Antonia Maria Tulino

Impact of antenna correlation on the capacity of multiantenna channels

This paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels. The analysis is not restricted to the popular separable correlation model, but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature. For arbitrary signal-to-noise ratios (SNR), the characterization is conducted in the regime of large numbers of antennas. For the low- and high-SNR regions, in turn, we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power, bandwidth, and rate.

High-SNR power offset in multiantenna communication

The analysis of the multiple-antenna capacity in the high-SNR regime has hitherto focused on the high-SNR slope (or maximum multiplexing gain), which quantifies the multiplicative increase as a function of the number of antennas. This traditional characterization is unable to assess the impact of prominent channel features since, for a majority of channels, the slope equals the minimum of the number of transmit and receive antennas. Furthermore, a characterization based solely on the slope captures only the scaling but it has no notion of the power required for a certain capacity. This paper advocates a more refined characterization whereby, as a function of SNR|/sub dB/, the high-SNR capacity is expanded as an affine function where the impact of channel features such as antenna correlation, unfaded components, etc., resides in the zero-order term or power offset. The power offset, for which we find insightful closed-form expressions, is shown to play a chief role for SNR levels of practical interest.

Capacity-achieving input covariance for single-user multi-antenna channels

We characterize the capacity-achieving input covariance for multi-antenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenvectors are found for zero-mean channels with arbitrary fading profiles and a wide range of correlation and keyhole structures. For the eigenvalues, in turn, we present necessary and sufficient conditions as well as an iterative algorithm that exhibits remarkable properties: universal applicability, robustness and rapid convergence. In addition, we identify channel structures for which an isotropic input achieves capacity.

Network MIMO With Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation, and Reduced-Complexity Scheduling

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.

Performance of space-time codes for a large number of antennas

We study the asymptotic behavior of space-time codes when the number of transmit and receive antennas grows to infinity. Specifically, we determine the behavior of pairwise error probabilities with maximum-likelihood (ML) decoding and with three types of receiver interfaces: the ML interface, the linear zero-forcing (ZF) interface, and the linear minimum-mean-square-error (MMSE) interface. Two situations are studied: when the number of receiving antennas grows to infinity while the number of transmitting antennas is finite, and when both numbers grow to infinity but their ratio remains constant. We show that with ML or linear interfaces the asymptotic performance of space-time codes is determined by the Euclidean distances between codewords. Moreover, with the two linear interfaces examined here the number r of receive antennas must be much larger than the number t of transmit antennas to avoid a sizeable loss of performance; on the other hand, when r /spl Gt/ t, the performance of these linear interfaces comes close to that of ML. The dependence of error probabilities on Euclidean distance is valid for intermediate signal-to-noise ratios (SNRs) even when the number of antennas is small. Simulations validate our theoretical findings, and show how asymptotic results may be substantially valid even in a nonasymptotic regime: thus, even for few antennas, off-the-shelf codes may outperform space-time codes designed ad hoc.

Achievable Sum Rate of MIMO MMSE Receivers: A General Analytic Framework

This paper investigates the achievable sum rate of multiple-input multiple-output (MIMO) wireless systems employing linear minimum mean-squared error (MMSE) receivers. We present a new analytic framework which exploits an interesting connection between the achievable sum rate with MMSE receivers and the ergodic mutual information achieved with optimal receivers. This simple but powerful result enables the vast prior literature on ergodic MIMO mutual information to be directly applied to the analysis of MMSE receivers. The framework is particularized to various Rayleigh and Rician channel scenarios to yield new exact closed-form expressions for the achievable sum rate, as well as simplified expressions in the asymptotic regimes of high and low signal-to-noise ratios (SNRs). These expressions lead to the discovery of key insights into the performance of MIMO MMSE receivers under practical channel conditions.

A new family of MMSE multiuser receivers for interference suppression in DS/CDMA systems employing BPSK modulation

We deal with interference suppression in asynchronous direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shift keying modulation. Such an interference may arise from other users of the network, from external low-rate systems, as well as from a CDMA network coexisting with the primary network to form a dual-rate network. We derive, for all of these cases, a new family of minimum mean-square-error detectors, which differ from their conventional counterparts in that they minimize a modified cost function. Since the resulting structure is not implementable with acceptable complexity, we also propose some suboptimum systems. The statistical analysis reveals that both the optimum and the suboptimum receivers are near-far resistant, not only with respect to the other users, but also with respect to the external interference. We also present a blind and a recursive least squares-based, decision-directed implementation of the receivers wherein only the signature and the timing of the user to be decoded and the signaling time and the frequency offset of the external interferer are assumed known. Finally, computer simulations show that the proposed adaptive algorithm outperforms the classical decision-directed RLS algorithm.

Support Recovery With Sparsely Sampled Free Random Matrices

Consider a Bernoulli-Gaussian complex <i>n</i>-vector whose components are <i>V</i>_i = <i>X</i>_i<i>B</i>_i, with <i>X</i>_i ~ <i>C N</i>(0, <i>P</i>_x) and binary <i>B</i>_i mutually independent and iid across <i>i</i>. This random <i>q</i>-sparse vector is multiplied by a square random matrix <b>U</b>, and a randomly chosen subset, of average size <i>n p</i>, <i>p</i> ∈ [0,1], of the resulting vector components is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where <b>U</b> is typically a matrix with iid components, to allow <b>U</b> satisfying a certain freeness condition. This class of matrices encompasses Haar matrices and other unitarily invariant matrices. We use the replica method and the decoupling principle of Guo and Verdú, as well as a number of information-theoretic bounds, to study the input-output mutual information and the support recovery error rate in the limit of <i>n</i> → ∞. We also extend the scope of the large deviation approach of Rangan and characterize the performance of a class of estimators encompassing thresholded linear MMSE and <i>l</i>₁ relaxation.

Spectral efficiency of multicarrier CDMA

We analyze the spectral efficiency (sum-rate per subcarrier) of randomly spread synchronous multicarrier code-division multiple access (MC-CDMA) subject to frequency-selective fading in the asymptotic regime of number of users and bandwidth going to infinity with a constant ratio. Both uplink and downlink are considered, either conditioned on the subcarrier fading coefficients (for nonergodic channels) or unconditioned thereon (for ergodic channels). The following receivers are analyzed: a) jointly optimum receiver, b) linear minimum mean-square error (MMSE) receiver, c) decorrelator, and d) single-user matched filter.

Design of reduced-rank MMSE multiuser detectors using random matrix methods

Reduced-rank minimum mean-squared error (MMSE) multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in long-sequence code-division multiple-access (CDMA) systems. In this paper, we consider the design of reduced-rank MMSE receivers in a general framework which includes fading, single and multiantenna receivers, as well as direct-sequence CDMA (DS-CDMA) and multicarrier CDMA (both uplink and downlink). In all these cases, random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reduced-rank receiver.