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.
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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.
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- NSF-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
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Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
