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Let ${\mathbf{s}}_k=\frac{1}{\sqrt{N}}(v_{1k},...,v_{Nk})^T,$ $k=1,...,K$,where $\{v_{ik},i,k$ $=1,...\}$ are independent and identically distributedrandom variables with $Ev_{11}=0$ and $Ev_{11}^2=1$. Let${\mathbf{S}}_k=({\mathbf{s}}_1,...,{\mathbf{s}}_{k-1},$${\mathbf{s}}_{k+1},...,{\mathbf{s}}_K)$, ${\mathbf{P}}_k=\operatorname{diag}(p_1,...,$ $p_{k-1},p_{k+1},...,p_K)$ and$\beta_k=p_k{\mathbf{s}}_k^T({\mathbf{S}}_k{\mathbf{P}}_k{\mathbf{S}}_k^T+\sigma^2{\mathbf{I}})^{-1}{\mathbf{s}}_k$, where $p_k\geq 0$ and the $\beta_k$ is referred to as thesignal-to-interference ratio (SIR) of user $k$ with linear minimum mean-squareerror (LMMSE) detection in wireless communications. The joint distribution ofthe SIRs for a finite number of users and the empirical distribution of allusers' SIRs are both investigated in this paper when $K$ and $N$ tend toinfinity with the limit of their ratio being positive constant. Moreover, thesum of the SIRs of all users, after subtracting a proper value, is shown tohave a Gaussian limit.

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