Phase-Difference Ambiguity Resolution for a Single-Frequency Signal in the Near-Field Using a Receiver Triplet

Abstract

The problem of ambiguity in the phase-difference of a signal received by widely-spaced receivers is considered. It is shown that a collinear receiver triplet with a specific configuration combined with a proposed algorithm can be utilized for phase-difference disambiguation. The identifiability condition is that the difference of the two smaller inter-receiver spacings is not greater than a half-wavelength of the impinging signal and is greater than zero. The effect of the emitter location relative to the receiver array and the effect of noise are studied. Analytic formulae for the MSE (mean squared error) under Gaussian white noise are obtained and are used to directly determine performance versus SNR (signal-to-noise ratio) given the emitter location and the receiver configuration. Performance is found to exhibit an SNR threshold effect that depends on the emitter location and the sensor configuration. The analytic performance predictions are found to be close to the performance obtained in simulation.