Adaptive Detection Algorithms for Channel Matrix-Based Cognitive Radar/Sonar

The classical problem of radar/sonar target adaptive detection relies on both a primary data set (consisting of possibly target returns plus noise), and a secondary or training data set (consisting of noise only data samples). Kelly derived a generalized likelihood-ratio test (GLRT) statistic for this problem when based on a radar data model that characterizes clutter via the data covariance matrix. Cognitive radar/sonar, however, has adopted a data model that characterizes both target and clutter via the use of channel matrices because it simplifies the desired waveform optimization. The present work derives a GLRT statistic for the classical adaptive detection problem but when based on the cognitive radar/sonar data model that uses channel matrices to characterize all waveform dependent components in the presence of additive Gaussian colored noise. The resulting GLRT statistic clearly illustrates the value of waveform diversity for channel estimation.