Exact detection probability and fluctuation loss for a partially correlated Rayleigh target

Theoretical methods are well known for the determination of the probability of detection for fluctuating and non-fluctuating targets when N pulses of signal pulse noise are integrated incoherently. Previously, correlation of the pulses has been considered to be complete or nonexistent during the integration time. This analysis extends the detection theory to include detection of the sum of N partially correlated pulses. A Rayleigh target whose in-phase and quadrature components have exponential correlation is used as the model. The fluctuation loss for a Gauss-Markov signal is determined as a function of number of pulses integrated, the correlation between pulses, and the specified detection and false alarm probabilities. This exact loss is compared to Barton's approximation.