MULTIPLE-INPUT multiple-output (MIMO) systems are

Transcription

1 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST MIMO Wireless Communication Channel Phenomenology Daniel W. Bliss, Member, IEEE, Amanda M. Chan, and Nicholas B. Chang Abstract Wireless communication using multiple-input multiple-output (MIMO) systems enables increased spectral efficiency and link reliability for a given total transmit power. Increased capacity is achieved by introducing additional spatial channels which are exploited using space-time coding. The spatial diversity improves the link reliability by reducing the adverse effects of link fading and shadowing. The choice of coding and the resulting performance improvement are dependent upon the channel phenomenology. In this paper, experimental channel-probing estimates are reported for outdoor environments near the personal communication services frequency allocation (1790 MHz). A simple channel parameterization is introduced. Channel distance metrics are introduced. Because the bandwidth of the channel-probing signal (1.3 MHz) is sufficient to resolve some delays in outdoor environments, frequency-selective fading is also investigated. Channel complexity and channel stationarity are investigated. Complexity is associated with channel-matrix singular value distributions. Stationarity is associated with the stability of channel singular value and singular vector structure over time. Index Terms Channel coding, information theory, multipath channels, multiple-input multiple-output (MIMO) systems. I. INTRODUCTION MULTIPLE-INPUT multiple-output (MIMO) systems are a natural extension of developments in antenna array communication. While the advantages of multiple receive antennas, such as gain and spatial diversity, have been known and exploited for some time [1] [3], the use of transmit diversity has been investigated more recently [4], [5]. Finally, the advantages of MIMO communication, exploiting the physical channel between many transmit and receive antennas, are currently receiving significant attention [6] [8]. Because MIMO communication capacity is dependent upon channel phenomenology, studying and parameterizing this phenomenology is of significant interest [9] [19]. This paper makes a number of contributions to this area of study. First, while most experimental results have focused on indoor phenomenology, the phenomenology investigated here focuses on outdoor environments. Second, results for both stationary and vehicle-mounted moving transmitters are Manuscript received March 19, 2003; revised September 27, This work was supported by the U.S. Air Force under Air Force Contract F C D. W. Bliss and A. M. Chan are with Advanced Sensor Techniques Group, MIT Lincoln Laboratory, Lexington, MA USA ( bliss@ll.mit.edu, achan@ll.mit.edu. N. Chang is with the Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI USA ( changn@eecs.umich.edu). Digital Object Identifier /TAP reported. Third, experimental phenomenological results are reported for both 4 4 and relatively large 8 8 MIMO systems, including channel stationarity, both in time and frequency. Fourth, two metrics of channel variation are introduced. One metric provides a measure of capacity loss assuming that receiver beamformers are constructed using incorrect channel estimates, which is useful to determine performance losses due to channel nonstationarity (either in time or frequency). The other metric is sensitive to the shape of the channel eigenvalue distribution, which is appropriate for space-time coding optimization, assuming a uniformed transmitter (UT) (that is transmitters without channel state information). Finally, a simple channel parameterization is provided which empirically matches channel eigenvalue distributions well and provides a simple approach to generate representative simulated channels for space-time coding optimization. MIMO systems provide a number of advantages over singleantenna communication. Sensitivity to fading is reduced by the spatial diversity provided by multiple spatial paths. Under certain environmental conditions, the power requirements associated with high spectral-efficiency communication can be significantly reduced by avoiding the compressive region of the information theoretic capacity bound. This is done by distributing energy amongst multipath modes in the environment. Spectral efficiency is defined as the total number of bits per second per Hz transmitted from one array to the other. Because MIMO systems use antenna arrays, interference can be mitigated naturally. In this paper, outdoor MIMO channel phenomenology near the PCS frequency allocation, 1.79 GHz, is discussed. The channel-probing signal has a bandwidth of 1.3 MHz. This bandwidth is sufficient to resolve some delays, inducing frequency-selective fading in outdoor environments. In Sections II and III, information theoretic capacity of MIMO communication systems and channel estimation are reviewed. Channel difference metrics are introduced in Section IV. Performance of MIMO communication systems and optimal selection of space-time coding are dependent upon the complexity of the channel [20], [21]. This phenomenology for outdoor environments is investigated using MIMO channel-probing experiments. The results are interpreted using a simple parameterization introduced in Section V. The channel phenomenology experiments are described in Section VI, and the experimental results, reporting estimates of channel complexity and stationarity, are discussed in Section VII. II. CHANNEL CAPACITY The information theoretic capacity of MIMO systems has been discussed widely [6] [8]. It is assumed for the sake of the X/04$ IEEE

2 2074 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 following discussion that the receiver can accurately estimate a pseudostationary channel. Given this assumption, there are two types of spectral-efficiency bounds: informed transmitter (IT) and UT, depending on whether or not channel estimates are fed back to the transmitter. For narrowband MIMO systems, the coupling between the transmitter and receiver can be modeled using where is the (number of receive by transmit antenna) channel matrix, containing the complex attenuation between each transmit and receive antenna, is an matrix containing the samples of the transmit array vector, is an matrix containing the samples of the complex receive-array output, and is an matrix containing zero-mean complex Gaussian noise. It is often useful to investigate the structure of the channel matrix and the mean-square attenuation independently. This can be achieved by studying the root-mean-square normalized channel matrix (1) (2) If (6) is not satisfied for some smaller., it will not be satisfied for any B. UT If the channel is not known at the transmitter, then the optimal transmission strategy is to transmit equal power with each antenna,, [7]. Assuming that the receiver can accurately estimate the channel, but the transmitter does not attempt to optimize its output to compensate for the channel, the maximum spectral efficiency is given by This is a common transmit constraint as it may be difficult to provide the transmitter channel estimates. Similarly to the IT case, the UT spectral-efficiency bound is purely a function of the channel-matrix singular values. Expressing the channel matrix with a singular vector decomposition,, the capacity is a function of eigenvalues, but not of the eigenvectors, of (7) (3) where is the mean-square transmitter-to-receiver attenuation, is the normalized channel matrix, and indicates the Frobenius norm. where the singular-value entries of the diagonal matrix given by. (8) are A. IT There are a variety of possible transmitter constraints. Here it is assumed that the fundamental limitation is the total power transmitted. The optimization of the noise-normalized transmit covariance matrix is constrained by the total noise-normalized transmit power. Allowing different transmit powers at each antenna, this constraint can be enforced using the form. The results of the channel-spectral-efficiency bounds discussions presented in [8] are repeated here. The capacity can be achieved if the channel is known by both the transmitter and receiver, giving C. Frequency-Selective Channels In environments where there is frequency-selective fading, the channel matrix is a function of frequency. As has been discussed in [22], the resulting capacity is a function of this fading structure. Exploiting the fact that frequency channels are orthogonal, the capacity in frequency-selective fading can be calculated using an extension of (5) and (7). For the UT, this leads to the frequency-selective spectral-efficiency bound (4) where the notation indicates determinant, indicates Hermitian conjugate, and indicates an identity matrix of size. Solving for the optimal, the resulting capacity is given by (5) where the distance between frequency samples is given by, and -bin frequency-partitioned channel matrix is given by (9) where is an diagonal matrix with entries, whose values are the top eigenvalues of. The values must satisfy (6)... (10) The approximation is exact if the supported delay range of the channel is sampled sufficiently.

3 BLISS et al.: MIMO WIRELESS COMMUNICATION CHANNEL PHENOMENOLOGY 2075 For the IT channel capacity, power is optimally distributed amongst both spatial modes and frequency channels. The capacity can be expressed (11) which is maximized by (5) with the appropriate substitutions for the frequency-selective channel, and diagonal entries in in (6) are selected from the eigenvalues of. Because of the block diagonal structure of, the space-frequency noise-normalized transmit covariance matrix is a block diagonal matrix, normalized so that. III. ESTIMATION The Gaussian probability density function for a multivariate, signal-in-the-mean, statistical model of the received signal is given by (12) where is the noise covariance matrix. The maximum-likelihood estimate of is given by (13) assuming that the reference signals in are known and is nonsingular. As one might intuit from the structure of (13), if a signal s sole use is channel estimation, then the choice of, such that is proportional to the identity matrix (that is equal-power orthogonal signals) is optimal for channel probing in finite signal-to-noise ratio (SNR) environments. However, if joint channel and signal detection is used, then orthogonal signals are not necessarily optimal for link performance. The previous channel-estimation discussion explicitly assumed flat fading. However, the frequency-selective channels can be estimated by first estimating a finite impulse-response MIMO channel which can be transformed to the frequency domain. A finite impulse-response extension of (1) is given by introducing delayed copies of at delays so that the transmit matrix has dimension resulting wideband channel matrix has the dimension. (14). The (15) Using this form, an effective channel filter is associated with each transmit-to-receive antenna link. Assuming regular delay sampling, the explicit frequency-selective form can be constructed using a discrete Fourier transform or equivalently (16) (17) where the -point discrete Fourier transform is represented by and the Kronecker product is represented by. IV. CHANNEL DIFFERENCE METRICS A variety of metrics are possible. Here, two metrics are discussed. Both metrics are ad hoc, but are motivated by limiting forms of the information theoretic capacity. The first metric, discussed in Section IV-A, is sensitive to the differences in channel eigenvalue distributions. While there are an unlimited number of channel eigenvalue distributions that can provide a particular capacity, for a given mean channel attenuation and power, performance of space-time codes is sensitive to the shape of the distribution. Because the optimization of UT space-time codes depends upon the eigenvalue distribution but not the eigenvector structure, the metric introduced in Section IV-A is an appropriate metric for investigating this issue. Specifically, space-time codes must select a rate versus redundancy operating point [20], [21]. The optimal operating point is a function of the shape of the channel eigenvalue distribution. This metric is used to estimate the channel parameter introduced in Section V-C. The second metric, discussed in Section IV-B, is sensitive to differences in both the singular-value distribution and the channel eigenvector structure. In general, MIMO receivers employ some sort of beamformer to coherently combine the signals impinging upon each receive antenna. In dynamic environments (either in time or frequency) channel estimates can quickly become inaccurate. A measure of the adverse effects of using these stale estimates is provided by this metric. Effectively, this metric provides a measure of the fractional capacity loss in the low SNR (or equivalently low spectral-efficiency) limit. Because performance in the low SNR limit is not affected by interference introduced by the other transmit antennas, MIMO systems operating at higher SNR will experience greater interference and thus worse performance. Consequently, this metric is an optimistic estimate of the expected performance due to dynamic channels. A. Eigenvalue-Based Metric As was mentioned in Section II, MIMO capacity is only a function of the channel singular values. Equivalently, capacity is invariant under channel-matrix transformations of the form (18)

4 2076 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 where and are arbitrary unitary matrices. Consequently, for some applications it is useful to employ a metric which is also invariant under this transformation. Because capacity is a function of the structure of the channel singular-value distribution, the metric should be sensitive to this structure. The channel capacity is a function of. A natural metric would employ the distance between the capacity for two channel matrices at the same average total received power, that is, the same where is the column of the channel matrix associated with transmitter. In the low SNR limit, the optimal receive beamformer is given by the matched response given in. If some other beamformer is employed,, then signal energy is lost, adversely affecting the capacity (23) One possible reason that a beamformer might use the wrong matched spatial filter is channel nonstationarity. Assuming the SNR is sufficiently low, the fractional capacity loss is given by (19) However, there are two problems with this definition. First, the difference is a function of. Second, there is degeneracy in singular values that gives a particular capacity. To address the first issue the difference can be investigated in a high SNR limit, resulting in (24) (20) where indicates the th largest eigenvalue of. To increase the sensitivity to the shape of the eigenvalue distribution, the metric is defined to be the Euclidean difference, assuming that each eigenvalue is associated with an orthogonal dimension, resulting in which is the power-weighted mean estimate, where is defined to be the inner product between the good and bad unit-norm array responses for the th transmitter. It is generally desirable for metrics to be symmetric with respect to and, thus avoiding moral attributions with regard to channel matrices. Using the previous discussion as motivation, a symmetric form of fractional capacity loss is given by (25) (21) B. Fractional Receiver-Loss Metric In this section a power-weighted mean metric is introduced. The metric takes into account both the eigenvalue and eigenvector structure of the channels. It is motivated by the effect of receive beamformer mismatch on capacity. Starting with (7), the low SNR UT capacity approximation is given by (22) where the power-weighted average is evaluated over transmitters. The metric presented in (25) provides an estimate of the loss in capacity if the incorrect channel is assumed in a low SNR environment. In general, the loss of capacity is much more significant if operating in a high spectral efficiency, and therefore high SNR regime. If only spatial mitigation is employed (as opposed to a combination of spatial processing and multiuser detection [23], [24]), a slight channel mismatch will introduce significant interference, and thus strongly adversely affect demodulation performance. V. CHANNEL PHENOMENOLOGY A. Singular Values The singular-value distribution of, or the related eigenvalue distribution of, is a useful tool for understanding the expected performance of MIMO communication systems. From the discussion in Section II, it can be seen that the channel capacity is a function of channel singular values, but not the singular-vector structure of the channel. Thus, channel phenomenology can be investigated by studying the statistics of channel singular-value distributions.

5 BLISS et al.: MIMO WIRELESS COMMUNICATION CHANNEL PHENOMENOLOGY 2077 B. Channel Parameterization A commonly employed model assumes the channel is proportional to a matrix,, where the entries are independently drawn from a unit-norm complex circular Gaussian distribution. While the distribution is convenient, it does suffer from a singular-value distribution that is overly optimistic for many environments. One solution is to introduce spatial correlations using the transformation [10] [12]. While this approach is limited [8], it produces simply more realistic channels than the uncorrelated Gaussian model. The spatial correlation matrices can be factored so that and, where and are unitary matrices, and and are positive semidefinite diagonal matrices. When the arrays are located in environments that are significantly different, then correlations seen by one array will typically be much stronger than the other, and the effect of either the left or right will dominate the shaping of the channel matrix singular-value distribution. Conversely, if the environments are similar then one would expect that. In practice, similar channel matrix singular-value distributions can be achieved given either assumption. However, the required values of and, are, of course, different. For the experiments discussed in this paper, both arrays are in similar environments and a symmetric form seems a reasonable model. Assuming that the number of transmit and receive antennas are equal and have similar spatial correlation characteristics, the diagonal matrices can be set equal,, producing the new random channel matrix (26) (27) where is used to set overall scale, is given by the size of, and and indicate random unitary matrices. The form of given here is somewhat arbitrary, but has the satisfying characteristics that as a rank-one channel matrix is produced, and as a spatially uncorrelated Gaussian matrix is produced; thus, the parameterization can easily approximate, in a statistical sense, nearly all environments. This stochastic channel parameterization has the advantage that it is not dependent upon the particular causes of the correlation, or details of the arrays or environment. The normalization for is chosen so that the expected value of is. The model can be related to the ergodic or mean capacity [8] (averaged over an ensemble channel). Exploiting the fact that MIMO capacity is convex cap, a bound on the mean capacity is given by (28) This bound is not necessarily tight, but is useful for illustrating the effects of channel parameter value on capacity. In Fig. 1, Fig. 1. Ratio of bounds on mean UT capacity of =0:2, 0.4, 0.6 to =1. the ratio of capacity bounds for 0.2, 0.4, and 0.6 for a 4 4 MIMO system is displayed. In practice, the ratio of bounds tends to produce slightly optimistic capacity results at values of. The essential features are accurate. Assuming that the space-time coding takes the channel statistics into account for values of 0.6 or greater, performance loss is not overwhelming. A second interesting feature is that at very high SNR the ratio of capacity slowly approaches 1. This is because at very high SNR even strongly attenuated channel modes become useful. Modeling approaches that introduce reduced effective numbers of antennas do not reproduce this phenomenon well. C. Channel Parameter Estimation An estimate for associated with particular transmit and receive locations is given by minimizing the mean-square metric given in (21) (29) where indicates the estimated value of. Here the expectation, denoted by, indicates averaging is over an ensemble of for a given and an ensemble of for given transmit and receiver sites. It is worth noting that this approach does not necessarily provide an unbiased estimate of. Estimates of, using the metric introduced in here, are dependent upon the received SNR. To reduce the bias, one can add complex Gaussian noise to to produce, mimicking the integrated SNR of the estimate of. Data presented here has sufficiently high SNR such that can be estimated within. VI. EXPERIMENT The experimental system employed is a slightly modified version of the Massachusetts Institute of Technology (MIT) Lincoln Laboratory system used previously [3], [23], [25] [27]. The transmit array consists of up to eight arbitrary waveform transmitters. The transmitters can support up to a 2 MHz bandwidth. These transmitters can be used independently, as two groups of four coherent transmitters or as a single coherent group of eight transmitters. The transmit systems can be deployed in the laboratory or in vehicles. When operating coherently as a multiantenna transmit system, the individual

6 2078 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 TABLE I LIST OF TRANSMIT SITES Fig. 2. Scatter plot of mean-squared SISO link attenuation, a, versus link range for the outdoor environment near the PCS frequency allocation. The error bars indicate a range of 61 standard deviation of the estimates at a given site. transmitters can send independent sequences using a common local oscillator. Synchronization between transmitters and receiver and transmitter geolocation is provided by GPS receivers in the transmitters and receivers. The MIT Lincoln Laboratory array receiver system is a highperformance 16-channel receiver system that can operate over a range of 20 MHz to 2 GHz, supporting a bandwidth of up to 8 MHz. The receiver can be deployed in the laboratory or in a stationary bread truck. A. MIT Campus Experiment The experiments were performed during July and August 2002 on and near the MIT campus. These outdoor experiments were performed in a frequency allocation near the PCS band (1.79 GHz). The transmitters periodically emitted 1.7 s bursts containing a combination of channel-probing and space-time-coding waveforms. A variety of coding and interference regimes were explored for both moving and stationary transmitters. The space-time-coding results are beyond the scope of this paper and are discussed elsewhere [23], [24]. Channel-probing sequences using both four and eight transmitters were used. The receive antenna array was placed on top of a tall one-story building (Brookline St. and Henry St.) surrounded by two- and three-story buildings with a parking lot along one side. Different four or eight antenna subsets of the 16-channel receiver were used to improve statistical significance. The nearly linear receive array had a total aperture of less than 8 m, arranged as three subapertures of less than 1.5 m each. The transmit arrays were located on the top of vehicles within 2 km of the receive array. On each vehicle four antennas were approximately located at the vertices of a square, with separation of greater than two to three wavelengths. When operating as an eight-element transmitter, two adjacent parked vehicles were used, connected by a cable that distributed a local oscillator signal. The channel-probing sequence supports a bandwidth of 1.3 MHz with a length of 1.7 ms repeated ten times. All four or eight transmitters emitted nearly orthogonal signals simultaneously. Fig. 3. CDF of channel a estimates, normalized by the mean a for each site, for SISO, and MIMO systems. VII. EXPERIMENTAL RESULTS Channel-complexity and channel-stationarity performance results are presented in this section. A list of transmit sites used for these results is presented in Table I. The table includes distance between transmitter and receiver, velocity of transmitter, the number of transmit antennas, and the estimated for the transmit site. Uncertainty in is determined using the bootstrap technique [28]. Cumulative distribution functions (CDF) reported here are evaluated over appropriate entries from Table I. The systematic uncertainty in the estimation of caused by estimation bias, given the model, is less than A. Attenuation The peak-normalized mean-squared single-input singleoutput (SISO) attenuation (path gain) averaged over transmit and receive antenna pairs for a given transmit site is displayed in Fig. 2 for the outdoor environment. The uncertainty in the estimate is evaluated using a bootstrap technique. B. Channel Complexity Channel complexity is presented using three different approaches. Variation in estimates, eigenvalue CDFs, and estimate CDFs are presented. In Fig. 3, CDFs of estimates normalized by mean for each transmit site are displayed. CDFs are displayed for narrowband SISO, 4 4, and 8 8 MIMO systems. As one would expect, because of the spatial diversity, the variation in mean antenna-pair received power decreases dramatically as the number of antenna pairs increases. This

7 BLISS et al.: MIMO WIRELESS COMMUNICATION CHANNEL PHENOMENOLOGY 2079 Fig. 4. CDF of narrowband channel eigenvalue distributions for MIMO systems: (a) simulated Gaussian channel and (b) experimental results. demonstrates one of the most important statistical effects that MIMO links exploit to improve communication link robustness. For example, if one wanted to operate with a probability of 0.9 to close the link, one would have to operate the SISO link with an excess SISO SNR ( ) margin of over 15 db. The MIMO systems received the added benefit of array gain, which is not accounted for in the figure. In Figs. 4 and 5, CDFs of eigenvalues are presented for 4 4 and 8 8 mean-squared-channel-matrix-element-normalized narrowband channel matrices,. Both simulated Gaussian channels and experimental results are displayed. Superficially, the distributions of the simulated and experimental distributions are similar. However, closer inspection reveals that the experimental distributions cover a greater range of eigenvalues. This is the result of the steeper channel-eigenvalues distribution that is observed in the experimental data compared to the simulated Gaussian channel. The experimental CDFs are evaluated over all site lists. Some care must be taken in interpreting these figures because eigenvalues are not independent. Nonetheless, the steepness of the CDFs is remarkable. One might interpret this to indicate that optimized space-time codes should operate with a relatively high probability of success. The CDFs for estimates are presented in Fig. 6. The mean values of for each environment are While one might expect smaller variation in the 8 8 systems because of the much larger number of paths, this effect may have been exaggerated in Fig. 6 because of the limited number of 8 8 sites available in the experiment. Fig. 5. CDF of narrowband channel eigenvalue distributions for MIMO systems: (a) simulated Gaussian channel and (b) experimental results. Fig. 6. CDF of estimates for and MIMO systems. The values of the channel-complexity parameter,, are, of course, dependent upon the details of the environment and the geometry of the transmit and receive arrays. As can be seen in Table I, the values of vary from one transmit site to another transmit site. Furthermore, one would anticipate significantly different values of in unlike environments, such as the open plains of the Midwest or in highly elevated towers. The dependency upon array geometries is somewhat less clear. Because the arrays employed in this experiment are spatially undersampled, the received signal experiences significant spatial aliasing. Increasing the array aperture may help resolve closely spaced scatterers; this occurs at the expense of folding other widely spaced scatterers back on similar array responses. Consequently, while perturbations in array geometries certainly affect particular received signals, these perturbations are not expected to affect strongly the statistical properties of the channel; thus values of are not expected to be a strong function of array geometry.

8 2080 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 Fig. 8. Example time variation of power-weighted mean cos, fh(t );H(t)g, for stationary and moving MIMO systems. Fig. 7. Eigenvalues,, ofhh as a function of time for (a) stationary and (b) moving transmitters. The same overall attenuation, estimated at t = 0, is used for all time samples. This point can be demonstrated by constraining the choice of receive antennas used for calculating. By excluding or requiring antennas to be consecutive and calculating under these constraints, sensitivity to antenna separation can be investigated. In the following table, three sets of constraints are implemented. In the first column, all receive antennas are used. In the second column, employed antennas are separated by at least two unused antennas. In the third column, only consecutive antennas are used. There is a slight bias for greater antenna separation to produce larger values of, which is consistent with the expectation that greater antenna separation produces more random channel matrices. However, this trend is very subtle, and in all cases, the results are statistically consistent with being independent of antenna separation at these relatively large antenna separations. C. Channel Stationarity The temporal variation of eigenvalues of for stationary and moving transmitters is displayed in Fig. 7. In this figure the normalization is fixed, allowing for overall shifts in attenuation. As one would expect, the eigenvalues of the moving transmitter vary significantly more than those of the stationary environment. However, the eigenvalues of the stationary transmitter do vary somewhat. While the transmitters and receivers are physically stationary, the environment does move. This effect is particularly noticeable near busy roads. Furthermore, while the multiple antennas are driven using the same local oscillator, given Fig. 9. CDF of time variation of power-weighted mean cos, fh(t ); H(t)g, for stationary MIMO system. Contours of CDF probabilities of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 are displayed. Because there is little variation, all curves are compressed near of 1. the commercial grade transmitters, there are always some small relative-frequency offsets. The example variation is given for transmit sites #7 and #14. While the moving-transmitter eigenvalues fluctuate more than those of the stationary transmitter, the values are remarkably stable in time. Conversely, an example of the time variation of the power-weighted mean metric [from (25)], displayed in Fig. 8, varies significantly for the moving transmitter within 10 ms. This indicates that the eigenvector structure varies significantly, while the distribution of eigenvalues tends to be more stable. In the example, the stationary transmitter is located at site #7, and the moving transmitter is located at #14. Over the same period, the stationary transmitter is relatively stable. CDFs for stationary and moving transmitters are displayed in Figs. 9 and 10. In the figures, 4 4 MIMO experiment sites with a speed less than or equal to 0.2 m/s were considered to be stationary (sites: 7, 9, 16, and 18), and those with speeds greater than 5 m/s were considered to be moving (sites: 10, 12 15, 17). As was discussed in Section IV-B, the performance implications of a particular value of depend upon the operating SNR and the receiver design. At low SNR, the fractional UT capacity loss due to receiver mismatch is given directly by the value of. At high SNR, if interference mitigation is primarily achieved through spatial antenna processing, then the performance loss can be significantly worse. This is because contamination from interfering transmit antennas is allowed to overwhelm the intended signals at the outputs of inaccurate beamformers. Furthermore, the significant variation of the moving transmitter is an indication that implementing an IT MIMO system would be

9 BLISS et al.: MIMO WIRELESS COMMUNICATION CHANNEL PHENOMENOLOGY 2081 delay spread, and the resulting frequency-selective fading, is both a function of environment and link length. Consequently, some care must be taken in interpreting this result. Fig. 10. CDF of time variation of power-weighted mean cos, fh(t ); H(t)g, for moving MIMO system. Contours of CDF probabilities of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 are displayed. VIII. SUMMARY In this paper, outdoor MIMO channel phenomenology was discussed. Data from an experiment performed on and near the MIT campus was used to study the phenomenology. The phenomenology was investigated from the perspective of the singular-value distributions of the channel matrices. A channel parameterization approach was introduced. Two channel-difference metrics were introduced. The first was used to estimate the channel parameter. The second metric was employed to demonstrate significant channel variation both as a function of time and frequency. Fig. 11. Example of frequency-selective variation of the power-weighted mean cos, fh(f ); H(f )g. ACKNOWLEDGMENT Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government. The authors would like to thank the excellent MIT Lincoln Laboratory staff involved in the MIMO experiment, in particular S. Tobin, J. Nowak, L. Duter, J. Mann, B. Downing, P. Priestner, B. Devine, T. Tavilla, A. McKellips and G. Hatke. The authors would also like to thank the MIT New Technology Initiative Committee for their support. The authors would also like to thank K. Forsythe, A. Yegulalp, and D. Ryan of MIT Lincoln Laboratory and V. Tarokh of Harvard University for their thoughtful comments. The authors would like to thank N. Sunkavally of MIT for his contributions to the experiment and the analysis. Fig. 12. CDF of frequency-selective variation of the power-weighted mean cos, fh(f ); H(f )g. Contours of CDF probabilities of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 are displayed. very challenging for the moving transmitter, but might be viable for some stationary MIMO systems. D. Frequency-Selective Fading An example of the frequency variation of the power-weighted mean is displayed in Fig. 11. The variation is indicated using the metric presented in (25). In the example, the stationary transmitter is located at site #7. Relatively small frequency offsets induce significant changes in. The CDF of the frequency-selective channel variation is displayed in Fig. 12 (using sites: 7, 9, 16, and 18). This sensitivity indicates that there is significant resolved delay spread and that to safely operate using the narrowband assumption, bandwidths less than 100 khz should be employed. It is worth noting that REFERENCES [1] W. C. Jakes, Microwave Mobile Communications. New York: Wiley, [2] R. A. Monzingo and T. W. Miller, Introduction to Adaptive Arrays. New York: Wiley, [3] K. W. Forsythe, D. W. Bliss, and C. M. Keller, Multichannel adaptive beamforming and interference mitigation in multiuser CDMA systems, in Proc. 33rd Asilomar Conf. Signals, Systems & Computers, vol. 1, Pacific Grove, CA, Oct. 1999, pp [4] A. Wittneben, Base station modulation diversity for digital SIMUL- CAST, in Proc. IEEE Vehicular Technology Conf., 1991, pp [5] V. Weerackody, Diversity for direct-sequence spread spectrum using multiple transmit antennas, in Proc. IEEE ICC, vol. 3, Geneva, 1993, pp [6] G. J. Foschini, Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas, Bell Labs Tech. J., vol. 1, no. 2, pp , [7] I. E. Telatar, Capacity of multi-antenna Gaussian channels, Eur. Trans. Telecommun., vol. 10, no. 6, pp , Nov.-Dec [8] D. W. Bliss, K. W. Forsythe, A. O. Hero, and A. F. Yegulalp, Environmental issues for MIMO capacity, IEEE Trans. Signal Processing, vol. 50, pp , Sept [9] P. Marinier, G. Y. Delisle, and C. L. Despins, Temporal variations of the indoor wireless millimeter-wave channel, IEEE Trans. Antennas Propagat., pp , June [10] D. Gesbert, H. Bolcskei, D. A. Gore, and A. J. Paulraj, Performance evaluation for scattering MIMO channel models, in Proc. 34th Asilomar Conf. Signals, Systems & Computers, vol. 1, Pacific Grove, CA, Oct. 2000, pp [11] D.-S. Shui, G. J. Forschini, M. J. Gans, and J. M. Kahn, Fading correlation and its effect on the capacity of multielement antenna systems, IEEE Trans. Commun., vol. 48, pp , Mar

10 2082 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 8, AUGUST 2004 [12] D. Chizhik, F. Rashid-Forrokhi, J. Ling, and A. Lozano, Effect of antenna separation on the capacity of blast in correlated channels, IEEE Commun. Lett., vol. 4, pp , Nov [13] D. Hampicke, C. Schneider, M. Landmann, A. Richter, G. Sommerkorn, and R. S. Thoma, Measurement-based simulation of mobile radio channels with multiple antennas using a directional parametric data model, in Proc. IEEE Vehicular Technology Conf., vol. 2, 2001, pp [14] M. Stoytchev and H. Safar, Statistics of the MIMO radio channel in indoor environments, in Proc. IEEE Vehicular Technology Conf., vol. 3, 2001, pp [15] D. P. McNamara, M. A. Beach, and P. N. Fletcher, Experimental investigation of the temporal variation of MIMO channels, in Proc. IEEE Vehicular Technology Conf., vol. 2, 2001, pp [16] C. C. Martin, N. R. Sollenberger, and J. H. Winters, MIMO radio channel measurements: Performance comparison of antenna configurations, in Proc. IEEE Vehicular Technology Conf., vol. 2, 2001, pp [17] J. F. Kepler, T. P. Krauss, and S. Mukthavaram, Delay spread measurements on a wideband MIMO channel at 3.7 GHz, in Proc. IEEE Vehicular Technology Conf., vol. 4, 2002, pp [18] T. Svantesson, A double-bounce channel model for multi-polarized MIMO systems, in Proc. IEEE Vehicular Technology Conf., vol. 2, 2002, pp [19] J. P. Kermoal, L. Schumacher, K. I. Pedersen, P. E. Mogensen, and F. Frederiksen, A stochastic MIMO radio channel model with experimental validation, IEEE J. Select. Areas Commun., vol. 20, pp , August [20] L. Zheng and D. Tse, Optimal diversity-multiplexing tradeoff in multiple antenna fading channels, in Proc. 35th Asilomar Conf. Signals, Systems & Computers, Pacific Grove, CA, Nov [21] H. E. Gamal, On the robustness of space-time coding, IEEE Trans. Signal Processing, vol. 50, pp , Oct [22] G. G. Raleigh and J. M. Cioffi, Spatio-temporal coding for wireless communications, IEEE Trans. Commun., vol. 46, pp , Mar [23] D. W. Bliss, P. H. Wu, and A. M. Chan, Multichannel multiuser detection of space-time turbo codes: Experimental performance results, in Proc. 36th Asilomar Conf. Signals, Systems & Computers, Pacific Grove, CA, Nov [24] D. W. Bliss, Robust MIMO wireless communication in the presence of interference using ad hoc antenna arrays, presented at the Proc. Military Communications Conf., MILCOM 2003, Boston, MA, Oct [25], Angle of arrival estimation in the presence of multiple access interference for CDMA cellular phone systems, in Proc IEEE Sensor Array and Multichannel Signal Processing Workshop, Cambridge, MA, Ma [26] C. M. Keller and D. W. Bliss, Cellular and PCS propagation measurements and statistical models for urban multipath on an antenna array, in Proc IEEE Sensor Array and Multichannel Signal Processing Workshop, Cambridge, MA, Mar. 2000, pp [27] D. W. Bliss, Robust MIMO wireless communication in the presence of interference using ad hoc antenna arrays, presented at the MILCOM, Boston, MA, Oct [28] B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans. Bristol, U.K.: Society for Industrial and Applied Mathematics, Daniel W. Bliss (M 97) received the B.S.E.E. degree in electrical engineering from Arizona State University, Tuscon, in 1989 and the M.S. and Ph.D. degrees in physics from the University of California at San Diego, in 1995 and 1997, respectively. Employed by General Dynamics from 1989 to 1991, he designed avionics for the Atlas-Centaur launch vehicle and performed research and development of fault-tolerant avionics. As a member of the Superconducting Magnet Group at General Dynamics from 1991 to 1993, he performed magnetic field calculations and optimization for high-energy particle accelerator superconducting magnets. His doctoral work rom 1993 to 1997, was in the area of high-energy particle physics, searching for bound states of gluons, studying the two-photon production of hadronic final states, and investigating innovative techniques for lattice gauge theory calculations. Since 1997, he has been employed by MIT Lincoln Laboratory, where he is currently a Staff Member at in the Advanced Sensor Techniques Group, where he focuses on multiantenna adaptive signal processing, primarily for communication systems, and on parameter estimation bounds, primarily for geolocation. His current research topics include algorithm development for multichannel multiuser detectors (MCMUD) and information theoretic bounds and space-time coding for MIMO communication systems. parameterization. Amanda M. Chan received the B.S.E.E. and M.S.E.E. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 2000 and 2002, respectively. Currently, she is an Associate Staff Member in the Advanced Sensor Techniques Group, MIT Lincoln Laboratory, Lexington, MA. Her interests are in channel phenomenology. She has previously worked with implementation of synthetic aperture geolocation of cellular phones. Most recently, she has worked on the implementation of MIMO channel Nicholas B. Chang received the B.S.E. degree in electrical engineering (magna cum laude) from Princeton University, Princeton, NJ and the M.S.E. degree in electrical engineering from the University of Michigan, Ann Arbor, in 2002 and 2004, respectively. He worked for MIT Lincoln Laboratory, Lexington, MA, in 2001 and 2002, focusing on synthetic aperture geolocation of wireless systems and channel phenomenology of MIMO communications systems. He is currently a Graduate Student in the Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor. Mr. Chang is a Member of Tau Beta Pi and Sigma Xi, the Scientific Research Society.