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Title: Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications
Authors: Pan, G.-M.
Guo, M.-H.
Zhou, W. 
Keywords: Central limit theorems
Empirical distribution
Random matrices
Random quadratic forms
Stieltjes transform
Issue Date: Feb-2007
Source: Pan, G.-M., Guo, M.-H., Zhou, W. (2007-02). Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications. Annals of Applied Probability 17 (1) : 181-206. ScholarBank@NUS Repository.
Abstract: Let sk = 1/√N (v1k,...,vNk) T, k = 1,..., K, where [vik, i, k = 1,...} are independent and identically distributed random variables with Ev11 =0 and Ev 11 2 = 1. Let Sk = (S1,...,s k-1, sk+1,...,sK), Pk = diag(p 1,..., pk-1, pk+1,...,pK) and βk = pksk T(SkP kSk T + σ2I)-1 sk, where pk ≥ 0 and the βk 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. © Institute of Mathematical Statistics, 2007.
Source Title: Annals of Applied Probability
ISSN: 10505164
DOI: 10.1214/105051606000000718
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