Memory Approximate Message Passing

• URL: http://arxiv.org/abs/2106.02237v1
• Date: Fri, 4 Jun 2021 03:37:14 GMT
• Title: Memory Approximate Message Passing
• Authors: Lei Liu, Shunqi Huang, Brian M. Kurkoski
• Abstract summary: This paper proposes a memory AMP (MAMP), in which a long-memory matched filter is proposed for interference suppression. A state evolution is derived to characterize the performance of MAMP. For all right-unitarily-invariant matrices, the optimized MAMP converges to OAMP/VAMP, and thus is Bayes-optimal if it has a unique fixed point.
• Score: 9.116196799517262
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable for other matrix ensembles, especially for ill-conditioned ones. To handle this difficulty, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP requires high-complexity linear minimum mean square error estimator. To solve the disadvantages of AMP and OAMP/VAMP, this paper proposes a memory AMP (MAMP), in which a long-memory matched filter is proposed for interference suppression. The complexity of MAMP is comparable to AMP. The asymptotic Gaussianity of estimation errors in MAMP is guaranteed by the orthogonality principle. A state evolution is derived to asymptotically characterize the performance of MAMP. Based on the state evolution, the relaxation parameters and damping vector in MAMP are optimized. For all right-unitarily-invariant matrices, the optimized MAMP converges to OAMP/VAMP, and thus is Bayes-optimal if it has a unique fixed point. Finally, simulations are provided to verify the validity and accuracy of the theoretical results.

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