Optimization Methods for Secure and Energy Efficient MIMO System

In this modern era, wireless networks continue to expand worldwide and play a pronounced role in daily life. However, wireless communication has become vulnerable to intelligent invaders in the network. Hence, the security aspects of wireless communication have been the center of modern-era research. Physical Layer Security (PLS) schemes have been proven to be very effective against potential eavesdroppers thanks to their low-complexity nature compared to encryption techniques. Therefore, this thesis is dedicated to the physical layer security of multiple-input multiple-output (MIMO) systems. More specifically, we provide efficient optimization techniques to maximize the achievable secrecy rate of MIMO Wiretap channels (WTC). First, we present novel numerical approaches to finding the achievable secrecy rate of the MIMO WTC subject to multiple power constraints. There is a challenge in deriving computationally efficient solutions to the secrecy rate maximization problem because the secrecy rate is expressed as a difference of convex functions (DC) of the transmit covariance matrix. However, to deal with it, we provided local optimization methods, such as the accelerated DC algorithm (ADCA) and a numerical method named partial best response algorithm (PBRA) based on the concave-convex equivalent reformulation of the secrecy capacity problem. Along with it, we provide a convex reformulation for degraded channels. Interestingly, our experiments have shown that the local optimization methods achieve global optimality for the secrecy rate maximization problem under power constraints. In this regard, we provide analytical proof with Karush-Kuhn-Tucker (KKT) conditions to validate our observation. Motivated by our finding, we propose an accelerated gradient projection algorithm with adaptive momentum parameters (AGPnc) that directly solves the secrecy rate maximization problem rather than the equivalent convex-concave form. We then extend the scope of our research of physical layer security enhancement by considering the Intelligent reflecting surface (IRS)-aided MIMO WTC system, as the IRS has achieved enormous attention recently for enhancement in spectral efficiency. In this context, we provided a numerical solution for the problem of maximizing the achievable secrecy rate of the considered system by jointly optimizing the input covariance matrix and the IRS phase shifts. The proposed is an iterative method based on block successive maximization (BSM) where each iteration is done in closed form. We then extend our research further toward maximizing the secrecy energy efficiency (SEE) of the (IRS)-aided MIMO WTC system. In relation to the SEE maximization problem, we provide a low-complexity based local optimization method. The challenge of this considered problem is the coupling between design variables in both the objective and the constraint. The main idea of the proposed method is to apply a penalty dual decomposition based alternating gradient projection (PDDAPG) method to obtain an efficient solution. Thanks to the low complexity nature of proposed methods, these methods can scale favourably with large-scale wireless systems, which has been an inherent issue of the existing studies. In this way, the contributions of this thesis will significantly impact future research in the field of physical layer security, especially toward the future generation of wireless communication.