Optimal and simple near optimal non‐coherent detection in amplify‐and‐forward two‐way relaying over fast fading channels

Abstract

Two-way relaying tends to become a celebrated technique in communication networks because of its unique characteristic in establishing a two-step bilateral information exchange mechanism between users' pairs, as well as, arranging a virtual spatial diversity scenario. In this paper, two-way relaying under amplify-and-forward strategy, and fast Rayleigh fading environment is considered. We investigate two distinct cases in which the relay retransmits users' superposed signals, either directly or after complex conjugation in two- or three-phase modalities. We derive the optimal detection rule which is inherently computational complex. Two closed-form suboptimal structures are proposed to circumvent this formidable problem. In the first form, we incorporate the destination noise into the relay counterpart, and assume Gaussian conditional distribution for the received signal in the latter. The first detector is designed using less stringent approximation and consequently has a better performance, whereas the second one benefits from a very low computational complexity and simple implementation and is more suitable for applications with strict computational and energy constraints such as sensor networks. Furthermore, we consider the imperfect self-channel information case and extend the corresponding results. Bit error rate analyses and accompanying computer simulations show an improvement of about 5 dB over existing methods.