Central limit theorem for signal-to-interference ratio of reduced rank linear receiver

作者：Pan G M^*; Zhou W

来源：Annals of Applied Probability, 2008, 18(3): 1232-1270.

DOI：10.1214/07-AAP477

• random quadratic forms
• SIR
• random matrices
• empirical distribution
• Stieltjes transform
• central limit theorem

Let s(k) = 1/root N(nu(1k),...,nu(Nk))(T), with {nu(ik),i,k = 1,...} independent and, identically distributed complex random variables. Write S-k = (s(1),..., s(k-1), s(k+1),...,s(K)), P-k = diag(p(1),...,p(k-1), p(k+l), p(K)), R-k = (SkPkSk* + sigma I-2) and A(km) = [s(k), R(k)s(k),..., R(k)(m-1)s(k)]. Define beta(km) = p(k)s(k)*A(km)(A(km)* x R(k)Ak(m))(-1)A(km)*s(k), referred to as the signal-to-interference ratio (SIR) of user k 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].

• 出版日期2008-6