### Abstract

This paper considers a belief propagation algorithm over pairwise graphical models to develop low-complexity iterative multiple-input multiple-output (MIMO) detectors. The pairwise graphical model is a bipartite graph where a pair of variable nodes are related by an observation node represented by the bivariate Gaussian function obtained by marginalizing the posterior joint probability density under the Gaussian input assumption. Specifically, we consider two types of pairwise models: the fully connected and ring-type. The pairwise graphs are sparse, compared with the conventional graphical model introduced by Bickson et al., insofar as the number of edges connected to an observation node (edge degree) is only two. Consequently, the computations are much easier than those of maximum likelihood (ML) detection, which are similar to the belief propagation (BP) that is run over the fully connected bipartite graph. The link level performance for non-Gaussian input is evaluated via simulations, and the results show the validity of the proposed algorithms. We also customize the algorithm with Gaussian input assumption to obtain the Gaussian BP run over the two pairwise graphical models, and for the ring-type, we prove its convergence to the linear minimum mean square error (MMSE) estimates. Since the maximum a posterior (MAP) estimator for Gaussian input is equivalent to the linear MMSE estimator, it shows the optimality of the scheme for Gaussian input.

Original language | English |
---|---|

Article number | 6665044 |

Pages (from-to) | 2363-2377 |

Number of pages | 15 |

Journal | IEEE Transactions on Vehicular Technology |

Volume | 63 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Automotive Engineering
- Aerospace Engineering
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Vehicular Technology*,

*63*(5), 2363-2377. [6665044]. https://doi.org/10.1109/TVT.2013.2291245

}

*IEEE Transactions on Vehicular Technology*, vol. 63, no. 5, 6665044, pp. 2363-2377. https://doi.org/10.1109/TVT.2013.2291245

**Low-complexity MIMO detection based on belief propagation over pairwise graphs.** / Yoon, Seokhyun; Chae, Chan-Byoung.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Low-complexity MIMO detection based on belief propagation over pairwise graphs

AU - Yoon, Seokhyun

AU - Chae, Chan-Byoung

PY - 2014/1/1

Y1 - 2014/1/1

N2 - This paper considers a belief propagation algorithm over pairwise graphical models to develop low-complexity iterative multiple-input multiple-output (MIMO) detectors. The pairwise graphical model is a bipartite graph where a pair of variable nodes are related by an observation node represented by the bivariate Gaussian function obtained by marginalizing the posterior joint probability density under the Gaussian input assumption. Specifically, we consider two types of pairwise models: the fully connected and ring-type. The pairwise graphs are sparse, compared with the conventional graphical model introduced by Bickson et al., insofar as the number of edges connected to an observation node (edge degree) is only two. Consequently, the computations are much easier than those of maximum likelihood (ML) detection, which are similar to the belief propagation (BP) that is run over the fully connected bipartite graph. The link level performance for non-Gaussian input is evaluated via simulations, and the results show the validity of the proposed algorithms. We also customize the algorithm with Gaussian input assumption to obtain the Gaussian BP run over the two pairwise graphical models, and for the ring-type, we prove its convergence to the linear minimum mean square error (MMSE) estimates. Since the maximum a posterior (MAP) estimator for Gaussian input is equivalent to the linear MMSE estimator, it shows the optimality of the scheme for Gaussian input.

AB - This paper considers a belief propagation algorithm over pairwise graphical models to develop low-complexity iterative multiple-input multiple-output (MIMO) detectors. The pairwise graphical model is a bipartite graph where a pair of variable nodes are related by an observation node represented by the bivariate Gaussian function obtained by marginalizing the posterior joint probability density under the Gaussian input assumption. Specifically, we consider two types of pairwise models: the fully connected and ring-type. The pairwise graphs are sparse, compared with the conventional graphical model introduced by Bickson et al., insofar as the number of edges connected to an observation node (edge degree) is only two. Consequently, the computations are much easier than those of maximum likelihood (ML) detection, which are similar to the belief propagation (BP) that is run over the fully connected bipartite graph. The link level performance for non-Gaussian input is evaluated via simulations, and the results show the validity of the proposed algorithms. We also customize the algorithm with Gaussian input assumption to obtain the Gaussian BP run over the two pairwise graphical models, and for the ring-type, we prove its convergence to the linear minimum mean square error (MMSE) estimates. Since the maximum a posterior (MAP) estimator for Gaussian input is equivalent to the linear MMSE estimator, it shows the optimality of the scheme for Gaussian input.

UR - http://www.scopus.com/inward/record.url?scp=84902970516&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902970516&partnerID=8YFLogxK

U2 - 10.1109/TVT.2013.2291245

DO - 10.1109/TVT.2013.2291245

M3 - Article

VL - 63

SP - 2363

EP - 2377

JO - IEEE Transactions on Vehicular Technology

JF - IEEE Transactions on Vehicular Technology

SN - 0018-9545

IS - 5

M1 - 6665044

ER -