Design of filters for reliable and secure communications conditional mean estimation at the eavesdropper

This paper considers the problem of filter design with secrecy constraints, where two legitimate parties, Alice and Bob, communicate in the presence of an eavesdropper, Eve, over multiple-input multiple-output (MIMO) Gaussian channels. In particular, we consider the design of transmit and receive filters that minimize the mean-squared error (MSE) between the legitimate parties subject to a certain eavesdropper MSE level, in the situation where the eavesdropper MIMO channel is a degraded version of the main MIMO channel. We analyze the penalty in terms of MSE in the eavesdropper channel due to the assumption that optimal linear receive filters are used, while the eavesdropper employs nonlinear conditional mean estimation instead. This penalty is also shown to be negligible in regions of operational interest. We present a set of numerical results to illustrate the main conclusions.