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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.