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This paper shows that increasing SNR is not necessarily sufficient to improve ROC performance, that is, increase the probability of detection for a given false alarm probability. The general optimal detector is derived with no assumptions on the stationarity of the input noise process or the form of the input signal model.

A CFAR detector commonly used for the detection of unresolved targets normalizes the background vaiiance by dividing the detection filter output by the local sample standard deviation. A number of researchers have measured the experimental false alarm probability of this detector and found it to be higher than the probability predicted by a Gaussian density funclion. This is the case even when the filter output statistics are known to be Gaussian distributed. A number of attempts have been made to heuiistically construct distribulions which exhibit the heavy tails associated with the measured false alarm probability (eg. sum oftwo Gaussian densities or the modified gamma density).This paper presents a first principles derivalion of the detector false alarm density function based upon the assumption that the filter output is Gaussian distributed. The resulting false alarm density function is veiy nearly Gaussian out to about 3.5 standard deviations. Past 3.5 standard deviations the tails ofthe derived density function are markedly heavier than the corresponding Gaussian tails. The parameters of this new density function are easily estimated from the filter output. The analytic results are validated using a ChiSquare goodness-of-fit test and experimental measurements of the false alarm density.

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