In this paper , we devise theoretical grounds for constructing channel models for Multi-input Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we give here has already been fruitfully explored with success in the context of Bayesian spectrum analysis and parameter estimation. For each channel model, we conduct an asymptotic analysis (in the number of antennas) of the achievable transmission rate using tools from random matrix theory. A central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations. The results are both useful in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks .

The linear vector--valued channel x 7! Q n M n x+z with z and M n denoting additive white Gaussian noise and independent random matrices, respectively, is analyzed in the asymptotic regime as the dimensions of the matrices and vectors involved become large. The asymptotic eigenvalue distribution of the channel's covariance matrix is given in terms of an implicit equation for its Stieltjes transform as well as an explicit expression for its moments. Additionally, almost all eigenvalues are shown to converge towards zero as the number of factors grows over all bounds. This effect cumulates the total energy in a vanishing number of dimensions. The channel model addressed generalizes the model introduced in [1] for communication via large antennas arrays to N --fold scattering per propagation path. As a byproduct, the multiplicative free convolution is shown to extend to a certain class of asymptotically large non--Gaussian random covariance matrices. Index terms --- random matrices, Stieltjes transform, channel models, fading channels, antenna arrays, multiplicative free convolution, S--transform, Catalan numbers

We study the performance of joint signaturereceiver optimization for Direct Sequence (DS)-Code Division Multiple Access (CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over a noiseless channel. We study the performance of a Random Vector Quantization (RVQ) scheme in which the codebook entries are independent and isotropically distributed. Assuming the interfering signatures are independent, and have independent, identically distributed elements, we evaluate the received Signal-to-Interference plus Noise Ratio (SINR) in the large system limit as the number of users, processing gain, and feedback bits B all tend to infinity with fixed ratios. This SINR is evaluated for both the matched filter and linear Minimum Mean Squared Error (MMSE) receivers. Furthermore, we show that this large system SINR is the maximum that can be achieved over any sequence of codebooks. Numerical results show that with the MMSE receiver one feedback bit per signature coefficient achieves close to single-user performance. We also consider a less complex and suboptimal reduced-rank signature optimization scheme in which the user's signature is constrained to lie in a lower dimensional subspace. The optimal subspace coefficients are scalar-quantized and relayed to the transmitter. The large system performance of the quantized reduced-rank scheme can be approximated, and numerical results show that it performs in the vicinity of the RVQ bound. Finally, we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference.

This paper adresses the behaviour of the mutual information of correlated MIMO Rayleigh channels when the numbers of transmit and receive antennas converge to + ∞ at the same rate. Using a new and simple approach based on Poincaré-Nash inequality and on an integration by parts formula, it is rigorously established that the mutual information converges to a Gaussian random variable whose mean and variance are evaluated. These results confirm previous evaluations based on the powerful but non rigorous replica method. It is believed that the tools that are used in this paper are simple, robust, and of interest for the communications engineering community.

We present a large-system performance analysis of blind and group-blind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain N , the number of users K, and the number of received signal samples M , all go to infinity, while keeping the ratios K/N and M/N fixed. Under such a scenario, we characterize the asymptotic performance of the direct-matrix inversion (DMI) blind linear MMSE receiver, the subspace blind linear MMSE receiver, and the group-blind linear hybrid receiver. We first derive the asymptotic average output signal-to-interference-plus-noise ratio (SINR), for each of these receivers. Our results reveal an interesting "saturation" phenomenon: The output SINR of each of these receivers converges to a finite limit as the signal-to-noise ratio (SNR) of the desired user increases, which is in stark contrast to the fact that the output SINR achieved by the exact linear MMSE receiver can get arbitrarily large. This indicates that the capacity of a wireless system with blind or group-blind multiuser receivers is not only interference-limited, but also estimation-error-limited. We then show that for both the blind and group-blind receivers, the output residual interference has an asymptotic Gaussian distribution, independent of the realizations of the spreading sequences. The Gaussianity indicates that in a large system, the bit error rate (BER) is related to the SINR simply through the Q function.

The use of multi-antenna arrays in both transmission and reception has been shown to dramatically increase the throughput of wireless communication systems. As a result there has been considerable interest in characterizing the ergodic average of the mutual information for realistic correlated channels. Here, an approach is presented that provides analytic expressions not only for the average, but also the higher cumulant moments of the distribution of the mutual information for zero-mean Gaussian MIMO channels with the most general multipath covariance matrices when the channel is known at the receiver. These channels include multi-tap delay paths, as well as general channels with covariance matrices that cannot be written as a Kronecker product, such as dual-polarized antenna arrays with general correlations at both transmitter and receiver ends. The mathematical methods are formally valid for large antenna numbers, in which limit it is shown that all higher cumulant moments of the distribution, other than the first two scale to zero. Thus, it is confirmed that the distribution of the mutual information tends to a Gaussian, which enables one to calculate the outage capacity. These results are quite accurate even in the case of a few antennas, which makes this approach applicable to realistic situations.

Abstract: This paper presents an asymptotic analysis of multi-signature Code-Division Multiple Access (CDMA) in the presence of frequency-selective channels. We characterize the sum spectral efficiency and spectral efficiency regions for both the optimal and Linear Minimum Mean Squared Error (LMMSE) multiuser receivers. Both i.i.d. signatures and isometric signatures, which are orthogonal at each transmitter, are considered. Our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio. The spectral efficiency of the LMMSE receiver is determined from the asymptotic output Signal-to-Interference-Plus Noise Ratio (SINR). Our results rely on approximating certain covariance matrices with unitarily invariant matrices that are asymptotically free. This approximation is shown to be very accurate through comparison with both simulation and an ‘incremental-signature ’ analysis, which can be used to compute asymptotic moments. Also, a novel proof of the convergence of the empirical spectral distribution of the signal correlation matrix is presented. From these results, we derive the optimal coding-spreading tradeoff, which maximizes the LMMSE spectral efficiency, for the case of a single user with multiple i.i.d. signatures. Simulation studies demonstrate that the asymptotic results accurately predict the performance of finite-size systems of interest. The resulting expressions are used to highlight and infer properties of the multi-signature CDMA system, including the benefit of orthogonal relative to i.i.d. signatures, and the tradeoff between spectral efficiency and the versatility of providing a variable data rate

Abstract — The impact of scattering condition and array configuration on performances are inseparable in early analyses of multiple-antenna systems. An array-independent scattering model is introduced where three basic scattering mechanisms are modeled. Performance results become more intrinsic property of the scattering channel itself. For linear arrays of length L in an environment of total angle spread |Ω|, the ergodic capacity is shown to increase linearly with L|Ω | for large arrays. When antenna arrays reduce to practical sizes, the capacity scaling depends on the SNR as well. This implies that the number of antennas used should also depend on the SNR. In terms of outage capacity, the trade-off between spatial multiplexing gain and diversity gain is shown to be very sensitive to the underlying scattering mechanisms. Finally, as |Ω | varies with the propagation range, the trade-off among multiplexing gain, diversity gain, and propagation range is studied. Index Terms — Multiple antennas, multiple-input multipleoutput (MIMO) systems, physical channel modeling, antenna

Polynomial expansion detectors introduced in [1] combined with recent results in random matrix theory were found to be powerful low-complexity tools to mitigate interference on multiple-input multiple-output (MIMO) communication channels [2]. The random matrix model of communication via antenna arrays proposed in [3] characterizes the channel in terms of its asymptotic eigenvalue distribution by a single parameter. Reference [4] generalises the polynomial expansion in [2] to multiple-input-multiple-output (MIMO) communication channels promising very good performance at complexity per bit that grows only linearly with the number of antennas. The reliability of the results reported in [4] strongly depends on the accuracy of the used asymptotic random matrix model to describe the antenna array channel. In this paper, we provide performance results of said receiver in terms of bit error rate and signal-to-interference ratio for communication over real-world MIMO channels that were measured recently in our office in Vienna. Computer simulations show that, for more than 5 antennas, performance with measured data is close to the prediction found with the asymptotic random matrix models used in [4] and only little behind the performance of far more complex receivers, such as the linear MMSE receiver, that involve matrix inversions to combat crosstalk. 1.

A random matrix model is introduced that probabilistically describes the multi--path propagation between a transmitting and receiving antenna array with a limited number of scatterers for indoor environments. The model allows to analytically calculate signal--to--interference-- and--noise ratios and channel capacities for communication systems that apply, similar to the BLAST [1] proposal, antenna arrays at both ends of the wireless link to boost spectral efficiency. I.