A new CFAR detection test for radar

In a well-known paper [2], Reed, Mallett, and Brennan (RMB ) discuss an adaptive procedure for the detection of a signal of known form in the presence of noise (or interference) which is assumed to be Gaussian, but whose covariance matrix is totally unknown. Two sets of input data are distinguished and are called for convenience the primary and the secondary input data. The primary data allow for the possibility of signal presence, while the secondary inputs are assumed to contain only noise, independent of and statistically identical to the noise components of the primary data. In the RMB procedure, the secondary inputs are used to form an estimate of the noise covariance, from which a weight vector for the detection of the known signal is determined. This weight vector is applied then to the primary data in the form of a standard colored-noise matched filter. The implication is that the output of this filter is compared with a threshold in order to achieve signal detection. However, no special rule is given for the determination of the threshold needed to control the probability of a false alarm ( PFA ) . In [l] Kelly used the generalized likelihood ratio to derive a hypothesis test for the above problem. This test exhibits the desirable property that its PFA is independent of the covariance matrix (level and structure) of the actual noise encountered; i.e., it is a CFAR (constant false alarm rate) test. However, the derivation of Kelly’s test statistic is complicated. A new related test is developed in this paper. This test is based on the optimal decision rule for a known signal template and a known noise covariance matrix. Then this classical test variable is normalized to have a unit variance. In the usual case of an unknown noise covariance matrix, the maximum likelihood estimate