Linear Precoding for Relay Networks with Finite-Alphabet Constraints

In this paper, we investigate the optimal precoding scheme for relay networks with finite-alphabet constraints. We show that the previous work utilizing various design criteria to maximize either the diversity or the transmission rate with the Gaussian inputs assumption may lead to significant loss for a practical system with finite constellation set constraint. A linear precoding scheme is proposed to maximize the transmission rate, i.e., the mutual information, for relay networks. We exploit the structure of the optimal precoding matrix, and develop a unified two-step iterative algorithm utilizing the theory of convex optimization and optimization on the complex Stiefel manifold. Numerical examples show that this novel iterative algorithm achieves significant gains compared to its conventional counterpart.