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On the Effect of a Signal Delay on Cross-Spectral Correlation Function

This paper presents a thorough analysis of the effects which a signal delay caused to cross-spectral cyclostationary characteristics for the case of relatively simple harmonizable signals. The signal of interest and its delayed version are observed by the antenna system being modeled as two receivers whose coordinates are assumed known and remained constant. The signal measurement is carried out in a presence of an interference that overlaps the signal in both time and frequency domain but not in the cyclic frequency domain, where the signal possesses unique cyclic frequency pattern. Cross-spectral characteristics for stationary and cyclostationary cases are presented and analyzed in the form of analytical expression, followed by the simulation results using Mote Carlo method. Paper highlights different statistical properties of the estimates evaluated for these two cases and with possible applications such as time difference of arrival problem considered.