Blind demixing for low-latency communication

Abstract

In the next generation wireless networks, lowlatency 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. 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 arbitrary initialization point. Numerical experiments have been carried out in the settings with different types of encoding matrices to demonstrate the algorithmic advantages, performance gains and sample efficiency of the Riemannian optimization algorithms.

Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow

“…is the preprocessed data vector transmitted by the i-th node. Over m channel access opportunities (e.g., time slots), the received signals at fusion center in the frequency domain can be written as [13], [15]…”

“…as the first entry and the second through the N -th entries of x t i , respectively. Based on the assumption thatx i = q i e 1 for i = 1, · · · , s, (15) and (16) can be reformulated as…”

“…and each α i is the alignment parameter. It is easily seen that if α h t i (13), β h t i (14), α x t i (15) and β x t i (16) obey…”

“…Even though the work [12] has proposed a type of CSI at sensor nodes, called No CSI, the receiver still needs to obtain the statistical channel knowledge. Recently, blind demixing has become a powerful tool to elude channel-state-information (i.e., without channel estimation at both transmitters and receivers) thereby enabling low-latency communications [13], [14], [15]. Specifically, in blind demixing, a sequence of source signals can be recovered from the sum of bilinear measurements without the knowledge of channel information [16].…”

“…Nevertheless, the theoretical guarantees for the regularized gradient [13] provide pessimistic convergence rate and require carefullydesigned initialization. The Riemannian trust-region optimization algorithm without regularization was further proposed in [15] to improve the convergence rate. However, the secondorder algorithm brings unique challenges in providing statistical guarantees.…”