(UWB) Multiple InputâMultiple Output (MIMO) - TTU CAE Network

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Time-Reversed Ultrawideband (UWB) Multiple Input–Multiple Output (MIMO) Based on Measured Spatial Channels

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Chenming Zhou, Member, IEEE, Nan Guo, Member, IEEE, and Robert Caiming Qiu, Senior Member, IEEE

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Abstract—Ultrawideband (UWB) technology is envisioned for future wireless high-data-rate transmission. A UWB system with multiple antennas takes advantage of the rich scattering environment to increase the data rate. On the other hand, given rich multipath, time reversal (TR) uses scatterers to create space and time focalization at a target point by coherent addition of all scattered contributions at that point. This paper analyzes the performance of an impulse TR-multiple-input–multiple-output (MIMO)-UWB system with a simple one-correlator receiver. The performance analyses are based on UWB spatial channels measured in an office environment.

16 Index Terms—Impulse multiple-input–multiple-output 17 (MIMO), intersymbol interference (ISI), multipath, spatial 18 focusing, time reversal (TR), ultrawideband (UWB).

I. I NTRODUCTION

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LTRAWIDEBAND (UWB) transmission has recently emerged as a potential candidate for future high-data-rate applications [1]–[7]. Impulsive transmission with short pulse duration makes the multipath components resolvable, which, 24 in turn, leads to immunity to the multipath fading. On the 25 other hand, however, capturing multipath energy distributed 26 in dense multipath components becomes a challenge. Time 27 reversal (TR) signal processing, which is a signal processing 28 technique popular in acoustics [8], has recently been applied 29 to electromagnetics [9]–[20]. A tutorial of TR and an extensive 30 review of literature for UWB communications is given in [13], 31 [48]. An attractive aspect of TR signal processing is the fact 32 that it makes use of multipath propagation. UWB impulsive 20

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radio is extremely interesting in this context, since hundreds 33 or thousands of paths are available (see, e.g., [16] and [18]). 34 Given a specific time and location, TR precoding has been 35 mathematically proved to be the optimum in the sense that it 36 maximizes the amplitude of the field at that time and location 37 [21]. It is then called spatiotemporal matched filter [22] because 38 it is analogous to a matched filter both in time and space. It 39 is also called transmit matched filter since the matched filter 40 is put at the transmitter side. However, TR alone may not 41 effectively reduce the channel delay spread, considering the 42 fact that it maximizes the peak amplitude but does not impose 43 any constraint at its sidelobe level. As shown in [20], multiple 44 antennas at the transmitter [i.e., multiple-input–single-output 45 (MISO)-TR] are then required to suppress the intersymbol 46 interference (ISI). The MISO-TR scheme also achieves array 47 gain with a factor of M (antenna number) by automatically 48 aligning the arrival peak [12]. MISO-TR has been extensively 49 investigated in the past years (e.g., [23] and [24]), and a natural 50 extension is to exploit the scenario of multiple-input–multiple- 51 output (MIMO) for TR signaling. 52 The MIMO technique uses multiple antennas at both ends 53 of the wireless link and is believed to be the most promising 54 approach to effectively use the transmission spectrum and 55 power. This technology has been extensively studied recently 56 [25], [26]. It has been shown that the channel capacity for 57 a MIMO system is increased as the number of antennas in- 58 creases. MIMO is mostly used in conjunction with orthogonal 59 frequency-division multiplexing (OFDM), which is a modula- 60 tion technology that is part of the IEEE 802.16 standard and 61 will also be part of the IEEE 802.11n high-throughput standard 62 due to its potentially high-data-rate capability. In addition to 63 the benefit from flat fading, MIMO also benefits from the rich 64 scattering of the channel. The use of multiple antennas and 65 space–time signal processing in a UWB system has been an 66 interesting topic [27]–[29]. 67 MIMO-UWB is a concept that can be implemented in several 68 alternative ways; in addition to the aforementioned OFDM 69 MIMO, another way is based on a scheme using impulse 70 radio to transmit pulses in one or multiple frequency bands, 71 such as the multiband UWB solution [30]. Here, we propose 72 the use of TR precoding combined with MIMO [14], which 73 we call impulse MIMO-TR. Note that we are interested in 74 the limits of UWB signals, i.e., pulses with ultrashort dura- 75 tion and extremely wide bandwidth. The proposed MIMO-TR 76 aims at implementing MIMO directly in the time domain and, 77

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

Manuscript received April 3, 2008; revised September 17, 2008 and December 8, 2008. This work was supported in part by the Office of Naval Research under Grant N00014-07-1-0529, by the National Science Foundation under Grant ECS-0622125, by the Army Research Laboratory and the Army Research Office under STIR Grant W911NF-06-1-0349, and by the Defense University Research Instrumentation Program under Grant W911NF-05-10111. The review of this paper was coordinated by Dr. K. T. Wong. C. Zhou is with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA (e-mail: czhou@ cmu.edu). N. Guo is with the Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38505 USA (e-mail: nguo@ tntech.edu). R. C. Qiu is with the Department of Electrical and Computer Engineering, Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38505 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2008.2012109

0018-9545/$25.00 © 2009 IEEE

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gain of 10 log10 (M N ) dB can be achieved by using a MIMO 136 system with M antennas at the transmitter and N antennas at 137 the receiver. We also investigate the performance based on the 138 bit energy at the receiver. We compare the performances for dif- 139 ferent scenarios [i.e., MIMO, MISO, and single-input–single- 140 output (SISO)], considering one-correlator receiver. 141 In practice, when a pulse is short and the data rate is low, 142 the above conditions (resolvable multipath and no ISI) tend 143 to be satisfied. However, for the case of high data rates and 144 relatively wide pulses, the conditions will no longer hold. 145 The performance of such a practical system is investigated 146 through Monte Carlo simulation. There are no data (on the 147 channel model of multiple antennas) that meet the need of 148 this research for spatial–temporal focusing; we have conducted 149 a series of channel measurements in an office environment. 150 The measurements are performed in the time domain, and the 151 CLEAN algorithm [45], [46] is employed to extract the channel 152 impulse response (CIR) from the measured data. 153 TR with multiuser UWB communications has been studied 154 by some other researchers (e.g., [41]–[44]), and the single-user 155 scenario has been considered in this paper. 156 The structure of this paper is given as follows. The principle 157 of TR signal processing and its suboptimum receiver—one- 158 correlator receiver—are introduced in Section II. The system 159 performance analysis for single antenna at both ends is given 160 in Section III. Then, the performance analysis is extended to 161 multiple-antenna scenarios in Sections IV and V. The exper- 162 imental description regarding the channel measurements are 163 shown in Section VI. Numerical results based on the measured 164 spatial channels are given in Section VII. Finally, we conclude 165 this paper in Section VIII. 166

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hence, is believed to be a simpler scheme than its frequencydomain counterpart. However, most research on UWB-MIMO is carried out in the frequency domain; very few time-domain 81 UWB MIMO results are reported. Sibille [31] proposed the 82 use of maximal ratio combining (MRC) RAKE combining to 83 accomplish the temporal alignment of received pulses, which 84 causes huge complexity at the receiver. However, pulses are 85 automatically aligned by using TR precoding at the cost of 86 increased transmitter complexity. It is shown in [32] that TR 87 precoding can achieve the same error performance as the MRC 88 combining scheme. 89 Separating the data streams at the receiver is challenging 90 for parallel data transmission. For the traditional narrowband 91 MIMO, singular-value decomposition (SVD) is usually applied 92 to decompose the channel into several independent subchan93 nels. For multitone UWB signals with gigahertz bandwidth, 94 however, applying SVD to each frequency tone significantly 95 increases the system complexity. In [33], a zero-forcing scheme 96 is proposed to separate N parallel transmitted data streams for 97 each resolvable multipath component. In this paper, considering 98 the good spatial–temporal focusing characteristics provided by 99 TR, we will show that TR precoding can also decompose the 100 channel, with reasonable complexity. The primary motivation 101 of this work is to investigate a system structure that has a good 102 tradeoff between complexity and performance. MIMO-TR is 103 such a structure. 104 Although MIMO-TR can achieve high data rates by parallel 105 data transmission, the applications of MIMO-TR are not limited 106 to support high data rates. With a beamforming approach, 107 where all the transmitter antenna elements transmit the same 108 information bit, a high signal-to-noise ratio (SNR) can be 109 obtained at the receiver, and hence, the transmission distance 110 can be greatly extended, depending on the number of antennas 111 employed in the array. It is shown in this paper that given the 112 same transmission power, the peak SNR at the receiver grows 113 linearly with M (the number of transmitter antenna elements) 114 and N (the number of receiver antenna elements). 115 The philosophy behind TR is the so-called transmit centric 116 processing, i.e., processing the signal at the transmitter side 117 before transmission to combat the deteriorating effects of the 118 channel. The motivation is from the fact that the power and 119 computation resources are generally more readily available at 120 the transmitter side. The main advantage of transmit centric 121 processing is the possibility to simplify the receivers, which 122 is desirable in the case of one central node serving for many 123 distributed sensor nodes. 124 Due to the favorable spatial–temporal focusing of the 125 MIMO-TR technique, the energy of a receive signal tends to 126 focus into a geometric spot and into a time instant. We propose 127 the use of a simple correlation receiver with one correlator to 128 capture the peak energy and ignore the rest of the energy as in129 terference. By doing this, the receiver complexity can be greatly 130 reduced since there are no channel estimation and equalization 131 in the receiver. However, as we will show later, the performance 132 of such a simple receiver can still achieve the additive white 133 Gaussian noise (AWGN) bound under ideal conditions that all 134 the multipath components are resolvable and that there is no 135 ISI in the system, given the same transmitted power. An energy 78

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II. P RINCIPLE OF TR S IGNAL P ROCESSING

A. Spatial–Temporal Focusing Through TR: Exploitation of Space–Time Symmetry

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TR cannot be understood, at first thought, as a simple 170 scheme: moving the matched filter to the transmitter side as 171 a TR filter. There is deep physics in the scheme to exploit 172 the spatial–temporal focusing, which is unique to impulsive 173 UWB signals. The physical foundation of TR is the space–time 174 symmetry, e.g., in general relativity. To avoid digressing very 175 far, we only outline—trying our best to use communications 176 engineering language—the physical mechanism behind the TR 177 scheme since much confusion has been caused in the literature 178 due to the lack of understanding of this mechanism. The main 179 motivation of this summary of known physical results is to 180 strike the point that the space–time symmetry cannot be taken 181 for granted: it must first be examined before it is used widely. 182 So far, this symmetry principle is established only for some 183 very simplistic physical regions. The experimental approach 184 must be used for realistic system settings to empirically support 185 this claim. The state-of-the-art status of theoretical justification 186 for the principle of space–time symmetry in a macroscope phe- 187 nomenon level is far from satisfactory, particularly for realistic 188 UWB communications applications. 189 It is well known that space–time symmetry is universally true 190 in physics. Radio waves follow the law of electromagnetics: 191

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ZHOU et al.: TIME-REVERSED UWB MIMO BASED ON MEASURED SPATIAL CHANNELS

The knowledge of symmetry (reciprocity) properties of a field frequently facilitates the determination of explicit field solutions [35]. For this purpose, one considers certain auxiliary or 195 adjoint problems related to the original field problem in such a 196 way as to reveal the space–time symmetry of the original field. 197 If the field, problems are phrased in terms of Green’s 198 functions—or CIR in linear system terms—which describe 199 the field response to a “point-source excitation,” with the 200 desired properties appearing most succinctly as symmetries in 201 these Green’s functions. A rigorous derivation of these sym202 metries in inhomogeneous lossy media, which is the case of 203 UWB communications, is very difficult. Rather, some insight 204 can be gained using simplified physical model. Experimen205 tal results are used to approximately establish the symme206 tries for realistic environments, e.g., indoors,1 and intravehicle 207 environments [14]. 208 For homogeneous media, or vacuums, the symmetries are an209 alytically established in [35, ch. 1]. If field symmetries exist, the 210 properties of the electromagnetic Green’s functions (and, thus, 211 CIRs) can be inferred prior to their explicit determination. In an 212 unbounded homogeneous stationary region, the field equations 213 are invariant under arbitrary linear space–time displacements, 214 i.e., the solutions are functions of the differences r − r and 215 t − t , where a pair of any space–time points (r, t) and (r , t ) 216 is considered. Mathematically, the Green’s function has the 217 symmetric form

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Fig. 1. Block diagram of the optimum transceiver design. (a) Matched Filter. (b) TR.

B. TR: Spatial–Temporal Matched Filter at Transmitter

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g(r, r ; t, t ) = g(r − r ; t − t ).

(1)

If we exchange the space–time point (r, t) with (r , t ), im219 plying (r − r; t − t), then the Green’s function is invariant. 220 In other words, when the spatial locations of two antennas are 221 switched, implying r − r, and the time is reversed, implying 222 t − t, the resultant Green’s function is identical to the original 223 one. Equation (1) is exactly the foundation of the so-called 224 TR scheme, requiring both TR of the CIR measured in one 225 direction and the exchange of two spatial locations of the 226 involved antenna pair. 227 Equation (1) is valid for the unbounded homogeneous sta228 tionary region with point-source excitation (ideal impulsive 229 antenna). For a general medium (channel), the adjoint-field 230 problem needs to be solved, using a temporal and spatial 231 reflection transformation [35]. As shown above, for the general 232 lossy bounded inhomogeneous and moving region with non233 point-source excitation (realistic UWB antennas), the adjoint234 field problem is open. Some simple physical media are solved, 235 including the following [35]: 1) free space (unbounded and 236 homogeneous) with point-source excitation; 2) homogeneous 237 medium with point-source excitation for both bounded re238 gions; 3) free space with an electrical dipole current excitation; 239 4) free space with planar stratified scattering structures with 240 Hertz potential excitation; and 5) bounded cylindrical regions 241 (a uniform waveguide of arbitrary cross section transverse to 242 the guide axis and bounded by perfectly conducting walls).

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the authors’ best knowledge, this is the first reported experimental result in the field of UWB communications regarding the channel’s space–time symmetry.

Consider a communication system illustrated in Fig. 1(a). 244 Here, p(t) is the transmitted pulse waveform, and h(t) denotes 245 the impulse response of the multipath channel. The received 246 signal before c1 (t) can be written as r(t) = p(t) ∗ h(t) + 247 n(t) = y(t) + n(t), where n(t) is AWGN with a two-sided 248 power spectral density of N0 /2, and y(t) = p(t) ∗ h(t). Given 249 r(t), a matched filter y(−t), which is matched to y(t), provides 250 the maximum signal-to-noise power ratio at its output. The 251 matched filter here can be virtually decomposed into two filters, 252 with the first filter matched to the CIR h(t) and the second one 253 matched to the pulse waveform p(t). As shown in Fig. 1(a), 254 this decomposition can be done by setting c1 (t) = h(−t) and 255 c2 (t) = p(−t). 256 We shall now consider what happens if we move the receiver 257 front-end matched filter c1 (t) to the transmitter but still keep the 258 filter c2 (t) at the receiver, as depicted in Fig. 1(b). This leads 259 to a TR system that is of interest in this paper. Note that this 260 operation actually makes the receiver suboptimum, as will be 261 shown later. However, by doing this, we simplify the receiver 262 structure and make more effective use of the transmitter energy 263 by concentrating it in the favorable frequency regions. 264 We still let c2 (t) = p(−t) and wish to find the optimum c1 (t) 265 such that it maximizes the SNR at the output of c2 (t), which is 266 given by 267 2 +∞ ∗ 2 P (f )P (f )C1 (f )H(f )df

SNR1 =

−∞

N0

+∞ −∞

(2)

2

|P (f )| df

under the constraint of fixed transmitted power, which is 268 defined by 269 +∞ P1 = |P (f )C1 (f )|2 df. −∞

(3)

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Here, P (f ), H(f ), C1 (f ), and C2 (f ) are the Fourier transforms of p(t), h(t), c1 (t), and c2 (t), respectively. Note that the denominator of (2) does not depend on C1 (f ). To maximize 273 (2), equivalently, we need to maximize the ratio

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+∞ 2 |P (f )|2 C1 (f )H(f )df ρ=

−∞

+∞

−∞

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.

(4)

|P (f )C1 (f )|2 df

According to Schwartz inequality, we have 2 +∞ P (f )C1 (f )H(f )P ∗ (f )df −∞

+∞ +∞ 2 ≤ |P (f )C1 (f )| df · |P ∗ (f )H(f )|2 df. (5)

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−∞

Substituting (5) into (4) yields

+∞ ρ≤ |P ∗ (f )H(f )|2 df −∞

(6)

with equality holding only when C1 (f ) = λ1 H ∗ (f ), or in the time domain, c1 (t) = λ1 h(−t), where λ1 is a constant that is 278 chosen to satisfy the power constraint (3). 279 We then have proved that a time-reversed precoding is opti280 mum in terms of SNR, given c2 (t) = p(−t). 276 277

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Channel estimation is a difficult task, and in a TR system, 296 this task is shifted to the transmitter side. We are interested 297 in a suboptimum receiver filter, and the transfer function of 298 which is matched to P ∗ (f ), instead of the optimum one 299 P (f )H(f )H ∗ (f ). This case is exactly the scenario if we move 300 the first channel matched filter c1 (t) to the transmitter side, as 301 discussed at the beginning of this section. The following sec- 302 tion studies TR system performance with such a suboptimum 303 receiver, namely, the one-correlator receiver, first for a single- 304 antenna system, which is later extended to a multiple-antenna 305 system. 306 The proposed scheme is suboptimal and of low complexity 307 compared to many optimal criteria. Consider a joint opti- 308 mization scenario, where h(t) is given and we wish to find 309 the optimum pair of c1 (t) and c2 (t) under the constraint of 310 fixed transmitted power (denoted as P2 ). If the signal has 311 finite time duration, the optimum transmitted waveform is the 312 eigenfunction corresponding to the maximum eigenvalue of the 313 TR operator of the CIR h(t) [40]. We should, however, note that 314 other eigenvalues may contain significant information about the 315 channel; thus, putting as much energy to just one frequency 316 (to optimize in terms of SNR) may decrease channel capacity 317 substantially—leading to low channel capacity. We still need 318 to implement a water-filling algorithm to achieve the optimum 319 capacity. When signal duration is infinite, i.e., T = ∞, this 320 optimization leads to a sinusoidal transmitted waveform, as 321 shown in [39]. In other words, we need to concentrate all the 322 transmitted power to the frequency with maximum transmission 323 capability. 324

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−∞

D. Suboptimum Receiver Filter for TR System: One-Correlator Receiver

III. P ERFORMANCE A NALYSIS

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C. Optimum Receiver Filter for TR System

A. System Description

We now consider another case. Given TR precoding, i.e., C1 (f ) = H ∗ (f ), we wish to optimize the receiver filter 284 c2 (t) (maximizing SNR) under the fixed transmitted power 285 constraint of 282 283

+∞

(7)

−∞ AQ5

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The receiving SNR at the output of c2 (t) can be expressed as Similarly, we refer to Schwartz inequality and have the SNR formulation as follows: 2 SNR ≤

+∞ −∞

|P (f )H ∗ (f )H(f )|2 df N0

(8)

with equality holding only when C2 (f ) = λ2 P ∗ (f )H(f ) × H ∗ (f ). It is suggested that the optimal receiver filter for a TR 291 system should be a filter whose impulse response is in the form 292 of λ2 p(−t) ∗ h(t) ∗ h(−t). This result is actually a validation 293 of the matched filter theory.

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Consider a single-user transmission. The transmitted signals 327 before precoding can be expressed as 328 s(t) =

+∞

i=−∞

|P (f )H ∗ (f )|2 df.

P2 =

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si (t) =

+∞

Eb bi p(t − iTb )

(9)

i=−∞

where Eb is the transmitted bit energy, and bi ∈ {±1} is 329 the ith information bit. Binary antipodal modulation has been 330 considered in this paper. p(t) is the UWB pulse with a width 331 of Tp , and assume that the pulse takes care of the impacts 332 of circuits and antennas at the both sides. The energy of p(t) 333 +∞ is normalized to unity, i.e., Ep = −∞ p2 (t)dt = 1. Tb is the 334 bit interval. Generally, we have Tb Tp to avoid possible ISI 335 caused by the multipath channel. In this paper, we will show 336 that by using a MIMO-TR technology, Tb and Tp could take the 337 same level without significant performance degradation. 338 For the sake of simplicity, we assume that there is no per-path 339 pulse distortion [34] caused by the channel. If per-path pulse 340 distortion does occur, a number of taps can be used to represent 341 the per-path impulse response, as done in [36], such that the 342 tap-delay-line model in (10) is still valid in its mathematical 343 form, but not physically interpreting the physics phenomenon. 344


In this case, the received signals are just a series of replicas 346 of the transmitted signals, with different attenuations and time 347 delays. The CIR then can be modeled as 345

h(t) =

L

αl δ(t − τl )

(10)

l=1

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where L is the number of multipath components, and αl and τl are their individual amplitudes and delays. Note that each term in (10) does not necessarily correspond to a physical path.

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B. Matched Filter Performance Bound

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If there is no TR and a single antenna is employed at both the transmitter and the receiver, the received signal can be expressed as

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ri (t) =

L

αl si (t − τl ) + n(t).

(11)

l=1

The optimum receiver for the above signal would be a matched filter matched to the signal part of ri (t). Such a receiver would achieve the performance bound, namely, matched filter bound, which is described as 2GEb (12) Pe = Q N0

∞ √ 2 where Q(x) = x (1/ 2π)e−y /2 dy is the Q-function, G = +∞ 360 −∞ |h(t)|2 dt is the channel gain, and Eb represents the trans361 mitted bit energy. The bit energy measured at the receiver side ˜b . 362 is denoted by E 363 In reality, it is believed that the performance bound in (12) 364 requires a very complex receiver and, thus, is hard to achieve 365 due to the complicated UWB multipath channel. In this section, 366 we will show that by using TR precoding at the transmitter, the 367 AWGN performance bound can be achieved with a simple one368 correlator receiver under some conditions. 359

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C. MISO-TR Performance Analysis Based on Transmit Bit Energy Eb

Before we consider MIMO-TR, let us start with a simpler scenario of SISO-TR. Consider a nonrealistic case where we use a short pulse so that the propagation delay difference between any adjacent multipath components is always larger 375 than the pulse duration Tp . In addition, we assume that Tb is 376 sufficient enough so that there is no ISI. 377 For SISO-TR, the received signal can be expressed as 371

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scenario. It is apparent that hSISO (t) is an autocorrelation with 380 eq a peak occurring at t = T . The magnitude of√ the peak √ √ is equal 381 +∞ to G, i.e., hSISO (t = T ) = −∞ |h(t)|2 dt/ G = G. 382 eq Due to its autocorrelation nature, most of the energy is 383 focused in the central (main) peak of the CIR hSISO (t). Since 384 eq we assume that there are no interpulse interference (IPI), ISI, 385 and pulse distortion, we can use a filter matched to the main 386 component of the received signal. It is proved in the following 387 that even by using such a simple receiver (with one correlator), 388 we can achieve the same performance as the matched filter 389 bound. 390 The main component of the receiving signal can be ex- 391 pressed as 392 √ rimain (t) = G Eb bi p(t − iTb − T ). (14) We then use a filter matched to p(t) to pick up the energy lying 393 in the aforementioned main component of the received signal. 394 The performance can be characterized using the following 395 analytical formula: 396 2GEb PeSISO = Q . (15) N0

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riSISO (t) = si (t) ∗ c(t) ∗ h(t) + n(t)

1 √ = si (t) ∗ h(T − t) ∗ h(t) + n(t) G (t) + n(t) (13) = si (t) ∗ hSISO eq √ 378 where c(t) = h(T −t)/ G is the prefilter code, and hSISO (t) = eq √ 379 h(T − t) ∗ h(t)/ G is the equivalent CIR for the SISO-TR

Comparing (12) and (15), it is evident that a TR system with 397 a one-correlator receiver can achieve the same performance 398 as a system without TR but with an ideal matched filter. The 399 same conclusion has been obtained by other researchers [32], 400 [47] through different approaches in the pre-RAKE systems. 401 Therefore, for a TR system with a one-correlator receiver, we 402 have the following observation: On the one hand, TR filter 403 improves the system performance by precoding the transmitted 404 signal to concentrate the transmitted power to the spectral 405 regions with less attenuation and, thus, make more effective 406 use of transmitted power; in contrast, system performance is 407 degraded by using a nonoptimum receiver (a one-correlator 408 receiver). Remarkably, the result in this section implies that 409 the improvement by placing a channel-matched TR filter at the 410 transmitter is exactly equal to the degradation caused by not 411 using such an optimum filter at the receiver. Again, this result 412 is true in the absence of ISI and IPI—a stringent condition. 413 In the following, we will extend this result to a scenario of 414 TR with multiple antennas. 415 IV. MIMO-TR: F OCUSING S PATIAL –T EMPORAL E NERGY TO A S HARP P EAK

A. MIMO-TR Precoding

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When a short pulse is sent to the channel, the radiated energy 419 is distributed among different spatial locations and spread in 420 time over a large number of pulses at any observation location 421 (due to multipath). Since a TR mirror—here, antenna arrays at 422 both MIMO terminals—can be viewed as a “channel sampler,” 423 more antennas imply more spatial sampling points, which 424 means that more energy can be captured. A MIMO-TR (4 × 4) 425 system configuration is illustrated in Fig. 2. Let hmn (t) denote 426 the CIR between the mth antenna at the transmitter and nth 427 antenna at the receiver, and let cm (t) be the corresponding 428

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Fig. 2. TR precoded MIMO communication system, with M = 4, and N = 4.

Fig. 3. Timing for the peak of the received signal in a TR system. The peak of the equivalent CIR will occur exactly at the time t = T , independent of the element location, antenna type, and channel.

429

prefilter code employed in the mth antenna branch at the M × N MIMO-TR system, the code

430 transmitter. In a general 431 cm (t) can be written as

cm (t) = Am

N

hmn (T − t)

(16)

n=1

where T is the length of the filter required to implement the TR operation [20], and Am is the power scaling factor to 434 normalize the total transmission power from different antenna 435 branches. It should be noted that different power allocation 436 schemes can be implemented by choosing different factors Am 437 [23]. In this paper, Am ’s are set to be equal for all the antenna 438 elements, i.e., 432 433

Am = A =

1

M

N

(17)

Gmn

m=1 n=1

+∞ where Gmn = −∞ |hmn (t)|2 dt is the channel gain of CIR hmn (t). Obtaining the TR precoding waveform cm (t) for the mth 442 antenna branch is straightforward. First, a sounding pulse w(t) 443 is sent through all the N antennas in the receiver to the trans444 mitter. Second, the receiving signals at each transmitter antenna

439 440 441

branch are then recorded, digitized, and time reversed. The 445 noise-free signal received by the mth antenna at the transmitter 446 can be expressed as follows: ym (t) = N n=1 hmn (t) ∗ w(t). 447 The foundation for using backward channel sounding is channel 448 reciprocity. For MIMO channels, no experimental confirmation 449 of this assumption has been done. If the sounding pulse w(t) is 450 sufficiently short, we can directly use the time-reversed version 451 of ym (T − t) as the precoding cm (t). Otherwise, deconvolution 452 effort is necessary to remove the pulse effect from the received 453 sounding signal. 454 One of the attractive characteristics of TR is that its temporal 455 focal point can be adjusted by a change in the parameter T . 456 The principle of timing alignment for TR for the mth antenna 457 element is illustrated by Fig. 3. If the same initial timing 458 between antenna elements in the same array is assumed (this 459 is a reasonable assumption because all the antenna elements of 460 an array use the same clock), all the peaks of the fields appear 461 at the receiver at the same time instant, independent of the 462 element location, antenna type, and channel. It turns out that 463 the peaks are aligned automatically. For a MISO case, all the 464 energy from different transmitter elements coherently adds up 465 at time T at the receive antenna. For a MIMO case, the energy 466 from different transmitter elements (viewed as several different 467 MISO arrays) will focus at each individual antenna element at 468 the receiver. 469


470 471

For MIMO-TR, the signal captured by the nth receive antenna can be expressed as M

rin (t) = si (t) ∗

{cm (t) ∗ hmn (t)} + n(t).

PeMIMO

All the signals captured by different antennas at the receiver can be combined directly, and the combined signal ri (t) can be expressed as ri (t) = si (t) ∗

N M

{cm (t) ∗ hmn (t)} + n(t)

n=1 m=1

= si (t) ∗ A

M N

n=1 m=1

N

hmk (T − t) ∗ hmn (t)

k=1

+ n(t)

N


  hmk (T − t) ∗ hmn (t) =A   n=1 m=1 k=1,k=n  N 

Interference

N M m=1 n=1

Rmn (t − T )

(20)

Signal

where Rmn (t) = hmn (−t) ∗ hmn (t) is the autocorrelation of hmn (t). Let us use a 4 × 4 MIMO example to illustrate (20). 477 It can be seen from (20) that hMIMO (t) consists of 64 terms, eq 478 corresponding to 16 autocorrelations and 48 cross correlations. 479 These 16 autocorrelation terms will coherently add up due to 480 its automatic alignment characteristic addressed in this section. 481 In contrast, these 48 cross correlation terms adds up noncoher482 ently. As a result, the desired autocorrelation part forms a strong 483 peak and dominates in the received signal. 484 At t = T , the amplitude of the peak in hMIMO can be eq 485 approximated by the contributions of all the autocorrelation 486 terms as 475 476

A

N M

Gmn

m=1 n=1

487 488

" ¯ b /N0 ). PeMIMO = Q( 2M N GE

(24)

As a special case when N = 1, we have the performance of 495 a MISO-TR system with a one-correlator receiver as 496   M = Q 2 Gm Eb /N0  .

(25)

m=1

k=1

N M

¯ denote the averaged channel gain over the whole 492 Let G ¯ = (1/M N ) M N Gmn . 493 M × N channels, where G m=1 n=1 We have 494

PeMISO

(23)

m=1 n=1

(19)

n=1 m=1

+A

  M N = Q 2 Gmn Eb /N0  .

IE E Pr E oo f

hMIMO (t) = A eq

M N

where ≈ is used because the contributions from all the cross 489 correlation terms to the main peak have been ignored. In the 490 absence of ISI and IPI, it follows that 491

(18)

m=1

472 473 474

7

M N = Gmn .

(21)

m=1 n=1

The signal on the main component of the received signal is then approximated as M N main ri (t) ≈ Gmn Eb b(i)p(t − iTb − T ) + n(t) m=1 n=1

(22)

When M = 1 and N = 1, (24) reduces to (15) for the SISO- 497 TR scenario. It is straightforward from (25) that the perfor- 498 mance of a MIMO-TR system depends on the following three 499 parameters: the number of antennas M and N and the energy 500 ¯ Statistical characterization 501 of the multipath (channel gain G). ¯ of G is important. 502 ˜b 503 B. Performance Analysis Based on the Receive Bit Energy E The above analysis, e.g., (24), is based on the bit energy 504 Eb on the transmitter side. Since a lot of literatures analyze 505 ˜b , this 506 the performance based on the receiver side bit energy E ˜b . The one- 507 section also derives the performance formula for E correlator receiver proposed in this paper is not optimum. The 508 optimum receiver should be a receiver matched to the whole 509 receive waveform of (24). Then, the performance bound for 510 such a receiver would" be the matched filter bound, which is 511 ˜b /N0 )) (assuming bipolar modu- 512 expressed as Pe = Q( (2E lation). We introduce a new metric, namely, the peak energy 513 ˜b ), denoting the 514 ratio κ, which is defined as κ = (Epeak /E energy ratio of the peak to the total received energy. Here, 515 Epeak represents the energy of the signal peak. As a result, the 516 performance " of the one-correlator receiver can be expressed as 517 ˜b κ/N0 ). Pe = Q( 2E 518 +∞ 2 Let νmn,ij = −∞ |hmn (−t) ∗ hij (t)| dt − Imn,ij for 519 cross correlation (m = i, n = j) and νmn,ij = νmn = GRmn − 520 Gmn for autocorrelation (m = i, n = j). Here, Imn,ij = 521 +∞ |hmn (−t)∗ hij (t)|t=0 = −∞ hmn (t)×hij (t)dt, and GRmn = 522 +∞ 2 −∞ |Rmn (t)| dt is the channel gain of the equivalent 523 CIR Rmn (t). Here, we can see that the cross correlation 524 νmn,ij represents the sidelobe energy of the equivalent CIR 525 hmn,ij . 526 For MIMO-TR, the peak energy ratio κMIMO can be ex- 527 press in (26), shown at the bottom of the next page, where 528

8


N ¯ ν¯ = 1/M N · M n=1 νmn , and I = 1/[M N (N − 1)] · N M m=1 N 530 n=1 m=1 k=1,k=n Imn,mk . Assuming that CIRs are not 531 correlated with each other, i.e., I¯ ≈ 0, we have 529

¯2 G . ¯2 +G

κMIMO ≈ 532

A A2

(28)

max |heq (r0 , r1 , t)|2

.

(33)

t

For the scenario of MISO-TR, the equivalent CIR for different 556 users can be expressed as 557

Gm

#

M

νm + A

Gm

¯2 G $2 = 1 ¯2 . ¯+G Mν

heq (r0 , r0 , t) (29) =

m=1

For SISO-TR, we have

M

1 hm (r0 , −t) ∗ hm (r0 , t) √ " m=1 M hm (r0 , t)2

heq (r0 , r1 , t) G2 . ν + G2

M

1 hm (r0 , −t) ∗ hm (r1 , t) (34) √ " m=1 M hm (r0 , t)2

IE E Pr E oo f

κ=

(30)

As a sanity check, when N = 1, (27) reduces to the MISO case (29). When M = 1 and N = 1, (27) reduces to the SISO case (30). 538 It then can be seen from (28) and (29) that the performances 539 of both the MIMO and MISO scenarios depend on the number 540 of transmit antenna elements M . If we increase M , we actually 541 improve the focusing and then get better performance. A com542 parison of (27) and (29) shows that the peak energy ratio κ for a 543 MISO system is better than that of a MIMO system, particularly 544 when N is large, and that the performance improvement caused 545 by the increase of M for a MISO system is faster than that of a 546 MIMO system.

535 536 537

548

t

$2

M

m=1

547

(32)

The spatial focusing can be characterized by the metric 554 directivity D(r0 , r1 ), which is defined as 555

D(r0 , r1 ) =

¯2 G ≈ 2 ¯2 . ¯+G Mν

m=1 M

553

max |heq (r0 , r0 , t)|2

For MISO-TR, we have #

534

heq (r0 , r1 , t) = h(r0 , −t) ∗ h(r1 , t).

For large N , we have κMIMO

533

(27)

2N −1 ¯ MN ν

For the unintended user, the equivalent CIR would be

V. MIMO-TR: S PATIAL M ULTIPLEXING

A. Enhanced Spatial Focusing With Multiple Antennas

Let h(r0 , t) represent the CIR for the intended receiver located in the position r0 (x0 , y0 , z0 ), and let h(r1 , t) denote the CIR of another unintended user at the position r1 (x1 , y1 , z1 ). 552 The equivalent CIR for the intended user would be

549 550 551

heq (r0 , r0 , t) = h(r0 , −t) ∗ h(r0 , t).

(31)

M N

Gmn +

m=1 n=1

κMIMO ≈ 2

N M

N

νmn,mk +

n=1 m=1 k=1,k=n

& ¯ + (N − 1)I¯ 2 G = % & 2N −1 ¯ + (N − 1)I¯ 2 ν¯ + G

M N m=1 n=1

=

where hm (r0 , t) denotes the CIR between the mth element in 558 the transmit array and the receiver located in r0 . 559 For simplicity, the receiver has been restricted to move along 560 a straight line in the measurements carried out in this paper. 561 Under this condition, (33) can be simplified as 562 max |heq (r0 , 0, t)|2

D(r0 , d) =

t

(35)

max |heq (r0 , d, t)|2 t

where d is the distance between the unintended receiver and 563 the intended receiver (focal point) located at r0 . For the case 564 where the antenna elements are not distributed along a line, but 565 in some shapes (e.g., circle, square, etc.), (35) will still be valid 566 if we replace the scalar d with a vector d, where d = r1 − r0 . 567 The value of directivity D(r0 , d) determines how well we 568 can, by employing TR, focus the transmitted energy into an 569 intended point of interest. A similar metric has been used in 570 [38]. Our previous paper [10] uses the same metric to inves- 571 tigate the spatial focusing of the UWB signal in the hallway 572 environment by simulation. In this paper, we experimentally 573

N M

2

N

Imn,mk

n=1 m=1 k=1,k=n

νmn +

M N m=1 n=1

Gmn +

N M

N

2 Imn,mk

n=1 m=1 k=1,k=n

%

MN

(26)


evaluate this parameter by moving the receiver away from the intended focusing point r0 and study how rapidly the receiving energy drops with this moving. 577 We expect the spatial focusing can be enhanced by employ578 ing multiple antennas at the transmitter, which will be shown 579 experimentally in this paper. If the spatial focusing is good 580 enough, we can take advantage of this property and transmit 581 signals in a parallel fashion. 574

575 576

582

B. Spatial Multiplexing With Multiple Antennas

Consider a communication link consisting of M transmitting antennas and N receiving antennas. The input data are serialto-parallel converted into N streams bn (t), which are precoded by cn (t) through FIR filters and modulated. Eventually, the 587 signals are sent to M transmitting antennas for simultaneous 588 transmission. After the signal passes through the channel and is 589 corrupted by AWGN, the nth receiving branch extracts the data 590 stream bn (t). 591 Let S(t) = [s1 (t), s2 (t), . . . , sN (t)] and R(t) = [r1 (t), 592 r2 (t), . . . , rN (t)] denote the transmitting and receiving signals, 593 respectively. We have R(t) = S(t) ∗ C(t) ∗ H(t), where C(t) 594 is the precoding matrix, and H(t) is the time-domain impulse 595 response matrix defined by   h11 (t) . . . h1N (t)   .. .. .. H(t) =  (36)  (M × N ). . . . 583

hM 1 (t) . . .

hM N (t)

We define the equivalent impulse response matrix (EIRM) as Heq (t) = H(t) ∗ C(t). Then, we have R(t) = S(t) ∗ Heq (t). 598 The EIRM is the target of interest. The objective is to transform 599 the EIRM into a desirable form by selecting a good code 600 matrix C(t). 601 To avoid ISI, the ideal EIRM will be in the form   0 a1 δ(t) . . .  ..  (N × N ) .. Heq (t) =  ... (37) . . 

596 597

0

...

an δ(t)

C(t) ∗ H(t) ≈ Hideal eq (t).



ˆ )H(f ˆ )=H ˆ eq (f ) C(f ˆ ), H(f ˆ ), and H ˆ eq (f ) are the Fourier transforms of 611 where C(f the matrices C(t), H(t), and Heq (t), respectively. 612 The solution for the above function is 613 ˆ −1 (f ). ˆ )=H ˆ eq (f )H C(f The above solution assumes that the channel matrix H(f ) 614 is square and invertible. For a general M ∗ N matrix H, the 615 solution will be 616 .−1 ˆ )=H ˆ eq (f )H(f ˆ ) H ˆ H (f )H(f ˆ ) C(f . (38)

M

Rhi1 (t)  i=1   ..  .  M  Heff (t) =  hin (−t) ∗ hi1 (t)   i=1  ..  .  M  hiN (−t) ∗ hi1 (t) i=1

Once we have the frequency-domain matrix C(f ), the time- 617 domain matrix C(t) can be numerically obtained by applying 618 inverse fast Fourier transformation to C(f ). Note that the trans- 619 form of a matrix is a process of term-by-term transformation. 620 Generally, the inversion of a matrix is ill-conditioned, and small 621 errors (e.g., the measurement error caused by noise) in any 622 matrix X will give rise to significant errors in its inverse matrix 623 X−1 . Even measurement is perfect, and there is no error in X; 624 X may not be invertible. Many techniques for the regularization 625 of this problem have been studied [22]. 626 2) Solution 2—TR: Considering the signal processing in- 627 volved in the previous inverse filter solution, another simpler 628 solution would be TR. In this case, the precoding matrix would 629 simply be CTR (t) = H (−t), where the superscript “ ” in the 630 notation denotes transpose operation. We have 631   h11 (−t) . . . hM 1 (−t)   .. .. .. CTR (t) =   (N × M ). (39) . . . h1N (t)

where (a1 , . . . , an ) are the matrix coefficients. 603 We hope that we can find a matrix C(t) that satisfies the 604 following equation: 602

Then, the problem will be how to find a suitable C(t). Two 605 solutions can be used to achieve the goal. 606 1) Solution 1—Inverse Filter: This approach is optimal in 607 the sense that, theoretically, the ideal formula presented above 608 can be exactly achieved. 609 Thinking the problem in the frequency domain, we have 610

IE E Pr E oo f

584 585 586

9

...

M

.

hi1 (−t) ∗ hin (t)

...

Rhin (t)

...

i=1

.. ...

M i=1



M

hi1 (−t) ∗ hiN (t)    ..  .  M  hin (−t) ∗ hiN (t)   (N × N ) i=1   ..  .  M  RhiN (t) i=1

M

...

hM N (−t)

In practice, CTR (t) can be readily obtained by channel sounding, and no extra computation is needed. Let Heff (t) = CTR (t) ∗ H(t). Then, Heff (t) can be expressed in (40), shown at the bottom of the page, where we have

i=1

..

...

hiN (−t) ∗ hin (t)

.

...

i=1

(40)

632 633 634 635

10


Fig. 4. UWB spatial channel measurement: experiment setup. 636 637 638

made an assumption that matrix convolution is a term-by-term convolution. In a general form, the received signal r(t) can be expressed as M N rn (t) = sj (t)∗ hij (−t)∗hin (t) , j=1

n = 1, 2, . . . , N.

i=1

(41) The received signal r(t) can be reformulated to a more convenient form as follows: rn (t) = sn (t)∗

M

IE E Pr E oo f

639 640

Rhin (t)+On (t),

i=1

n = 1, 2, . . . , N

(42)

M where On (t) = N j=1,j=n sj (t) ∗ [ i=1 hij (−t) ∗ hin (t)]. 642 Assuming good spatial focusing, the received signal can 643 be approximated by the following formula: rn (t) ≈ sn (t) ∗ M 644 i=1 Rhin (t), where we have ignored the contributions from 645 the cross correlation part On (t). Under this condition, the 646 corresponding impulse response matrix will be in the form of a 647 diagonal matrix, i.e.,  M R (t) . . . 0 hi1     i=1   .. .. .. Heff (t) =   (N ×M ) (43) . . .   M   RhiN (t) 0 ... 641

Fig. 5.

UWB spatial channel measurement: experiment environment.

= scom (t) ∗

m=1 j=1

= scom (t) ∗

where the impulse matrix has been decomposed into parallel 649 channels. This decomposition gives us several independent 650 subchannels and, thus, increases the data rate. 651 TR spatial multiplexing discussed in this section is another 652 application of TR-MIMO in addition to the application of 653 beamforming. The precodings for the two different scenarios 654 are different. As a sanity check, in the following, we will show 655 that scenario A (spatial multiplexing) is reduced to scenario B 656 (beamforming) when all the independent channels transmit the 657 same information, namely, sn (t) = scom (t). 658 Under this condition, the receiving signal can be combined 659 together directly and is expressed as

M N j=1

r(t) =

rn (t)

n=1

 M  N N  = scom (t) ∗ hij (−t) ∗ hin (t)  n=1

j=1

i=1

hij (−t) ∗ him (t)

i=1

hij (−t) ∗

N

him (t) .

(44)

m=1

i=1

hMIMO (t) eq

=

M N j=1

hij (−t) ∗

i=1

N

hMIMO (t) eq

=A

M N j=1

i=1

660

him (t) .

m=1

Considering the power allocation factor A, we have hij (−t) ∗

N

661

him (t)

m=1

which is consistent with the result derived previously in (20). VI. UWB S PATIAL C HANNEL M EASUREMENT

A. Experiment Setup (Fig. 4) N

The equivalent impulse response can thus be modeled as

i=1

648

M N N

662

663 664

Major equipment used in the measurements include 1) a 665 waveform generator for triggering the pulser; 2) a UWB pulser 666 that generates Gaussian-like pulses with a root mean square 667 pulsewidth of approximate 250 ps; 3) a wideband low-noise 668 amplifier (LNA) with bandwidth over 10 GHz and a noise figure 669 less than 1.5 dB; 4) a Tektronix CSA8000 digital sampling 670

AQ6


11

IE E Pr E oo f

TABLE I COMPARISON OF κ FOR DIFFERENT SCENARIOS

oscilloscope (DSO) with a 20-GHz sampling module 80E03; and 5) a pair of omnidirectional antennas with a relatively flat 673 gain over the signal band. To maintain synchronization, the 674 same waveform generator is employed to trigger the DSO. The 675 major frequency components of the system are from 750 MHz 676 to 1.6 GHz. A simplified block diagram of the experiment setup 677 can be found in Fig. 4. 678 A virtual antenna array is employed in the experiments. The 679 elements of the array are spaced far enough so that there is no 680 significant correlation between two adjacent channels. This can 681 be achieved by setting the spacings between any two adjacent 682 antenna elements greater than 20 cm, which corresponds to the 683 half wavelength of the lowest frequency. The value of 20 cm 684 is found to be sufficient after some trials of bigger values. The 685 MIMO antenna coupling is considered in [17]. In Fig. 5, four 686 virtual elements are equally spaced along a line. The heights of 687 the antennas are set to 1.4 m. The receiving antenna is moved to 688 different locations, and individual channels were sounded and 689 measured sequentially. No line of sight is available for all the 690 measurements. 671 672

691

B. Experiment Environment

A set of measurements has been performed in the office area of Clement Hall 400 at the Tennessee Technological University. 694 Fig. 5 shows the experimental layout for these experiments. 695 In Fig. 5 (also in Table I), Tn denotes the nth element of the 696 transmitting array, and Rn denotes the receiver located in the 697 nth position. The environment for the experiment is a typical 698 office area with abundance of wooden and metallic furniture 699 (chairs, desks, bookshelves, and cabinets). 692 693

Fig. 6. CLEAN algorithm employed to extract impulse response from the received signals.

C. Measurement Results and Spatial Focusing Analysis

700

A typical receiving waveform is shown in Fig. 6. The 701 CLEAN algorithm is employed to extract CIRs from the re- 702 ceived waveforms. 703 We first investigate the spatial focusing of a MISO-TR sys- 704 tem. Consider downlink transmission. Assume that there are 705 two users separated by a distance d, with one of them as the 706 target user (focal point) and the other as the undesired user. 707 Each user has one receive antenna and a transmit antenna array 708 with four elements. The equivalent CIRs for the target user and 709 the undesired user of 0.2 m away are shown in Fig. 7(a) and (b), 710 respectively. The equivalent CIRs for different users are 711

12


Fig. 7. Demonstration of MISO-TR spatial focusing by the equivalent CIR. (a) Equivalent CIR for the target user. (b) Equivalent CIR for the unintended user with 0.2 m away from the target user.

VII. N UMERICAL R ESULTS

IE E Pr E oo f

Fig. 8. Spatial focusing characterized by the parameter directivity D(r0 , d).

calculated by using (34). As we can see in Fig. 7, the signal is very strong for the target user, while it is almost behind the background noise for the undesired user with a short distance of 0.2 m away. 716 We further investigate the variation of the directivity D, as 717 defined in Section V-A, with respect to different distances d. 718 A comparison of spatial focusing for MISO-TR and SISO719 TR is shown in Fig. 8. In the SISO-TR case, it is observed 720 that energy drops by more than 15 dB when the undesired 721 receiver is located 0.2 m away from the intended user. This 722 number will slightly change when the unintended receiver 723 moves to a farther place. In Fig. 8, the “SISO average” curve 724 represents the average directivity of the four SISO-TR cases. It 725 is observed that the “MISO” directivity curve drops much faster 726 than the “SISO average” curve, implying that spatial focusing 727 is improved by employing an antenna array at the transmitter. 728 With a four-element array at the transmitter, energy drops by 729 22 dB when the unintended receiver is 0.2 m away from the 730 target receiver. 712

713 714 715

731

Table I shows a comparison of κ (defined in Section IV-B) for 732 different scenarios. In Table I, the calculating of parameters ν, 733 G2 , and κ are all based on the measured UWB spatial channels. 734 The approximated (“Appro”) values of κ for MIMO and MISO 735 scenarios are calculated using (28) and (29), respectively. The 736 experiment (“Exper”) values are directly measured from the 737 equivalent CIRs of MISO and MIMO scenarios. Table I shows 738 that (28) and (29) can approximate the measured value well. 739 The slight difference between the approximated value and the 740 measured value is due to the disturbances of the cross correla- 741 tion terms (the interference from the other antennas), which is 742 hard to be included in an analytical formula. 743 Based on the measured UWB spatial channels, we conduct 744 Monte Carlo simulations to investigate the performance of 745 the one-correlator receiver and compare them under different 746 scenarios: SISO, MISO, and MIMO. In our simulation, the 747 second-order derivative of Gaussian pulse has been used as the 748 transmitted pulse p(t), which is mathematically defined as 749

p(t) = 1 − 4π

#

t − tc w

$2

e−2π(

t−tc w

2

)

(45)

where w is the parameter controlling the width of the pulse 750 (and, therefore, the frequency bandwidth of the transmit signal), 751 and tc is the parameter to shift the pulse to the middle of 752 the window. In the following simulation, we let w = 1 ns and 753 tc = 0.5 ns. To avoid the presence of severe ISI in the system, 754 we add an interpulse guard time Tg . Therefore, we have Tb = 755 w + Tg . Moreover, Tg can be used to adjust the transmission 756 data rate in the simulation. Unless stated otherwise, we let 757 Tg = w, corresponding to a data rate of 500 Mb/s. 758 Throughout this paper, we assume perfect synchronization, 759 and the transmitter has the full knowledge of the channel 760 information. To make the comparison fair, performances of 761 SISO and MISO scenarios have been averaged over all the 762 corresponding specific channels that virtually form the MIMO 763


Fig. 10. BER performance in terms of transmitted bit energy. Ebtx here represents the transmitted bit energy. Both ISI and IPI have been considered.

SISO SISO MISO channel, i.e., Pave = (1/16) 16 , and Pave = i=1 Pi 4 MISO 765 (1/4) P . i=1 i 766 A comparison of BER performance for different scenarios 767 with both ISI and IPI is shown in Fig. 9. The performance 768 bound for AWGN channel is also plotted as a reference. In 769 Fig. 9 we can see that given the same SNR at the receiver side, 770 MISO-TR has the best performance, and MIMO-TR is slightly 771 better than SISO-TR scenario. This is due to the best temporal 772 focusing provided by MISO-TR. It should be noted that these 773 comparisons are based on the received SNR. In reality, however, 774 given the same transmitted power, the SNR at the receiver 775 side for MIMO-TR is much higher than that of MISO-TR, 776 which will make MIMO-TR outperform MISO-TR, as will be 777 illustrated in the following. 778 Fig. 10 shows the BER performances for the SISO, MISO, 779 and MIMO scenarios under the same transmitted power con780 straint, with different transmission data rates. For the MIMO 781 scenario, all the four antennas transmit the same bit informa782 tion, i.e., the beamforming approach has been applied to in783 crease the SNR at the receiver side. Both IPI and ISI have been 764

Fig. 11. BER performance for a 2 × 2 TR-MIMO system. ISI, IPI, and interchannel interference have been considered.

considered. As we can see in Fig. 10, MIMO-TR outperforms 784 MISO-TR, and MISO-TR outperforms SISO-TR. Tests were 785 conducted for data rates of 500 and 225 Mb/s. As expected, an 786 increase in the data rate leads to a performance degradation. For 787 a data rate of 250 Mb/s, a power gain of about 13 dB (compared 788 with SISO-TR) is achieved by employing a 4 × 4 MIMO array. 789 The power gain in a system with ISI and IPI is slightly higher 790 than the theoretical power gain 10 log10 (M N ), as derived in 791 Section IV-A, where we assume that there are no ISI and IPI. 792 To illustrate the concept of spatial multiplexing for MIMO- 793 TR, we study a simple scenario of 2 × 2 MIMO-TR system. 794 As stated in Section V, the signal will first be serial-to-parallel 795 converted into two streams, precoded with TR precoding, 796 and then sent to two transmitting antennas for simultaneous 797 transmission. The signal passes through the channel and is 798 corrupted by AWGN. Fig. 11 shows the BER performance for 799 the two parallel subchannels. Compared with the beamforming 800 approach addressed previously, one more interference source 801 from interchannels need to be considered in the spatial multi- 802 plexing simulation. 803

IE E Pr E oo f

Fig. 9. BER performance in terms of received bit energy. IPI and ISI have been considered. SISO result is the average of 16 channels, and MISO is the average of four channels.

13

VIII. C ONCLUSION

804

TR is considered in the framework of UWB MIMO. Ex- 805 perimental measurements have been used to evaluate the per- 806 formance. Multiple antennas are found to be very useful in a 807 UWB system. The working principles for MIMO in a UWB 808 system is fundamentally different from that for a narrowband 809 flat-fading wireless system. The fading is not a concern for 810 UWB communications. The leading mechanism behind UWB 811 MIMO is to exploit the space–time focusing that is unique to an 812 impulse signal. The design philosophy is to use deterministic 813 signal model as digital subscriber line, rather than the statistic 814 fading signal in a narrowband system. This reported work is 815 the first step toward the nonfading transmission [19] for UWB 816 systems. The time-reversed MIMO matrix is combined with the 817 physical channel to form an effective matrix channel that can be 818 treated deterministically [19]. 819 One feasible scheme of combining the MIMO with the 820 one-finger correlator has been demonstrated. Some further 821

14


simplification of the transceiver can be done using a chirp UWB system. When a pair of chirp waveforms in the transmitter and receiver is used to replace the second-order Gaussian 825 pulse as the modulation waveform, the new scheme may prove 826 to be useful for some high-data-rate communications with a 827 relatively low cost [16], [18]. What we have learned from the 828 past is that too many multipath fingers force us to walk away 829 from the famous RAKE structure to reduce the transceiver cost. 830 For example, for a transmitted pulse of 1 ns, a dense multipath 831 spread of 1000 ns is observed in a metal cavity in [16] and 832 [18], and it is believed that TR is necessary to capture the 833 spread multipath energy. As suggested in this paper, the MIMO 834 transmission with TR can be further used to make full use of 835 the space–time channel responses at the same time. The work 836 reported here thus paves the way for the potential solution of the 837 communication problem in some RF harsh environments like a 838 metal cavity. 822

823 824

839

ACKNOWLEDGMENT

AQ7

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The authors would like to thank Dr. B. Sadler, Dr. S. K. Das, and Dr. R. Ulman for the helpful discussions and the anony842 mous reviewers for their thorough reading of the manuscript 843 and their constructive suggestions. 840 841

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[38] S. M. Emami, J. Hansen, A. D. Kim, G. Papanicolaou, A. J. Paulraj, D. Cheung, and C. Prettie, “Predicted time reversal performance in wireless communications using channel measurements,” IEEE Commun. Lett., 2004. [39] E. J. Badhdady, Lectures on Communications System Theory. New York: McGraw-Hill, 1961, ch. 14. [40] M. R. Bell, “Information theory and radar waveform design,” IEEE Trans. Inf. Theory, vol. 39, no. 5, pp. 1578–1597, Sep. 1993. [41] H. T. Nguyen, I. Z. K. Kovacs, and P. C. F. Eggers, “A time reversal transmission approach for multiuser UWB communications,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3216–3224, Nov. 2006. [42] H. T. Nguyen, I. Z. K. Kovacs, and P. C. F. Eggers, “A time reversal transmission potential for multiuser UWB communications,” IEEE Trans. Antennas Propag., pp. 1–13, 2005. [43] H. T. Nguyen, P. Kyritsi, and P. C. F. Eggers, “Time reversal technique for multi-user wireless communication with single tap receiver,” in Proc. 16th IST Mobile Wireless Commun. Summit, 2007, pp. 1–5. [44] H. T. Nguyen, J. B. Andersen, G. F. Pedersen, P. Kyritsi, and P. C. F. Eggers, “Time reversal in wireless communications: A measurement-based investigation,” IEEE Trans. Wireless Commun., vol. 5, no. 8, pp. 2242–2252, Aug. 2006. [45] R. J. Cramer, “An evaluation of ultrawideband propagation channels,” Ph.D. dissertation, Univ. Southern Calif., Los Angeles, CA, Dec. 2000. [46] R. M. Buehrer, “Ultra-wideband propagation measurements and modeling final report,” in DARPA NETEX Program. Blacksburg, VA: Virginia Polytechnic Inst. State Univ., Jan. 2004, p. 333. [47] R. Esmailzadeh, E. Sourour, and M. Nakagawa, “PreRAKE combining in time-division duplex CDMA mobile communications,” IEEE Trans. Veh. Technol., vol. 48, no. 3, pp. 795–801, May 1999. [48] N. Guo, R. C. Qiu, Q. Zhang, B. M. Sadler, Z. Hu, P. Zhang, Y. Song, and C. M. Zhou, Handbook of Sensor Networks. Singapore: World Scientific, 2009, ch. Time Reversal for Ultra-Wideband Communications: Architecture and Test-bed, pp. 1–41.

Nan Guo (S’96–M’99) received the M.S. degree in telecommunications engineering from Beijing University of Posts and Telecommunications, Beijing, China, in 1990 and the Ph.D. degree in communications and electronic systems from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 1997. In September 1990, he became a faculty member with UESTC. In January 1997, he joined the Center for Wireless Communications, University of California, San Diego. From December 1999 to January 2002, he was a Research/System Engineer with Golden Bridge Technology, Inc., West Long Branch, NJ, where he was deeply involved in 3G code division multiple access system design, intellectual property development, and standardization activities. From June 2002 to February 2003, he was a Research Engineer with the System Group, Ansoft Corporation, Elmwood Park, NJ, where his major responsibility was software development, with emphasis on functionality modeling of emerging technologies. Since 2004, he has been with the Center for Manufacturing Research, Tennessee Technological University, Cookeville, doing R&D and laboratory work. He has over 15 years of industrial and academic experience in R&D, teaching, and hands-on work. His research interests are in the area of wireless communications. His recent focus is on radio system design, optimization, and implementation.

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Robert Caiming Qiu (S’93–M’96–SM’01) received the Ph.D. degree in electrical engineering from New York University, NY. He is currently a Professor with the Department of Electrical and Computer Engineering, Center for Manufacturing Research, Tennessee Technological University (TTU), Cookeville. His current interest is in wireless communication and networking systems, particularly ultrawideband (UWB). He was the Founder-CEO and President of Wiscom Technologies, Inc., Clark, NJ, which manufactured and marketed WCDMA chipsets. Wiscom was sold to Intel in 2003. Prior to Wiscom, he was with GTE Laboratories, Inc. (now Verizon), Waltham, MA, and Bell Laboratories, Lucent, Whippany, NJ. He has worked in wireless communications, radio propagation, digital signal processing, EM scattering, composite absorbing materials, radio-frequency microelectronics, ultrawideband, underwater acoustics, and fiber optics. He is the author of over 40 technical papers and four book chapters. He is the holder of over ten U.S. patents pending in WCDMA. He contributed to 3GPP and IEEE standards bodies and delivered invited seminars to institutions, including Princeton University, Princeton, NJ, and the U.S. Army Research Laboratory. He served on the advisory board of the New Jersey Center for Wireless Telecommunications. He is an Associate Editor for the International Journal of Sensor Networks (Interscience) and Wireless Communication and Mobile Computing (Wiley). He is a Guest Book Editor for Ultra-Wideband (UWB) Wireless Communications (Wiley, 2005) Dr. Qiu received the Kinslow Research Award from TTU. He serves as a Member of Technical Program Committee for GLOBE-COM, WCNC, and MILCOM. He serves as an Associate Editor for the IEEE TRANSACTIONS ON V EHICULAR T ECHNOLOGY . He is a Guest Book Editor for three Special Issues on UWB, including the IEEE JOURNAL ON SELECTED AREAS IN C OMMUNICATIONS and the IEEE T RANSACTIONS ON V EHICULAR TECHNOLOGY.

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997 Chenming Zhou (S’05–M’08) was born in Jiangxi, 998 China, in 1979. He received the B.S. degree in 999 physics from Changsha University of Science and 1000 Technology, Changsha, China, in 2000, the M.S. 1001 degree in optical science from Beijing University of 1002 Technology, Beijing, China, in 2003, and the Ph.D. 1003 degree in electrical engineering from Tennessee 1004 Technological University, Cookeville, in 2008. 1005 He is currently a Research Scientist with the De1006 partment of Electrical and Computer Engineering, 1007 Carnegie Mellon University, Pittsburgh, PA. His gen1008 eral research interests include radio propagation, wireless sensor network, and 1009 radio-frequency systems.

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AUTHOR QUERIES AUTHOR PLEASE ANSWER ALL QUERIES

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AQ1 = Note that UWB was defined here as Ultrawideband for consistency throughout. Edit okay? AQ2 = Write out STIR. AQ3 = What does RAKE stand for? Please define it first here. AQ4 = What does CLEAN stand for? Please define it first here. AQ5 = Looks like there’s a missing equation here. AQ6 = Table VI-B was changed to Table 1, which was not mentioned anywhere in the text. Correct? AQ7 = Please provide volume and issue number in Ref. [8]. AQ8 = Please provide page range in Ref. [15]. AQ9 = Please provide issue number in Ref. [23]. AQ10 = Please provide publication update in Ref. [38]. AQ11 = Please provide volume and issue number in Ref. [42]. AQ12 = Please provide complete list of authors in Ref. [46]. AQ13 = Write out GLOBE-COM, WCNC, and MILCOM in full.

Note that reference [10] and [12], [13] and [24], [14] and [33] are the same. Ref. [12], [24] and [33] was deleted, citations and bibliographic list were renumbered accordingly. Please check. END OF ALL QUERIES

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Time-Reversed Ultrawideband (UWB) Multiple Input–Multiple Output (MIMO) Based on Measured Spatial Channels

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Chenming Zhou, Member, IEEE, Nan Guo, Member, IEEE, and Robert Caiming Qiu, Senior Member, IEEE

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Abstract—Ultrawideband (UWB) technology is envisioned for future wireless high-data-rate transmission. A UWB system with multiple antennas takes advantage of the rich scattering environment to increase the data rate. On the other hand, given rich multipath, time reversal (TR) uses scatterers to create space and time focalization at a target point by coherent addition of all scattered contributions at that point. This paper analyzes the performance of an impulse TR-multiple-input–multiple-output (MIMO)-UWB system with a simple one-correlator receiver. The performance analyses are based on UWB spatial channels measured in an office environment.

16 Index Terms—Impulse multiple-input–multiple-output 17 (MIMO), intersymbol interference (ISI), multipath, spatial 18 focusing, time reversal (TR), ultrawideband (UWB).

I. I NTRODUCTION

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LTRAWIDEBAND (UWB) transmission has recently emerged as a potential candidate for future high-data-rate applications [1]–[7]. Impulsive transmission with short pulse duration makes the multipath components resolvable, which, 24 in turn, leads to immunity to the multipath fading. On the 25 other hand, however, capturing multipath energy distributed 26 in dense multipath components becomes a challenge. Time 27 reversal (TR) signal processing, which is a signal processing 28 technique popular in acoustics [8], has recently been applied 29 to electromagnetics [9]–[20]. A tutorial of TR and an extensive 30 review of literature for UWB communications is given in [13], 31 [48]. An attractive aspect of TR signal processing is the fact 32 that it makes use of multipath propagation. UWB impulsive 20

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radio is extremely interesting in this context, since hundreds 33 or thousands of paths are available (see, e.g., [16] and [18]). 34 Given a specific time and location, TR precoding has been 35 mathematically proved to be the optimum in the sense that it 36 maximizes the amplitude of the field at that time and location 37 [21]. It is then called spatiotemporal matched filter [22] because 38 it is analogous to a matched filter both in time and space. It 39 is also called transmit matched filter since the matched filter 40 is put at the transmitter side. However, TR alone may not 41 effectively reduce the channel delay spread, considering the 42 fact that it maximizes the peak amplitude but does not impose 43 any constraint at its sidelobe level. As shown in [20], multiple 44 antennas at the transmitter [i.e., multiple-input–single-output 45 (MISO)-TR] are then required to suppress the intersymbol 46 interference (ISI). The MISO-TR scheme also achieves array 47 gain with a factor of M (antenna number) by automatically 48 aligning the arrival peak [12]. MISO-TR has been extensively 49 investigated in the past years (e.g., [23] and [24]), and a natural 50 extension is to exploit the scenario of multiple-input–multiple- 51 output (MIMO) for TR signaling. 52 The MIMO technique uses multiple antennas at both ends 53 of the wireless link and is believed to be the most promising 54 approach to effectively use the transmission spectrum and 55 power. This technology has been extensively studied recently 56 [25], [26]. It has been shown that the channel capacity for 57 a MIMO system is increased as the number of antennas in- 58 creases. MIMO is mostly used in conjunction with orthogonal 59 frequency-division multiplexing (OFDM), which is a modula- 60 tion technology that is part of the IEEE 802.16 standard and 61 will also be part of the IEEE 802.11n high-throughput standard 62 due to its potentially high-data-rate capability. In addition to 63 the benefit from flat fading, MIMO also benefits from the rich 64 scattering of the channel. The use of multiple antennas and 65 space–time signal processing in a UWB system has been an 66 interesting topic [27]–[29]. 67 MIMO-UWB is a concept that can be implemented in several 68 alternative ways; in addition to the aforementioned OFDM 69 MIMO, another way is based on a scheme using impulse 70 radio to transmit pulses in one or multiple frequency bands, 71 such as the multiband UWB solution [30]. Here, we propose 72 the use of TR precoding combined with MIMO [14], which 73 we call impulse MIMO-TR. Note that we are interested in 74 the limits of UWB signals, i.e., pulses with ultrashort dura- 75 tion and extremely wide bandwidth. The proposed MIMO-TR 76 aims at implementing MIMO directly in the time domain and, 77

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AQ1


Manuscript received April 3, 2008; revised September 17, 2008 and December 8, 2008. This work was supported in part by the Office of Naval Research under Grant N00014-07-1-0529, by the National Science Foundation under Grant ECS-0622125, by the Army Research Laboratory and the Army Research Office under STIR Grant W911NF-06-1-0349, and by the Defense University Research Instrumentation Program under Grant W911NF-05-10111. The review of this paper was coordinated by Dr. K. T. Wong. C. Zhou is with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA (e-mail: czhou@ cmu.edu). N. Guo is with the Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38505 USA (e-mail: nguo@ tntech.edu). R. C. Qiu is with the Department of Electrical and Computer Engineering, Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38505 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2008.2012109

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gain of 10 log10 (M N ) dB can be achieved by using a MIMO 136 system with M antennas at the transmitter and N antennas at 137 the receiver. We also investigate the performance based on the 138 bit energy at the receiver. We compare the performances for dif- 139 ferent scenarios [i.e., MIMO, MISO, and single-input–single- 140 output (SISO)], considering one-correlator receiver. 141 In practice, when a pulse is short and the data rate is low, 142 the above conditions (resolvable multipath and no ISI) tend 143 to be satisfied. However, for the case of high data rates and 144 relatively wide pulses, the conditions will no longer hold. 145 The performance of such a practical system is investigated 146 through Monte Carlo simulation. There are no data (on the 147 channel model of multiple antennas) that meet the need of 148 this research for spatial–temporal focusing; we have conducted 149 a series of channel measurements in an office environment. 150 The measurements are performed in the time domain, and the 151 CLEAN algorithm [45], [46] is employed to extract the channel 152 impulse response (CIR) from the measured data. 153 TR with multiuser UWB communications has been studied 154 by some other researchers (e.g., [41]–[44]), and the single-user 155 scenario has been considered in this paper. 156 The structure of this paper is given as follows. The principle 157 of TR signal processing and its suboptimum receiver—one- 158 correlator receiver—are introduced in Section II. The system 159 performance analysis for single antenna at both ends is given 160 in Section III. Then, the performance analysis is extended to 161 multiple-antenna scenarios in Sections IV and V. The exper- 162 imental description regarding the channel measurements are 163 shown in Section VI. Numerical results based on the measured 164 spatial channels are given in Section VII. Finally, we conclude 165 this paper in Section VIII. 166

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hence, is believed to be a simpler scheme than its frequencydomain counterpart. However, most research on UWB-MIMO is carried out in the frequency domain; very few time-domain 81 UWB MIMO results are reported. Sibille [31] proposed the 82 use of maximal ratio combining (MRC) RAKE combining to 83 accomplish the temporal alignment of received pulses, which 84 causes huge complexity at the receiver. However, pulses are 85 automatically aligned by using TR precoding at the cost of 86 increased transmitter complexity. It is shown in [32] that TR 87 precoding can achieve the same error performance as the MRC 88 combining scheme. 89 Separating the data streams at the receiver is challenging 90 for parallel data transmission. For the traditional narrowband 91 MIMO, singular-value decomposition (SVD) is usually applied 92 to decompose the channel into several independent subchan93 nels. For multitone UWB signals with gigahertz bandwidth, 94 however, applying SVD to each frequency tone significantly 95 increases the system complexity. In [33], a zero-forcing scheme 96 is proposed to separate N parallel transmitted data streams for 97 each resolvable multipath component. In this paper, considering 98 the good spatial–temporal focusing characteristics provided by 99 TR, we will show that TR precoding can also decompose the 100 channel, with reasonable complexity. The primary motivation 101 of this work is to investigate a system structure that has a good 102 tradeoff between complexity and performance. MIMO-TR is 103 such a structure. 104 Although MIMO-TR can achieve high data rates by parallel 105 data transmission, the applications of MIMO-TR are not limited 106 to support high data rates. With a beamforming approach, 107 where all the transmitter antenna elements transmit the same 108 information bit, a high signal-to-noise ratio (SNR) can be 109 obtained at the receiver, and hence, the transmission distance 110 can be greatly extended, depending on the number of antennas 111 employed in the array. It is shown in this paper that given the 112 same transmission power, the peak SNR at the receiver grows 113 linearly with M (the number of transmitter antenna elements) 114 and N (the number of receiver antenna elements). 115 The philosophy behind TR is the so-called transmit centric 116 processing, i.e., processing the signal at the transmitter side 117 before transmission to combat the deteriorating effects of the 118 channel. The motivation is from the fact that the power and 119 computation resources are generally more readily available at 120 the transmitter side. The main advantage of transmit centric 121 processing is the possibility to simplify the receivers, which 122 is desirable in the case of one central node serving for many 123 distributed sensor nodes. 124 Due to the favorable spatial–temporal focusing of the 125 MIMO-TR technique, the energy of a receive signal tends to 126 focus into a geometric spot and into a time instant. We propose 127 the use of a simple correlation receiver with one correlator to 128 capture the peak energy and ignore the rest of the energy as in129 terference. By doing this, the receiver complexity can be greatly 130 reduced since there are no channel estimation and equalization 131 in the receiver. However, as we will show later, the performance 132 of such a simple receiver can still achieve the additive white 133 Gaussian noise (AWGN) bound under ideal conditions that all 134 the multipath components are resolvable and that there is no 135 ISI in the system, given the same transmitted power. An energy 78

AQ3


II. P RINCIPLE OF TR S IGNAL P ROCESSING

A. Spatial–Temporal Focusing Through TR: Exploitation of Space–Time Symmetry

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TR cannot be understood, at first thought, as a simple 170 scheme: moving the matched filter to the transmitter side as 171 a TR filter. There is deep physics in the scheme to exploit 172 the spatial–temporal focusing, which is unique to impulsive 173 UWB signals. The physical foundation of TR is the space–time 174 symmetry, e.g., in general relativity. To avoid digressing very 175 far, we only outline—trying our best to use communications 176 engineering language—the physical mechanism behind the TR 177 scheme since much confusion has been caused in the literature 178 due to the lack of understanding of this mechanism. The main 179 motivation of this summary of known physical results is to 180 strike the point that the space–time symmetry cannot be taken 181 for granted: it must first be examined before it is used widely. 182 So far, this symmetry principle is established only for some 183 very simplistic physical regions. The experimental approach 184 must be used for realistic system settings to empirically support 185 this claim. The state-of-the-art status of theoretical justification 186 for the principle of space–time symmetry in a macroscope phe- 187 nomenon level is far from satisfactory, particularly for realistic 188 UWB communications applications. 189 It is well known that space–time symmetry is universally true 190 in physics. Radio waves follow the law of electromagnetics: 191

AQ4


The knowledge of symmetry (reciprocity) properties of a field frequently facilitates the determination of explicit field solutions [35]. For this purpose, one considers certain auxiliary or 195 adjoint problems related to the original field problem in such a 196 way as to reveal the space–time symmetry of the original field. 197 If the field, problems are phrased in terms of Green’s 198 functions—or CIR in linear system terms—which describe 199 the field response to a “point-source excitation,” with the 200 desired properties appearing most succinctly as symmetries in 201 these Green’s functions. A rigorous derivation of these sym202 metries in inhomogeneous lossy media, which is the case of 203 UWB communications, is very difficult. Rather, some insight 204 can be gained using simplified physical model. Experimen205 tal results are used to approximately establish the symme206 tries for realistic environments, e.g., indoors,1 and intravehicle 207 environments [14]. 208 For homogeneous media, or vacuums, the symmetries are an209 alytically established in [35, ch. 1]. If field symmetries exist, the 210 properties of the electromagnetic Green’s functions (and, thus, 211 CIRs) can be inferred prior to their explicit determination. In an 212 unbounded homogeneous stationary region, the field equations 213 are invariant under arbitrary linear space–time displacements, 214 i.e., the solutions are functions of the differences r − r and 215 t − t , where a pair of any space–time points (r, t) and (r , t ) 216 is considered. Mathematically, the Green’s function has the 217 symmetric form

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Fig. 1. Block diagram of the optimum transceiver design. (a) Matched Filter. (b) TR.

B. TR: Spatial–Temporal Matched Filter at Transmitter

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g(r, r ; t, t ) = g(r − r ; t − t ).

(1)

If we exchange the space–time point (r, t) with (r , t ), im219 plying (r − r; t − t), then the Green’s function is invariant. 220 In other words, when the spatial locations of two antennas are 221 switched, implying r − r, and the time is reversed, implying 222 t − t, the resultant Green’s function is identical to the original 223 one. Equation (1) is exactly the foundation of the so-called 224 TR scheme, requiring both TR of the CIR measured in one 225 direction and the exchange of two spatial locations of the 226 involved antenna pair. 227 Equation (1) is valid for the unbounded homogeneous sta228 tionary region with point-source excitation (ideal impulsive 229 antenna). For a general medium (channel), the adjoint-field 230 problem needs to be solved, using a temporal and spatial 231 reflection transformation [35]. As shown above, for the general 232 lossy bounded inhomogeneous and moving region with non233 point-source excitation (realistic UWB antennas), the adjoint234 field problem is open. Some simple physical media are solved, 235 including the following [35]: 1) free space (unbounded and 236 homogeneous) with point-source excitation; 2) homogeneous 237 medium with point-source excitation for both bounded re238 gions; 3) free space with an electrical dipole current excitation; 239 4) free space with planar stratified scattering structures with 240 Hertz potential excitation; and 5) bounded cylindrical regions 241 (a uniform waveguide of arbitrary cross section transverse to 242 the guide axis and bounded by perfectly conducting walls).

218

1 To

the authors’ best knowledge, this is the first reported experimental result in the field of UWB communications regarding the channel’s space–time symmetry.

Consider a communication system illustrated in Fig. 1(a). 244 Here, p(t) is the transmitted pulse waveform, and h(t) denotes 245 the impulse response of the multipath channel. The received 246 signal before c1 (t) can be written as r(t) = p(t) ∗ h(t) + 247 n(t) = y(t) + n(t), where n(t) is AWGN with a two-sided 248 power spectral density of N0 /2, and y(t) = p(t) ∗ h(t). Given 249 r(t), a matched filter y(−t), which is matched to y(t), provides 250 the maximum signal-to-noise power ratio at its output. The 251 matched filter here can be virtually decomposed into two filters, 252 with the first filter matched to the CIR h(t) and the second one 253 matched to the pulse waveform p(t). As shown in Fig. 1(a), 254 this decomposition can be done by setting c1 (t) = h(−t) and 255 c2 (t) = p(−t). 256 We shall now consider what happens if we move the receiver 257 front-end matched filter c1 (t) to the transmitter but still keep the 258 filter c2 (t) at the receiver, as depicted in Fig. 1(b). This leads 259 to a TR system that is of interest in this paper. Note that this 260 operation actually makes the receiver suboptimum, as will be 261 shown later. However, by doing this, we simplify the receiver 262 structure and make more effective use of the transmitter energy 263 by concentrating it in the favorable frequency regions. 264 We still let c2 (t) = p(−t) and wish to find the optimum c1 (t) 265 such that it maximizes the SNR at the output of c2 (t), which is 266 given by 267 2 +∞ ∗ 2 P (f )P (f )C1 (f )H(f )df

SNR1 =

−∞

N0

+∞ −∞

(2)

2

|P (f )| df

under the constraint of fixed transmitted power, which is 268 defined by 269 +∞ P1 = |P (f )C1 (f )|2 df. −∞

(3)

4


Here, P (f ), H(f ), C1 (f ), and C2 (f ) are the Fourier transforms of p(t), h(t), c1 (t), and c2 (t), respectively. Note that the denominator of (2) does not depend on C1 (f ). To maximize 273 (2), equivalently, we need to maximize the ratio

270

271 272

+∞ 2 |P (f )|2 C1 (f )H(f )df ρ=

−∞

+∞

−∞

274

.

(4)

|P (f )C1 (f )|2 df

According to Schwartz inequality, we have 2 +∞ P (f )C1 (f )H(f )P ∗ (f )df −∞

+∞ +∞ 2 ≤ |P (f )C1 (f )| df · |P ∗ (f )H(f )|2 df. (5)

275

−∞

Substituting (5) into (4) yields

+∞ ρ≤ |P ∗ (f )H(f )|2 df −∞

(6)

with equality holding only when C1 (f ) = λ1 H ∗ (f ), or in the time domain, c1 (t) = λ1 h(−t), where λ1 is a constant that is 278 chosen to satisfy the power constraint (3). 279 We then have proved that a time-reversed precoding is opti280 mum in terms of SNR, given c2 (t) = p(−t). 276 277

294 295

Channel estimation is a difficult task, and in a TR system, 296 this task is shifted to the transmitter side. We are interested 297 in a suboptimum receiver filter, and the transfer function of 298 which is matched to P ∗ (f ), instead of the optimum one 299 P (f )H(f )H ∗ (f ). This case is exactly the scenario if we move 300 the first channel matched filter c1 (t) to the transmitter side, as 301 discussed at the beginning of this section. The following sec- 302 tion studies TR system performance with such a suboptimum 303 receiver, namely, the one-correlator receiver, first for a single- 304 antenna system, which is later extended to a multiple-antenna 305 system. 306 The proposed scheme is suboptimal and of low complexity 307 compared to many optimal criteria. Consider a joint opti- 308 mization scenario, where h(t) is given and we wish to find 309 the optimum pair of c1 (t) and c2 (t) under the constraint of 310 fixed transmitted power (denoted as P2 ). If the signal has 311 finite time duration, the optimum transmitted waveform is the 312 eigenfunction corresponding to the maximum eigenvalue of the 313 TR operator of the CIR h(t) [40]. We should, however, note that 314 other eigenvalues may contain significant information about the 315 channel; thus, putting as much energy to just one frequency 316 (to optimize in terms of SNR) may decrease channel capacity 317 substantially—leading to low channel capacity. We still need 318 to implement a water-filling algorithm to achieve the optimum 319 capacity. When signal duration is infinite, i.e., T = ∞, this 320 optimization leads to a sinusoidal transmitted waveform, as 321 shown in [39]. In other words, we need to concentrate all the 322 transmitted power to the frequency with maximum transmission 323 capability. 324

IE E Pr E oo f

−∞

D. Suboptimum Receiver Filter for TR System: One-Correlator Receiver

III. P ERFORMANCE A NALYSIS

281

C. Optimum Receiver Filter for TR System

A. System Description

We now consider another case. Given TR precoding, i.e., C1 (f ) = H ∗ (f ), we wish to optimize the receiver filter 284 c2 (t) (maximizing SNR) under the fixed transmitted power 285 constraint of 282 283

+∞

(7)

−∞ AQ5

286 287 288

The receiving SNR at the output of c2 (t) can be expressed as Similarly, we refer to Schwartz inequality and have the SNR formulation as follows: 2 SNR ≤

+∞ −∞

|P (f )H ∗ (f )H(f )|2 df N0

(8)

with equality holding only when C2 (f ) = λ2 P ∗ (f )H(f ) × H ∗ (f ). It is suggested that the optimal receiver filter for a TR 291 system should be a filter whose impulse response is in the form 292 of λ2 p(−t) ∗ h(t) ∗ h(−t). This result is actually a validation 293 of the matched filter theory.

289 290

326

Consider a single-user transmission. The transmitted signals 327 before precoding can be expressed as 328 s(t) =

+∞

i=−∞

|P (f )H ∗ (f )|2 df.

P2 =

325

si (t) =

+∞

Eb bi p(t − iTb )

(9)

i=−∞

where Eb is the transmitted bit energy, and bi ∈ {±1} is 329 the ith information bit. Binary antipodal modulation has been 330 considered in this paper. p(t) is the UWB pulse with a width 331 of Tp , and assume that the pulse takes care of the impacts 332 of circuits and antennas at the both sides. The energy of p(t) 333 +∞ is normalized to unity, i.e., Ep = −∞ p2 (t)dt = 1. Tb is the 334 bit interval. Generally, we have Tb Tp to avoid possible ISI 335 caused by the multipath channel. In this paper, we will show 336 that by using a MIMO-TR technology, Tb and Tp could take the 337 same level without significant performance degradation. 338 For the sake of simplicity, we assume that there is no per-path 339 pulse distortion [34] caused by the channel. If per-path pulse 340 distortion does occur, a number of taps can be used to represent 341 the per-path impulse response, as done in [36], such that the 342 tap-delay-line model in (10) is still valid in its mathematical 343 form, but not physically interpreting the physics phenomenon. 344


In this case, the received signals are just a series of replicas 346 of the transmitted signals, with different attenuations and time 347 delays. The CIR then can be modeled as 345

h(t) =

L

αl δ(t − τl )

(10)

l=1

349 350

where L is the number of multipath components, and αl and τl are their individual amplitudes and delays. Note that each term in (10) does not necessarily correspond to a physical path.

351

B. Matched Filter Performance Bound

352

If there is no TR and a single antenna is employed at both the transmitter and the receiver, the received signal can be expressed as

348

353 354

ri (t) =

L

αl si (t − τl ) + n(t).

(11)

l=1

The optimum receiver for the above signal would be a matched filter matched to the signal part of ri (t). Such a receiver would achieve the performance bound, namely, matched filter bound, which is described as 2GEb (12) Pe = Q N0

∞ √ 2 where Q(x) = x (1/ 2π)e−y /2 dy is the Q-function, G = +∞ 360 −∞ |h(t)|2 dt is the channel gain, and Eb represents the trans361 mitted bit energy. The bit energy measured at the receiver side ˜b . 362 is denoted by E 363 In reality, it is believed that the performance bound in (12) 364 requires a very complex receiver and, thus, is hard to achieve 365 due to the complicated UWB multipath channel. In this section, 366 we will show that by using TR precoding at the transmitter, the 367 AWGN performance bound can be achieved with a simple one368 correlator receiver under some conditions. 359

369 370

C. MISO-TR Performance Analysis Based on Transmit Bit Energy Eb

Before we consider MIMO-TR, let us start with a simpler scenario of SISO-TR. Consider a nonrealistic case where we use a short pulse so that the propagation delay difference between any adjacent multipath components is always larger 375 than the pulse duration Tp . In addition, we assume that Tb is 376 sufficient enough so that there is no ISI. 377 For SISO-TR, the received signal can be expressed as 371

372 373 374

scenario. It is apparent that hSISO (t) is an autocorrelation with 380 eq a peak occurring at t = T . The magnitude of√ the peak √ √ is equal 381 +∞ to G, i.e., hSISO (t = T ) = −∞ |h(t)|2 dt/ G = G. 382 eq Due to its autocorrelation nature, most of the energy is 383 focused in the central (main) peak of the CIR hSISO (t). Since 384 eq we assume that there are no interpulse interference (IPI), ISI, 385 and pulse distortion, we can use a filter matched to the main 386 component of the received signal. It is proved in the following 387 that even by using such a simple receiver (with one correlator), 388 we can achieve the same performance as the matched filter 389 bound. 390 The main component of the receiving signal can be ex- 391 pressed as 392 √ rimain (t) = G Eb bi p(t − iTb − T ). (14) We then use a filter matched to p(t) to pick up the energy lying 393 in the aforementioned main component of the received signal. 394 The performance can be characterized using the following 395 analytical formula: 396 2GEb PeSISO = Q . (15) N0

IE E Pr E oo f

355 356 357 358

5

riSISO (t) = si (t) ∗ c(t) ∗ h(t) + n(t)

1 √ = si (t) ∗ h(T − t) ∗ h(t) + n(t) G (t) + n(t) (13) = si (t) ∗ hSISO eq √ 378 where c(t) = h(T −t)/ G is the prefilter code, and hSISO (t) = eq √ 379 h(T − t) ∗ h(t)/ G is the equivalent CIR for the SISO-TR

Comparing (12) and (15), it is evident that a TR system with 397 a one-correlator receiver can achieve the same performance 398 as a system without TR but with an ideal matched filter. The 399 same conclusion has been obtained by other researchers [32], 400 [47] through different approaches in the pre-RAKE systems. 401 Therefore, for a TR system with a one-correlator receiver, we 402 have the following observation: On the one hand, TR filter 403 improves the system performance by precoding the transmitted 404 signal to concentrate the transmitted power to the spectral 405 regions with less attenuation and, thus, make more effective 406 use of transmitted power; in contrast, system performance is 407 degraded by using a nonoptimum receiver (a one-correlator 408 receiver). Remarkably, the result in this section implies that 409 the improvement by placing a channel-matched TR filter at the 410 transmitter is exactly equal to the degradation caused by not 411 using such an optimum filter at the receiver. Again, this result 412 is true in the absence of ISI and IPI—a stringent condition. 413 In the following, we will extend this result to a scenario of 414 TR with multiple antennas. 415 IV. MIMO-TR: F OCUSING S PATIAL –T EMPORAL E NERGY TO A S HARP P EAK

A. MIMO-TR Precoding

416 417 418

When a short pulse is sent to the channel, the radiated energy 419 is distributed among different spatial locations and spread in 420 time over a large number of pulses at any observation location 421 (due to multipath). Since a TR mirror—here, antenna arrays at 422 both MIMO terminals—can be viewed as a “channel sampler,” 423 more antennas imply more spatial sampling points, which 424 means that more energy can be captured. A MIMO-TR (4 × 4) 425 system configuration is illustrated in Fig. 2. Let hmn (t) denote 426 the CIR between the mth antenna at the transmitter and nth 427 antenna at the receiver, and let cm (t) be the corresponding 428

6


IE E Pr E oo f

Fig. 2. TR precoded MIMO communication system, with M = 4, and N = 4.

Fig. 3. Timing for the peak of the received signal in a TR system. The peak of the equivalent CIR will occur exactly at the time t = T , independent of the element location, antenna type, and channel.

429

prefilter code employed in the mth antenna branch at the M × N MIMO-TR system, the code

430 transmitter. In a general 431 cm (t) can be written as

cm (t) = Am

N

hmn (T − t)

(16)

n=1

where T is the length of the filter required to implement the TR operation [20], and Am is the power scaling factor to 434 normalize the total transmission power from different antenna 435 branches. It should be noted that different power allocation 436 schemes can be implemented by choosing different factors Am 437 [23]. In this paper, Am ’s are set to be equal for all the antenna 438 elements, i.e., 432 433

Am = A =

1

M

N

(17)

Gmn

m=1 n=1

+∞ where Gmn = −∞ |hmn (t)|2 dt is the channel gain of CIR hmn (t). Obtaining the TR precoding waveform cm (t) for the mth 442 antenna branch is straightforward. First, a sounding pulse w(t) 443 is sent through all the N antennas in the receiver to the trans444 mitter. Second, the receiving signals at each transmitter antenna

439 440 441

branch are then recorded, digitized, and time reversed. The 445 noise-free signal received by the mth antenna at the transmitter 446 can be expressed as follows: ym (t) = N n=1 hmn (t) ∗ w(t). 447 The foundation for using backward channel sounding is channel 448 reciprocity. For MIMO channels, no experimental confirmation 449 of this assumption has been done. If the sounding pulse w(t) is 450 sufficiently short, we can directly use the time-reversed version 451 of ym (T − t) as the precoding cm (t). Otherwise, deconvolution 452 effort is necessary to remove the pulse effect from the received 453 sounding signal. 454 One of the attractive characteristics of TR is that its temporal 455 focal point can be adjusted by a change in the parameter T . 456 The principle of timing alignment for TR for the mth antenna 457 element is illustrated by Fig. 3. If the same initial timing 458 between antenna elements in the same array is assumed (this 459 is a reasonable assumption because all the antenna elements of 460 an array use the same clock), all the peaks of the fields appear 461 at the receiver at the same time instant, independent of the 462 element location, antenna type, and channel. It turns out that 463 the peaks are aligned automatically. For a MISO case, all the 464 energy from different transmitter elements coherently adds up 465 at time T at the receive antenna. For a MIMO case, the energy 466 from different transmitter elements (viewed as several different 467 MISO arrays) will focus at each individual antenna element at 468 the receiver. 469


470 471

For MIMO-TR, the signal captured by the nth receive antenna can be expressed as M

rin (t) = si (t) ∗

{cm (t) ∗ hmn (t)} + n(t).

PeMIMO

All the signals captured by different antennas at the receiver can be combined directly, and the combined signal ri (t) can be expressed as ri (t) = si (t) ∗

N M

{cm (t) ∗ hmn (t)} + n(t)

n=1 m=1

= si (t) ∗ A

M N

n=1 m=1

N


k=1

+ n(t)

N


  hmk (T − t) ∗ hmn (t) =A   n=1 m=1 k=1,k=n  N 

Interference

N M m=1 n=1

Rmn (t − T )

(20)

Signal

where Rmn (t) = hmn (−t) ∗ hmn (t) is the autocorrelation of hmn (t). Let us use a 4 × 4 MIMO example to illustrate (20). 477 It can be seen from (20) that hMIMO (t) consists of 64 terms, eq 478 corresponding to 16 autocorrelations and 48 cross correlations. 479 These 16 autocorrelation terms will coherently add up due to 480 its automatic alignment characteristic addressed in this section. 481 In contrast, these 48 cross correlation terms adds up noncoher482 ently. As a result, the desired autocorrelation part forms a strong 483 peak and dominates in the received signal. 484 At t = T , the amplitude of the peak in hMIMO can be eq 485 approximated by the contributions of all the autocorrelation 486 terms as 475 476

A

N M

Gmn

m=1 n=1

487 488

" ¯ b /N0 ). PeMIMO = Q( 2M N GE

(24)

As a special case when N = 1, we have the performance of 495 a MISO-TR system with a one-correlator receiver as 496   M = Q 2 Gm Eb /N0  .

(25)

m=1

k=1

N M

¯ denote the averaged channel gain over the whole 492 Let G ¯ = (1/M N ) M N Gmn . 493 M × N channels, where G m=1 n=1 We have 494

PeMISO

(23)

m=1 n=1

(19)

n=1 m=1

+A

  M N = Q 2 Gmn Eb /N0  .

IE E Pr E oo f

hMIMO (t) = A eq

M N

where ≈ is used because the contributions from all the cross 489 correlation terms to the main peak have been ignored. In the 490 absence of ISI and IPI, it follows that 491

(18)

m=1

472 473 474

7

M N = Gmn .

(21)

m=1 n=1

The signal on the main component of the received signal is then approximated as M N main ri (t) ≈ Gmn Eb b(i)p(t − iTb − T ) + n(t) m=1 n=1

(22)

When M = 1 and N = 1, (24) reduces to (15) for the SISO- 497 TR scenario. It is straightforward from (25) that the perfor- 498 mance of a MIMO-TR system depends on the following three 499 parameters: the number of antennas M and N and the energy 500 ¯ Statistical characterization 501 of the multipath (channel gain G). ¯ of G is important. 502 ˜b 503 B. Performance Analysis Based on the Receive Bit Energy E The above analysis, e.g., (24), is based on the bit energy 504 Eb on the transmitter side. Since a lot of literatures analyze 505 ˜b , this 506 the performance based on the receiver side bit energy E ˜b . The one- 507 section also derives the performance formula for E correlator receiver proposed in this paper is not optimum. The 508 optimum receiver should be a receiver matched to the whole 509 receive waveform of (24). Then, the performance bound for 510 such a receiver would" be the matched filter bound, which is 511 ˜b /N0 )) (assuming bipolar modu- 512 expressed as Pe = Q( (2E lation). We introduce a new metric, namely, the peak energy 513 ˜b ), denoting the 514 ratio κ, which is defined as κ = (Epeak /E energy ratio of the peak to the total received energy. Here, 515 Epeak represents the energy of the signal peak. As a result, the 516 performance " of the one-correlator receiver can be expressed as 517 ˜b κ/N0 ). Pe = Q( 2E 518 +∞ 2 Let νmn,ij = −∞ |hmn (−t) ∗ hij (t)| dt − Imn,ij for 519 cross correlation (m = i, n = j) and νmn,ij = νmn = GRmn − 520 Gmn for autocorrelation (m = i, n = j). Here, Imn,ij = 521 +∞ |hmn (−t)∗ hij (t)|t=0 = −∞ hmn (t)×hij (t)dt, and GRmn = 522 +∞ 2 −∞ |Rmn (t)| dt is the channel gain of the equivalent 523 CIR Rmn (t). Here, we can see that the cross correlation 524 νmn,ij represents the sidelobe energy of the equivalent CIR 525 hmn,ij . 526 For MIMO-TR, the peak energy ratio κMIMO can be ex- 527 press in (26), shown at the bottom of the next page, where 528

8


N ¯ ν¯ = 1/M N · M n=1 νmn , and I = 1/[M N (N − 1)] · N M m=1 N 530 n=1 m=1 k=1,k=n Imn,mk . Assuming that CIRs are not 531 correlated with each other, i.e., I¯ ≈ 0, we have 529

¯2 G . ¯2 +G

κMIMO ≈ 532

A A2

(28)

max |heq (r0 , r1 , t)|2

.

(33)

t

For the scenario of MISO-TR, the equivalent CIR for different 556 users can be expressed as 557

Gm

#

M

νm + A

Gm

¯2 G $2 = 1 ¯2 . ¯+G Mν

heq (r0 , r0 , t) (29) =

m=1

For SISO-TR, we have

M

1 hm (r0 , −t) ∗ hm (r0 , t) √ " m=1 M hm (r0 , t)2

heq (r0 , r1 , t) G2 . ν + G2

M

1 hm (r0 , −t) ∗ hm (r1 , t) (34) √ " m=1 M hm (r0 , t)2

IE E Pr E oo f

κ=

(30)

As a sanity check, when N = 1, (27) reduces to the MISO case (29). When M = 1 and N = 1, (27) reduces to the SISO case (30). 538 It then can be seen from (28) and (29) that the performances 539 of both the MIMO and MISO scenarios depend on the number 540 of transmit antenna elements M . If we increase M , we actually 541 improve the focusing and then get better performance. A com542 parison of (27) and (29) shows that the peak energy ratio κ for a 543 MISO system is better than that of a MIMO system, particularly 544 when N is large, and that the performance improvement caused 545 by the increase of M for a MISO system is faster than that of a 546 MIMO system.

535 536 537

548

t

$2

M

m=1

547

(32)

The spatial focusing can be characterized by the metric 554 directivity D(r0 , r1 ), which is defined as 555

D(r0 , r1 ) =

¯2 G ≈ 2 ¯2 . ¯+G Mν

m=1 M

553

max |heq (r0 , r0 , t)|2

For MISO-TR, we have #

534

heq (r0 , r1 , t) = h(r0 , −t) ∗ h(r1 , t).

For large N , we have κMIMO

533

(27)

2N −1 ¯ MN ν

For the unintended user, the equivalent CIR would be

V. MIMO-TR: S PATIAL M ULTIPLEXING

A. Enhanced Spatial Focusing With Multiple Antennas

Let h(r0 , t) represent the CIR for the intended receiver located in the position r0 (x0 , y0 , z0 ), and let h(r1 , t) denote the CIR of another unintended user at the position r1 (x1 , y1 , z1 ). 552 The equivalent CIR for the intended user would be

549 550 551

heq (r0 , r0 , t) = h(r0 , −t) ∗ h(r0 , t).

(31)

M N

Gmn +

m=1 n=1

κMIMO ≈ 2

N M

N

νmn,mk +

n=1 m=1 k=1,k=n

& ¯ + (N − 1)I¯ 2 G = % & 2N −1 ¯ + (N − 1)I¯ 2 ν¯ + G

M N m=1 n=1

=

where hm (r0 , t) denotes the CIR between the mth element in 558 the transmit array and the receiver located in r0 . 559 For simplicity, the receiver has been restricted to move along 560 a straight line in the measurements carried out in this paper. 561 Under this condition, (33) can be simplified as 562 max |heq (r0 , 0, t)|2

D(r0 , d) =

t

(35)

max |heq (r0 , d, t)|2 t

where d is the distance between the unintended receiver and 563 the intended receiver (focal point) located at r0 . For the case 564 where the antenna elements are not distributed along a line, but 565 in some shapes (e.g., circle, square, etc.), (35) will still be valid 566 if we replace the scalar d with a vector d, where d = r1 − r0 . 567 The value of directivity D(r0 , d) determines how well we 568 can, by employing TR, focus the transmitted energy into an 569 intended point of interest. A similar metric has been used in 570 [38]. Our previous paper [10] uses the same metric to inves- 571 tigate the spatial focusing of the UWB signal in the hallway 572 environment by simulation. In this paper, we experimentally 573

N M

2

N

Imn,mk

n=1 m=1 k=1,k=n

νmn +

M N m=1 n=1

Gmn +

N M

N

2 Imn,mk

n=1 m=1 k=1,k=n

%

MN

(26)


evaluate this parameter by moving the receiver away from the intended focusing point r0 and study how rapidly the receiving energy drops with this moving. 577 We expect the spatial focusing can be enhanced by employ578 ing multiple antennas at the transmitter, which will be shown 579 experimentally in this paper. If the spatial focusing is good 580 enough, we can take advantage of this property and transmit 581 signals in a parallel fashion. 574

575 576

582

B. Spatial Multiplexing With Multiple Antennas

Consider a communication link consisting of M transmitting antennas and N receiving antennas. The input data are serialto-parallel converted into N streams bn (t), which are precoded by cn (t) through FIR filters and modulated. Eventually, the 587 signals are sent to M transmitting antennas for simultaneous 588 transmission. After the signal passes through the channel and is 589 corrupted by AWGN, the nth receiving branch extracts the data 590 stream bn (t). 591 Let S(t) = [s1 (t), s2 (t), . . . , sN (t)] and R(t) = [r1 (t), 592 r2 (t), . . . , rN (t)] denote the transmitting and receiving signals, 593 respectively. We have R(t) = S(t) ∗ C(t) ∗ H(t), where C(t) 594 is the precoding matrix, and H(t) is the time-domain impulse 595 response matrix defined by   h11 (t) . . . h1N (t)   .. .. .. H(t) =  (36)  (M × N ). . . . 583

hM 1 (t) . . .

hM N (t)

We define the equivalent impulse response matrix (EIRM) as Heq (t) = H(t) ∗ C(t). Then, we have R(t) = S(t) ∗ Heq (t). 598 The EIRM is the target of interest. The objective is to transform 599 the EIRM into a desirable form by selecting a good code 600 matrix C(t). 601 To avoid ISI, the ideal EIRM will be in the form   0 a1 δ(t) . . .  ..  (N × N ) .. Heq (t) =  ... (37) . . 

596 597

0

...

an δ(t)

C(t) ∗ H(t) ≈ Hideal eq (t).



ˆ )H(f ˆ )=H ˆ eq (f ) C(f ˆ ), H(f ˆ ), and H ˆ eq (f ) are the Fourier transforms of 611 where C(f the matrices C(t), H(t), and Heq (t), respectively. 612 The solution for the above function is 613 ˆ −1 (f ). ˆ )=H ˆ eq (f )H C(f The above solution assumes that the channel matrix H(f ) 614 is square and invertible. For a general M ∗ N matrix H, the 615 solution will be 616 .−1 ˆ )=H ˆ eq (f )H(f ˆ ) H ˆ H (f )H(f ˆ ) C(f . (38)

M

Rhi1 (t)  i=1   ..  .  M  Heff (t) =  hin (−t) ∗ hi1 (t)   i=1  ..  .  M  hiN (−t) ∗ hi1 (t) i=1

Once we have the frequency-domain matrix C(f ), the time- 617 domain matrix C(t) can be numerically obtained by applying 618 inverse fast Fourier transformation to C(f ). Note that the trans- 619 form of a matrix is a process of term-by-term transformation. 620 Generally, the inversion of a matrix is ill-conditioned, and small 621 errors (e.g., the measurement error caused by noise) in any 622 matrix X will give rise to significant errors in its inverse matrix 623 X−1 . Even measurement is perfect, and there is no error in X; 624 X may not be invertible. Many techniques for the regularization 625 of this problem have been studied [22]. 626 2) Solution 2—TR: Considering the signal processing in- 627 volved in the previous inverse filter solution, another simpler 628 solution would be TR. In this case, the precoding matrix would 629 simply be CTR (t) = H (−t), where the superscript “ ” in the 630 notation denotes transpose operation. We have 631   h11 (−t) . . . hM 1 (−t)   .. .. .. CTR (t) =   (N × M ). (39) . . . h1N (t)

where (a1 , . . . , an ) are the matrix coefficients. 603 We hope that we can find a matrix C(t) that satisfies the 604 following equation: 602

Then, the problem will be how to find a suitable C(t). Two 605 solutions can be used to achieve the goal. 606 1) Solution 1—Inverse Filter: This approach is optimal in 607 the sense that, theoretically, the ideal formula presented above 608 can be exactly achieved. 609 Thinking the problem in the frequency domain, we have 610

IE E Pr E oo f

584 585 586

9

...

M

.

hi1 (−t) ∗ hin (t)

...

Rhin (t)

...

i=1

.. ...

M i=1



M

hi1 (−t) ∗ hiN (t)    ..  .  M  hin (−t) ∗ hiN (t)   (N × N ) i=1   ..  .  M  RhiN (t) i=1

M

...

hM N (−t)

In practice, CTR (t) can be readily obtained by channel sounding, and no extra computation is needed. Let Heff (t) = CTR (t) ∗ H(t). Then, Heff (t) can be expressed in (40), shown at the bottom of the page, where we have

i=1

..

...

hiN (−t) ∗ hin (t)

.

...

i=1

(40)

632 633 634 635

10


Fig. 4. UWB spatial channel measurement: experiment setup. 636 637 638

made an assumption that matrix convolution is a term-by-term convolution. In a general form, the received signal r(t) can be expressed as M N rn (t) = sj (t)∗ hij (−t)∗hin (t) , j=1

n = 1, 2, . . . , N.

i=1

(41) The received signal r(t) can be reformulated to a more convenient form as follows: rn (t) = sn (t)∗

M

IE E Pr E oo f

639 640

Rhin (t)+On (t),

i=1

n = 1, 2, . . . , N

(42)

M where On (t) = N j=1,j=n sj (t) ∗ [ i=1 hij (−t) ∗ hin (t)]. 642 Assuming good spatial focusing, the received signal can 643 be approximated by the following formula: rn (t) ≈ sn (t) ∗ M 644 i=1 Rhin (t), where we have ignored the contributions from 645 the cross correlation part On (t). Under this condition, the 646 corresponding impulse response matrix will be in the form of a 647 diagonal matrix, i.e.,  M R (t) . . . 0 hi1     i=1   .. .. .. Heff (t) =   (N ×M ) (43) . . .   M   RhiN (t) 0 ... 641

Fig. 5.

UWB spatial channel measurement: experiment environment.

= scom (t) ∗

m=1 j=1

= scom (t) ∗

where the impulse matrix has been decomposed into parallel 649 channels. This decomposition gives us several independent 650 subchannels and, thus, increases the data rate. 651 TR spatial multiplexing discussed in this section is another 652 application of TR-MIMO in addition to the application of 653 beamforming. The precodings for the two different scenarios 654 are different. As a sanity check, in the following, we will show 655 that scenario A (spatial multiplexing) is reduced to scenario B 656 (beamforming) when all the independent channels transmit the 657 same information, namely, sn (t) = scom (t). 658 Under this condition, the receiving signal can be combined 659 together directly and is expressed as

M N j=1

r(t) =

rn (t)

n=1

 M  N N  = scom (t) ∗ hij (−t) ∗ hin (t)  n=1

j=1

i=1

hij (−t) ∗ him (t)

i=1

hij (−t) ∗

N

him (t) .

(44)

m=1

i=1

hMIMO (t) eq

=

M N j=1

hij (−t) ∗

i=1

N

hMIMO (t) eq

=A

M N j=1

i=1

660

him (t) .

m=1

Considering the power allocation factor A, we have hij (−t) ∗

N

661

him (t)

m=1

which is consistent with the result derived previously in (20). VI. UWB S PATIAL C HANNEL M EASUREMENT

A. Experiment Setup (Fig. 4) N

The equivalent impulse response can thus be modeled as

i=1

648

M N N

662

663 664

Major equipment used in the measurements include 1) a 665 waveform generator for triggering the pulser; 2) a UWB pulser 666 that generates Gaussian-like pulses with a root mean square 667 pulsewidth of approximate 250 ps; 3) a wideband low-noise 668 amplifier (LNA) with bandwidth over 10 GHz and a noise figure 669 less than 1.5 dB; 4) a Tektronix CSA8000 digital sampling 670

AQ6


11

IE E Pr E oo f

TABLE I COMPARISON OF κ FOR DIFFERENT SCENARIOS

oscilloscope (DSO) with a 20-GHz sampling module 80E03; and 5) a pair of omnidirectional antennas with a relatively flat 673 gain over the signal band. To maintain synchronization, the 674 same waveform generator is employed to trigger the DSO. The 675 major frequency components of the system are from 750 MHz 676 to 1.6 GHz. A simplified block diagram of the experiment setup 677 can be found in Fig. 4. 678 A virtual antenna array is employed in the experiments. The 679 elements of the array are spaced far enough so that there is no 680 significant correlation between two adjacent channels. This can 681 be achieved by setting the spacings between any two adjacent 682 antenna elements greater than 20 cm, which corresponds to the 683 half wavelength of the lowest frequency. The value of 20 cm 684 is found to be sufficient after some trials of bigger values. The 685 MIMO antenna coupling is considered in [17]. In Fig. 5, four 686 virtual elements are equally spaced along a line. The heights of 687 the antennas are set to 1.4 m. The receiving antenna is moved to 688 different locations, and individual channels were sounded and 689 measured sequentially. No line of sight is available for all the 690 measurements. 671 672

691

B. Experiment Environment

A set of measurements has been performed in the office area of Clement Hall 400 at the Tennessee Technological University. 694 Fig. 5 shows the experimental layout for these experiments. 695 In Fig. 5 (also in Table I), Tn denotes the nth element of the 696 transmitting array, and Rn denotes the receiver located in the 697 nth position. The environment for the experiment is a typical 698 office area with abundance of wooden and metallic furniture 699 (chairs, desks, bookshelves, and cabinets). 692 693

Fig. 6. CLEAN algorithm employed to extract impulse response from the received signals.

C. Measurement Results and Spatial Focusing Analysis

700

A typical receiving waveform is shown in Fig. 6. The 701 CLEAN algorithm is employed to extract CIRs from the re- 702 ceived waveforms. 703 We first investigate the spatial focusing of a MISO-TR sys- 704 tem. Consider downlink transmission. Assume that there are 705 two users separated by a distance d, with one of them as the 706 target user (focal point) and the other as the undesired user. 707 Each user has one receive antenna and a transmit antenna array 708 with four elements. The equivalent CIRs for the target user and 709 the undesired user of 0.2 m away are shown in Fig. 7(a) and (b), 710 respectively. The equivalent CIRs for different users are 711

12


Fig. 7. Demonstration of MISO-TR spatial focusing by the equivalent CIR. (a) Equivalent CIR for the target user. (b) Equivalent CIR for the unintended user with 0.2 m away from the target user.

VII. N UMERICAL R ESULTS

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Fig. 8. Spatial focusing characterized by the parameter directivity D(r0 , d).

calculated by using (34). As we can see in Fig. 7, the signal is very strong for the target user, while it is almost behind the background noise for the undesired user with a short distance of 0.2 m away. 716 We further investigate the variation of the directivity D, as 717 defined in Section V-A, with respect to different distances d. 718 A comparison of spatial focusing for MISO-TR and SISO719 TR is shown in Fig. 8. In the SISO-TR case, it is observed 720 that energy drops by more than 15 dB when the undesired 721 receiver is located 0.2 m away from the intended user. This 722 number will slightly change when the unintended receiver 723 moves to a farther place. In Fig. 8, the “SISO average” curve 724 represents the average directivity of the four SISO-TR cases. It 725 is observed that the “MISO” directivity curve drops much faster 726 than the “SISO average” curve, implying that spatial focusing 727 is improved by employing an antenna array at the transmitter. 728 With a four-element array at the transmitter, energy drops by 729 22 dB when the unintended receiver is 0.2 m away from the 730 target receiver. 712

713 714 715

731

Table I shows a comparison of κ (defined in Section IV-B) for 732 different scenarios. In Table I, the calculating of parameters ν, 733 G2 , and κ are all based on the measured UWB spatial channels. 734 The approximated (“Appro”) values of κ for MIMO and MISO 735 scenarios are calculated using (28) and (29), respectively. The 736 experiment (“Exper”) values are directly measured from the 737 equivalent CIRs of MISO and MIMO scenarios. Table I shows 738 that (28) and (29) can approximate the measured value well. 739 The slight difference between the approximated value and the 740 measured value is due to the disturbances of the cross correla- 741 tion terms (the interference from the other antennas), which is 742 hard to be included in an analytical formula. 743 Based on the measured UWB spatial channels, we conduct 744 Monte Carlo simulations to investigate the performance of 745 the one-correlator receiver and compare them under different 746 scenarios: SISO, MISO, and MIMO. In our simulation, the 747 second-order derivative of Gaussian pulse has been used as the 748 transmitted pulse p(t), which is mathematically defined as 749

p(t) = 1 − 4π

#

t − tc w

$2

e−2π(

t−tc w

2

)

(45)

where w is the parameter controlling the width of the pulse 750 (and, therefore, the frequency bandwidth of the transmit signal), 751 and tc is the parameter to shift the pulse to the middle of 752 the window. In the following simulation, we let w = 1 ns and 753 tc = 0.5 ns. To avoid the presence of severe ISI in the system, 754 we add an interpulse guard time Tg . Therefore, we have Tb = 755 w + Tg . Moreover, Tg can be used to adjust the transmission 756 data rate in the simulation. Unless stated otherwise, we let 757 Tg = w, corresponding to a data rate of 500 Mb/s. 758 Throughout this paper, we assume perfect synchronization, 759 and the transmitter has the full knowledge of the channel 760 information. To make the comparison fair, performances of 761 SISO and MISO scenarios have been averaged over all the 762 corresponding specific channels that virtually form the MIMO 763


Fig. 10. BER performance in terms of transmitted bit energy. Ebtx here represents the transmitted bit energy. Both ISI and IPI have been considered.

SISO SISO MISO channel, i.e., Pave = (1/16) 16 , and Pave = i=1 Pi 4 MISO 765 (1/4) P . i=1 i 766 A comparison of BER performance for different scenarios 767 with both ISI and IPI is shown in Fig. 9. The performance 768 bound for AWGN channel is also plotted as a reference. In 769 Fig. 9 we can see that given the same SNR at the receiver side, 770 MISO-TR has the best performance, and MIMO-TR is slightly 771 better than SISO-TR scenario. This is due to the best temporal 772 focusing provided by MISO-TR. It should be noted that these 773 comparisons are based on the received SNR. In reality, however, 774 given the same transmitted power, the SNR at the receiver 775 side for MIMO-TR is much higher than that of MISO-TR, 776 which will make MIMO-TR outperform MISO-TR, as will be 777 illustrated in the following. 778 Fig. 10 shows the BER performances for the SISO, MISO, 779 and MIMO scenarios under the same transmitted power con780 straint, with different transmission data rates. For the MIMO 781 scenario, all the four antennas transmit the same bit informa782 tion, i.e., the beamforming approach has been applied to in783 crease the SNR at the receiver side. Both IPI and ISI have been 764

Fig. 11. BER performance for a 2 × 2 TR-MIMO system. ISI, IPI, and interchannel interference have been considered.

considered. As we can see in Fig. 10, MIMO-TR outperforms 784 MISO-TR, and MISO-TR outperforms SISO-TR. Tests were 785 conducted for data rates of 500 and 225 Mb/s. As expected, an 786 increase in the data rate leads to a performance degradation. For 787 a data rate of 250 Mb/s, a power gain of about 13 dB (compared 788 with SISO-TR) is achieved by employing a 4 × 4 MIMO array. 789 The power gain in a system with ISI and IPI is slightly higher 790 than the theoretical power gain 10 log10 (M N ), as derived in 791 Section IV-A, where we assume that there are no ISI and IPI. 792 To illustrate the concept of spatial multiplexing for MIMO- 793 TR, we study a simple scenario of 2 × 2 MIMO-TR system. 794 As stated in Section V, the signal will first be serial-to-parallel 795 converted into two streams, precoded with TR precoding, 796 and then sent to two transmitting antennas for simultaneous 797 transmission. The signal passes through the channel and is 798 corrupted by AWGN. Fig. 11 shows the BER performance for 799 the two parallel subchannels. Compared with the beamforming 800 approach addressed previously, one more interference source 801 from interchannels need to be considered in the spatial multi- 802 plexing simulation. 803

IE E Pr E oo f

Fig. 9. BER performance in terms of received bit energy. IPI and ISI have been considered. SISO result is the average of 16 channels, and MISO is the average of four channels.

13

VIII. C ONCLUSION

804

TR is considered in the framework of UWB MIMO. Ex- 805 perimental measurements have been used to evaluate the per- 806 formance. Multiple antennas are found to be very useful in a 807 UWB system. The working principles for MIMO in a UWB 808 system is fundamentally different from that for a narrowband 809 flat-fading wireless system. The fading is not a concern for 810 UWB communications. The leading mechanism behind UWB 811 MIMO is to exploit the space–time focusing that is unique to an 812 impulse signal. The design philosophy is to use deterministic 813 signal model as digital subscriber line, rather than the statistic 814 fading signal in a narrowband system. This reported work is 815 the first step toward the nonfading transmission [19] for UWB 816 systems. The time-reversed MIMO matrix is combined with the 817 physical channel to form an effective matrix channel that can be 818 treated deterministically [19]. 819 One feasible scheme of combining the MIMO with the 820 one-finger correlator has been demonstrated. Some further 821

14


simplification of the transceiver can be done using a chirp UWB system. When a pair of chirp waveforms in the transmitter and receiver is used to replace the second-order Gaussian 825 pulse as the modulation waveform, the new scheme may prove 826 to be useful for some high-data-rate communications with a 827 relatively low cost [16], [18]. What we have learned from the 828 past is that too many multipath fingers force us to walk away 829 from the famous RAKE structure to reduce the transceiver cost. 830 For example, for a transmitted pulse of 1 ns, a dense multipath 831 spread of 1000 ns is observed in a metal cavity in [16] and 832 [18], and it is believed that TR is necessary to capture the 833 spread multipath energy. As suggested in this paper, the MIMO 834 transmission with TR can be further used to make full use of 835 the space–time channel responses at the same time. The work 836 reported here thus paves the way for the potential solution of the 837 communication problem in some RF harsh environments like a 838 metal cavity. 822

823 824

839

ACKNOWLEDGMENT

AQ7

IE E Pr E oo f

The authors would like to thank Dr. B. Sadler, Dr. S. K. Das, and Dr. R. Ulman for the helpful discussions and the anony842 mous reviewers for their thorough reading of the manuscript 843 and their constructive suggestions. 840 841

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887 888 889 AQ8 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 AQ9 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963


[38] S. M. Emami, J. Hansen, A. D. Kim, G. Papanicolaou, A. J. Paulraj, D. Cheung, and C. Prettie, “Predicted time reversal performance in wireless communications using channel measurements,” IEEE Commun. Lett., 2004. [39] E. J. Badhdady, Lectures on Communications System Theory. New York: McGraw-Hill, 1961, ch. 14. [40] M. R. Bell, “Information theory and radar waveform design,” IEEE Trans. Inf. Theory, vol. 39, no. 5, pp. 1578–1597, Sep. 1993. [41] H. T. Nguyen, I. Z. K. Kovacs, and P. C. F. Eggers, “A time reversal transmission approach for multiuser UWB communications,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3216–3224, Nov. 2006. [42] H. T. Nguyen, I. Z. K. Kovacs, and P. C. F. Eggers, “A time reversal transmission potential for multiuser UWB communications,” IEEE Trans. Antennas Propag., pp. 1–13, 2005. [43] H. T. Nguyen, P. Kyritsi, and P. C. F. Eggers, “Time reversal technique for multi-user wireless communication with single tap receiver,” in Proc. 16th IST Mobile Wireless Commun. Summit, 2007, pp. 1–5. [44] H. T. Nguyen, J. B. Andersen, G. F. Pedersen, P. Kyritsi, and P. C. F. Eggers, “Time reversal in wireless communications: A measurement-based investigation,” IEEE Trans. Wireless Commun., vol. 5, no. 8, pp. 2242–2252, Aug. 2006. [45] R. J. Cramer, “An evaluation of ultrawideband propagation channels,” Ph.D. dissertation, Univ. Southern Calif., Los Angeles, CA, Dec. 2000. [46] R. M. Buehrer, “Ultra-wideband propagation measurements and modeling final report,” in DARPA NETEX Program. Blacksburg, VA: Virginia Polytechnic Inst. State Univ., Jan. 2004, p. 333. [47] R. Esmailzadeh, E. Sourour, and M. Nakagawa, “PreRAKE combining in time-division duplex CDMA mobile communications,” IEEE Trans. Veh. Technol., vol. 48, no. 3, pp. 795–801, May 1999. [48] N. Guo, R. C. Qiu, Q. Zhang, B. M. Sadler, Z. Hu, P. Zhang, Y. Song, and C. M. Zhou, Handbook of Sensor Networks. Singapore: World Scientific, 2009, ch. Time Reversal for Ultra-Wideband Communications: Architecture and Test-bed, pp. 1–41.

Nan Guo (S’96–M’99) received the M.S. degree in telecommunications engineering from Beijing University of Posts and Telecommunications, Beijing, China, in 1990 and the Ph.D. degree in communications and electronic systems from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 1997. In September 1990, he became a faculty member with UESTC. In January 1997, he joined the Center for Wireless Communications, University of California, San Diego. From December 1999 to January 2002, he was a Research/System Engineer with Golden Bridge Technology, Inc., West Long Branch, NJ, where he was deeply involved in 3G code division multiple access system design, intellectual property development, and standardization activities. From June 2002 to February 2003, he was a Research Engineer with the System Group, Ansoft Corporation, Elmwood Park, NJ, where his major responsibility was software development, with emphasis on functionality modeling of emerging technologies. Since 2004, he has been with the Center for Manufacturing Research, Tennessee Technological University, Cookeville, doing R&D and laboratory work. He has over 15 years of industrial and academic experience in R&D, teaching, and hands-on work. His research interests are in the area of wireless communications. His recent focus is on radio system design, optimization, and implementation.

1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032

Robert Caiming Qiu (S’93–M’96–SM’01) received the Ph.D. degree in electrical engineering from New York University, NY. He is currently a Professor with the Department of Electrical and Computer Engineering, Center for Manufacturing Research, Tennessee Technological University (TTU), Cookeville. His current interest is in wireless communication and networking systems, particularly ultrawideband (UWB). He was the Founder-CEO and President of Wiscom Technologies, Inc., Clark, NJ, which manufactured and marketed WCDMA chipsets. Wiscom was sold to Intel in 2003. Prior to Wiscom, he was with GTE Laboratories, Inc. (now Verizon), Waltham, MA, and Bell Laboratories, Lucent, Whippany, NJ. He has worked in wireless communications, radio propagation, digital signal processing, EM scattering, composite absorbing materials, radio-frequency microelectronics, ultrawideband, underwater acoustics, and fiber optics. He is the author of over 40 technical papers and four book chapters. He is the holder of over ten U.S. patents pending in WCDMA. He contributed to 3GPP and IEEE standards bodies and delivered invited seminars to institutions, including Princeton University, Princeton, NJ, and the U.S. Army Research Laboratory. He served on the advisory board of the New Jersey Center for Wireless Telecommunications. He is an Associate Editor for the International Journal of Sensor Networks (Interscience) and Wireless Communication and Mobile Computing (Wiley). He is a Guest Book Editor for Ultra-Wideband (UWB) Wireless Communications (Wiley, 2005) Dr. Qiu received the Kinslow Research Award from TTU. He serves as a Member of Technical Program Committee for GLOBE-COM, WCNC, and MILCOM. He serves as an Associate Editor for the IEEE TRANSACTIONS ON V EHICULAR T ECHNOLOGY . He is a Guest Book Editor for three Special Issues on UWB, including the IEEE JOURNAL ON SELECTED AREAS IN C OMMUNICATIONS and the IEEE T RANSACTIONS ON V EHICULAR TECHNOLOGY.

1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 AQ13 1061 1062 1063 1064

IE E Pr E oo f

964 965 966 AQ10 967 968 969 970 971 972 973 974 975 976 AQ11 977 978 979 980 981 982 983 984 985 986 AQ12 987 988 989 990 991 992 993 994 995 996

997 Chenming Zhou (S’05–M’08) was born in Jiangxi, 998 China, in 1979. He received the B.S. degree in 999 physics from Changsha University of Science and 1000 Technology, Changsha, China, in 2000, the M.S. 1001 degree in optical science from Beijing University of 1002 Technology, Beijing, China, in 2003, and the Ph.D. 1003 degree in electrical engineering from Tennessee 1004 Technological University, Cookeville, in 2008. 1005 He is currently a Research Scientist with the De1006 partment of Electrical and Computer Engineering, 1007 Carnegie Mellon University, Pittsburgh, PA. His gen1008 eral research interests include radio propagation, wireless sensor network, and 1009 radio-frequency systems.

15

AUTHOR QUERIES AUTHOR PLEASE ANSWER ALL QUERIES

IE E Pr E oo f

AQ1 = Note that UWB was defined here as Ultrawideband for consistency throughout. Edit okay? AQ2 = Write out STIR. AQ3 = What does RAKE stand for? Please define it first here. AQ4 = What does CLEAN stand for? Please define it first here. AQ5 = Looks like there’s a missing equation here. AQ6 = Table VI-B was changed to Table 1, which was not mentioned anywhere in the text. Correct? AQ7 = Please provide volume and issue number in Ref. [8]. AQ8 = Please provide page range in Ref. [15]. AQ9 = Please provide issue number in Ref. [23]. AQ10 = Please provide publication update in Ref. [38]. AQ11 = Please provide volume and issue number in Ref. [42]. AQ12 = Please provide complete list of authors in Ref. [46]. AQ13 = Write out GLOBE-COM, WCNC, and MILCOM in full.

Note that reference [10] and [12], [13] and [24], [14] and [33] are the same. Ref. [12], [24] and [33] was deleted, citations and bibliographic list were renumbered accordingly. Please check. END OF ALL QUERIES

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