Songbin Liu

Songbin Liu

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Publications

You can also find my articles on my Google Scholar profile.

Optimality of Approximate Message Passing Algorithms for Spiked Matrix Models with Rotationally Invariant Noise

Published in , 2024

We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this problem and provide a simple and concise characterization of their dynamics in the high-dimensional limit. At each iteration, these algorithms exploit prior knowledge about the noise structure by applying a non-linear matrix denoiser to the eigenvalues of the observed matrix and prior information regarding the signal structure by applying a non-linear iterate denoiser to the previous iterates generated by the algorithm. We exploit our result on the dynamics of these algorithms to derive the optimal choices for the matrix and iterate denoisers. We show that the resulting algorithm achieves the smallest possible asymptotic estimation error among a broad class of iterative algorithms under a fixed iteration budget.

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Decentralized Channel Estimation for the Uplink of Grant-Free Massive Machine-Type Communications

Published in IEEE Transactions on Communications, 2021

This paper studies the joint estimation of channel fading and user activity for the uplink of a grant-free massive machine-type communication system. Comparing with previous studies, we consider more practical aspects of the system, including non-i.i.d. signature matrices, low-resolution quantization, and random users activated by an unknown sparse rate. A new estimation algorithm, termed hybrid decentralized generalized expectation consistent (HyDeGEC), is then derived based on a hybrid network that applies scalar message passing for the prior inference and vector message passing for the likelihood inference. This new algorithm outperforms many state-of-the-art techniques in terms of robustness (to non-i.i.d. signatures), complexity (in computation per iteration), and/or estimation accuracy (of the channel and the activity rate). The state evolution of the algorithm is also analyzed, which, as validated by simulations, can capture precisely the algorithm’s per-iteration behavior in MSE. Summing up, the algorithm we propose here is practically effective, computationally efficient, and theoretically analyzable.

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