Central limit theorem for signal-to-interference ratio of reduced rank linear receiver

Abstract

Let ${\mathbf{s}}_k=\frac{1}{\sqrt{N}}(v_{1k},...,v_{Nk}{)}^T,$ with $\{v_{ik},i,k=1,...\}$ independent and identically distributed complex random variables. Write ${\mathbf{S}}_k=({\mathbf{s}}_1,...,{\mathbf{s}}_{k-1},{\mathbf{s}}_{k+1},...,{\mathbf{s}}_K),$ ${\mathbf{P}}_k=\mathrm{diag}(p_1,...,p_{k-1},p_{k+1},...,p_K)$, ${\mathbf{R}}_k=({\mathbf{S}}_k{\mathbf{P}}_k{\mathbf{S}}_k^{\ast }+{\sigma }^2\mathbf{I})$ and ${\mathbf{A}}_{km}=[{\mathbf{s}}_k,{\mathbf{R}}_k{\mathbf{s}}_k,...,{\mathbf{R}}_k^{m-1}{\mathbf{s}}_k]$. Define ${\beta }_{km}=p_k{\mathbf{s}}_k^{\ast }{\mathbf{A}}_{km}({\mathbf{A}}_{km}^{\ast }\times mathbf{R}_k{\mathbf{A}}_{km}{)}^{-1}{\mathbf{A}}_{km}^{\ast }{\mathbf{s}}_k$, referred to as the signal-to-interference ratio (SIR) of user $k$ under the multistage Wiener (MSW) receiver in a wireless communication system. It is proved that the output SIR under the MSW and the mutual information statistic under the matched filter (MF) are both asymptotic Gaussian when $N/K\to c>0$. Moreover, we provide a central limit theorem for linear spectral statistics of eigenvalues and eigenvectors of sample covariance matrices, which is a supplement of Theorem 2 in Bai, Miao and Pan [Ann. Probab. 35 (2007) 1532--1572]. And we also improve Theorem 1.1 in Bai and Silverstein [Ann. Probab. 32 (2004) 553--605].

arXiv commentPublished in at http://dx.doi.org/10.1214/07-AAP477 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• On asymptotics of eigenvectors of large sample covariance matrix
• On the signal-to-interference ratio of CDMA systems in wireless communications
• Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications

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