### Abstract

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

Pages (from-to) | 1300-1307 |

Journal | IEEE Transactions on Communications |

Volume | 55 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2007 |

MoE publication type | A1 Journal article-refereed |

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### Keywords

- Linear equalizers
- Mean field inference
- Turbo receivers
- Variational optimization

### Cite this

*IEEE Transactions on Communications*,

*55*(7), 1300-1307. https://doi.org/10.1109/TCOMM.2007.900609

}

*IEEE Transactions on Communications*, vol. 55, no. 7, pp. 1300-1307. https://doi.org/10.1109/TCOMM.2007.900609

**Soft-input soft-output equalizers for turbo receivers : A statistical physics perspective.** / Nissilä, Mauri; Pasupathy, Subbarayan.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Soft-input soft-output equalizers for turbo receivers

T2 - A statistical physics perspective

AU - Nissilä, Mauri

AU - Pasupathy, Subbarayan

PY - 2007

Y1 - 2007

N2 - Many algorithms in signal processing and digital communications must deal with the problem of computing the probabilities of the hidden state variables given the observations, i.e., the inference problem, as well as with the problem of estimating the model parameters. Such an inference and estimation problem is encountered, for e.g., in adaptive turbo equalization/demodulation where soft information about the transmitted data symbols has to be inferred in the presence of the channel uncertainty, given the received signal samples and a information provided by the decoder. An exact inference algorithm computes the a probability (APP) values for all transmitted symbols, but the computation of APPs is known to be an NP-hard problem, thus, rendering this approach computationally prohibitive in most cases. In this paper, we show how many of the well-known low-complexity soft-input soft-output (SISO) equalizers, including the channel-matched filter-based linear SISO equalizers and minimum mean square error (MMSE) SISO equalizers, as well as the expectation-maximization (EM) algorithm-based SISO demodulators in the presence of the Rayleigh fading channel, can be formulated as solutions to a variational optimization problem. The variational optimization is a well-established methodology for low-complexity inference and estimation, originating from statistical physics. Importantly, the imposed variational optimization framework provides an interesting link between the APP demodulators and the linear SISO equalizers. Moreover, it provides a new set of insights into the structure and performance of these widely celebrated linear SISO equalizers while suggesting their fine tuning as well.

AB - Many algorithms in signal processing and digital communications must deal with the problem of computing the probabilities of the hidden state variables given the observations, i.e., the inference problem, as well as with the problem of estimating the model parameters. Such an inference and estimation problem is encountered, for e.g., in adaptive turbo equalization/demodulation where soft information about the transmitted data symbols has to be inferred in the presence of the channel uncertainty, given the received signal samples and a information provided by the decoder. An exact inference algorithm computes the a probability (APP) values for all transmitted symbols, but the computation of APPs is known to be an NP-hard problem, thus, rendering this approach computationally prohibitive in most cases. In this paper, we show how many of the well-known low-complexity soft-input soft-output (SISO) equalizers, including the channel-matched filter-based linear SISO equalizers and minimum mean square error (MMSE) SISO equalizers, as well as the expectation-maximization (EM) algorithm-based SISO demodulators in the presence of the Rayleigh fading channel, can be formulated as solutions to a variational optimization problem. The variational optimization is a well-established methodology for low-complexity inference and estimation, originating from statistical physics. Importantly, the imposed variational optimization framework provides an interesting link between the APP demodulators and the linear SISO equalizers. Moreover, it provides a new set of insights into the structure and performance of these widely celebrated linear SISO equalizers while suggesting their fine tuning as well.

KW - Linear equalizers

KW - Mean field inference

KW - Turbo receivers

KW - Variational optimization

U2 - 10.1109/TCOMM.2007.900609

DO - 10.1109/TCOMM.2007.900609

M3 - Article

VL - 55

SP - 1300

EP - 1307

JO - IEEE Transactions on Communications

JF - IEEE Transactions on Communications

SN - 0090-6778

IS - 7

ER -