Multiple Antenna Communication Systems — An ... - CiteSeerX

Multiple Antenna Communication Systems — An Emerging Technology Paul Goud Jr., Christian Schlegel Witold A. Krzymien, Robert Hang Department of Electrical and Computer Engineering University of Alberta Edmonton, CANADA January 19, 2004

Abstract A recent development in wireless communications is the application of multiple-input multiple-output (MIMO) systems to radio communications via use of multiple antennas. In order to investigate the technology’s potential, an experimental MIMO system which contains two four-element antenna arrays (4 × 4) has been developed at the University of Alberta. The system is used to obtain MIMO channel measurements in a typical indoor office environment in the ISM band (902 - 928 MHz). Measurement campaigns were performed using different antenna spacings and two different types of antenna: half-wavelength (λ/2) centre-fed dipoles and dual polarized patches. The measurements are used to calculate channel capacities for an indoor 4 × 4 MIMO system. The measurements confirm the high capacity potential of a MIMO channel, with ergodic capacity of approximately 21 bits per channel use available with either antenna type at a signal-to-noise ratio of 20 dB if the antenna element separation is λ/2 or larger. An introduction to basic MIMO theory, a discussion of the University of Alberta wireless MIMO testbed, and observations regarding the measured indoor MIMO channel are presented in the paper.

1

Introduction

MIMO wireless systems, which use arrays of antennas instead of single transmit and receive antennas, hold the promise of providing data rates far exceeding those of conventional wireless systems [1]. Such MIMO systems operate by transmitting multiple signals in the same frequency band and at the same time over multiple transmit antennas. At the receiver, multiple antennas are also used and the received correlated signals are processed to separate the different transmitted data streams.

MIMO communications is made possible by the extension of receiver processing to include spatial dimensionality as well as time (spatio-temporal processing). Multiple propagation paths, as occur in a scattering propagation environment, become distinguishable at the MIMO receiver due to small differences in arrival times and can be used to carry additional information across the channel [2]. Although the idea of using multiple antennas is not new – it finds application in such techniques as diversity combining and beamforming - only MIMO systems approach the information carrying capacity potential of such channels. It is likely that future applications of MIMO technology include both fixed and mobile uses for indoor as well as outdoor environments. An example of a potential mobile application for MIMO communications has recently been studied in [3], which describes an investigation on using the technology for high speed (around 1 Mb/s) communication with subway trains. A MIMO system for residential fixed wireless access was developed by Iospan Wireless (now part of L-3 Communications Inc.) [4]. Another company, Antenova Ltd, is examining the use of MIMO for laptops and handheld consumer devices [5]. A MIMO chipset has already been developed by Airgo Networks, a start-up company in Silicon Valley [6]. A MIMO system with Nt transmit antennas and Nr receive antennas utilizes a channel with Nt Nr separate paths and the gains for these paths are described using an Nt × Nr matrix H. The information theoretic capacity, i.e., the maximum throughput of a MIMO channel, is dependent upon the characteristics of its transmission matrix H, in particular its singular values. As shown in Section 2, these depend on the propagation environment, which ultimately determines the capacity of MIMO channels. In general, a rich scattering environment, as occurs in indoor wireless communications, tends to produce channels with high capacity. Since wireless channels are inherently complex and difficult to characterize, obtaining channel measurements is the only accurate and reliable method of determining the yet not fully understood capacity potential of such MIMO systems. In order to measure the capacity of MIMO systems in typical propagation environments, a flexible and mobile MIMO testbed containing up to 4 × 4 arrays has been developed in the iCORE HCDC (High Capacity Digital Communications) laboratory at the University of Alberta, Canada. In this paper, we present results of several MIMO channel measurement campaigns for non-line of sight channels in an indoor office environment, using two different types of antennas: standard λ/2 dipole and specially designed dual-polarized patch antennas [7]. The singular values of the measured channel gain 2

matrices are calculated and analyzed along with the MIMO channel capacities. In Section 2 of this paper we discuss the capacity formulas for MIMO channels and explain the impact of system and propagation environmental parameters. We then discuss implementation issues along with the need to perform MIMO channel measurements in Section 3. Layering processing is described in Section 4. Section 5 gives a description of our testbed and our system validation tests. The MIMO testbeds that exist at other Universities are analyzed in Section 6 and compared to our design. In Section 7, we show how our campaigns were conducted and present the results for them. Finally, Section 8 gives conclusions and outlines planned future research.

2

The Multi-Antenna MIMO Channel

2.1

Channel Model and Capacity

A MIMO transmission system uses Nt transmit and Nr receive antennas. Each antenna i transmits symbols
from a complex symbol alphabet each with energy Esi per signaling interval, such that i Esi = Es is constant for each use of the channel. These transmit symbols are modulated by a suitable pulse waveform, up-converted to the desired transmission band, and sent over the Nt transmit antennas. The signals from the receive antennas are mixed down to baseband, sampled, and fed into the receiver. A basic block-level diagram of a MIMO system is shown in Figure 1. The wireless transmission channel is a linear channel, and, assuming that timing recovery has been accomplished, the received sampled signal yjl for the j th receive antenna at time l is given by Nt   Esi hij cil + ηjl yjl =

(1)

i=1

where ηjl is a sample of circularly symmetrical complex Gaussian noise with variance N0 , cil is the sampled transmitted signal and hij is the normalized complex path gain from transmit antenna j to receive antenna i. It contains all linear effects on the signal, such as propagation power loss and phase shifts, fading due to multipath, cross-talk, antenna coupling, and polarization. We have furthermore assumed that the symbol rate is low enough such that frequency selectivity caused by time-of-arrival differences between the various multipath replicas of the received signal is not an issue that manifests itself noticeably. This implies symbol rates of about 1 Mbaud or less for indoor transmission, and about 50 kbaud or less for outdoor situations [8]. 3

The entire MIMO channel can now succinctly be characterized by the linear algebraic relationship   √ Es1 √   Es2   (2) y = HAc + n; A =   . .   .  EsNt H is an Nt × Nr rectangular matrix of channel gains hij and c is a vector of Nt transmitted symbols cil . The information theoretic capacity of the discrete channel in (2) can be calculated from basic information theoretic concepts [9] as 

ρ + HEH CI = log2 det I + Nt where ρ =

Es N0

is the signal-to-noise ratio per symbol,  Es1 Es2 1   E=  Es 

[bits/channel use],

(3)

 ..

   

.

(4)

EsNt and H + is the conjugate transpose of H. Since the channel parameters are time-varying, CI is interpreted as the “instantaneous” channel capacity for a given channel realization H. For a time-varying channel this capacity has to be averaged over all realizations of the MIMO channel matrix H to calculate the ergodic channel capacity C = EH (CI ). Telatar [10] has presented closed form solutions for C in the case where the hij are independent complex Gaussian fading channel gains. The channel matrix H can be decomposed via the singular value decomposition (SVD) method [11] into the product H = U DV +

(5)

where U and V are unitary matrices, i.e., U U + = I, and V V + = I. The matrix D contains the singular values {dn } of H on its diagonal, which are the positive square roots of the non-zero eigenvalues of HH + or H + H. Note that D may not be a square matrix, which simply means that the number of non-zero singular values can be no larger than the minimum size of the matrix, and is in fact equal to its rank. The SVD allows us to write the channel equation in an equivalent form y = U DV + Ac + n ˜ = D˜ ˜ c+n U +y = y 4

(6)

˜ = V + Ac. This leads to parallel Gaussian channels y˜n = dn x where c ˜n + n˜n as shown in Figure 2. The capacity of the MIMO channel is now determined by the well-known waterfilling theorem [12] as

 

2  N N  d 2 En dn µ CI = = (7) log2 1 + n log2 N0 N0 n=1

n=1

where En is the energy per symbol allocated to channel n, and N = min(Nr , Nt ) is the rank of H. This capacity is achieved with the waterfilling power allocation: En = µ − En = 0; where µ is the waterfilling level such that




N0 ; d2n

N0 /d2n < µ

(8)

N0 /d2n ≥ µ

(9)

En = Es . If the channel is known at the transmitter, the signal

strategy shown in Figure 2, which is based on the SVD, achieves capacity by transforming the channel into a set of parallel channels. However, channel knowledge is not typically available at the transmitter, and the only choice we have is to distribute the energy uniformly over all component channels. This leads to the Symmetric Capacity

  N

N  d2n Es d2n Es = log2 1+ (10) log2 1 + Csym = Nt N0 Nt N0 n=1

n=1

Introducing λ(M ), the spectrum (set of eigenvalues) of M , and using the facts det(M ) =

λ(M ) and

(1 + λ(M )) = det(I + M ), we obtain the equivalent formulations:  



 N

d2n Es ρ ρ + + Csym = log2 1+ = log2 det I Nr + = log2 det I Nr + HH H H Nt N0 Nt Nt

(11)

n=1

Fundamentally, the capacity of a MIMO channel is governed by the singular values of H which determine the channel gains of the independent equivalent parallel channels.

2.2

Capacity Potential and Limitations of MIMO Channels

If the channel paths hij are uncorrelated, most channel realizations are of high rank with the eigenvalues of HH + distributed according to a Wishart distribution [10]. The case of equal singular values represents a limiting case where the rows hj of H are orthogonal and hj × hi = δij Nr , implying d2n = Nr , and the capacity is given by Chigh =

N  n=1



 d2n ρ Nr ρ = N log2 1 + log2 1 + Nt Nt 5

(12)

This capacity increases linearly with the minimum of the number of elements in either of the two antenna arrays. On the other hand, if component channels are completely correlated, such as occurs in scatterfree long-distance wireless connections, (e.g. in a satellite-ground radio link) all rows hj of H, the array response vectors, are approximately equal, and H has only one non-zero singular value, d2 = Nt Nr . As a result Clow ≈ log2 (1 + ρNr )

(13)

In this case the channel capacity grows only logarithmically with the number of (receive) antennas. Realworld situation will lie somewhere between these two extremes, with the capacity determined by the complex propagation environment in which the system has to function. This leads to the necessity to carefully analyze and measure such candidate environments to obtain precise values. In fact, for scatterfree propagation the array response vectors become correlated very rapidly (see also [13]) and the channel matrix H looses rank, turning the MIMO channel into nothing more than a fancy conventional wireless link. Furthermore, the capacity potential of a MIMO channel requires relatively high-power transmitters as can be shown as follows: if the signal-to-noise ratio ρ is low, a Taylor Series approximation of log(1+x) ≈ x for small x lets us develop both (12) and (13) as Chigh ≈ N

Nr ρ ; Nt

Clow ≈ Nr ρ

(14)

which now both grow linearly with the array sizes. This also indicates that for Nt ≤ Nr , which implies N = Nt , correlation in the channel has no effect on capacity for low SNR values. The sole effect of an increased number of antennas is that of gathering more received power. Communications is fundamentally power limited and the additional dimensionality offered by a “high-rank” MIMO channel cannot be exploited. From the physical model it is evident that the geometry of the propagation environment plays a significant role. The transmission strategy for both low-rank MIMO channels as well as low SNR MIMO channels is identical and straightforward. Concentrate all transmit power on a single antenna and use maximum-ratio combining of the Nr receive antennas to feed a single receiver. Of course, the transmit antenna array can be used to shape the transmitted beam to direct power to the desired receiver. These are the well-known traditional beamforming techniques.

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3

MIMO Channels in the Real World

In order to better understand MIMO channels in real-world environments, accurate MIMO channel measurements are needed. One issue with wireless channels is the large power variations that occur in the received signals due to multipath fading if one or both of the terminals are mobile. Figure 3 is a plot of the received signal power obtained from measurements with the HCDC MIMO testbed for a single transmit-receive antenna pair in an indoor office environment without automatic gain control. It illustrates the rich multipath environment, which results in power fluctuations. Clearly visible are the signal fades approximately every wavelength, i.e., every 30 cm. If a receiver moves through this signal field, the spatial fading pattern turns into time-varying signal fading. As can be appreciated, channel tracking under such conditions is a major challenge for MIMO systems, where there are Nr × Nt such channels which vary largely independently. Channel tracking, however, is essential for MIMO communications since the complex channel gain information is needed to separate the co-existing signals. In the absence of channel tracking, orthogonal space-time codes [14] or differential space-time modulation [15] have to be used, both severely limiting the achievable maximal data rates. Fortunately, and at first glance perhaps paradoxically, despite the power fluctuations that occur in the received signals, the MIMO channel capacity itself is very stable. This is due to the fact that the large number of component channel gains tend to average out, presenting an “average” MIMO channel to the receiver at all times. In other words, it is very unlikely that all of the channel paths will be in a deep fade at the same time provided that antenna spacing is sufficient. The capacity of the 4 × 4 MIMO channel, one of whose components is the fluctuating signal in Figure 3, is shown in Figure 4. Astonishingly, the channel capacity fluctuates with a standard deviation of only about 10% of the average.

4

Layered Processing

Apart from the fundamental problem of acquiring precise timing for the symbols, which we shall not discuss in this paper, MIMO receivers face the task of demodulating potentially very large signal sets. As an example, consider a 16 × 16 MIMO system with 8PSK modulation employed on each transmit antenna. Each space time symbol will therefore consist of 3×16 = 48 bits, which corresponds to 248 ≈ 3×1014 signal points. In order to handle such large symbol sets, maximum likelihood demodulation becomes infeasible

7

and advanced receiver processing techniques, such as signal layering pioneered by Foschini [16, 17], are required. Layering involves of separating the received space-time symbols into independent data streams corresponding to the different transmitted signals. This is done by a combination of nulling (zero-forcing) of interfering signals and successive cancellation of previously decoded signals. Foschini [16] shows that this method can achieve the capacity of the MIMO channel in the limit of large signal-to-noise ratios. This is not particularly surprising, since it is well established that successive interference cancellation can achieve the capacity of a multiple access channel [9, 18], in this case, a MIMO channel. One of the difficulties is that successive interference cancellation is very complex and entails long delays. A lower complexity alternative to (space-time)successive interference cancellation is to simply filter the received space-time symbol by an appropriate linear layering filter, such as a decorrelator or minimummean square error (MMSE) filter [19]. Both of these filters can achieve suppression of the interference caused by the channel gain correlation at the cost of enhancing the system noise. The performance of the MMSE filter is superior to that of the decorrelator for all values of the signal-to-noise ratio (SNR), and the two are equal as the SNR → ∞. Tse and Hanly [20] have calculated the residual noise of the MMSE filter for random channels, such as an ideal MIMO channel, from which capacities of the different layers can be calculated. Figure 5 shows the capacities of MMSE layered MIMO systems for two different values of Nr /Nt . The figure shows the achievable capacity normalized per dimension as a function of the available bit energy to noise power spectral density ratio, Eb /N0 . The figure shows two cases: (i) the left hand plot is for Nt /Nr = 2, i.e., there are twice as many transmit antennas used as receive antennas, and (ii) the right hand plot shows the reverse situation with Nt /Nr = 1/2, i.e., there are more receive antennas. Several observations can readily be made. If the system is “underloaded”, i.e., there are more receive antennas than transmit antennas – this can arise when a channel rank is significantly smaller than the size of the antenna arrays – then linear layering is very efficient in that the obtained capacities per transmit dimension is virtually identical to that obtainable with an ideal optimal receiver – shown as the solid “optimal” curve in the figure. On the other hand, if more transmit antennas are used, then linear layering may not be efficient, especially for large values of the SNR. Note that the results in Figure 5 are general in the sense that they apply to all MIMO systems as long a Nt , Nr are large. The MMSE linear layering filter requires the inverse of a Nr × Nr filter, which itself may be rather 8

complex for large systems and high target data rates. Specifically, the receiver needs to compute [18]  −1 M l,mmse = HH + + N0 I

(15)

Low complexity alternatives can be found by appealing to stationary iterative methods for solving linear algebraic equations which are computationally efficient methods to compute or approximate matrix inverses [21, 22]. Given a linear algebraic equation x = M −1 u,

(16)

xn+1 = xn − τ (M xn − u)

(17)

the stationary iterative solution

converges to the correct solution with an exponentially vanishing error as long as M is invertible. Applied to our system in [22] it is shown that (n+1)

x

1 = H +y − Nt 1 + Nr



  1  + HH + (N0 − 1)I x(n) Nt 1 + Nr

(18)

has the fastest convergence. The iterations are started with the arbitrary initial vector x(0) = H + y. Using random matrix theory, per dimension capacities can be calculated [23] and are shown in Figure 6 for various iterations of the optimal stationary iterative filter. The solid lines for n = 0 and n = ∞ indicate the capacities of the matched filter receiver (no iterations) and of the full-blown MMSE filter, respectively. The load Nt /Nr = 0.5. Note that in the range of about Eb /N0 = 2 − 6 dB simple iterative filters with two stages outperform matched filtering and virtually achieve the capacity of the more complex and nearly ideal MMSE filter. Furthermore, these values of Eb /N0 are quite reasonable, since the total symbol energy to noise power spectral density ratio Es /N0 = REb /N0 , where R is the rate of the MIMO system, which typically is very large. For example, with 20 antennas, 8-PSK, and rate 2/3 error control codes on each data stream, R = 40 bits. Therefore Es /N0 = 18 − 22 dB, which require high power transmitters. Even for larger values of the Eb /N0 , 2, 5 or at most 10 stages in an iterative filter approximation achieve most of the available information theoretic capacity. These values are independent of the size of the system, which could be hundreds of antennas, and therefore a multiple-stage filter is significantly less complex than an MMSE matrix inverter. The resulting layered channel can now be operated just like a conventional single-input, single-output channel, for which powerful turbo coding techniques approach capacity almost arbitrarily closely [24]. 9

5

Testbed Description

The mobile MIMO measurement system developed at the University of Alberta consists of independent transmitter and receiver stations. Each station is comprised of an FPGA (field programmable gate array) development board for baseband processing, a custom RF (radio frequency) module (for up-, or downconversion and power amplification) and a custom antenna array structure. A PC is used to process captured data from the receiver FPGA board. A photograph of one mobile station of our testbed (excluding the laptop computer and USB cable) is shown in 7.

5.1

Signal Processing Aspects

All signal processing functions are implemented on GVA-290 FPGA development boards manufactured by GV and Associates Inc. Each GVA-290 board contains four Analog Devices AD9762 DACs, four Analog Devices AD9432 ADCs, two Xilinx Virtex-E FPGAs and a Xilinx Spartan-II FPGA. Four-channel RF modules have been custom built for this project by SignalCraft Technologies Inc. Each transmit module receives the spread signals at an IF of 12.5 MHz and up-converts them to the ISM band (902-928 MHz). The signals can be amplified to a maximum output power of 20 dBm per channel. The receive module mirrors the functions of the transmit module. The four signals received from the antennas are amplified and down-converted from the ISM band to 12.5 MHz. On both sets of RF modules, only one local oscillator is used at each frequency stage to generate the carriers that mix with the four input signals. This ensures that no phase shifts are introduced between the four channels by the modules, and that the different received signals are not rotated with respect to each other. An FPGA image has been developed for the transmitter which generates and simultaneously transmits four filtered 500 kchips/s spread spectrum signals (see Figure 8). The spreading sequences used are orthogonal Walsh codes of length 32 multiplied by a pseudorandom m-sequence [25] to ensure good correlation properties. The chip pulse has a truncated square-root raised-cosine shape with a cutoff frequency of 500 kHz and a roll-off factor of 0.31. The four filtered signals are up-converted digitally to an IF of 12.5 MHz before being sent to the DACs. At the receiver (see Figure 9) all of the signal processing is performed on the FPGA development board. The four parallel down-converted signals are received at an IF of 12.5 MHz from the RF receive module. The

10

signals are sampled simultaneously by the ADCs at 50 Msps and passed into an FPGA. In the FPGA, the signals are digitally down-converted to baseband then decimated to 1 Msps (2 samples/chip). Subsequently, they are convolved through a square-root raised-cosine matched filter with the same characteristics as the modulation pulse shaping filter. A proprietary parallel synchronization algorithm [26] is used to synchronize the receiver. Each received signal is correlated with stored copies of the four PN-spread signals that were used in the transmitter. The correlation operation generates four gain values at each receive antenna. The four sets of gain values are arranged into a complex 4 × 4 correlation matrix for each sample instant. The individual matrix elements are squared and subsequently all 16 values are added together.

5.2

Electromagnetic Aspects

Two types of antenna arrays are used with our testbed. One array type is comprised of four (λ/2) centre-fed dipoles and the other consists of two dual-polarized patch antennas [7]. The centre-fed dipoles are created by mounting λ/4-length monopole antennas onto conductive sheets. For both array cases, the antennas were placed in a row so as to make a broadside array. Each patch antenna contains two co-located elements with orthogonal polarizations. Both antenna types have potential advantages and disadvantages with respect to increasing the capacity of the MIMO channel. Performing identical measurement campaigns with both array types allows the determination of which antenna type yields higher channel capacity. The patch antenna array has the potential advantage of employing two orthogonal polarizations while the dipole antenna array uses only a single polarization. This means that in a 4×4 MIMO system with patch antennas, ideally each transmitted signal is affected by only one significant interfering signal. It is then natural to conclude that reduced interference would lead to a higher MIMO channel capacity. However, the scattering that will occur in a multipath radio environment results in rapid loss of polarization separation. The dipole antenna has the potential advantage of having a uniform 360 degree radiation pattern in the plane perpendicular to itself, whereas the patch antenna has a radiation pattern that is nearly uniform over less than 180 degrees in the two perpendicular radiation planes. The dipole antenna’s wider radiation pattern leads one to expect it to provide a higher capacity since it creates a richer multipath environment. The transmitted signals from the dipole antenna array radiate in all directions resulting in reflections and scattering off more objects. Also, the receiver antennas would detect incoming waves from all directions

11

instead of only from a hemisphere. A consideration concerning the link budget is the efficiency of the antenna: what fraction of the electrical energy that enters the antenna connector actually radiates from the antenna as electromagnetic energy. Energy is lost due to antenna dielectrics and protective covers. A rough measurement of the efficiency of an antenna can be obtained using an unobstructed line-of-sight channel. For such a channel, the theoretical received power can be calculated using the transmission formula [27]. A comparison of the measured received power to the theoretical received power (assuming perfectly efficient antennas) will determine the antenna efficiencies. Efficiency measurements have been performed for both the dipole and patch antennas. Our testbed has been set up with one transmitter antenna and one receiver antenna. The transmitter and receiver stations have been placed a few metres apart. An efficiency of 74% for the dipole antenna and an 18% efficiency for the patch antenna have been measured and calculated. Thus, the dipole antenna has a clear advantage over the patch antenna if the link power budget is an issue. In order to verify that the polarization separation of our patch antenna arrays is good, experiments have been conducted to measure the cross polarization discrimination. The experiment measures the amount of power emitted in one polarity that is received by the antennas in the cross polarity. The experiment is performed by placing the two antennas of the receiver station very close (60 to 65 cm separation) to the antennas of the transmitter array. This separation is large enough to avoid near field electromagnetic effects but small enough to create a strong line-of-sight path with little multipath effects. Using this testbed set-up, each of the four transmitter signals is radiated separately from its corresponding antenna while the power at all four received antennas is measured. Table 1 shows the measured relative power of the received signals with cross polarization. As can be observed in the table, the powers of the received cross-polarized signals are 11.9 dB to 17.1 dB below the power of their corresponding received co-polarized signal. Although our measured cross polarization discrimination values are not as large as when the antennas are used in an ideal transmission environment [7], they are still large enough to ensure that cross-coupling will have a minimal effect on our channel gain measurements. In order to assess the error in the channel gain measurements obtained with our system, measurements have been made for an uncoupled line-of-sight (LOS) MIMO channel [29]. This LOS channel was created

12

by removing the antenna arrays and connecting the four RF outputs from the transmitter to the four RF inputs of the receiver with cables. For this uncoupled LOS channel, the diagonal elements (hii , i = 1, . . . 4) of the channel gain matrix correspond to the connected paths and should have the same magnitude. All the off-diagonal values (hij , i = j) represent the non-existent cross paths and should be zero. The deviation in the measured values from this expected result represents the system error. The averaged normalized results from 80 measurements are shown in Table 2 and demonstrate that the error introduced by the system is low. Measured gains of all connected paths are less than 0.5 dB of each other. The power measured in each of the non-existent cross channels is at least 27 dB below the power measured for connected paths.

6

MIMO Testbeds at Other Laboratories

Many universities and corporations around the world have developed testbeds in their labs and are conducting research in this area. An examination of the testbed designs and experimental activities of other teams adds perspective and truly shows why MIMO is an emerging technology. Of the many testbeds in existence, three are discussed below and compared to the University of Alberta MIMO testbed. These testbeds exist at Brigham Young University (Provo, UT), at the Virginia Polytechnic Institute and State University (Blacksburg, VA), and at the Canadian Communications Research Centre (Ottawa, ON). All three of the research teams have thus far used their testbeds for obtaining channel measurements. The MIMO testbed at Brigham Young University [28] is a flexible system that can be expanded up to a 16x16 architecture. It operates in the range 0.8 GHz to 6 GHz and the transmitter can amplify each BPSK signal up to 0.5 W. At the receiver, blocks of sampled data are captured and stored in a PC for off-line processing. Channel estimates are obtained using a correlation and averaging technique. The VT-STAR (Virginia Tech Space-Time Advanced Radio) testbed [29] is a 2x2 MIMO testbed that operates at 2050 MHz on a bandwidth of 750 kHz. The VT-STAR transmitter can radiate up to 28 dBm from each antenna. In contrast to the FPGA boards used in the University of Alberta testbed, VTSTAR uses DSP boards for implementation of their baseband algorithms. In addition, a different receiver algorithm employing a linear processing rule is used for estimating the MIMO channel parameters. The Radio Communications Technologies team at the Communications Research Centre have developed

13

a flexible PC based MIMO testbed [30] similar to that at the Brigham Young University. Their testbed can be scaled up to an 8x8 architecture. It requires a 25 MHz radio bandwidth and can be set to operate at any frequency in the range 20 MHz to 2.4 GHz. The transmitter can radiate up to 25 dBm from each antenna. MIMO channel estimates are derived at the receiver in a fashion similar to what is done on the University of Alberta testbed. A pseudo noise (PN) sequence spread signal is radiated from each transmit antenna and correlations are performed of the received signals with PN sequence copies stored at the receiver.

7

Measured Capacity Results

7.1

Details of Measurement Campaigns

The fifth floor of the ECERF (Electrical and Computer Engineering Research Facility) building on the University of Alberta campus was selected as the location for the indoor channel measurement campaigns. The ECERF building is constructed of steel, concrete and drywall which is typical of many modern office buildings. Four campaigns were performed in total. Three of the campaigns used antenna arrays of dipole antennas and one used dual polarized patch antennas. In all cases, the antennas at each station were placed so as to create a broadside array. For the three dipole antenna campaigns, the four antennas were spaced at distances of λ/8, λ/4 and λ/2 at both stations. For the patch antenna campaign, the two microstrip patch elements were spaced λ/2 apart. Once we had obtained channel gain data in our measurement campaigns, the matrices of measured gains were normalized according to

 H=G

Nr Nt ||G||2

(19)

where ||G||2 is the squared Frobenius norm of G, i.e., the sum of the squared magnitudes of the elements √ of G. Consequently, the Frobenius norm of H, normalized according to (19) becomes equal to Nr Nt . The purpose of normalizing the gain matrices is to eliminate the effect of propagation power loss on the calculated capacity. The MIMO channel capacities were calculated from H using equation (3) with ρ set to 20 dB. For comparison, idealized 4 × 4 MIMO channel matrices of uncorrelated gains have also been generated by a computer. Each element of each computer-generated matrix is created using an independent complex

14

Gaussian random number generator with zero mean and unit variance per dimension. The capacities of the computer-generated channels have been calculated using (3) after being normalized. Channel gain matrices generated in this fashion have been used in several MIMO capacity studies [31].

7.2

Channel Measurements and Comparisons

Figure 10 shows the complementary cumulative distribution function (CCDF) curves for the three dipole antenna campaigns along with the simulated Gaussian case [32]. Two observations can be made by comparing the curves. First, the mean capacity of the simulated Gaussian channel is about 2 bits/channel use higher than the highest mean capacity of the dipole configuration. This difference may be due to a small specular component present in the MIMO channel. Nevertheless, the measurements clearly demonstrate high available capacity. The second observation is that the capacity drops as the antennas are placed closer together, which is not surprising since greater correlation will occur between the received signals. Figure 11 shows the CCDF curves for the λ/2 spaced dipole and λ/2 spaced patch antenna cases [33]. A slightly higher capacity can be observed for the patch antenna array case. The CCDF curve for the λ/2 spaced dipole array in Figure 11 is slightly different from the curve for the λ/2 spaced dipole array in Figure 10. This is because different locations were used for the transmitter antenna array. Another meaningful comparison is that of the singular values (SV) of the channel gain matrices for the four different measurement campaigns. MIMO channels which exhibit higher channel capacity have singular values which are approximately equal while channels with lower capacity have fewer dominant singular values. Figure 12 shows the histogram of the measured SVs for the dipole antenna array campaign when λ/2 element spacing is used. The solid curve shows the theoretical Wishart distribution [10] for an independent Gaussian channel with twice as many receive as transmit antennas (i.e. with a number of significant SVs which is half the size of the array). Hence, the curve represents the distribution of SVs for a purely diffuse 2x4 MIMO channel. Its good match with the first cluster of the histogram suggests that there is about a rank two contribution from diffuse propagation components. The second cluster of SVs with large values around 3-3.5 likely results from specular propagation paths.

15

8

Conclusion and Future Outlook

As calculated from the data presented in Figure 11, the mean MIMO channel capacities for the two λ/2 separation cases are 21.3 bits/channel use (patch antenna case) and 21.1 bits/channel use (dipole case). It is worthwhile to compare these values to those derived from the limiting case equations (12) and (13). For ρ = 20 dB and Nt = Nr = 4, we can calculate Chigh = 26.6 bits/channel use and Clow = 8.6 bits/channel use. Thus, the mean capacities for our typical indoor office environment reach approximately 80 percent of the ideal upper limit case. A better appreciation of the potential data rate increase can be obtained with a different explanation of the upper limiting case equation (12). The capacity potential that is defined by this equation equals the capacity of Nt separate orthogonal channels, e.g., different frequency bands. Thus, with a 4 × 4 system using a 1 MHz frequency band, we obtain 80% of the capacity of single-antenna links using four 1 MHz bands. A second interesting conclusion that can be drawn from our results is that the CCDF capacity curve for the λ/2 spaced patch antenna case is slightly better than the CCDF capacity curve for the λ/2 spaced dipole antenna. Therefore, for our measurement location, the advantage of using dual polarized signals completely compensates the disadvantage of having antennas with a partial (hemispheric) radiation pattern. There are several intriguing extensions to the work that we have presented here. One is to obtain channel measurements for a much larger system (e.g. Nt = Nr = 16) to determine if the same throughput potential relative to the upper limit case exists, i.e., if there is enough scattering in the channel for large capacity gains. This question is undoubtedly dependent on the particular transmission environment (indoor, outdoor, indoor-outdoor, etc.), and measurements are currently under way. Finally, it will be valuable to expand our system to transmit data and establish how much of the MIMO channel capacity is achievable by different communication system structures . We are currently pursuing these research avenues. Acknowledgements The authors gratefully acknowledge the funding for this work provided by the Alberta Informatics Circle of Research Excellence (iCORE), TRLabs, the Natural Sciences and Engineering Research Council (NSERC), the Canadian Foundation for Innovation (CFI) and the National Sciences Foundation (NSF) of 16

the United States.

17

References [1] G.J. Foschini and M.J. Gans,“On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Communications, vol.6, no. 3, pp. 311-335, Mar. 1998. [2] M. Martone, Multiantenna Digital Radio Transmission. Norwood, MA: 1st edition, Artech House, 2002. [3] M. Lienard, P. Degauque, J. Baudet and D. Degardin, “Investigation on MIMO channels in subway tunnels,” IEEE Journal on Selected Areas in Communications, vol. 21 no. 3, pp. 332-339, Apr. 2003. [4] B. Harter, “Bringing fixed wireless home,” Broadbandweek.com, Dec. 2000. [5] J. Walko, “Antenova directs its antennas two ways,” TheWorkCircuit.com, July 31, 2003. [6] E. Auchard, “New Airgo chip attracts attention,” The Globe and Mail, Aug. 19, 2003. [7] K. Gosalia and G. Lazzi, “Reduced size, dual polarized microstrip patch antenna for wireless communications,” IEEE Transactions on Antennas and Propagation, vol. 51, no. 9, pp. 2182-2186, Sept. 2003. [8] Guidelines for Evaluation of Radio Transmission Technologies for IMT-2000, Recommendation ITU-R M.1225, 1997. [9] T. Cover and J. Thomas, Elements of Information Theory. New York: Wiley, 1991. [10] E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. on Telecomm. (ETT), vol. 10, no. 6, Nov. 1999, pp. 585-596. [11] R.A. Horn and J.C. Johnson, Matrix Analysis. New York: Cambridge University Press, 1990. [12] R.G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968. [13] D. Gesbert, H. B¨ olcskei, D.A. Gore, and A.J. Paulraj, “Outdoor MIMO wireless channels: models and performance prediction,” IEEE Transactions on Communications, vol. 50, no. 12, pp. 1926 - 1934, Dec. 2002. [14] V. Tarokh, H. Jafarkhani, and A.R. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Trans. Inform. Theory, Vol. 45, No. 5, pp. 1456–1467, July 1999. [15] B. Hughes, “Differential space-time modulation,” IEEE Trans. Inform. Theory, Vol. 46, No. 7, pp. 2567-2578, Nov. 2000. [16] G. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs Technical Journal, vol. 1, No. 2, , pp. 41 - 59, August 1996. [17] Wolniansky, P. Foschini, G. Golden, G. and Valenzuela, R. “V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel,” in Proc. URSI International Symposium on Signals, Systems, and Electronics, 1998 - ISSSE 98, pp. 295-300, Pisa, Italy, Sept. 1998. [18] S. Verdu, Multiuser Detection. U.K.: Cambridge University Press, 1998. [19] S. Haykin, Adaptive Filter Theory, 2nd Edition. New York: Prentice Hall, 1991. [20] D. Tse and S. Hanly, “Linear multiuser receivers: effective interference, effective bandwidth and user capacity,” IEEE Trans. Inform. Theory, vol. 45, pp. 641-657, Mar. 1999. [21] O. Axelson, Iterative Solution Methods, U.K.: Cambridge Univ. Press, 1994. [22] A. Grant and C. Schlegel, “Linear interference cancellation multiuser receivers,” IEEE Trans. on Communications, vol. 49, no. 10, pp. 1824-1834, Oct. 2001. [23] L. Trichard, J. Evans and I. Collings, “Large system analysis of linear multistage parallel interference cancellation,” IEEE Trans. on Communications, vol. 50, no. 11, pp. 1778 - 1786, Nov. 2002. [24] C. Schlegel and L. Perez, Trellis and Turbo Coding. New York: John Wiley and Sons, 2004. [25] R.E. Ziemer, R.L. Peterson, and D.E. Borth, Introduction to Spread-Spectrum Communications, Prentice Hall, 1995.

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[26] Z. Bagley, C. Schlegel et al, “Digital timing recovery operable at very low or zero SNR,” US Patent Application, filed January 2004. [27] H. Wesolowski, Mobile Communications Systems, p. 82. New York: John Wiley and Sons, Inc, 2002. [28] J. Wallace and M. Jensen, “Experimental characterization of the MIMO wireless channel: data acquisition and analysis,” IEEE Transactions on Wireless Communications, vol. 2, no. 2, pp. 335-343, March 2003. [29] R. Gozali, R. Mostafa, R. Palat, P. Robert, W. Newhall, B. Woerner and J. Reed, “MIMO channel capacity measurements using the VT-STAR architecture,” in Proc. IEEE Vehicular Technology Conference (VTC’02-Fall), pp. 884-888, Vancouver, Canada, Sept. 2002. [30] C. Squires, T. Willink and B. Gagnon, “A flexible platform for MIMO channel characterization and system evaluation,” in Proc. Wireless 2003 - The International Conference on Wireless Communications, pp. 441-450, Calgary, Canada, July 2003. [31] D. Chizhik, F. Rashid-Farrokhi, J. Ling, A. Lozano, “Effect of antenna separation on the capacity of BLAST in correlated channels,” IEEE Communications Letters, vol. 4, no. 11, pp. 337-339, Nov. 2000. [32] P. Goud Jr., C. Schlegel, R. Hang, W. Krzymien, Z. Bagley, S. Messerly, P. Watkins, V. Rajamani, “MIMO channel measurements for an indoor office environment,” in Proc. Wireless 2003 Conference, pp. 423-427, Calgary, Canada, July 2003. [33] P. Goud Jr., C. Schlegel, W. Krzymien, R. Hang, Z. Bagley, S. Messerly, M. Nham, V. Rajamani, “Indoor MIMO channel measurements using dual polarized patch antennas,” in Proc. IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, pp. 752-755, Victoria, Canada, Aug. 2003.

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9

Figures and Tables Radiating Transmitter Antenna 1 2 3 4

Relative Power Cross Path 1 (dB) -12.9 -17.1 -17.1 -16.9

Relative Power Cross Path 2 (dB) -12.3 -11.9 -14.7 -12.0

Table 1: Measured cross polarized power in the patch antenna arrays (relative to the main co-polarized path)

Channel Path h11 h12 h13 h14 h21 h22 h23 h24

Power (dB) -0.33 -34.23 -37.73 -32.62 -29.40 -0.16 -31.22 -37.47

Channel Path h31 h32 h33 h34 h41 h42 h43 h44

Power (dB) -30.13 -32.32 0.00 -34.33 -30.71 -31.84 -27.63 -0.26

Parallel RF Stages

....

....

Baseband Signals

Parallel RF Stages

Table 2: Average squared path gain values for an uncoupled LOS channel

Figure 1: Basic communication system for MIMO channels.

20

Received Baseband Signals

MIMO Channel

c

V

y

˜ c

Matrix Processor

N (0, N0 )

N = min(Nt , Nr )

+

+

y˜1

N (0, N0 )

dN

+

+

c˜N

˜ y

Matrix Processor

d1 c˜1

U+

y˜N

Figure 2: Optimal signal processing if the channel is known at the transmitter.

0

Normalized Power (dB)

-10

-20

-30

-40

-50

-60

-70 0

5

10

15

20

25

30

35

40

Distance (m) Figure 3: Sample received power profile for an indoor office environment

21

Channel Capacity (bits/channel use)

25

20

15

Mean capacity: 21.3 bits/use Capacity standard deviation: 2.6 bits/use

10

5

0 0

5

10

15

25

20

30

35

40

Distance (m) Figure 4: Sample 4 × 4 MIMO channel capacity profile for an indoor office environment: ρ = 20 dB

10 Orthogonal

Capacity bits/dimension

Capacity bits/dimension

10

Optimal 1 MMSE

Optimal MMSE

1

0.1

0.1 -2

Orthogonal

0

2.5

5

7.5

10 12.5

Eb N0 [dB]

-2

0

2.5

5

7.5

10 12.5

Eb N0 [dB]

Figure 5: Achievable capacities with linear MMSE layering of an ideal MIMO channel.

22

Capapcity bits/dimension

10

AWGN Capacity n=∞ n = 10 n=5

MMSE Capacity 1

n=2 n=1 n=0 Matched Filters

0.1 -2

0

2

4

6

8

10

12

14

16 Eb /N0

Figure 6: Achievable spectral efficiencies using iterative linear layering filters.

Figure 7: One station of the mobile MIMO testbed

23

Walsh Coded Signal Generator

500 kchips/s 50 Msps

M Sequence

Pulse Shaping Filter

Image Suppression

Pulse Shaping Filter

Image Suppression

Filter To Digital DAC Quadrature Modulator

Filter

Generator

Figure 8: Block diagram of the transmitter signal processing chain (single channel)

Controller

50 Msps ADC1 Input

ADC2 Input

1 Msps Digital Quadrature Demodulator Digital Quadrature Demodulator

ADC3 Input Digital Quadrature Demodulator ADC4 Input Digital Quadrature Demodulator

50 : 1 Decimation

50 : 1 Decimation

50 : 1 Decimation

50 : 1 Decimation

Pulse Matched Filter Square

Pulse Matched Filter

Walsh and Despreading Sum

Pulse Matched Filter Pulse Matched Filter

Channel Gains

Figure 9: Block diagram of the receiver signal processing chain

24

Peak Detector

Probability Capacity > Abscissa

λ/8 Spaced Dipole Array λ/4 Spaced Dipole Array λ/2 Spaced Dipole Array Simulated Gaussian

1

0.8

0.6

0.4

0.2

0

10

12

14

16

18

20

22

24

26

28

30

Channel Capacity (bits/use) Figure 10: CCDF of the measured channel capacity: ρ = 20 dB

25

Probability Capacity > Abscissa

λ/2 Spaced Dipole Array λ/2 Spaced Patch Array Simulated Gaussian

1

0.8

0.6

0.4

0.2

0

10

12

14

16

18

20

22

24

26

28

30

Channel Capacity (bits/use) Figure 11: CCDF of the measured channel capacity: ρ = 20 dB

26

1000 900 800

Specular components

Bin Count

700

Diffuse components

600 500 400 300 200 100 0

0

0.5

1

1.5

2

2.5

3

3.5

4

Singular Values Figure 12: Histogram of SVs from the λ/2 separated dipole measurements

27