Minimum MSE Relaying for Arbitrary Signal Constellations in Coded Relay Networks

In this paper a soft relaying scheme for coded relay networks combining the benefits of classical Decode-Forward (DF) and Amplify-Forward (AF) is extended to higher order modulation schemes. In order to minimize the mean-squared- error at the destination, the conditional expectation value of the symbol after soft-output channel decoding at the relay is transmitted. The main idea of this scheme called Decode- Estimate-Forward (DEF) is to exploit coding gain like DF while still preserving reliability information as AF. This approach was presented by the authors for BPSK in coded systems, but the extension to arbitrary modulation alphabets presented here allows for more flexible system designs. The performance of the proposed relay function is compared to classical AF and DF in a wide variety of scenarios like AWGN and Rayleigh fading channels as well as different numbers and constellations of relays.