Convergence Analysis of the Variance in Gaussian Belief Propagation

Su, Qinliang; Wu, Yik-Chung

doi:10.1109/tsp.2014.2345635

Cited by 32 publications

(21 citation statements)

References 29 publications

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“…Therefore, we have MSE G M P (v −1 ) > MSE G M P (v l −1 ) due tov −1 >v l −1 . As a result, we have the inequality (a) in (38). Hence, we obtain Corollary 2.…”

Section: Iteration #7mentioning

confidence: 60%

Gaussian Message Passing for Overloaded Massive MIMO-NOMA

Liu

Yuen

Guan

et al. 2019

IEEE Trans. Wireless Commun.

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This paper considers a low-complexity Gaussian Message Passing (GMP) scheme for a coded massive Multiple-Input Multiple-Output (MIMO) systems with Non-Orthogonal Multiple Access (massive MIMO-NOMA), in which a base station with N s antennas serves N u sources simultaneously in the same frequency. Both N u and N s are large numbers, and we consider the overloaded cases with N u > N s . The GMP for MIMO-NOMA is a message passing algorithm operating on a fully-connected loopy factor graph, which is well understood to fail to converge due to the correlation problem. In this paper, we utilize the largescale property of the system to simplify the convergence analysis of the GMP under the overloaded condition. First, we prove that the variances of the GMP definitely converge to the mean square error (MSE) of Linear Minimum Mean Square Error (LMMSE) multi-user detection. Secondly, the means of the traditional GMP will fail to converge when N u /N s < ( √ 2 − 1) −2 ≈ 5.83. Therefore, we propose and derive a new convergent GMP called scale-andadd GMP (SA-GMP), which always converges to the LMMSE multi-user detection performance for any N u /N s > 1, and show that it has a faster convergence speed than the traditional GMP with the same complexity. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results presented.

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“…Therefore, we have MSE G M P (v −1 ) > MSE G M P (v l −1 ) due tov −1 >v l −1 . As a result, we have the inequality (a) in (38). Hence, we obtain Corollary 2.…”

Section: Iteration #7mentioning

confidence: 60%

Gaussian Message Passing for Overloaded Massive MIMO-NOMA

Liu

Yuen

Guan

et al. 2019

IEEE Trans. Wireless Commun.

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“…In [5], [6], necessary and sufficient conditions for asymptotic convergence of the Gaussian BP algorithm are studied. The purpose of this paper is to study the convergence rate of the Gaussian BP algorithm.…”

Section: Introductionmentioning

confidence: 99%

Convergence rate analysis of Gaussian belief propagation for Markov networks

Zhang

2020

IEEE/CAA J. Autom. Sinica

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Gaussian Belief Propagation (BP) algorithm is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density functions from a high dimensional joint density function over a Markov network in a finite number of iterations when the underlying Gaussian graph is acyclic. It is also known more recently that the algorithm produces correct marginal means asymptotically for cyclic Gaussian graphs under the condition of walk summability. This paper extends this convergence result further by showing that the convergence is exponential under the walk summability condition, and provides a simple bound for the convergence rate.

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“…Three sufficient conditions for the convergence of GaBP in loopy graphs are known: diagonaldominance [25], [26], convex decomposition [24] and walksummability [27]. Recently, a necessary and sufficient variance convergence condition of GaBP is given in [28]. For the GMPID based on the pairwise graph, a sufficient condition of the mean convergence is given in [31] and it is shown that 1) the covariance matrices definitely converge, 2) if they converge, the means of GMPID coincide with the true marginal means.…”

Section: Introductionmentioning

confidence: 99%

Convergence Analysis and Assurance for Gaussian Message Passing Iterative Detector in Massive MU-MIMO Systems

Liu

Yuen

Guan

et al. 2016

IEEE Trans. Wireless Commun.

107

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Abstract-This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) algorithm for massive Multiuser Multiple-Input Multiple-Output (MU-MIMO) system, in which a base station with M antennas serves K Gaussian sources simultaneously. Both K and M are very large numbers, and we consider the cases that K < M . The GMPID is a low-complexity message passing algorithm based on a fully connected loopy graph, which is well understood to be not convergent in some cases. As it is hard to analyse the GMPID directly, the large-scale property of the massive MU-MIMO is used to simplify the analysis. Firstly, we prove that the variances of the GMPID definitely converge to the mean square error of Minimum Mean Square Error (MMSE) detection. Secondly, we propose two sufficient conditions that the means of the GMPID converge to those of the MMSE detection. However, the means of GMPID may not converge when K/M ≥ ( √ 2 − 1) 2 . Therefore, a new convergent GMPID called SA-GMPID (scale-and-add GMPID) , which converges to the MMSE detection in mean and variance for any K < M and has a faster convergence speed than the GMPID, but has no higher complexity than the GMPID, is proposed. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results.

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Convergence Analysis of the Variance in Gaussian Belief Propagation

Cited by 32 publications

References 29 publications

Gaussian Message Passing for Overloaded Massive MIMO-NOMA

Gaussian Message Passing for Overloaded Massive MIMO-NOMA

Convergence rate analysis of Gaussian belief propagation for Markov networks

Convergence Analysis and Assurance for Gaussian Message Passing Iterative Detector in Massive MU-MIMO Systems

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