Sonar Array Detection ofGaussian Signals inGaussian Noise
N.J. Bershad, P. Feintuch · 1974
A statistical testispostulated fordetecting, withan M-element hydrophone array, a Gaussian signalin spatially independent Gaussian noiseofunknownpower. Thetestisan extension ofthe uniformly-most-powerful (UMP)unbiased testfora two-element array.Theoutputsignal-to-noise ratio ofthetestiscalculated and, fora large numberofindependent space-time samples, isshownto beno better thana mean-level detector (MLD).Receiver operating characteristic curves (ROC)fortheMLD are computedand comparedtotheROC curvesfortheoptimum(Bayes) parametric detector. Theinputsignal-to-noise power ratios required toprovide a detection probability of0.5differby lessthan0.2dB fora fifty-element arraywithwidevariation infalse-alarm probability and time-bandwidth product. Thisresult suggeststhatboththe extendedbivariate UMP unbiased testandtheMLD perform close to the unknown UMP unbiased testforindependence of a multivariate Gaussian distribution.