Iterative deconvolution in noncoherent systems

The application of iterative deconvolution techniques to the squared-magnitude function of a complex-valued signal degraded by convolution with a known complex function is considered. The observed and desired complex signal phase functions are treated as random processes. One possible iteration for the mean of the squared-magnitude of the desired signal is considered. The role of the probability density functions of the unknown phases is discussed, and the case where all phases are completely random is considered in more detail. It is shown that a computable iteration is obtained only in this special case. The problem has application in areas such as radar where noncoherent sensors are used to receive signals which are inherently complex-valued.