A Riemannian Geometric Approach to Blind Signal Recovery for Grant-Free Radio Network Access

We propose a new nonconvex framework for blind multiple signal demixing and recovery. The proposed Riemannian geometric approach extends the well known constant modulus algorithm to facilitate grant-free wireless access for simultaneous demixing and recovery of multiple signal demixing and recovery. We formulate the problem as non-convex problem optimization problem integrated with the signal orthogonality constraint in the form of Riemannian Orthogonal CMA (ROCMA). Unlike traditional stochastic gradient solutions that require large data samples, parameter tuning, and careful initialization, we leverage Riemannian geometry and transform the orthogonality requirement of recovered signals into a Riemannian manifold optimization. Our solution demonstrates full recovery of multiple access signals without large data sample size or special initialization with high probability of success.