Operating Characteristics for Continuous Square-Law Detection in Gaussian Noise

摘要

The exact detection probabilities and false-alarm probabilities for continuous square-law detection of a signal in Gaussian noise are calculated, with no restrictive assumptions about the size of the observation-time-bandwidth products. Two cases are considered: they are called the low-frequency (LF) and narrowband (NB) cases. In both cases, the signal has coherent and incoherent components. Results for the detection probability versus signal-to-noise ratio (S/N), with false-alarm probability as a parameter, are given for both the LF and NB cases for observation-time-bandwidth products equal to 2 sup n (n = 0(1)7) and for the fraction of coherent signal power equal to 0, .2, 1. For a specifed detection probability of .5 and false-alarm probabilities of 1/(10 sup n)(n = 1(1)8), the required S/N is also plotted for the same range of time-bandwidth products and fractions of coherent signal power as above. (Author)