A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large Dimensional Signals

TL;DR

This paper analyzes the asymptotic distribution of the SINR at the output of the LMMSE estimator for large-dimensional signals, showing it converges to a Gaussian distribution with variance decreasing as signal dimension grows.

Contribution

It establishes a central limit theorem for the SINR in large-dimensional settings, extending the understanding of estimator performance in high-dimensional regimes.

Findings

SINR fluctuations converge to Gaussian distribution

Variance of fluctuations decreases inversely with signal dimension

Applicable to multi-antenna and spread spectrum models

Abstract

This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multi-antenna as well as spread spectrum transmission models. The expression of the deterministic approximation of the SINR in the large dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.