Error Performance of Two-Channel Phase-Measurement Systems

The problem of measuring a constant phase difference between two sinusoids which have been corrupted by two additive noise processes is investigated. For the case in which both noise processes are Gaussian and the signal-to-noise ratio is high, the variance of the time-averaged phase-difference estimate is found as a single integral over the noise power spectral densities and cross spectral density. Arbitrary cross correlation is allowed between the two noise processes. Two cases of practical interest are considered: 1) the noise processes have identical, rectangular power spectral densities and are statistically independent; 2) an idealized radio direction finding situation in which two spatially separated sensors are immersed in an isotropic, planar noise field. For the statistically independent case, a universal curve is presented which permits determination of phase-estimate standard deviation for arbitrary signal-to-noise ratio and for a wide range of bandwidths and integration times.