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 ad...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 69; pp. 6515 - 6529
Main Authors: Feres, Carlos, Ding, Zhi
Format: Journal Article
Language:English
Published: New York IEEE 2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
blind signal recovery
Channel noise
Constant-modulus algorithm
Convergence
Cost function
Heuristic algorithms
Internet of Things
Iterative methods
Minimization
Optimization
Phase retrieval
Recovery
Signal processing algorithms
Signal reconstruction
Wirtinger Flow
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2021.3103038