Blind Deconvolution Meets Phase Retrieval in Optical Wireless Communications

Optical wireless communication becomes a key enabling technology for achieving ultra-high data rate requirements in beyond 5G systems. In this paper, to reduce both channel signaling overhead and hardware cost in optical wireless communications, we present a blind deconvolutional phase retrieval approach to recover the source signals from phaseless measurements without a priori channel information. To deal with the coupled challenges of phaseless measurements and bilinear signaling model, we recast the signal recovery problem into a rank-one matrices recovery problem via matrix lifting, followed by relaxing each phaseless matrix measurement into its convex hull. We further propose a difference-of-convex-functions (DC) programming algorithm to solve the low-rank matrix optimization problem. This is achieved by proposing the DC representation for the rank function based on the convex Ky Fan k-norm, thereby exactly detecting the fixed-rank constraints. The numerical results demonstrate that the proposed DC approach outperforms the state-of-the-art methods in terms of signal recovery performance and the robustness to the noise.