Linear Minimum Variance Estimation with Complex Phase Errors

The linear minimum variance estimator of a random signal, received multiplied by a complex Gaussian phase error and added to random noise, is investigated. The results apply to the propagation of images through the turbulent atmosphere, fading channels, and synthetic-aperture radar. Among others, a result is that the multiplicative error can be replaced by an additive error, usually white. The best signal modulation is found in two important special cases.