Blind Channel Estimation for Amplify-and-Forward Two-Way Relay Networks Employing M-PSK Modulation

TL;DR

This paper introduces blind channel estimation algorithms for AF two-way relay networks using M-PSK modulation, reducing training overhead and improving spectral efficiency compared to traditional pilot-based methods.

Contribution

It proposes a deterministic maximum likelihood algorithm for M-PSK signals and an alternative for BPSK, enhancing channel estimation without extensive training.

Findings

DML estimator is consistent and effective at high SNR for M-PSK with order > 2.

BPSK requires a specialized algorithm for better performance.

DML outperforms LS in symbol-error rate, offering a better accuracy-spectral efficiency tradeoff.

Abstract

We consider the problem of channel estimation for amplify-and-forward (AF) two-way relay networks (TWRNs). Most works on this problem focus on pilot-based approaches which impose a significant training overhead that reduces the spectral efficiency of the system. To avoid such losses, this work proposes blind channel estimation algorithms for AF TWRNs that employ constant-modulus (CM) signaling. Our main algorithm is based on the deterministic maximum likelihood (DML) approach. Assuming M-PSK modulation, we show that the resulting estimator is consistent and approaches the true channel with high probability at high SNR for modulation orders higher than 2. For BPSK, however, the DML performs poorly and we propose an alternative algorithm that performs much better by taking into account the BPSK structure of the data symbols. For comparative purposes, we also investigate the Gaussian maximum-likelihood (GML) approach which treats the data symbols as Gaussian-distributed nuisance parameters. We derive the Cramer-Rao bound and use Monte-Carlo simulations to investigate the mean squared error (MSE) performance of the proposed algorithms. We also compare the symbol-error rate (SER) performance of the DML algorithm with that of the training-based least-squares (LS) algorithm and demonstrate that the DML offers a superior tradeoff between accuracy and spectral efficiency.