Performance characteristics of passive coherence estimators

Two dimensional coherence processing is commonly used for passive detection in acoustic sensor systems. Modern coherence processors, well suited for this purpose, include the magnitude squared coherence (MSC) estimator and the normalized correlation envelope (NCE) estimator. These are biased estimators, whose performance characteristics are not well understood and are exceptionally difficult to analyze. However, by developing a rather unique bias correcting function, the detection performance of biased estimators is derived as a function of both the input signal and the processor parameters, Design parameters, which optimize detection, are determined for both the MSC and the NCE estimators. In applications where the number of degrees of freedom (or time bandwidth product) of a target signal is severely limited, detection performance can be enhanced by signal overcontainment within the processor bandwidth. Performance data are presented in formats appropriate for selecting processor parameters which are optimum for a given application. Practical guidelines are given to avoid misapplying the theoretical results in cases where there are many narrowband interfering signals in the spectral region of a target signal.