Abstract

The issues of privacy and security in wireless communication networks have taken on an increasingly important role as these networks continue to flourish worldwide. Traditionally, security is viewed as an independent feature with little or no relation to the remaining data communication tasks and, therefore, state-of-the-art cryptographic algorithms are insensitive to the physical nature of the wireless medium. This talk introduces yet another physical-layer security paradigm, based on an estimation-theoretic problem formulation rather than the information-theoretic one: We consider the problem of filter design with secrecy constraints in the classical wiretap scenario, where two legitimate parties communicate in the presence of an eavesdropper. In particular, we consider the design of transmit and receive filters that minimize the mean-squared error (MSE) between the legitimate parties whilst guaranteeing a certain eavesdropper MSE level subject to a total average power constraint, in the situation where the main channel and the wiretap channel consist of a bank of parallel independent degraded Gaussian channels (a scenario representative of orthogonal frequency division multiplexing (OFDM) communications systems). The traditional problem of filter design for point-to-point communications systems can be easily cast into the framework of convex optimization theory by using standard tools from majorization theory or matrix-monotone functions. In contrast, the problem of filter design with secrecy constraints is much more complex. We address this problem by putting forth a novel mathematical framework, revolving around the notions of D-sets, D-functions and D-optimization problems, that enables the transformation of the original optimization problem into a convex one. We derive the form of the optimal receive filter and the optimal transmit filter. We also derive the form of the optimal filters in the asymptotic regimes of low and high available power. We will complement theoretical insight with various numerical results. This represents joint work with João Xavier from the Technical University of Lisbon, Portugal.