Performance Analysis of Constant-False-Alarm-Rate Detectors Using Characteristic Functions

Constant-false-alarm-rate (CFAR) detectors in sonar and radar are often implemented by forming the ratio of an unnormalized decision statistic from a test cell to an estimate of the noise background power and comparing it to a decision threshold. Evaluation of the performance in terms of the detection and false alarm probabilities is traditionally done through the use of the probability density function (pdf) of the background power estimate and the cumulative distribution function (cdf) of the unnormalized test cell. An alternative approach is presented in this paper where the pdf, cdf, and other properties of the CFAR decision statistic are described as a function of the characteristic functions of the unnormalized test cell and the background power estimate. The characteristic-function-based approach is appealing because of its generally simpler form compared to the pdfs and cdfs of both the background power estimator and standard signal models (deterministic, Gaussian fluctuating, Rician, and gamma-fluctuating intensity). The technique is demonstrated through several examples including background power estimators formed using a weighted average (e.g., an exponential averager), an order-statistic filter, and correlated Gaussian data. The broad utility of the approach is illustrated by evaluating false alarm and detection performance of a cell-averaging normalizer for a significantly fluctuating signal in heavy-tailed clutter and by assessing how much nonstationarity in the background noise power is required for normalizing before incoherent integration to perform better than normalizing after.