SINR Constrained Beamforming for a MIMO Multi-User Downlink System: Algorithms and Convergence Analysis

Consider a multiple-input multiple-output (MIMO) downlink multi-user channel. A well-studied problem in such a system is the design of linear beamformers for power minimization with the quality of service (QoS) constraints. The most representative algorithms for solving this class of problems are the so-called minimum mean square error (MMSE)-second-order cone programming (SOCP) algorithm [Visotksy and Madhow, “Optimum Beamforming Using Transmit Antenna Arrays,” Proc. IEEE Veh. Technol. Conf., May 1999, vol. 1, pp. 851-856] , [Wong, Zheng, and Ng, “Convergence Analysis of Downlink MIMO Antenna System Using Second-Order Cone Programming,” Proc. 62nd IEEE Veh. Technol. Conf., Sep. 2005, pp. 492-496] and the uplink-downlink duality (UDD) algorithm [Codreanu, Tolli, Juntti, and Latva-Aho, “Joint Design of Tx-Rx Beamformers in MIMO Downlink Channel,” IEEE Trans. Signal Process., vol. 55, no. 9, pp. 4639-4655, Sep. 2007]. The former is based on alternating optimization of the transmit and receive beamformers; while the latter is based on the well-known uplink-dowlink duality theory. Despite their wide applicability, the convergence to Karush-Kuhn-Tucker (KKT) solutions of both algorithms is still open in the literature. In this paper, we rigorously establish the convergence of these algorithms for QoS-constrained power minimization (QCPM) problem with both single stream and multiple streams per user cases. Key to our analysis is the development and analysis of a new MMSE-DUAL algorithm, which connects the MMSE-SOCP and the UDD algorithm. Our numerical experiments show that 1) all these algorithms can almost always reach points with the same objective value irrespective of initialization and 2) the MMSE-SOCP/MMSE-DUAL algorithm works well while the UDD algorithm may fail with an infeasible initialization

Optimization of secure wireless communications for IoT networks in the presence of eavesdroppers

The problem motivates this paper is that securing the critical data of 5G based wireless IoT network is of significant importance. Wireless 5G IoT systems consist of a large number of devices (low-cost legitimate users), which are of low complexity and under strict energy constraints. Physical layer security (PLS) schemes, along with energy harvesting, have emerged as a potential candidate that provides an effective solution to address this issue. During the data collection process of IoT, PHY security techniques can exploit the characteristics of the wireless channel to ensure secure communication. This paper focuses on optimizing the secrecy rate for simultaneous wireless information and power transfer (SWIPT) IoT system, considering that the malicious eavesdroppers can intercept the data. In particular, the main aim is to optimize the secrecy rate of the system under signal to interference noise ratio (SINR), energy harvesting (EH), and total transmits power constraints. We model our design as an optimization problem that advocates the use of additional noise to ensure secure communication and guarantees efficient wireless energy transfer. The primary problem is non-convex due to complex objective functions in terms of transmit beamforming matrix and power splitting ratios. We have considered both the perfect channel state information (CSI) and the imperfect CSI scenarios. To circumvent the non-convexity of the primary problem in perfect CSI case, we proposed a solution based on the concave-convex procedure (CCCP) iterative algorithm, which results in a maximum local solution for the secrecy rate. In the imperfect CSI scenario, we facilitate the use of S-procedure and present a solution based on the iterative successive convex approximation (SCA) approach. Simulation results present the validations of the proposed algorithms. The results provide an insightful view that the proposed iterative method based on the CCCP algorithm achieves higher secrecy rates and lower computational complexity in comparison to the other algorithms

SINR Constrained Beamforming for a MIMO Multi-User Downlink System: Algorithms and Convergence Analysis

Consider a multiple-input multiple-output (MIMO) downlink multi-user channel. A well-studied problem in such a system is the design of linear beamformers for power minimization with the quality of service (QoS) constraints. The most representative algorithms for solving this class of problems are the so-called minimum mean square error (MMSE)-second-order cone programming (SOCP) algorithm [Visotksy and Madhow, “Optimum Beamforming Using Transmit Antenna Arrays,” Proc. IEEE Veh. Technol. Conf., May 1999, vol. 1, pp. 851-856] , [Wong, Zheng, and Ng, “Convergence Analysis of Downlink MIMO Antenna System Using Second-Order Cone Programming,” Proc. 62nd IEEE Veh. Technol. Conf., Sep. 2005, pp. 492-496] and the uplink-downlink duality (UDD) algorithm [Codreanu, Tolli, Juntti, and Latva-Aho, “Joint Design of Tx-Rx Beamformers in MIMO Downlink Channel,” IEEE Trans. Signal Process., vol. 55, no. 9, pp. 4639-4655, Sep. 2007]. The former is based on alternating optimization of the transmit and receive beamformers; while the latter is based on the well-known uplink-dowlink duality theory. Despite their wide applicability, the convergence to Karush-Kuhn-Tucker (KKT) solutions of both algorithms is still open in the literature. In this paper, we rigorously establish the convergence of these algorithms for QoS-constrained power minimization (QCPM) problem with both single stream and multiple streams per user cases. Key to our analysis is the development and analysis of a new MMSE-DUAL algorithm, which connects the MMSE-SOCP and the UDD algorithm. Our numerical experiments show that 1) all these algorithms can almost always reach points with the same objective value irrespective of initialization and 2) the MMSE-SOCP/MMSE-DUAL algorithm works well while the UDD algorithm may fail with an infeasible initialization.This is a manuscript of an article from IEEE Transactions on Signal Processing 64 (2016): 2920, DOI: 10.1109/TSP.2016.2529590. Posted with permission.</p