Comparison of two angle of arrival averaging strategies

The accuracy of direction finding (DF) systems can often be improved by using techniques for the time averaging of information from multiple data records, particularly when the signal-to-noise ratio is low. In certain DF systems, the emitter angle of arrival (AOA) is computed from the phase angle of a complex-valued signal. For this type of DF systems, there are two closely related but distinctly different approaches to AOA averaging. The first approach directly averages the complex signal samples and then computes the value of AOA from the phase angle of the resultant average. The second approach reverses the order of operations of the first approach by first computing the phase angle of each complex signal sample and then averaging the computed individual phase angles. Under the assumption that the complex signal samples processed by the AOA estimator are i.i.d. Gaussian distributed, this paper presents a theoretical proof to demonstrate the superiority of the first approach that was observed through experiments with off-the-air data.