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

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dc.creatorPan, Guang-Ming
dc.creatorGuo, Mei-Hui
dc.creatorZhou, Wang
dc.date2007-03-01
dc.date.accessioned2026-07-07T07:49:34Z
dc.date.available2026-07-07T07:49:34Z
dc.descriptionLet ${\mathbf{s}}_k=\frac{1}{\sqrt{N}}(v_{1k},...,v_{Nk})^T,$ $k=1,...,K$, 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.
dc.descriptionPublished 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)
dc.identifierhttps://arxiv.org/abs/math/0703014
dc.identifierhttp://arxiv.org/abs/math/0703014
dc.identifierAnnals of Applied Probability 2007, Vol. 17, No. 1, 181-206
dc.identifierdoi:10.1214/105051606000000718
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124897
dc.subjectProbability
dc.subject15A52, 62P30 (Primary) 60F05, 62E20 (Secondary)
dc.titleAsymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications
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