Signal-Detection Studies, with Applications

Curves are given relating the probability βT of detection of a signal in noise to the signal-to-noise power-ratio S/N, to the proportion α of false detections that can be tolerated, and to the time available (more specifically, to the number m of independent squared samples of the envelope of the filter output that are averaged in making a single attempt at detection). For the curves, three types of sinusoidal signals are assumed, according as the amplitude is constant, varies at random very slowly (fading), or varies as rapidly as the filtered noise itself. The second case is of course very unfavorable for reliable detection, and the third is also if one is limited to one or two sample points. The curves are applied to problems of optimizing radar parameters such as pulse energy, scan rate, averaging time, etc. The Appendix gives the mathematical background for the foregoing and then proceeds to consider additional types of signal (dc and arbitrary Gaussian) and methods of detection (failure to rectify or take the envelope, counting of samples above a threshold, and averaging by continuous integration).