Measurements on the Impact of Sparse Multipath Components on the LOS MIMO Channel Capacity Andreas Knopp, Robert T. Schwarz, Christian A. Hofmann, Mohamed Chouayakh, Berthold Lankl Munich University of the Bundeswehr, Institute for Communications Engineering, 85579 Neubiberg, Germany.
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pinging from the walls, the bottom, the ceiling and from largescale objects. As a difference to Non-LOS (NLOS) indoor transmission channels, where the radiated waves are subject to several transmissions and reflections, in in-room channels scattering effects are of less relevance. Furthermore, in-room channels are usually characterized by low mobility indicating the commonly utilized Rayleigh-fading channel model to be widely inapplicable. Consequently, new measurements and modeling approaches become necessary. Brief descriptions of the measurement strategy and equipment in section III are followed in section IV by the results, starting with a discussion of the practical relevance of the antenna setup rules given in [3]. Afterwards, we will investigate the impact of strong multipath signal parts on the channel capacity of optimized LOS in-room channels in section IV-B and discuss the most relevant characteristics of those multipath signals which are beneficial for the MIMO channel capacity. The analysis is mainly performed by means of two new performance measures which are presented in section II-B. We concentrate on a 4 × 4 MIMO system as it is most relevant for the upcoming WLAN standard IEEE 802.11n.
Abstract— The channel capacity of indoor Line-Of-Sight MIMO channels is affected by the geometrical antenna setup. In theory there exist rules for the design of LOS channels with optimum channel eigenvalue profile providing maximum capacity. These prescripts are only valid in the absence of multipath signals. By measurements we investigate the relevance of such design rules in real-world MIMO channels consisting of a LOS signal component as well as multipath parts. For that purpose two new performance measures are introduced and shown to be very adequate to distinguish capacity variations which are caused by changes in receive power from those that are caused by differing eigenvalue profiles of the channel matrix. Even sparse multipath signals turn out to be capable of distinctly enhancing the measured spectral efficiency in low-rank channels, while for the high-rank case any multipath components get almost negligible. More important, the geometrical antenna setup not only affects the LOS signal, but also the remaining signal parts. Moreover, the angles of arrival determine, how multipath components affect the LOS channel capacity.
I. I NTRODUCTION Multiple Input-Multiple Output (MIMO) transmission systems promise high channel capacity gains and reliability improvements for fixed bandwidth and transmit power [1], [2]. In order to fully exploit the channel capacity benefits offered by the MIMO technology, it is very important to obtain sufficient knowledge on the transmission channel and its capacityaffecting parameters. Recently, it has been shown theoretically as well as by measurements that especially in Line-Of-Sight (LOS) transmission channels the geometrical antenna setup impacts on the accessible channel capacity [3]–[7]. Presuming uniform linear arrays (ULAs) as the commonly chosen antenna arrangement, the inter antenna array spacing as well as the arrangement of the arrays at the transmitter (Tx) as well as the receiver (Rx) have turned out to be the most important impact factors. In order to construct pure-LOS channels with optimal channel eigenvalues, in [3] a theoretical prescript for the choice of the ULA antenna spacing has been presented. The approach is based on a spherical wave model which has been shown to be superior to the plane wave model in terms of its capacity prediction accuracy [4], [5]. Contrarily to the pure-LOS theory in [3], LOS channel measurements, which provide a statistical data base covering different indoor locations and high numbers of measured positions, have shown the capacity to be only slightly dependending on the antenna arrangement and spacing [6], [7]. Such in-room locations, which are also the focus of this paper, are characterized by a strong LOS signal component as well as several dominant multipath signal components im-
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II. P ERFORMANCE MEASURES FOR ANALYSIS A. The MIMO Channel Spectral Efficiency For the analysis of MIMO channels the channel capacity generally is the most meaningful performance measure. According to [1] and [2] for a MIMO system consisting of N transmit antennas and M receive antennas the time invariant channel spectral efficiency C, which denotes the channel capacity normalized by the transmission bandwidth (unit [Bit/sec/Hz])1 , for a frequency selective MIMO-channel in the absence of channel knowledge at the Tx is calculated σ2 1 log2 det IM + x2 H(f )H H (f ) df . (1) C= B B ση Here, B denotes the transmission bandwidth, IM ∈ NM ×M is the identity matrix, σx2 denotes the mean transmit power that is allocated to each transmit antenna and ση2 denotes the noise power per receive antenna. In the equation uncorrelated transmit signals and equal power at each Tx antenna are presumed. Furthermore, (.)H abbreviates the complex conjugate transpose. For our measurements in this paper we propose the σ2 strategy of working with σx2 and in the consequence leaving η
1 we
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use the terms ”capacity” and ”spectral efficiency” synonymously, here
IEEE ISWCS 2007
obtained by taking the measured HH H and setting all entries on the subdiagonal to zero. This way a CTM is presumed leading to a maximum-value determinant coinciding with a identical power norm ||H||2F of the channel matrix3 , where the power is incorporated in the remaining, non-zero main diagonal entries as given by the truly measured channel. As ||H||2F = tr{HH H }holds4 , in Cref the included power actually remains unchanged, but the omission of the subdiagonal entries ”artificially” turns the true channel into a channel which clearly results in a maximum determinant. This way a reference channel of maximum multiplexing gain is created while keeping the original channel properties in terms of LOS power / path loss. In order to calculate the denominator Cref 2 the value ζLOS is introduced. It denotes the mean path loss between the Rx and Tx antenna arrays which is approximately calculated from the distance d among the array center points 2 = (λ/4πd)2 . and the center wavelength λ according to ζLOS To incorporate this path loss becomes necessary as we use σx2 /ση2 instead of the SNR at the Rx inputs in equation (1). 2 a slight approximation is accepted as the Clearly, using ζLOS distance between different pairs of antennas somewhat varies, but for practical antenna spacings the introduced error gets negligible. Clearly, this measure is sensible for the case of LOS channels only. By means of this, the numerator as well as the denominator presume full-rank channels which differ in their incorporated power. Thus, they are widely independent from the multiplexing gain of H(f ). The denominator takes into account the power of the pure LOS channel without any multipath signals and the numerator regards the LOS signal part as well as the multipath signal parts. Thus, P provides a measure for the receive power alterations due to the multipath components (MPCs) impinging at the Rx input. The codomain of this measure is defined by the receive power. In theory P tends to zero if no receive power impinges at the Rx, and it is theoretically upper limited by the case where the transmit power radiated by the Tx arrives at the Rx without any losses. Hence, both bounds strongly depend upon the chosen scenario and no sensible absolute values can be provided. Instead, the criterion of interest is the deviation of P from P = 1. It reflects how much the receive power is altered by reflected waves compared to the pure LOS case, where it obtains P = 1. The second measure, which is called ”multiplexing measure” M, is defined
the measured channel transfer functions (CTFs) within the channel transfer matrix H(f ) unchanged with respect to their incorporated path loss. This strategy is different from normalizing H(f ) by factoring out the path loss and finally replacing 2 σx 2 by the SNR at the receiver inputs, as it is regularly done. ση Our proposed method has several advantages with respect to the evaluation of measured data which are discussed in more detail for example in [7]. As this discussion is not a focus of this paper, for the moment it should be sufficient to be aware that the SISO CIRs, which we use to form the MIMO channel, are truly scaled with respect to their power as the path loss is included. This for example means that changing the distance between Tx and Rx also causes an alteration of the channel capacity even if the eigenvalue profile of the channel transfer matrix (CTM) remains unchanged. Therefore, our strategy appears to be able of best representing the physical nature of the channel as it incorporates both capacity-affecting effects: the path loss and the eigenvalue profile of the channel transfer matrix. Based on such deliberations, further measures would be helpful which enable the user to distinguish between the two impact factors. Such measures are presented in the next section. They are especially designed for LOS channels. B. The ”Power Measure” and the ”Multiplexing Measure” Discussing the performance of MIMO systems, well configured antenna setups regularly aim at the multiplexing gain maximization of the underlying MIMO channel, i.e. the construction of high-rank2 MIMO channel transfer matrices. If reflections are introduced, on the one hand they are very probable of changing the CTM eigenvalue profile compared to the pure LOS case, but on the other hand they may increase or decrease the receive power at the receiver input. From this point of view it would be very advantageous if it was possible to separate both effects for analysis. Having available corresponding measures it could for example be quantified which of the both effects has the most important impact and should be primarily regarded in terms of system design. Hence, we introduce the following two independent measures: The first measure we call ”power measure” P and we define P
LOS (2) Cref /Cref M 2 σ 1 log2 1 + σx2 H(f )H H (f ) df B η m=1 B mm = . σ2 2 min{M, N } log2 1 + σx2 ζLOS max{M, N }
=
M
=
η
Here [U ]mm denotes the m-th entry on the main diagonal of matrix U . P is intended to characterize the increase / decrease in receive power due to multipath signal components. P builds the ratio between a quantity Cref and the maximum spectral efficiency which would occur if the LOS signals existed without any multipath signal components and concurrently had LOS ). The measure Cref is an optimum eigenvalue profile (Cref
=
(3) C/Cref
2 σ log2 det IM + σx2 H(f )H H (f ) df η B . M σ2 log2 1 + σx2 H(f )H H (f ) df B
m=1
η
mm
It aims at quantifying the margin between the actual channel and a full-rank channel of identical power with respect to the channel capacity. This way the measure M obtains value 1 for the case of a physical channel which has full rank
2 With respect to the MIMO channel capacity in this paper the terms ”lowrank” channel and ”high-rank” channel denote the cases of suboptimal and optimal channel eigenvalue profiles, respectively.
||.||F denotes the Frobenius-norm. denotes the trace operator
3 Here 4 ”tr”
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already, i.e. Cref = C. The multiplexing measure M builds the ratio between the true spectral efficiency of the MIMO channel H(f ) and Cref . The codomain of this measure is M ∈ [Cmin /Cref , 1] ≈ [1/M, 1]. Thus, the power in H(f ) is secondary and the focus lies on the multiplexing gain. In the context of the measurement analysis the practical relevance of the measures will become more striking. III. D ETAILS ON THE M EASUREMENTS A. Measurement Equipment For our measurements we used an enhanced version of our fast MIMO channel sounder which was already used for earlier measurement campaigns, e.g. [6], [7]. The most important technical data of the improved channel sounder, which was practically used for the first time in this paper, are summarized in the following table: measurable size of MIMO channel carrier frequency measurement bandwidth resolution measurement time per MIMO channel matrix temporal resolution measurement SNR maximum transmit power maximum continuous measurement time span MIMO CTM snapshots per continuous measurement
2 × 2 ... 8 × 8 2.35 GHz 80 MHz 12 Bit 204.8 µs (8 × 8) 12.5 ns > 40 dB 16 dBm ≈8s 1...250
We used λ/2 monopole antennas which were arranged as an ULA on a wooden board. The equipment as well as the antenna arrays are depicted in figure 1. For the estimation of the channel parameters we applied a method which is equivalent to the BLUE (Best Linear Unbiased Estimator) [8] in order to achieve lowest variance of the estimation results.
Fig. 1. measurement setup and equipment (8 × 8 MIMO channel sounder). top figure: perpendicular antenna orientation, metal board positioned laterally to the LOS propagation path (”setup 1”), bottom figures: metal reflection layers positioned behind Tx and Rx, respectively
stress the power-dominance of the LOS signal component and reduce the impact of reflected waves which we mainly expected to impinge from the surrounding plasterboard-walls. Furthermore, the room was furnished solely by single-person working desks and chairs, no furniture, cupboards or closets acting as additional scattering objects were present. The left hand part of figure 2 shows the joint AOD/AOA angular spectrum which was measured accordingly. At each frequency sample of the measured, frequency selective channel this angular spectrum was simply calculated applying the well known method of performing a 2-D fourier transform of the measured 8 × 8 MIMO CTM [9]. Afterwards the results of the different frequency bins were averaged for noise reduction. It can be observed that the main receive signal energy impinges from the LOS propagation direction, where it must be kept in mind that only AOAs/AODs in horizontal direction can be resolved. This particularly means that reflections from the bottom or the ceiling can not be distinguished from the LOS signal. Those reflections clearly could not be totally suppressed due to the low height of the room, but the antenna pattern of the antennas masked the corresponding AODs and AOAs and again stressed the horizontal (LOS) propagation direction. The figure meaningfully shows the LOS direction being the preferred propagation direction. No comparably
B. Measurement Procedure In [6], [7] we presented results of measurement campaigns in different in-room environments where we statistically evaluated the spatial capacity variations depending on the Tx-Rx antenna positions. Concurrently, we investigated the dependence of the measured spectral efficiency on the chosen antenna setup and inter antenna array spacing. As the main result of that earlier papers this dependence could be observed much less than it would have been expected from theory. Although a higher capacity could be measured after applying the rules for the construction of high-rank LOS channels, the degradation between high-rank and low-rank LOS configurations ranged only around 10% or even below. Obviously, the measured capacity was influenced by reflected or even scattered multipath signals which interfere the LOS propagation path and alter the phase angle relations among the entries of the CTM. Therefore, in this paper we try to investigate the impact of reflected signals on the measured MIMO capacity in more detail. Hence, we applied the following measurement strategy: at first, we located our measurement system in the center of a large conference room of size 24 × 10 × 3m. We chose a comparatively narrow Tx-Rx distance of 2.3m in oder to
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nometalboardsinthevicinityofthesetup 40
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−80 −80 −60 −40 −20 0 AoD[◦ ]
41 39 37 35 33 31 29 27
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Fig. 2. joint AOD/AOA angular spectra, Tx-Rx distance=2.3m, LOS propagation path corresponding to AOA=AOD=0, brightness directly proportional to arriving signal energy, left: LOS only, right: LOS+2 reflections
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Fig. 4. left hand part: impact of antenna orientation and setup on the measured LOS channel capacity, right hand part: introducing MPCs and 2 /σ 2 = 107 , see fig. 3 for explanation of abbreviations impact of AOA, σx η
IV. R ESULTS A. Antenna Arrangement and Spacing in pure LOS Channels
Fig. 3. left hand part: investigated antenna array orientations (top view), right hand part: possible positions of metal boards (top view)
We started our analysis with a practical test of Bohagen’s prescript which in theory enables the construction of highrank LOS channels. According to [3], if a broadside ULAantenna orientation is presumed, the antenna separation product (ASPopt ) leading to a full-rank LOS MIMO channel with good accuracy is calculated by
strong reflections could be observed, elsewhere. This antenna arrangement in the sequel was used for our investigations. Thus, section IV-A starts by a discussion of the practical relevance of high-rank channel construction methods, before in section IV-B we add large, metal boards at different positions around the measurement setup in order to introduce multipath signals. An example for a typical angular spectrum with LOS and MPCs is also depicted in the right hand part of figure 2. During the discussion of the results we distinguish between different antenna orientations, antenna spacings and positions of the metal reflection layers. All the possible setups are shown in figure 3. Additionally, corresponding abbreviations are provided which are used in the sequel. An exemplary measurement setup is depicted in figure 1. For each characteristic setup at least 250 MIMO channel realizations consisting of 16 · 103 channel impulse responses were combined in a data set for statistical evaluation. As an example, the pureLOS case with broadside antenna orientation is taken as a single, characteristic setup. Hence, we measured 5 different Tx-Rx positions in the vicinity of the center of the room in order to provoke changing scattering components, where at each position 50 MIMO channel realizations were consecutively allocated for noise and error reduction. During the 50 measurements the channel was assured to be quasi-static. For the capacity calculation the measured bandwidth of 80 MHz was split up into segments of 4 MHz-bandwidth and each segment was treated to be a single channel realization. This again is equivalent to slightly changing the Tx-Rx positions resulting in different phase angles of interfering signal parts at a particular frequency. Thus, for a single, characteristic setup we evaluated a data set of at least 5 · 103 MIMO channels.
ASPopt = dT dR = (d·λ·κ) / V, κ ∈ {k ∈ N : V k}, (4) where V = max{M, N } and V k means that k is not divisible by V . Here the distances dT , dR and d are denoted according to figure 3. For the given Tx-Rx distance of our measurement setup of d = 2.3m and the center wavelength of the transmission band of λ = 0.1277m we obtain ASPopt = 0.2937 · κ/M , where we presume the setup to be endowed with the identical number of Tx and Rx antennas. For our survey we chose M = N = 4 and κ = 1. For dT = dR we obtained dT (λ) = dR (λ) = 27.1cm. Clearly, the chosen ASPopt (λ) only is exactly valid at the center frequency λ, but according to Bohagen’s results in [3] no alterations of the resulting channel capacity are to be expected for B
