A parametric approach to optimal soft signal relaying in wireless parallel-relay systems

This paper proposes an optimal estimate-forward strategy, termed Z-forwarding, for 2-hop parallel-relay systems. The previous tanh-forwarding strategy, which is optimized for the single-relay system is shown to be no longer optimal for a parallel-relay system. Instead, a new, parametrically-optimized Z-forwarding strategy is proposed, where the relay re-transmits a nonlinear but piece-wise linear function of the log-likelihood ratio (LLR) of the source signal. By analytically formulating the end-to-end bit error rate (BER), optimal thresholds that minimize the BER are computed as a function of all the source-relay and relay-destination channels. Maximum likelihood (ML) detector is also developed for the destination to recoup all the diversity gains from the multiple relays. It is shown that Z-forwarding strategy delivers a performance comparable to tanh-forwarding in a single relay system, but considerably better than tanh-forwarding (as well as amplify-forward and decode-forward) in a parallel-relay system.