Abstract
The analysis of the arithmetic mean constant false-alarm rate (CFAR) normalizing processor for nonfluctuating targets entails consideration ion of the moderately complicated F-distribution. For Swerling 1 targets, the CFAR performance equations are quite simple. The mean signal-to-interference ratio (SIR), ϒ ─M, required as a function of probability of detection, P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> , false-alarm probabil ity, P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</sub> , and number of normalization cells, M, is given by ϒ─M = (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> / P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/M</sup> / (1-P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l/M</sup> ). A graph of the CFAR loss, the increased SIR relative to that required when the interference power is known (so that CFAR processing is not required), is given. The data indicate that the CFAR loss, in decibels, is halved when the number of normalization cells is doubled. This result is a special case of the more general gamma density fluctuation model. The more general case is derived and specialized to Swerling 1 and 3 target models.
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