Optimal Precoder Designs for Sum-Utility Maximization in SWIPT-Enabled Multi-User MIMO Cognitive Radio Networks

In this paper, we study a generalized framework that combines the three major techniques for 5G communication systems such as the multi-user multi-input multi-output (MuMIMO) techniques for spectral efficiency enhancement, the cognitive radio (CR) techniques for spectrum sharing, and the simultaneous wireless information and power transfer (SWIPT) techniques for convenient power supplies, which is called a MuMIMO-CR-SWIPT network. In this system, we have one base-station that simultaneously supports multiple information decoding (ID) and energy harvesting users under a condition that interference power to the primary ID (P-ID) receivers stays below a certain threshold. With this scenario, our goal is to design an optimal precoder that maximizes the sum-utility cost function for the ID users while satisfying the transmit power constraint at the BS, the energy requirement at each EH user, and the interference power constraint at each P-ID user. As we consider a general sum-utility cost function that puts together different target utilities in a general MuMIMO-CR-SWIPT environment, the previous works for each of the MuMIMO, CR, and SWIPT systems are casted as particular solutions of our framework. The problem has been considered to be challenging, since the weighted minimum mean-squared error problem transformation no longer resolves the non-convexity of the original problem. In this paper, we settle such an issue by demonstrating that the WMMSE transformation guarantees zero-duality gap between the primal and dual problems. Based on the observation, we attain the optimal precoder by solving the dual problem through the sub-gradient ellipsoid method. We also propose a simplified algorithm for the case of a single ID user, which is shown to achieve the globally optimum. Finally, we demonstrate the optimality and efficiency of the proposed algorithms through numerical simulation results.