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

Abstract

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 11 2 = 1. Let Sk = (S1,...,s k-1, sk+1,...,sK), Pk = diag(p 1,..., pk-1, pk+1,...,pK) and βk = pksk T(SkP kSk T + σ2I)-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. © Institute of Mathematical Statistics, 2007.