Optimum radar signal processing in clutter

This paper considers the joint optimization of a class of radar signals and filters in a number of clutter-pins-noise environments. The radar signal processor in this case will be optimum in the sense that its output at the time of target detection yields the maximum ratio of peak signal power to total interference power. If the interference at the input to this signal processor is a Gaussian random process, this processor also yields the maximum probability of detection for a given value of false-alarm probability. The signals used are pulse trains and the filters are tapped delay lines. The purpose of signal design is to determine the optimum complex weighting for each pulse of the pulse train. Filter design yields the optimum complex weighting for the output taps of the delay line. Filter design for a specified signal is considered first. This is followed by combined signal and filter design and matched filter design. Constrained signal and filter design is investigated last. It should be emphasized that the optimizations require a knowledge of the clutter time-frequency distribution. For practical situations, when the clutter distribution is unknown, an adaptive filter is proposed that automatically provides the optimum filter weights for a given transmitted signal. When the clutter has a range-time extent less than the equivalent range-time extent of the signal, filter design alone yields nearly optimum performance. As the clutter becomes extended in range-time, it is necessary to consider jointly the design of signal and filter to obtain an optimum radar signal processor. In this report it is suggested that the signal be designed under the assumption of the clutter being extended over a broad range of Dopplers and that the signal processor consist of a bank of adaptive filters. Then each filter output yields the maximum ratio of peak signal to total interference power for this signal design.