Asymptotic Distributions of the Signal-to-interference Ratios of Lmmse Detection in Multiuser Communications

Let sk = 1 √ N (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)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.