Detectors for Estimate-and-Forward Wireless Relay Networks

Relay radios are used to improve the quality of point-to-point wireless links with respect to achievable rates and symbol error rates (SER). Under these metrics, the estimate-and-forward (EF) protocol has the best performance in a wide variety of cases. The EF protocol is defined as the relaying protocol in which the relay forwards an estimate of its received information. Although optimal estimates have been identified in the literature, an implementable detector at the receiver still remains to be found. In this paper, we solve this open problem by using a piecewise linear approximation of the minimum mean square error (MMSE) estimate (pLAM) of the received symbol at the relay. In the three-node cooperative wireless relay network, this new piecewise linear approximation leads to an analytical form of the detector at the destination. Furthermore, we show that the symbol error rates of this new framework closely approximate the true performance of EF when using a MMSE estimate of the received symbol at the relay. Finally, we provide several examples where we apply this new pLAM approach to multiple modulation schemes such as BPSK and 16-QAM, in both one- and two-way relay networks.