Effects of signal fluctuation on the detection of pulse signals in noise

The Neyman-Pearson statistical theory on testing hypotheses has in previous work been applied to the problem of the detection of nonfluctuating constant-amplitude signals embedded in noise. This work is extended in this paper to the case of signal power fluctuating according to a prescribed probability distribution. The effect on system performance of possible correlation between successive signal pulses is taken into account. The introduction of signal fluctuation leads in general to some loss in system performance as compared to the case of nonfluctuating signals. This loss is most pronounced when there is complete correlation between successive signals, and is quite small when successive signals are independent of one another.