Precoder Design for Amplify and Forward Relaying With Complex Field Network Coding

In this correspondence, multiuser relay systems with amplify and forward relaying protocol are considered. To make transmission delays as short as possible, the concept of complex field network coding is applied. The relays transmit for all users simultaneously instead of using conventional relaying transmissions over orthogonal channels such as time-division multiplexing for each user. Three transmission schemes with two or three time-slot delays and symbol rates 1/2, 2/3, and 1 are examined. Based on the derived pairwise error probability expressions, optimal precoders achieving the maximum diversity and best coding gains are designed without changing the original ergodic capacity regions. Simulation results are provided to verify the proposed designs.