Optimization of the Receive Filter and Transmit Sequence for Active Sensing

This paper discusses the joint design of receive filters and transmit signals for active sensing applications such as radar and active sonar. The goal is to minimize the mean-square error (MSE) of target's scattering coefficient estimate in the presence of clutter and interference, which is equivalent to maximizing the signal-to-clutter-plus-interference ratio. A discrete-time signal model is assumed and practical constant-modulus or low peak-to-average-power ratio (PAR) constraints are imposed on the transmit signal. Several optimization methods are proposed for this joint design. Furthermore, the MSE criterion is expressed in the frequency domain and a corresponding MSE lower bound is derived. Numerical examples for different types of interferences are included to demonstrate the effectiveness of the proposed designs.