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 Ev112=1. Let Sk=(s1,..,.sk.1,.sk+1,..,.sK), Pk=diag.(p1,..,.pk.1,.pk+1,..,.pK) and .k=pkskT(SkPkSkT+.2I).1sk, where pk.0 and the .k 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.