The Annals of Applied Probability

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

Guang-Ming Pan, Mei-Hui Guo, and Wang Zhou

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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.

Article information

Source
Ann. Appl. Probab., Volume 17, Number 1 (2007), 181-206.

Dates
First available in Project Euclid: 13 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1171377181

Digital Object Identifier
doi:10.1214/105051606000000718

Mathematical Reviews number (MathSciNet)
MR2292584

Zentralblatt MATH identifier
1221.15055

Subjects
Primary: 15A52 62P30: Applications in engineering and industry
Secondary: 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory

Keywords
Random quadratic forms SIR random matrices empirical distribution Stieltjes transform central limit theorems

Citation

Pan, Guang-Ming; Guo, Mei-Hui; Zhou, Wang. Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications. Ann. Appl. Probab. 17 (2007), no. 1, 181--206. doi:10.1214/105051606000000718. https://projecteuclid.org/euclid.aoap/1171377181


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