On the signal-to-interference ratio of CDMA systems in wireless communications

• 成果类型: Article
• 署名作者: Bai, Z. D.; Silverstein, Jack W.
• 署名单位: Northeast Normal University - China; North Carolina State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000637
• 发表日期: 2007
• 页码: 81-101
• 关键词: eigenvalues; matrices

摘要

Let {s(ij): i, j = 1,2....} consist of i.i.d. random variables in C with Es-11 = 0, E/s(11)/(2) = 1. For each positive integer N, let s(k) = s(k) (N) = (s(1k), s(2k),..., s(Nk))(T), 1 <= k <= K, with K = K(N) and K/N -> c > 0 as N -> infinity. Assume for fixed positive integer L, for each N and k <= K, alpha(k) = (alpha(k)(1),..., alpha k(L))(T) is random, independent of the s(ij), and the empirical distribution of (alpha(1),..., alpha(K)), with probability one converging weakly to a probability distribution H on C-L. Let beta(k) = beta(k)(N) = (alpha(k) (1)s(K)(T),..., alpha(k)(L)s(k)(T))(T) and set C = C(N) = (1/N) Sigma(K)(k=2) beta(k)beta(*)(k). Let sigma(2) > 0 be arbitrary. Then define SIR1 = (1/N)beta(*)(1)(C + sigma I-2)(-1) beta(1), which represents the best signal-to-interference ratio for user I with respect to the other K-I users in a direct-sequence code-division multiple-access system in wireless communications. In this paper it is proven that, with probability 1, SIR1 tends, as N -> infinity, to the limit E-l,l'=1(L) alpha(1) (l)alpha(1) (l')a(l,l'), where A = (a(l,l')) is nonrandom, Hermitian positive definite, and is the unique matrix of such type satisfying A = (cE (alpha alpha*)/(1+alpha* A alpha) + sigma(2) I-L)(-1), where alpha is an element of C-L has distribution H. The result generalizes those previously derived under more restricted assumptions.