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## Research Article Low Complexity MLSE Equalization in Highly Dispersive Rayleigh Fading Channels

### Citations

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Error bounds for convolutional codes and an asymptotically optimum decoding algorithm
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(Show Context)
Citation Context ... to mitigate the effect of ISI, in order to produce reliable estimates of the transmitted information. In the early 1970s, Forney proposed an optimal equalizer [1] based on the Viterbi algorithm (VA) =-=[2]-=-, able to optimally estimate the most likely sequence of transmitted symbols. The VA was proposed a few years before for the optimal decoding of convolutional error-correction codes. Shortly afterward... |

1572 |
Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate”,
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Citation Context ...stimate the most likely sequence of transmitted symbols. The VA was proposed a few years before for the optimal decoding of convolutional error-correction codes. Shortly afterward, the BCJR algorithm =-=[3]-=-, also known as the maximum a posterior probability (MAP) algorithm, was proposed, able to produce optimal estimates of the transmitted symbols. The development of an optimal MLSE equalizer was an ext... |

1125 | Wireless Communications,
- Goldsmith
- 2005
(Show Context)
Citation Context ...uared error (MMSE) equalizer and the decision feedback equalizer (DFE) [5–7], and variants thereof, are often used in systems where the channel memory is too long for optimal equalizers to be applied =-=[4, 8]-=-. Orthogonal frequency division multiplexing 2 EURASIP Journal on Advances in Signal Processing (OFDM) modulation can be used to completely eliminate the effect of multipath on the system performance ... |

644 |
Neural computations of decisions in optimization problems.
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Citation Context ...he performance of the proposed equalizer in sparse channels, are presented) is developed for equalization in M-QAMmodulated systems with extremely long memory. Using the Hopfield neural network (HNN) =-=[15]-=- as foundation, this equalizer has complexity quadratic in the data block length and approximately independent of the channel memory length for practical systems. (In practical systems, the data block... |

178 |
OFDM Wireless LANs: A Theoretical and Practical Guide.
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Citation Context ...ver, is very susceptible to Doppler shift, suffers from a large peak-toaverage power ratio (PAPR), and requires large overhead when the channel delay spread is very long compared to the symbol period =-=[4, 9]-=-. There are a number of communication channels that have extremely long memory. Among these are underwater channels (UAC), magnetic recording channels (MRC), power line channels (PLC), and microwave c... |

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75 | Improved models for the generation of multiple uncorrelated Rayleigh fading waveforms
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(Show Context)
Citation Context ...00 MHz, the symbol period is Ts = 3.7μs and the relative speed between the transmitter and receiver is v = 3 km/h. To simulate the fading effect on each tap, the Rayleigh fading simulator proposed in =-=[33]-=- is used to generate uncorrelated fading vectors. Least Squares (LS) channel estimation is used to determine an estimate for the CIR, in order to include the effect of imperfect channel state informat... |

61 |
Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference
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(Show Context)
Citation Context ...qualization is necessary in the receiver to mitigate the effect of ISI, in order to produce reliable estimates of the transmitted information. In the early 1970s, Forney proposed an optimal equalizer =-=[1]-=- based on the Viterbi algorithm (VA) [2], able to optimally estimate the most likely sequence of transmitted symbols. The VA was proposed a few years before for the optimal decoding of convolutional e... |

45 | Digital Baseband Transmission and Recording. - Bergmans - 1996 |

44 |
Markov chain monte carlo algorithms for CDMA and MIMO communication systems,”
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(Show Context)
Citation Context ...N in escaping less optimal basins of attraction simulated annealing and asynchronous neuron updates are often used. Markov Chain Monte Carlo (MCMC) algorithms are used together with Gibbs sampling in =-=[32]-=- to aid optimization in the solution space. According to [32], however, the complexity of the MCMC algorithms may become prohibitive due to the so called stalling problem, which result from low probab... |

32 | Equalization concepts for EDGE
- Gerstacker, Schober
- 2002
(Show Context)
Citation Context ...e of N symbols chosen from an alphabet D containing M complex symbols, rk is the kth received symbol, nk is the kth Gaussian noise sample N (0, σ2), and hj is the jth coefficient of the estimated CIR =-=[7]-=-. The equalizer is responsible for reversing the effect of the channel on the transmitted symbols in order to produce the sequence of transmitted symbols with maximum confidence. To optimally estimate... |

22 | A maximum-likelihood sequence estimator with decision-feedback equalization - Lee, Hill - 1977 |

14 | The soft-feedback equalizer for turbo equalization of highly dispersive channels - Lopes, Barry - 2006 |

14 | Channel-estimation-based adaptive equalization of underwater acoustic signals - Stojanovic, Freitag, et al. - 1999 |

14 |
Artificial Neural Networks
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- 1988
(Show Context)
Citation Context ... electronic components, they constructed a recurrent neural network and derived the characteristic equations for the network. The set of equations that describe the dynamics of the system is given by =-=[26]-=- Ci dui dt = −ui τi + ∑ j Ti j Ii + Ii, Vi = g(ui), (1) with Tij , the dots, describing the interconnections between the amplifiers, u1–uN the input voltages of the amplifiers, V1–VN the output voltag... |

8 | Improved MMSE estimation of correlated MIMO channels using 16 EURASIP Journal on Advances in Signal Processing a structured correlation estimator - Czink, Matz, et al. - 2005 |

8 |
A neural network for detection of signals in communication
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(Show Context)
Citation Context ... the cross-correlation matrix of the complex received symbols such that XH = XTi − jXTq = Xi + jXq, (7) implying that it is Hermitian. Therefore, XTi = Xi is symmetric and XTq = −Xq is skew symmetric =-=[22, 23]-=-. By using the symmetric properties of X, (5) can be expanded and rewritten as L = −1 2 [ sTi Xisi + s T q Xqsq + 2s T q Xqsi ] − [ sTi Ii + s T q Iq ] , (8) which in turn can be rewritten as [22–25] ... |

5 | Improved spatialtemporal equalization for EDGE: a fast selective-direction MMSE timing recovery algorithm and two-stage soft-output equalizer - Zeng, Ye, et al. - 2001 |

4 | Low complexity MMSE-SIC equalizer employing time-domain recursion for OFDM systems - Park, Whang, et al. - 2008 |

4 | Neural network implementation for an adaptive maximum-likelihood receiver - Provence - 1988 |

3 | Low complexity iterative MLSE equalization of M-QAM signals in extremely long Rayleigh fading channels
- Myburgh, Olivier
- 2009
(Show Context)
Citation Context ...unt of interfering symbols in these channels, the use of conventional optimal equalization algorithms are infeasible. In this paper, a low complexity MLSE equalizer, first presented by the authors in =-=[14]-=-, (in this paper, the M-QAM HNN MLSE equalizer in [14] is presented in much greater detail. Here, a complete complexity analysis, as well as the performance of the proposed equalizer in sparse channel... |

2 | An improved algorithm of MMSE multiuser detection for CDMA systems - Dayong, Yang, et al. - 2005 |

2 | Improved adaptive MMSE detector for downlink multi-cell MIMO signals - Zhou, Zhou - 2004 |

2 | Low complexity code multiplexed pilot aided adaptive MMSE equalizerfor CDMA systems - Rong, Guangqiu - 2008 |

2 |
Maximum likelihood sequence estimation of communication signals by a Hopfield neural network
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(Show Context)
Citation Context ... the cross-correlation matrix of the complex received symbols such that XH = XTi − jXTq = Xi + jXq, (7) implying that it is Hermitian. Therefore, XTi = Xi is symmetric and XTq = −Xq is skew symmetric =-=[22, 23]-=-. By using the symmetric properties of X, (5) can be expanded and rewritten as L = −1 2 [ sTi Xisi + s T q Xqsq + 2s T q Xqsi ] − [ sTi Ii + s T q Iq ] , (8) which in turn can be rewritten as [22–25] ... |

2 | A neural network communication equalizer with optimized solution capability - Chen, Sheu, et al. - 1996 |

2 |
Paralleled hardware annealing in multilevel Hopfield neural networks for optimal solutions
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(Show Context)
Citation Context ...he modulation alphabet size. A multilevel decision function can be realized by adding several bipolar decision functions and shifting each by a predetermined value, and scaling the result accordingly =-=[29, 30]-=-. To realize a Q-level decision function for use in an −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 g( u ) −30 −20 −10 0 10 20 30 u φ = 10 φ = 15 φ = 20 Figure 4: The four-level decision function. M-QAM... |

2 |
Search of optimal solutions in multi-level neural networks
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(Show Context)
Citation Context ...he modulation alphabet size. A multilevel decision function can be realized by adding several bipolar decision functions and shifting each by a predetermined value, and scaling the result accordingly =-=[29, 30]-=-. To realize a Q-level decision function for use in an −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 g( u ) −30 −20 −10 0 10 20 30 u φ = 10 φ = 15 φ = 20 Figure 4: The four-level decision function. M-QAM... |