| Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications (2007) | |||||||||||||
Abstract | |||||||||||||
| Let $\mathbf{s}_{k}=\frac{1}{\sqrt{N}}(v_{1k},\ldots,v_{Nk})^{T}$ , 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 βk=pkskT(SkPkSkT+σ2I)−1sk, 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. | |||||||||||||
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