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Noise cancellation systems that in essence form the ratio between the detected videos of two different channels have frequently been used to reduce the effects of continuous external interference. As yet, no quantitative treatment of such systems is available in the literature. This paper examines the statistical properties of the cancelled video output and determines such quantities as false-alarm probability and probability of detection in terms of threshold setting and signal-to-interference ratio. In general, for optimum detectability two distinct thresholds are required (in contrast to conventional detection systems), although specific numerical results are given for the more practical, suboptimum cases of a single threshold and a symmetrical dual threshold. Both a nonfiuctuating target and a Rayleigh fading target are considered.