Abstract
In this chapter, we convert the signal detection in a C-RAN to an inference problem over a bipartite random geometric graph. By passing messages among neighboring nodes, message passing (a.k.a. belief propagation) provides an efficient way to solve the inference problem over a sparse graph. However, the traditional message-passing algorithm does not guarantee to converge, because the corresponding bipartite random geometric graph is locally dense and contains many short loops. As a major contribution of this chapter, we propose a randomized Gaussian message passing (RGMP) algorithm to improve the convergence. The proposed RGMP algorithm demonstrates significantly better convergence performance than the conventional message passing algorithms. In addition, we generalize the RGMP algorithm to a blockwise RGMP (B-RGMP) algorithm, which allows parallel implementation. The average computation time of B-RGMP remains constant when the network size increases.
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Notes
- 1.
If x does not follow a Gaussian distribution, the message-passing algorithm presented in this work gives an approximation of the linear MMSE estimation [3].
- 2.
A tree-type graph is an undirected graph in which any two nodes are connected by exactly one path, where a path is a sequence of edges which connect a sequence of vertices without repetition.
- 3.
A loop in a graph is a path that starts and ends at the same node.
- 4.
References
C. Fan, X. Yuan, and Y. J. Zhang, “Scalable uplink signal detection in C-RANs via randomized Gaussian message passing,” IEEE Transaction on Wireless Communications, vol. 16, no. 8, pp. 5187–5200, 2017.
D. Bickson, D. Dolev, O. Shental, P. H. Siegel, and J. K. Wolf, “Gaussian belief propagation based multiuser detection,” in Proc. of IEEE International Symposium on Information Theory (ISIT), 2008, pp. 1878–1882.
Y. Weiss and W. T. Freeman, “Correctness of belief propagation in Gaussian graphical models of arbitrary topology,” in Advances in neural information processing systems, 2000, pp. 673–679.
S. V. Vaseghi, Advanced digital signal processing and noise reduction. John Wiley & Sons, 2008.
F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 498–519, 2001.
T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 599–618, 2001.
L. Liu, C. Yuen, Y. L. Guan, Y. Li, and Y. Su, “A low-complexity Gaussian message passing iterative detector for massive MU-MIMO systems,” in Proc. of IEEE International Conference on Information and Communications Security (ICICS), 2015, pp. 1–5.
L. Liu, C. Yuen, Y. L. Guan, Y. Li, and Y. Su, “Convergence analysis and assurance for Gaussian message passing iterative detector in massive MU-MIMO systems,” IEEE Transactions on Wireless Communications, vol. 15, no. 9, pp. 6487–6501, 2016.
L. Liu, C. Yuen, Y. L. Guan, Y. Li, and C. Huang, “Gaussian message passing iterative detection for MIMO-NOMA systems with massive access,” in Proc. of IEEE Global Communications Conference (GLOBECOM), 2016, pp. 1–6.
I. Sohn, S. H. Lee, and J. G. Andrews, “Belief propagation for distributed downlink beamforming in cooperative MIMO cellular networks,” IEEE Transactions on Wireless Communications, vol. 10, no. 12, pp. 4140–4149, 2011.
P. Som, T. Datta, A. Chockalingam, and B. S. Rajan, “Improved large-MIMO detection based on damped belief propagation,” in Proc. of IEEE Information Theory Workshop (ITW), 2010, pp. 1–5.
M. Moretti, A. Abrardo, and M. Belleschi, “On the convergence and optimality of reweighted message passing for channel assignment problems,” IEEE Signal Processing Letters, vol. 21, no. 11, pp. 1428–1432, 2014.
J. Goldberger and H. Kfir, “Serial schedules for belief-propagation: Analysis of convergence time,” IEEE Transactions on Information Theory, vol. 54, no. 3, pp. 1316–1319, 2008.
D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proceedings of the National Academy of Sciences, vol. 106, no. 45, pp. 18 914–18 919, 2009.
S. Rangan, “Generalized approximate message passing for estimation with random linear mixing,” in IEEE International Symposium on Information Theory (ISIT), 2011, pp. 2168–2172.
Y. Shi, J. Zhang, B. O’Donoghue, and K. B. Letaief, “Large-scale convex optimization for dense wireless cooperative networks,” IEEE Transactions Signal Processing, vol. 63, no. 18, pp. 4729–4743, 2015.
R. Sun, Z.-Q. Luo, and Y. Ye, “On the expected convergence of randomly permuted ADMM,” arXiv preprint arXiv:1503.06387, 2015.
B. L. Ng, J. Evans, and S. Hanly, “Distributed downlink beamforming in cellular networks,” in Proc. of IEEE International Symposium on Information Theory (ISIT), 2007, pp. 6–10.
R. D. Yates, “A framework for uplink power control in cellular radio systems,” IEEE Journal on selected areas in communications, vol. 13, no. 7, pp. 1341–1347, 1995.
O. Axelsson, Iterative solution methods. Cambridge university press, 1996.
Q. Su and Y.-C. Wu, “On convergence conditions of Gaussian belief propagation.” IEEE Transactions on Signal Processing, vol. 63, no. 5, pp. 1144–1155, 2015.
R. Barrett, et al., Templates for the solution of linear systems: Building blocks for iterative methods. SIAM, 1994.
S. Wu, et al., “Low-complexity iterative detection for large-scale multiuser MIMO-OFDM systems using approximate message passing,” IEEE Journal of Selected Topics in Signal Processing, vol. 8, no. 5, pp. 902–915, 2014.
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Zhang, YJ.A., Fan, C., Yuan, X. (2019). Scalable Signal Detection: Randomized Gaussian Message Passing. In: Scalable Signal Processing in Cloud Radio Access Networks. SpringerBriefs in Electrical and Computer Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-15884-2_5
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