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

• 成果类型: Article
• 署名作者: Pan, Guang-Ming; Guo, Mei-Hui; Zhou, Wang
• 署名单位: National Sun Yat Sen University; National University of Singapore
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000718
• 发表日期: 2007
• 页码: 181-206
• 关键词: limiting spectral distribution; eigenvalues

摘要

Let s(k) = 1/root N (nu(1k),...,nu(Nk))(T), k = 1,...,K, where {nu(ik), i, k = 1,...} are independent and identically distributed random variables with E nu(11) = 0 and E nu(2)(11) = 1. Let S-k = (s(1),...,s(k-1), s(k+l),...,s(K)), P-k = diag(p(1),...,p(k-1), p(k+1),...,p(K)) and beta(k) = p(k)s(k)(T) (SkPkSkT + sigma I-2)(-1)s(k) where pk >= 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.