ASYMPTOTIC DISTRIBUTIONS OF THE SIGNAL-TO-INTERFERENCE RATIOS OF LMMSE DETECTION IN MULTIUSER COMMUNICATIONS
Guangming Pan, Meihui Guo, Zhou Wang, National Sun Yat · 2007
(v1k,...,vNk) T, k = 1,...,K, where {vik,i,k = 1,...} are independent and identically distributed random variables with Ev11 = 0 and Ev 2 11 = 1. Let Sk = (s1,...,sk−1, sk+1,...,sK), Pk = diag(p1,..., pk−1,pk+1,...,pK) and βk = pks T k (SkPkS T k + σ 2 I) −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. 1. Introduction. Consider