Soft Parallel Wireless Relay via Z-Forward

This paper considers soft-message forwarding in a 2-hop wireless network. Previous methods have only considered the source-relay channel quality but ignored the relay-destination channel quality, causing potential sub-optimality especially in a parallel-relay setting. This paper takes a centralized approach by accounting for all the individual channel-segments, and proposes a “Z-forward” strategy, in which the i-th relay represents the forward messages in a parameterized piece-wise linear form: θ_i-truncated log-likelihood ratio (LLR) of its reception. This message representation not only is numerically stable, and soft-information-preserving, but also allows us to analytically derive the end-to-end bit error rate (with maximal ratio combining (MRC)), and to compute the optimal values of θ_i numerically. The results confirm that previous message-forward proposals, however a good performance in a single-relay setting, will considerably degrade as the the number of relays increases. Next, to further simplify the design, we propose a single threshold θ for all the relays, in lieu of one for each, and show that it strikes a balance between performance and computation. Additionally, with Z-forward, we are able to derive the exact probability density function (pdf) of the final reception at the destination, and subsequently to develop the maximum likelihood (ML) estimator. Extensive simulations are presented to verify the efficiency of the new schemes.