Signal reconstruction from phase only information and application to blind system estimation

We propose a method for the reconstruction of a complex signal from its Fourier phase only, where the phase is known within a linear phase term, and the sequence's length is unknown. The case of the phase known exactly has received a lot of attention in the past, however, in most cases the phase can be estimated up to a linear phase term whose slope is unknown. Moreover, in most cases of interest, the exact length of the sequence which is to be recovered is unknown. As an application of the reconstruction from phase technique, we propose a method for blind channel identification.