Ambiguity functions, processing gains, and Cramer-Rao bounds for matched illumination radar signals

Ambiguity functions (AFs) are obtained for a radar using matched illumination (MI) transmit signals for the detection of range-spread targets in the presence of clutter. The transmit signals are adapted to target and interference spectra and are filtered optimally in the receiver; they are designed to maximize signal-to-interference-and-noise ratio (SINR) power ratios at receiver output. In this paper, expressions for processing gains, spread AFs, and Cramer-Rao bounds on range and Doppler estimates are derived based on likelihood functions. Here, for extended targets, AFs resulting from using optimal MI constant envelope waveforms obtained via phase retrieval techniques demonstrate superior resolution characteristics compared with classic linear frequency-modulated (LFM) signals employing optimal pulse compression. For various target and clutter spectral models, simulation results show that optimally filtered MI signals provide significantly enhanced SINR behavior compared with LFM radar signals. Hopefully, these results set the stage for the induction of MI signaling and receive techniques into conventional radar signal processing and pave the way for realization of one methodology for achieving cognition in radar systems.