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

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-plusnoise (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.

The development and application of random matrix theory in adaptive signal processing in the sample deficient regime

“…Note however that σ 2 MMSE does depend on the noise and channel characteristics as well as the lengths of the equalizer's feedforward and feedback filters. A similar relationship between the SINR's at the outputs of the linear equalizer and its corresponding MMSE equalizer is obtained in [38].…”

“…The analysis of training mode operation allows the analysis of the impact of channel time-variability and thus limited observations intervals to be handled in a clearer manner and provides useful insights into performance trade-offs. Other contributions to the performance analysis of equalizers also assume operation in the training mode [39], [38].…”

“…The transient behavior of the signal to interference plus noise ratio (SINR) at the output of the RLS estimator in a time-invariant channel is studied in [38]. The analysis therein is fairly general and the performance metric is given as a solution to a set of non-linear equations.…”

“…As such, [62] studies the signal-to-noise-puls-interference ratio (SINR) at the output of the LS-based linear equalizer for a time invariant frequency flat fading channel. A more general analysis in [38] characterizes the SINR at the output of the LS-based linear equalizer for time invariant frequency selective channels. Both works exploit random matrix theory results which, as elaborated in Section 2.7, while theoretically valid in the limit, are fairly accurate in modeling equalizer performance in practical finite observation time scenarios.…”

“…A signal prediction error is adopted as the performance metric and characterization of its mean square value is derived. In comparison to [38], in addition to handling the case of DFE equalization and evaluating the signal prediction MSE, the analysis technique is different and yields a greatly simplified closed-form result, which is exact when the received signal is Gaussian distributed. The derived expression is validated via Monte-Carlo simulations.…”