A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large Dimensional Signals

This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multi-antenna as well as spread spectrum transmission models. The expression of the deterministic approximation of the SINR in the large dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large dimension regime, and their variance is shown to decrease as the inverse of the signal dimension

Free Probability based Capacity Calculation of Multiantenna Gaussian Fading Channels with Cochannel Interference

During the last decade, it has been well understood that communication over multiple antennas can increase linearly the multiplexing capacity gain and provide large spectral efficiency improvements. However, the majority of studies in this area were carried out ignoring cochannel interference. Only a small number of investigations have considered cochannel interference, but even therein simple channel models were employed, assuming identically distributed fading coefficients. In this paper, a generic model for a multi-antenna channel is presented incorporating four impairments, namely additive white Gaussian noise, flat fading, path loss and cochannel interference. Both point-to-point and multiple-access MIMO channels are considered, including the case of cooperating Base Station clusters. The asymptotic capacity limit of this channel is calculated based on an asymptotic free probability approach which exploits the additive and multiplicative free convolution in the R- and S-transform domain respectively, as well as properties of the eta and Stieltjes transform. Numerical results are utilized to verify the accuracy of the derived closed-form expressions and evaluate the effect of the cochannel interference.Comment: 16 pages, 4 figures, 1 tabl

Performance Analysis of Massive MIMO Networks with Random Unitary Pilot Matrices

A common approach to obtain channel state information for massive MIMO networks is to use the same orthogonal training sequences in each cell. We call this the full-pilot reuse (FPR) scheme. In this paper, we study an alternative approach where each cell uses different sets of orthogonal pilot (DOP) sequences. Considering uplink communications with matched filter (MF) receivers, we first derive the SINR in the large system regime where the number of antennas at the base station, the number of users in each cell, and training duration grow large with fixed ratios. For tractability in the analysis, the orthogonal pilots are drawn from Haar distributed random unitary matrices. The resulting expression is simple and easy to compute. As shown by the numerical simulations, the asymptotic SINR approximates the finite-size systems accurately. Secondly, we derive the user capacity of the DOP scheme under a simple power control and show that it is generally better than that of the FPR scheme.Comment: Draf

Random Beamforming over Correlated Fading Channels

We study a multiple-input multiple-output (MIMO) multiple access channel (MAC) from several multi-antenna transmitters to a multi-antenna receiver. The fading channels between the transmitters and the receiver are modeled by random matrices, composed of independent column vectors with zero mean and different covariance matrices. Each transmitter is assumed to send multiple data streams with a random precoding matrix extracted from a Haar-distributed matrix. For this general channel model, we derive deterministic approximations of the normalized mutual information, the normalized sum-rate with minimum-mean-square-error (MMSE) detection and the signal-to-interference-plus-noise-ratio (SINR) of the MMSE decoder, which become arbitrarily tight as all system parameters grow infinitely large at the same speed. In addition, we derive the asymptotically optimal power allocation under individual or sum-power constraints. Our results allow us to tackle the problem of optimal stream control in interference channels which would be intractable in any finite setting. Numerical results corroborate our analysis and verify its accuracy for realistic system dimensions. Moreover, the techniques applied in this paper constitute a novel contribution to the field of large random matrix theory and could be used to study even more involved channel models.Comment: 35 pages, 5 figure

Random Beamforming over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach

In this work, we study the performance of random isometric precoders over quasi-static and correlated fading channels. We derive deterministic approximations of the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide simple provably converging fixed-point algorithms for their computation. Although these approximations are only proven exact in the asymptotic regime with infinitely many antennas at the transmitters and receivers, simulations suggest that they closely match the performance of small-dimensional systems. We exemplarily apply our results to the performance analysis of multi-cellular communication systems, multiple-input multiple-output multiple-access channels (MIMO-MAC), and MIMO interference channels. The mathematical analysis is based on the Stieltjes transform method. This enables the derivation of deterministic equivalents of functionals of large-dimensional random matrices. In contrast to previous works, our analysis does not rely on arguments from free probability theory which enables the consideration of random matrix models for which asymptotic freeness does not hold. Thus, the results of this work are also a novel contribution to the field of random matrix theory and applicable to a wide spectrum of practical systems.Comment: to appear in IEEE Transactions on Information Theory, 201

Transmitter Optimization in Multiuser Wireless Systems with Quality of Service Constraints

In this dissertation, transmitter adaptation for optimal resource allocation in wireless communication systems are investigated. First, a multiple access channel model is considered where many transmitters communicate with a single receiver. This scenario is a basic component of a. wireless network in which multiple users simultaneously access the resources of a wireless service provider. Adaptive algorithms for transmitter optimization to meet Quality-of-Service (QoS) requirements in a distributed manner are studied. Second, an interference channel model is considered where multiple interfering transmitter-receiver pairs co-exist such that a given transmitter communicates with its intended receiver in the presence of interference from other transmitters. This scenario models a wireless network in which several wireless service providers share the spectrum to offer their services by using dynamic spectrum access and cognitive radio (CR) technologies. The primary objective of dynamic spectrum access in the CR approach is to enable use of the frequency band dynamically and opportunistically without creating harmful interference to licensed incumbent users. Specifically, CR users are envisioned to be able to provide high bandwidth and efficient utilization of the spectrum via dynamic spectrum access in heterogeneous networks. In this scenario, a distributed method is investigated for combined precoder and power adaptation of CR transmitters for dynamic spectrum sharing in cognitive radio systems. Finally, the effect of limited feedback for transmitter optimization is analyzed where precoder adaptation uses the quantized version of interference information or the predictive vector quantization for incremental updates. The performance of the transmitter adaptation algorithms is also studied in the context of fading channels