Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications

Abstract

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 $E{v}_{11}=0$ and $E{v}_{11}^2=1$. Let ${\mathbf{S}}_k=({\mathbf{s}}_1,...,{\mathbf{s}}_{k-1},$ ${\mathbf{s}}_{k+1},...,{\mathbf{s}}_K)$, ${\mathbf{P}}_k=\mathrm{diag}(p_1,...,$ $p_{k-1},p_{k+1},...,p_K)$ 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 $p_k\ge 0$ and the ${\beta }_k$ 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.

Published at http://dx.doi.org/10.1214/105051606000000718 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• On the signal-to-interference ratio of CDMA systems in wireless communications

Cited by in corpus (2)

• Spectral distributions of adjacency and Laplacian matrices of random graphs
• Central limit theorem for signal-to-interference ratio of reduced rank linear receiver