Blind Demixing for Low-Latency Communication

In next-generation wireless networks, low-latency communication is critical to support emerging diversified applications, e.g., tactile Internet and virtual reality. In this paper, a novel blind demixing approach is developed to reduce the channel signaling overhead, thereby supporting low-latency communication. Specifically, we develop a low-rank approach to recover the original information only based on the single observed vector without any channel estimation. To address the unique challenges of multiple non-convex rank-one constraints, the quotient manifold geometry of the product of complex symmetric rank-one matrices is exploited. This is achieved by equivalently reformulating the original problem that uses complex asymmetric matrices to the one that uses Hermitian positive semidefinite matrices. We further generalize the geometric concepts of the complex product manifold via element-wise extension of the geometric concepts of the individual manifolds. The scalable Riemannian optimization algorithms, i.e., the Riemannian gradient descent algorithm and the Riemannian trust-region algorithm, are then developed to solve the blind demixing problem efficiently with low iteration complexity and low iteration cost. The statistical analysis shows that the Riemannian gradient descent with spectral initialization is guaranteed to linearly converge to the ground truth signals provided sufficient measurements. In addition, the Riemannian trust-region algorithm is provable to converge to an approximate local minimum from the arbitrary initialization point. Numerical experiments have been carried out in settings with different types of encoding matrices to demonstrate the algorithmic advantages, performance gains, and sample efficiency of the Riemannian optimization algorithms.