Unified Large System Analysis of MMSE and Adaptive Least Squares Receivers for a class of Random Matrix Channels

TL;DR

This paper provides a comprehensive large system analysis of MMSE and adaptive least squares receivers for random matrix channels, unifying their analysis and deriving key SINR expressions under various conditions.

Contribution

It introduces a unified analytical framework for both MMSE and ALS receivers, accommodating different precoding, training, and channel distributions, with explicit SINR formulas.

Findings

Derived asymptotic SINR expressions for MMSE and ALS receivers.

Established a fundamental relationship between ALS and MMSE SINR responses.

Demonstrated applications including throughput optimization with training sequence length.

Abstract

We present a unified large system analysis of linear receivers for a class of random matrix channels. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. We derive expressions for the asymptotic signal-to-interference-plus-noise (SINR) of the MMSE receiver, and both the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.