Distributed Channel Assignment and Precoder Design for Multiantenna Dynamic Spectrum Access Systems

We consider a cognitive radio (CR) network in which nodes employ multi-input multi-output (MIMO) for spatial multiplexing (realized through precoding matrices). Our objective is to jointly allocate available channels to various CR links such that no channel is allocated to more than one link, and simultaneously optimize the precoding matrices (one per allocated channel) at each transmitter so as to ensure fairness or maximize network throughput. For the fairness objective, we formulate the problem based on Nash bargaining (NB). The proposed bargaining problem is combinatorial with mixed variables. Even if we relax its integer variables, the problem is still non-convex. To tackle it, we first convexify the relaxed version and provide a timesharing interpretation of the new problem. Using dual decomposition, we develop an optimal distributed algorithm for this timesharing problem, which sheds light on how to design a distributed algorithm for the original bargaining problem. Our distributed algorithm allows CR users to propose their requested rates, negotiate their channel assignment, and configure their precoding matrices. Following the same approach, we also consider the network throughput maximization problem (NET-MAX). Using convexification and dual decomposition, a distributed algorithm for this problem is developed. Simulations confirm the convergence of our distributed algorithms to the globally optimal solutions of both the NB-based and NET-MAX problems. It is shown that the NB-based algorithm achieves much better fairness with moderate throughput reduction, compared with the NET-MAX algorithm. Our algorithms are applicable not only to MIMO CR ad hoc networks, but also to cellular MIMO/SISO networks (on the uplink) and OFDMA-based systems. Index Terms Cooperative games, Nash bargaining, fairness, dual decomposition, distributed algorithm, throughput maximization, cognitive radio, OFDMA, MIMO, MAC protocol, power allocation, frequency assignment.

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