Matched-Filter Envelope Detector Deflection Performance for a Correlated Phase Channel

In this paper, the effect of channel phase coherence upon a matched filter envelope detector output is investigated for a pulsed radar or active sonar. A novel model for the correlated channel phases allows the explicit calculation of the loss in detection performance using the deflection criteria. The theoretical model yields good agreement with simulations when the phase correlation coefficients between the first and last pulses are between 0.1 and 1.0. It is shown that a 3-dB loss in performance, as compared to the optimum detector for perfect coherence, requires phase correlation between adjacent pulses of
\rho_{i,i+1} = 0.91
, 0.96, and 0.96 for 10, 20, and 30 pulses, respectively. On the other hand, the same performance is obtained with a noncoherent combiner of the matched filter pulse returns when correlation between adjacent pulses,
\rho_{i,i+1} = 0.8
, 0.835, and 0.84 for 10, 20, and 30 pulses, respectively. If
\rho_{i,i+1}
is smaller than these quantities, one is better off performing noncoherent detection.