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Exact Detection Performance for Broadband Correlators

The detection of a broadband plane wave in an isotropic noise field is considered. The detection statistic used is the cross correlation of the sampled output from two sensors where the sampling rate equals the Nyquist rate and the time delay is an integer multiple of the sampling period. By restricting the number of points in the cross correlation to be even, the detection and false-alarm probbilities are obtained in closed form. Numerical results are presented for several special cases.