Widely Linear vs. Conventional Subspace-Based Estimation of SIMO Flat-Fading Channels: Mean-Squared Error Analysis

TL;DR

This paper compares the mean-squared error performance of widely linear and conventional subspace-based channel estimators for SIMO flat-fading channels with BPSK modulation, analyzing how ambiguity resolution impacts their relative effectiveness.

Contribution

It provides closed-form MSE expressions for both estimators under four ambiguity resolution scenarios, highlighting the impact of ambiguity information accuracy on estimator performance.

Findings

WL estimator outperforms conventional in low ambiguity information scenarios

Performance gap increases as ambiguity resolution becomes less accurate

Closed-form MSE expressions for different ambiguity scenarios are derived

Abstract

We analyze the mean-squared error (MSE) performance of widely linear (WL) and conventional subspace-based channel estimation for single-input multiple-output (SIMO) flat-fading channels employing binary phase-shift-keying (BPSK) modulation when the covariance matrix is estimated using a finite number of samples. The conventional estimator suffers from a phase ambiguity that reduces to a sign ambiguity for the WL estimator. We derive closed-form expressions for the MSE of the two estimators under four different ambiguity resolution scenarios. The first scenario is optimal resolution, which minimizes the Euclidean distance between the channel estimate and the actual channel. The second scenario assumes that a randomly chosen coefficient of the actual channel is known and the third assumes that the one with the largest magnitude is known. The fourth scenario is the more realistic case where pilot symbols are used to resolve the ambiguities. Our work demonstrates that there is a strong relationship between the accuracy of ambiguity resolution and the relative performance of WL and conventional subspace-based estimators, and shows that the less information available about the actual channel for ambiguity resolution, or the lower the accuracy of this information, the higher the performance gap in favor of the WL estimator.