Abstract: The matched filter is a common solution to the problem of detecting a known signal in noise. The matched filter is composed of the signal template to enhance the signal response and second order noise statistics to suppress the noise. The second order statistics of the noise are typically unknown. Fully adaptive implementations estimate these statistics from the noise present in the data to be filtered. If the signal is present, then it will be included in the estimate of the noise statistics used in the matched filter. Since these statistics are used by the matched filter to suppress noise, the signal will act to suppress itself, this is referred to as signal capture loss. In this paper an analytic model for signal capture loss is developed and experimentally verified. The use of the sample statistics to suppress the noise from which they are derived alters the noise rejection performance of the filter. Unlike the analysis of Reed et. al. which considers the use of the sample covariance to filter data which is independent of the sample covariance, the case of filtering the same data which was used to calculate the sample covariance is explicitly analyzed. This form of noise suppression is called self- whitening. The effect of self-whitening upon the noise rejection performance of the filter is analyzed and the results are verified experimentally. Signal capture loss and self-whitening are competing effects in terms of the number of samples used to form the sample covariance matrix. The output SNR includes both of these effects and is used to measure filter performance as a function of the number of samples. The output SNR performance is obtained by combining the results for signal capture loss with the self-whitening results. To obtain the performance of a fully adaptive filter relative to the optimal matched filter designed with the true population covariance, the results derived in this paper are combined with those of Reed et. al. !1
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