A Recursive Method for Signal Resolution

A recursive method is given for resolving signals overlapping in time. Assume that the signal waveform is known and several signals are received. The signals (of unknown number) may overlap with one another and the amount of time delay of each individual signal is unknown. The signals are corrupted with additive white Gaussian noise. The problem is to estimate the number, the amplitudes, and the time delays of the overlapping signals. Assume that at a certain instant tk-1 estimates have been made on the number of signals arriving in the time interval (O, tk-1) and the amplitudes and time delays of these signals. Using these estimates, we test at tk the hypothesis H1 that a new signal arrives at tk against the null hypothesis Ho that no new signal arrives. The decision gives the number of signals arriving in the time interval (0, tk); the parameters are then re-estimated. The overlapping signals are detected and resolved, and the estimates are improved at each stage. The system is analyzed in detail, and computer-simulated results are presented.