Detecting multipath signals with the matched-lag filter

A detection problem is considered for a single broadband source of unknown waveform and emission time. The signal travels to the receiver along multipath with unknown delays and temporal separation exceeding the inverse bandwidth of the signal. The received noise has uncertain variance. The travel times of the multipath are impractical to predict because of uncertainties in the environment. The presence or absence of the signal is estimated from the auto-correlation function. Instead of stochastically modeling the multipath in terms of their received auto-correlation function, receivers are constructed which constrain the signal-related lags in the auto-correlation function to have physically possible arrangements. For simple cases, this approach, called a matched-lag filter, yields probabilities of detection that are 1.35 times greater (for a false-alarm probability of 0.001) than conventional filters which base their decision on the signal-to-noise ratio in the autocorrelation function.