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Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications
Let ,
where are independent and identically distributed
random variables with and . Let
, and
\beta_k=p_k{\mathbf{s}}_k^T({\mathb
f{S}}_k{\mathbf{P}}_k{\mathbf{S}}_k^T+\sigma^2{\mathbf{I}})^{-1}{\math
bf{s}}_k, where and the is referred to as the
signal-to-interference ratio (SIR) of user 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 and 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.Comment: Published at http://dx.doi.org/10.1214/105051606000000718 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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