Fast converging adaptive detection of Doppler-shifted, range-distributed targets

A generalized likelihood ratio test (GLRT) for the adaptive detection of a target or targets that are Doppler-shifted and distributed in range is derived. The unknown parameters associated with the hypothesis test are the complex amplitudes in range of the desired target and the unknown covariance matrix of the additive interference, which is assumed to be characterized as complex zero-mean correlated Gaussian random variables. The target´s or targets´ complex amplitudes are assumed to be distributed across the entire input data block (sensor × range). The unknown covariance matrix is constrained to have the reasonable form of the identity matrix (the internal noise contribution) plus an unknown positive semidefinite (psdh) matrix (the external interference contribution). It is shown via simulation for a variety of interference scenarios that the new detector has the characteristic of having a bounded constant false alarm rate (CFAR), i.e., for our problem, the probability of false alarm P_F for a given detection threshold is bounded by the P_F that results when no external interference is present. It is also shown via simulation that the new detector converges relatively fast with respect to the number of sample vectors K necessary in order to achieve a given probability of detection P_D