Detection performance of the smooth coherence transform (SCOT)

When energy from a radiating source is received at two physically separated sensors, it is possible to detect the presence of that source and estimate signal travel time difference (τ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> ) to the sensors using the Smoothed Coherence Transform (SCOT). The purpose of the SCOT is to enhance travel time difference (τ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> ) estimation, however, to estimate (τ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> ) a SCOT peak must first be detected. This detection performance is the subject which will be considered in this paper. Detection performance (probability of detection) is evaluated when the SCOT is obtained using the Inverse Discrete Fourier Transform (IDFT) of the Complex Coherence Function (CCF) estimate. Results are presented for both wideband and narrow-band signals assuming zero-mean, stationary, Gaussian signal and noise processes.