Nonquadratic regularization for waveform optimization

An adaptive algorithm for eigen-based waveform optimization is presented. The algorithm is capable of improving the matched filter signal-to-interference-plus-noise ratio (SINR) of a radar operating in a colored interference environment while simultaneously constraining the shape of the matched filter response. To arrive at the algorithm cost function, the asymptotic behavior of the interference covariance matrix is examined, and a p-norm regularization term is considered. The resulting cost function consists of one term to improve SINR, and another term to constrain the shape of the matched filter response. This provides the waveform designer with a means of trading between SINR performance and matched filter response for a given application. The simulated performance of various steepest descent algorithms applied to waveforms in a colored interference environment is presented. These results show that a low-complexity stochastic gradient algorithm (in the spirit of LMS) is capable of improving radar performance in band-limited interference.