### Abstract

This paper is concerned with the challenging and timely problem of joint channel estimation and equalization for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. The resulting algorithm is based on the space alternating generalized expectation maximization-maximum a posteriori probability (SAGE-MAP) technique which is particularly well suited to multicarrier signal formats. The algorithm is implemented in the time-domain which enables one to use the Gaussian approximation of the transmitted OFDM samples. Consequently, the averaging process of the nonpilot data symbols becomes analytically possible resulting in a feasible and computationally efficient channel estimation algorithm leading to a receiver structure that yields also an equalized output from which the data symbols are detected with excellent symbol error rate (SER) performance. Based on this Gaussian approximation the exact Bayesian Cramér Rao lower bound (CRLB) as well as the convergence rate of the algorithm are derived analytically. To reduce the computational complexity of the algorithm, discrete Legendre orthogonal basis functions are employed to represent the rapidly time-varying fading channel. It is shown that, depending on the normalized Doppler frequency, only a small number of expansion coefficients is sufficient to approximate the channel very well and there is no need to know the correlation function of the input signal. The computational complexity of the algorithm is shown to be ∼O(NL) per detected data symbol and per SAGE-MAP algorithm cycle where N is the number of OFDM subcarriers and L is the number of multipath components.

Original language | English (US) |
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Article number | 6188536 |

Pages (from-to) | 4236-4253 |

Number of pages | 18 |

Journal | IEEE Transactions on Signal Processing |

Volume | 60 |

Issue number | 8 |

DOIs | |

State | Published - Jul 23 2012 |

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Electrical and Electronic Engineering

### Keywords

- Basis expansion model (BEM)
- SAGE-MAP algorithm
- joint channel estimation and equalization
- orthogonal frequency-division multiplexing (OFDM)
- rapidly varying wireless channels

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## Cite this

*IEEE Transactions on Signal Processing*,

*60*(8), 4236-4253. [6188536]. https://doi.org/10.1109/TSP.2012.2195657