Precoder Design for Multi-Hop Cognitive MIMO Relay Systems With Finite-Alphabet Inputs

This paper investigates the precoder design in a multi-hop multiple-input multiple-output (MIMO) relay system with cognitive radio. We assume that the source node (secondary user) sends data to the destination node (secondary user) by means of multiple relay nodes (secondary users), and that the source and relays simultaneously share the same frequency band with primary users. Unlike previous research, this paper assumes the inputs to be practical finite-alphabet signals, such as phase shift keying (PSK). Our objective is to maximize the mutual information of the overall system by optimizing the precoders at the source and relays under the constraints of the transmit power at each node and the interference power to the primary users. The precoder designs in two channel state information (CSI) cases, where the nodes know the perfect or statistical CSI, are both investigated. The formulated optimization problems are nondeterministic polynomial-time (NP)-hard and nonconvex, so the global optimal solution cannot be found within the polynomial time. However, by exploiting the structures of the optimization problems, we develop a new framework, which combines the iterative rank penalty (IRP) algorithm with the customized Uzawa algorithm, to solve them. Simulation results are provided to verify the efficacy of the proposed precoding algorithms.