arXiv subjects
Publications and source records attributed to Mei-Hui Guo.
To properly reflect the main purpose of this work, we have changed the paper title to: 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.
Let ${\mathbf{s}}_k=\frac{1}{\sqrt{N}}(v_{1k},...,v_{Nk})^T,$ $k=1,...,K$, where $\{v_{ik},i,k$ $=1,...\}$ are independent and identically distributed random variables with $Ev_{11}=0$ and $Ev_{11}^2=1$. Let ${\mathbf{S}}_k=({\mathbf{s}}_1,...,{\mathbf{s}}_{k-1},$ ${\mathbf{s}}_{k+1},...,{\mathbf{s}}_K)$, ${\mathbf{P}}_k=\operatorname {diag}(p_1,...,$ $p_{k-1},p_{k+1},...,p_K)$ and $β_k=p_k{\mathbf{s}}_k^T({\mathb f{S}}_k{\mathbf{P}}_k{\mathbf{S}}_k^T+σ^2{\mathbf{I}})^{-1}{\math bf{s}}_k$, where $p_k\geq 0$ and the $β_k$ is referred to as the signal-to-interference ratio (SIR) of user $k$ with linear minimum mean-square error (LMMSE) detection in wireless communications. The joint distribution of the SIRs for a finite number of users and the empirical distribution of all users' SIRs are both investigated in this paper when $K$ and $N$ tend to infinity with the limit of their ratio being positive constant. Moreover, the sum of the SIRs of all users, after subtracting a proper value, is shown to have a Gaussian limit.