Threshold Region Performance of Multi-Carrier Maximum Likelihood Direction of Arrival Estimator

This paper addresses the performance characterization of a direction of arrival (DoA) estimator in the low signal-to-noise-ratio (SNR) region. The case of a sensor array simultaneously collecting signals emitted at multiple carrier frequencies by a single source is considered. A maximum likelihood (ML) approach is used as a reference method for DoA estimation and its accuracy is characterized in terms of mean square error (MSE). It is well known that for SNR values included in the so-called threshold region, the DoA estimation accuracy decreases rapidly, due to the presence of outliers. This effect can be possibly mitigated when multiple frequency channels are jointly exploited. However, the capability to predict this performance degradation is fundamental either for assessing the robustness of an existing sensor or for supporting its design. Therefore, the scope of this paper is to introduce appropriate approximations to the MSE of a multifrequency ML DoA estimator in order to provide a reliable characterization of its performance in the threshold region. Two models for the source signals are considered and separately discussed, namely the deterministic (or conditional) and stochastic (or unconditional). An extensive simulated analysis is reported to prove the tightness of the approximations and to characterize the benefits steming from the exploitation of signals emitted at multiple carriers.