  Multichannel adaptive signal detection jointly uses the test and training
data to form an adaptive detector, and then make a decision on whether a target
exists or not. Remarkably, the resulting adaptive detectors usually possess the
constant false alarm rate (CFAR) properties, and hence no additional CFAR
processing is needed. Filtering is not needed as a processing procedure either,
since the function of filtering is embedded in the adaptive detector. Moreover,
adaptive detection usually exhibits better detection performance than the
filtering-then-CFAR detection technique. Multichannel adaptive signal detection
has been more than 30 years since the first multichannel adaptive detector was
proposed by Kelly in 1986. However, there are fewer overview articles on this
topic. In this paper we give a tutorial overview of multichannel adaptive
signal detection, with emphasis on Gaussian background. We present the main
deign criteria for adaptive detectors, investigate the relationship between
adaptive detection and filtering-then-CFAR detection, relationship between
adaptive detectors and adaptive filters, summarize typical adaptive detectors,
show numerical examples, give comprehensive literature review, and discuss some
possible further research tracks.
