The matched-lag filter: detecting broadband multipath signals with auto- and cross-correlation functions.
Signal detection is considered for uncertain noise variance and a broadband source of unknown waveform and emission time. The signal travels to the receivers along paths with unknown delays. Using a new "matched-lag filter," the presence or absence of the signal is estimated from the auto- and cross-correlation functions of the receptions. Like a matched filter, correlation functions provide the first stage of gain in signal-to-noise ratio because the paths are assumed to be partially coherent. The second stage achieves additional gain by searching only over physically possible arrangements of signals in the auto- and cross-correlation functions while excluding forbidden arrangements. These stages enable the matched-lag filter to behave like a matched filter within a matched filter. In an ideal case, simulations of the matched-lag filter yield probabilities of detection that are, with one and two receivers, 4.1 and 366 times, respectively, that obtained from the conventional energy detector at a false-alarm probability of 0.001. The matched-lag filter has applications to wireless communications and the detection of acoustic signals from animals, vehicles, ships, and nuclear blasts. The matched-lag filter more completely describes signal structure than stochastic detection and communication theories whose specified auto-correlation function does not prohibit forbidden arrangements.