False Alarm Rate for Rank Quantizer When Input Range Samples are not Independent

Under the assumption that the non-independent range samples fed into the rank quantizer form a first-order Markov sequence, the first threshold false alarm probability Pn is written in the form of a multiple integral, the multiplicity being equal to the number of samples or quantizer taps. The Rice model for narrow-band noise (clutter) is used to check the effect of correlation on Pn using the derived formula. For the limited case examined, correlation be tween samples decreases Pn as compared with the independent samples case.