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

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.

Error performance analysis of decode‐and‐forward and amplify‐and‐forward multi‐way relay networks with binary phase shift keying modulation

“…Compared with other TWRN protocols, such as digital network coding in which the relay performs XOR operations on bit streams from the two users [1,5], it has been shown that PNC requires smaller number of time slots for full information exchange [4]. The performance of TWRNs with PNC has been thoroughly analysed from the perspective of capacity [6,7], bit error rate (BER) [1,4,[8][9][10][11][12][13] and practical issues such as channel estimation and synchronisation [14][15][16][17].…”

Semi Blind Channel Estimation with Training-Based Pilot in AF Two-Way Relaying Networks

“…Unidirectional or one-way relaying supports in communication from a source to a destination user and has been studied in the literature [1]. On the other hand, in two-way relaying networks (TWRNs), the flow of information is bidirectional and the two users exchange data simultaneously with the relation of an intermediate relay node [2]. The comparison with one-way half-duplex relaying, bidirectional relaying is a spectrally more efficient relaying protocol [2].…”

“…On the other hand, in two-way relaying networks (TWRNs), the flow of information is bidirectional and the two users exchange data simultaneously with the relation of an intermediate relay node [2]. The comparison with one-way half-duplex relaying, bidirectional relaying is a spectrally more efficient relaying protocol [2]. Both amplify-and-forward and decode-and-forward protocols have been designedfor TWRNs.…”

Lower bounds on the estimation performance in low complexity quantize-and-forward cooperative systems

“…The CRB for the estimation of the channel parameters in a one-way AF cooperative system using flat-fading channels has been obtained in [18], while in [19], the CRB is obtained for an AF and DF system in which multiple frequency offsets are considered. Lower bounds for the two-way relaying channel, in which two terminals aided by a relay communicate with one another, have been obtained in [20][21][22][23] for the AF protocol.…”