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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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