Numerical Optimization Techniques for Secure Communications Over MIMO Channels

Abstract

As multimedia applications become more popular, wireless communication systems are expected to reliably provide increased data rates. Multiple Input Multiple Output (MIMO) technologies can meet this demand without using additional bandwidth or transmit power. MIMO is part of modern wireless communication standards. Another critical aspect of communications is to secure the confidentiality of data transmission. Cryptography accomplishes this at the upper layers of the protocol stack. At the physical layer, data travels unencrypted and can be secured by using the channel characteristics to ``hide'' data transmission from potential eavesdroppers. We consider a Gaussian MIMO wiretap channel and are looking for the maximal rate at which data can be transmitted both reliably and securely to the intended receiver: the secrecy capacity. This quantity is difficult to find analytically and is known precisely in only a few cases. This thesis proposes several numerical optimization methods, both stochastic and deterministic, to evaluate the secrecy capacity and to find the optimal transmit covariance matrix. The stochastic approaches are based on Monte-Carlo and on Differential Evolution (a genetic algorithm). The deterministic approaches are based on successive linear approximation. The accuracy of the results obtained with these methods is, in general, better than the one offered by popular numerical optimization tools such as CVX or YALMIP.