Efficacy analysis of the power-law detector for non-Rayleigh distributed reverberation in active sonar systems

Non-Rayleigh reverberation in active sonar systems causes an increase in the number of false alarms when detection algorithms are designed under the assumption that the reverberation is actually Rayleigh distributed. Many models have been used to represent non-Rayleigh reverberation and then build appropriate detectors including the Rayleigh mixture model, K-distribution, and McDaniel's model. The detectors for these models de-emphasize the tails of the distribution. Thus, a natural non-parametric alternative would be to use a power-law non-linearity with a power less than one. In this paper the efficacy is used to evaluate the power-law detector for the above reverberation models with a non-fluctuating target. For the K-distribution and McDaniel's model, it was seen that the power-law can achieve the same efficacy as the locally optimal non-linearity with a simpler implementation. However, choosing the optimal power-law requires modeling the reverberation with McDaniel's model and a numerical optimization, the former of which can result in mismatch errors if there is not a good fit with the observed reverberation. Thus, a different technique is considered in which the power is chosen so that the transformed data have the same higher order moment measure (skewness, kurtosis, or scintillation index) as the Rayleigh distribution. It wag seen that matching kurtosis resulted in the best average performance, but also the highest variability when the higher order moments must be estimated from auxiliary data. Matching the scintillation index provided the worst average performance, but the least variability, and matching the skewness was in between these extremes in terms of both average performance and variability.