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Traditional preamble detection algorithms have low accuracy in the
grant-based random access scheme in massive machine-type communication (mMTC).
We present a novel preamble detection algorithm based on Stein variational
gradient descent (SVGD) at the second step of the random access procedure. It
efficiently leverages deterministic updates of particles for continuous
inference. To further enhance the performance of the SVGD detector, especially
in a dense user scenario, we propose a normalized SVGD detector with momentum.
It utilizes the momentum and a bias correction term to reduce the preamble
estimation errors during the gradient descent process. Simulation results show
that the proposed algorithm performs better than Markov Chain Monte Carlo-based
approaches in terms of detection accuracy.

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