414 research outputs found
Iterative Deterministic Equivalents for the Performance Analysis of Communication Systems
In this article, we introduce iterative deterministic equivalents as a novel
technique for the performance analysis of communication systems whose channels
are modeled by complex combinations of independent random matrices. This
technique extends the deterministic equivalent approach for the study of
functionals of large random matrices to a broader class of random matrix models
which naturally arise as channel models in wireless communications. We present
two specific applications: First, we consider a multi-hop amplify-and-forward
(AF) MIMO relay channel with noise at each stage and derive deterministic
approximations of the mutual information after the Kth hop. Second, we study a
MIMO multiple access channel (MAC) where the channel between each transmitter
and the receiver is represented by the double-scattering channel model. We
provide deterministic approximations of the mutual information, the
signal-to-interference-plus-noise ratio (SINR) and sum-rate with
minimum-mean-square-error (MMSE) detection and derive the asymptotically
optimal precoding matrices. In both scenarios, the approximations can be
computed by simple and provably converging fixed-point algorithms and are shown
to be almost surely tight in the limit when the number of antennas at each node
grows infinitely large. Simulations suggest that the approximations are
accurate for realistic system dimensions. The technique of iterative
deterministic equivalents can be easily extended to other channel models of
interest and is, therefore, also a new contribution to the field of random
matrix theory.Comment: submitted to the IEEE Transactions on Information Theory, 43 pages, 4
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
A Deterministic Equivalent for the Analysis of Non-Gaussian Correlated MIMO Multiple Access Channels
Large dimensional random matrix theory (RMT) has provided an efficient
analytical tool to understand multiple-input multiple-output (MIMO) channels
and to aid the design of MIMO wireless communication systems. However, previous
studies based on large dimensional RMT rely on the assumption that the transmit
correlation matrix is diagonal or the propagation channel matrix is Gaussian.
There is an increasing interest in the channels where the transmit correlation
matrices are generally nonnegative definite and the channel entries are
non-Gaussian. This class of channel models appears in several applications in
MIMO multiple access systems, such as small cell networks (SCNs). To address
these problems, we use the generalized Lindeberg principle to show that the
Stieltjes transforms of this class of random matrices with Gaussian or
non-Gaussian independent entries coincide in the large dimensional regime. This
result permits to derive the deterministic equivalents (e.g., the Stieltjes
transform and the ergodic mutual information) for non-Gaussian MIMO channels
from the known results developed for Gaussian MIMO channels, and is of great
importance in characterizing the spectral efficiency of SCNs.Comment: This paper is the revision of the original manuscript titled "A
Deterministic Equivalent for the Analysis of Small Cell Networks". We have
revised the original manuscript and reworked on the organization to improve
the presentation as well as readabilit
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
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