An exact formula for the probability density of the phase error of a digital interferometer

The accuracy of an interferometer was analyzed by E.V. Stansfield, who derived approximate formulas for the variance of the phase error given that the received signal from each antenna is a sinusoid embedded in additive white Gaussian noise. These formulas are simple to use and provide useful insights into the performance of interferometric direction finding systems. However, they may be unreliable, as their derivation depends on certain assumptions which, in a strict sense, are invalid. In particular, an exact solution for the probability density of the phase error has, up to now, resisted mathematical analysis. This paper derives an exact formula for the probability density of the phase error of a digital interferometer based on the processing of non-overlapped signal data blocks. This result leads to an exact formula for the variance of the phase error, and thereby improves the accuracy with which the theoretical performance of a digital interferometer can be determined.