Performance sensitivity of array detectors to a p r i o r i spatial knowledge

Abstract

Performance of array detectors degrades when the a priori spatial knowledge of the signal direction or interfering noise direction is inaccurate. Two classes of signal waveforms are considered; one is the known-waveform signal, the other is the Gaussian signal. For the known-waveform-signal case, an explicit functional form is derived for the detectability index to characterize the degraded receiver-operating-characteristic (ROC) curve which is due to either mismatch of signal direction or inaccurate noise direction. For the Gaussian-signal case, the distribution of the sufficient statistic is shown to be a ’’generalized chi-square distribution.’’ Then, the performance and its sensitivity to the signal-direction mismatch are evaluated in terms of probability of detection (PD) and probability of false alarm (PF). Closed form expressions for PD and PF are shown for a single-frequency case. The array factor, which depends on the geometry of the array sensors, plays an important role in the sensitivity study. For the Gaussian signal in independent noise, the performance loss of the processor is a function of the array factor and the angular distance between the true source location and the assumed source location. For the known-waveform signal in independent noise, performance degradation is closely related to the array factor. The detectability index for the known-waveform signal, with directional noise, is related in a more complicated way to the array factor. In general, a low-directivity array is desirable in the incorrect signal-direction cases and a high-directivity array is desirable in the incorrect noise-direction cases. By comparing the relative detection performance degradation of the known-waveform signal processor with that of the Gaussian-signal processor, we conclude that the Gaussian-signal processor is less sensitive to the uncertainty than is the known-waveform processor. This is due to the fact that the received signal phase which is used in the known-waveform signal processor, is more sensitive to the inaccuracy of the spatial knowledge than is the received-signal energy which is used in the Gaussian-signal processor.