An official website of the United States government
We propose a new nonconvex framework for blind multiple signal demixing and recovery. The proposed Riemann geometric approach extends the well known constant modulus algorithm to facilitate grant-free wireless access. For multiple signal demixing and recovery, we formulate the problem as non-convex problem optimization problem with 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.
more »
« less
Wirtinger Flow Meets Constant Modulus Algorithm: Revisiting Signal Recovery for Grant-Free Access
In this work, we analyze the convergence of constant modulus algorithm (CMA) in blindly recovering multiple signals to facilitate grant-free wireless access. The CMA typically solves a non-convex problem by utilizing stochastic gradient descent. The iterative convergence of CMA can be affected by additive channel noise and finite number of samples, which is a problem not fully investigated previously. We point out the strong similarity between CMA and the Wirtinger Flow (WF) algorithm originally proposed for Phase retrieval. In light of the convergence proof of WF under limited data samples, we adopt the WF algorithm to implement CMA-based blind signal recovery. We generalize the convergence analysis of WF in the context of CMA-based blind signal recovery. Numerical simulation results also corroborate the analysis.
more »
« less
- PAR ID:
- 10281852
- Date Published:
- Journal Name:
- IEEE transactions on signal processing
- ISSN:
- 1941-0476
- Page Range / eLocation ID:
- Accepted
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The prospect of massive deployment of devices for Internet-of-Things (IoT) motivates grant-free access for simultaneously uplink transmission by multiple nodes. Blind demixing represents a promising technique for recovering multiple such source signals over unknown channels. Recent studies show Wirtinger Flow (WF) algorithm can be effective in blind demixing. However, existing theoretical results on WF step size selection tend to be conservative and slow down convergence rates. To overcome this limitation, we propose an improved WF (WF-OPT) by optimizing its step size in each iteration and expediting the convergence. We provide a theoretical guarantee on the strict contraction of WF-OPT and present the upper bounds of the contraction ratio. Simulation results demonstrate the expected convergence gains.more » « less
-
As applications of Internet-of-things (IoT) rapidly expand, unscheduled multiple user access with low latency and low cost communication is attracting growing more interests. To recover the multiple uplink signals without strict access control under dynamic co-channel interference environment, the problem of blind demixing emerges as an important obstacle for us to overcome. Without channel state information, successful blind demixing can recover multiple user signals more effectively by leveraging prior information on signal characteristics such as constellations and distribution. This work studies how forward error correction (FEC) codes in Galois Field can generate more effective blind demixing algorithms. We propose a constrained Wirtinger flow algorithm by defining a valid signal set based on FEC codewords. Specifically, targeting the popular polar codes for FEC of short IoT packets, we introduce signal projections within iterations of Wirtinger Flow based on FEC code information. Simulation results demonstrate stronger robustness of the proposed algorithm against noise and practical obstacles and also faster convergence rate compared to regular Wirtinger flow algorithm.more » « less
-
Blind deconvolution and phase retrieval are both fundamental problems with a growing interest in signal processing and communications. In this work, we consider the task of simultaneous blind deconvolution and phase retrieval. We show that this non-linear problem can be reformulated as a low-rank tensor recovery problem and propose an algorithm named TIHT-BDPR to recover the unknown parameters. We include a series of numerical simulations to illustrate the effectiveness of our proposed algorithm.more » « less
-
This work attempts to recover digital signals from a few stochastic samples in time domain. The target signal is the linear combination of one-dimensional complex sine components with R different but continuous frequencies. These frequencies control the continuous values in the domain of normalized frequency [0, 1), contrary to the previous research into compressed sensing. To recover the target signal, the problem was transformed into the completion of a low-rank structured matrix, drawing on the linear property of the Hankel matrix. Based on the completion of the structured matrix, the authors put forward a feasible-point algorithm, analyzed its convergence, and speeded up the convergence with the fast iterative shrinkage-thresholding (FIST) algorithm. The initial algorithm and the speed up strategy were proved effective through repeated numerical simulations. The research results shed new lights on the signal recovery in various fields.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
