Optimal power allocation and optimal linear encoding for parameter estimation in the presence of a smart eavesdropper

In this article, we consider secure transmission of a deterministic vector parameter from a transmitter to an intended receiver in the presence of a smart eavesdropper. The aim is to determine the optimal power allocation and optimal linear encoding strategies at the transmitter to maximize the estimation performance at the intended receiver under constraints on the estimation performance at the eavesdropper and on the transmit power. First, the A-optimality criterion is adopted by utilizing the Cramér-Rao lower bound as the estimation performance metric, and the optimal power allocation and optimal linear encoding strategies are characterized theoretically. Then, corresponding to the D-optimality criterion, the determinant of the Fisher information matrix is considered as the estimation performance metric. It is shown that the optimal linear encoding and optimal power allocation strategies lead to the same solution for this criterion. In addition, extensions of the theoretical results are provided to cases with statistical knowledge of systems parameters. Numerical examples are provided to investigate the optimal power allocation and optimal linear encoding strategies in different scenarios.