Minimax Robust Discrete-Time Matched Filters

The problem of designing finite-length discrete-time matched filters is considered for situations in which exact knowledge of the input signal and/or noise characteristics is not available. Such situations arise in many applications due to channel distortion, incoherencies, nonlinear effects, and other modeling uncertainties. In such cases it is often of interest to design a minimax robust matched filter, i.e., a nonadaptive filter with an optimum level of worst-case performance for the expected uncertainty class. This problem is investigated here for three types of uncertainty models for the input signal, namely, the mean-absolute, mean-square, and maximum-absolute distortion classes, and for a wide generality of norm-deviation models for the noise covariance matrix. Some numerical examples illustrate the robustness properties of the proposed designs.