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Title: Central limit theorem for signal-to-interference ratio of reduced rank linear receiver
Authors: Pan, G.M.
Zhou, W. 
Keywords: Central limit theorem
Empirical distribution
Random matrices
Random quadratic forms
Stieltjes transform
Issue Date: Jun-2008
Citation: Pan, G.M., Zhou, W. (2008-06). Central limit theorem for signal-to-interference ratio of reduced rank linear receiver. Annals of Applied Probability 18 (3) : 1232-1270. ScholarBank@NUS Repository.
Abstract: Let sk = 1/√N (v1k, . . . ,vNk) T, with {vik, i, k = 1, . . .} independent and identically distributed complex random variables. Write Sk = (s1, . . . , sk-1, sk+1, . . ,sK) Pk =diag(p1, . . . ,pk-1, pk+1, . . . ,p K), Rk = (SkPk Sk* + σ2I) and Akm = [sk, Rks k, . . . ,Rk m-1sk]. Define βkm = pksk*Akm (A km* × RkAkm)-11 A km*sk, 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 → 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]. © Institute of Mathematical. Statistics, 2008.
Source Title: Annals of Applied Probability
ISSN: 10505164
DOI: 10.1214/07-AAP477
Appears in Collections:Staff Publications

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