## 2016 |

## Journal Articles |

Vázquez, Manuel; Míguez, Joaquín On the Use of the Channel Second-Order Statistics in MMSE Receivers for Time- and Frequency-Selective MIMO Transmission Systems (Journal Article) EURASIP Journal on Wireless Communications and Networking, 2016 (1), 2016. (Abstract | Links | BibTeX | Tags: data estimation, Joint channel, Journal, MIMO, MMSE, Second-order statistics) @article{Vazquez2016, title = {On the Use of the Channel Second-Order Statistics in MMSE Receivers for Time- and Frequency-Selective MIMO Transmission Systems}, author = {Vázquez, Manuel A. and Míguez, Joaquín}, url = {http://jwcn.eurasipjournals.springeropen.com/articles/10.1186/s13638-016-0768-0}, doi = {10.1186/s13638-016-0768-0}, year = {2016}, date = {2016-12-01}, journal = {EURASIP Journal on Wireless Communications and Networking}, volume = {2016}, number = {1}, publisher = {Springer International Publishing}, abstract = {Equalization of unknown frequency- and time-selective multiple input multiple output (MIMO) channels is often carried out by means of decision feedback receivers. These consist of a channel estimator and a linear filter (for the estimation of the transmitted symbols), interconnected by a feedback loop through a symbol-wise threshold detector. The linear filter is often a minimum mean square error (MMSE) filter, and its mathematical expression involves second-order statistics (SOS) of the channel, which are usually ignored by simply assuming that the channel is a known (deterministic) parameter given by an estimate thereof. This appears to be suboptimal and in this work we investigate the kind of performance gains that can be expected when the MMSE equalizer is obtained using SOS of the channel process. As a result, we demonstrate that improvements of several dBs in the signal-to-noise ratio needed to achieve a prescribed symbol error rate are possible.}, keywords = {data estimation, Joint channel, Journal, MIMO, MMSE, Second-order statistics}, pubstate = {published}, tppubtype = {article} } Equalization of unknown frequency- and time-selective multiple input multiple output (MIMO) channels is often carried out by means of decision feedback receivers. These consist of a channel estimator and a linear filter (for the estimation of the transmitted symbols), interconnected by a feedback loop through a symbol-wise threshold detector. The linear filter is often a minimum mean square error (MMSE) filter, and its mathematical expression involves second-order statistics (SOS) of the channel, which are usually ignored by simply assuming that the channel is a known (deterministic) parameter given by an estimate thereof. This appears to be suboptimal and in this work we investigate the kind of performance gains that can be expected when the MMSE equalizer is obtained using SOS of the channel process. As a result, we demonstrate that improvements of several dBs in the signal-to-noise ratio needed to achieve a prescribed symbol error rate are possible. |

## 2014 |

## Journal Articles |

Yang,; Durisi, Giuseppe; Koch, Tobias; Polyanskiy, Yury Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength (Journal Article) IEEE Transactions on Information Theory, 60 (7), pp. 4232–4265, 2014, ISSN: 0018-9448. (Abstract | Links | BibTeX | Tags: channel dispersion, Decoding, error probability, finite blocklength regime, MIMO, MIMO channel, outage probability, quasi-static fading channel, Rayleigh channels, Receivers, Transmitters) @article{Yang2014, title = {Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength}, author = {Yang, W. and Durisi, Giuseppe and Koch, Tobias and Polyanskiy, Yury}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6802432 http://arxiv.org/abs/1311.2012}, issn = {0018-9448}, year = {2014}, date = {2014-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {60}, number = {7}, pages = {4232--4265}, publisher = {IEEE}, abstract = {This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output fading channels, with and without channel state information at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular 1 $,times,$ 2 single-input multiple-output Rician fading channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared with the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds.}, keywords = {channel dispersion, Decoding, error probability, finite blocklength regime, MIMO, MIMO channel, outage probability, quasi-static fading channel, Rayleigh channels, Receivers, Transmitters}, pubstate = {published}, tppubtype = {article} } This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output fading channels, with and without channel state information at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular 1 $,times,$ 2 single-input multiple-output Rician fading channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared with the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds. |

Cespedes, Javier; Olmos, Pablo; Sanchez-Fernandez, Matilde; Perez-Cruz, Fernando Expectation Propagation Detection for High-order High-dimensional MIMO Systems (Journal Article) IEEE Transactions on Communications, PP (99), pp. 1–1, 2014, ISSN: 0090-6778. (Abstract | Links | BibTeX | Tags: Approximation methods, computational complexity, Detectors, MIMO, Signal to noise ratio, Vectors) @article{Cespedes2014, title = {Expectation Propagation Detection for High-order High-dimensional MIMO Systems}, author = {Cespedes, Javier and Olmos, Pablo M. and Sanchez-Fernandez, Matilde and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6841617}, issn = {0090-6778}, year = {2014}, date = {2014-01-01}, journal = {IEEE Transactions on Communications}, volume = {PP}, number = {99}, pages = {1--1}, abstract = {Modern communications systems use multiple-input multiple-output (MIMO) and high-order QAM constellations for maximizing spectral efficiency. However, as the number of antennas and the order of the constellation grow, the design of efficient and low-complexity MIMO receivers possesses big technical challenges. For example, symbol detection can no longer rely on maximum likelihood detection or sphere-decoding methods, as their complexity increases exponentially with the number of transmitters/receivers. In this paper, we propose a low-complexity high-accuracy MIMO symbol detector based on the Expectation Propagation (EP) algorithm. EP allows approximating iteratively at polynomial-time the posterior distribution of the transmitted symbols. We also show that our EP MIMO detector outperforms classic and state-of-the-art solutions reducing the symbol error rate at a reduced computational complexity.}, keywords = {Approximation methods, computational complexity, Detectors, MIMO, Signal to noise ratio, Vectors}, pubstate = {published}, tppubtype = {article} } Modern communications systems use multiple-input multiple-output (MIMO) and high-order QAM constellations for maximizing spectral efficiency. However, as the number of antennas and the order of the constellation grow, the design of efficient and low-complexity MIMO receivers possesses big technical challenges. For example, symbol detection can no longer rely on maximum likelihood detection or sphere-decoding methods, as their complexity increases exponentially with the number of transmitters/receivers. In this paper, we propose a low-complexity high-accuracy MIMO symbol detector based on the Expectation Propagation (EP) algorithm. EP allows approximating iteratively at polynomial-time the posterior distribution of the transmitted symbols. We also show that our EP MIMO detector outperforms classic and state-of-the-art solutions reducing the symbol error rate at a reduced computational complexity. |

## Inproceedings |

Yang, Wei; Durisi, Giuseppe; Koch, Tobias; Polyanskiy, Yury Dispersion of Quasi-Static MIMO Fading Channels via Stokes' Theorem (Inproceeding) 2014 IEEE International Symposium on Information Theory, pp. 2072–2076, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4. (Abstract | Links | BibTeX | Tags: channel capacity, differential form integration, Dispersion, Fading, fading channels, fading distribution, integration, Manifolds, Measurement, MIMO, MIMO communication, quasistatic MIMO fading channels dispersion, quasistatic multiple-input multiple-output fading, radio transmitters, Random variables, Stoke Theorem, transmitter) @inproceedings{Yang2014b, title = {Dispersion of Quasi-Static MIMO Fading Channels via Stokes' Theorem}, author = {Yang, Wei and Durisi, Giuseppe and Koch, Tobias and Polyanskiy, Yury}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6875198}, isbn = {978-1-4799-5186-4}, year = {2014}, date = {2014-01-01}, booktitle = {2014 IEEE International Symposium on Information Theory}, pages = {2072--2076}, publisher = {IEEE}, address = {Honolulu}, abstract = {This paper analyzes the channel dispersion of quasi-static multiple-input multiple-output fading channels with no channel state information at the transmitter. We show that the channel dispersion is zero under mild conditions on the fading distribution. The proof of our result is based on Stokes' theorem, which deals with the integration of differential forms on manifolds with boundary.}, keywords = {channel capacity, differential form integration, Dispersion, Fading, fading channels, fading distribution, integration, Manifolds, Measurement, MIMO, MIMO communication, quasistatic MIMO fading channels dispersion, quasistatic multiple-input multiple-output fading, radio transmitters, Random variables, Stoke Theorem, transmitter}, pubstate = {published}, tppubtype = {inproceedings} } This paper analyzes the channel dispersion of quasi-static multiple-input multiple-output fading channels with no channel state information at the transmitter. We show that the channel dispersion is zero under mild conditions on the fading distribution. The proof of our result is based on Stokes' theorem, which deals with the integration of differential forms on manifolds with boundary. |

Valera, Isabel; Ruiz, Francisco; Perez-Cruz, Fernando Infinite Factorial Unbounded Hidden Markov Model for Blind Multiuser Channel Estimation (Inproceeding) 2014 4th International Workshop on Cognitive Information Processing (CIP), pp. 1–6, IEEE, Copenhagen, 2014, ISBN: 978-1-4799-3696-0. (Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian non parametrics, Bayesian nonparametric models, blind multiuser channel estimation, Channel estimation, degrees of freedom, detection problems, dispersive channel model, generative model, Hidden Markov models, HMM, inference algorithm, infinite factorial unbounded hidden Markov model, Markov chain Monte Carlo, Markov processes, MIMO, MIMO communication, MIMO communication systems, multiple-input multiple-output (MIMO), multiple-input multiple-output communication syste, receiver performance, Receivers, Signal to noise ratio, Transmitters, unbounded channel length, unbounded number, user detection) @inproceedings{Valera2014a, title = {Infinite Factorial Unbounded Hidden Markov Model for Blind Multiuser Channel Estimation}, author = {Valera, Isabel and Ruiz, Francisco J. R. and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6844506}, isbn = {978-1-4799-3696-0}, year = {2014}, date = {2014-01-01}, booktitle = {2014 4th International Workshop on Cognitive Information Processing (CIP)}, pages = {1--6}, publisher = {IEEE}, address = {Copenhagen}, abstract = {Bayesian nonparametric models allow solving estimation and detection problems with an unbounded number of degrees of freedom. In multiuser multiple-input multiple-output (MIMO) communication systems we might not know the number of active users and the channel they face, and assuming maximal scenarios (maximum number of transmitters and maximum channel length) might degrade the receiver performance. In this paper, we propose a Bayesian nonparametric prior and its associated inference algorithm, which is able to detect an unbounded number of users with an unbounded channel length. This generative model provides the dispersive channel model for each user and a probabilistic estimate for each transmitted symbol in a fully blind manner, i.e., without the need of pilot (training) symbols.}, keywords = {Bayes methods, Bayesian non parametrics, Bayesian nonparametric models, blind multiuser channel estimation, Channel estimation, degrees of freedom, detection problems, dispersive channel model, generative model, Hidden Markov models, HMM, inference algorithm, infinite factorial unbounded hidden Markov model, Markov chain Monte Carlo, Markov processes, MIMO, MIMO communication, MIMO communication systems, multiple-input multiple-output (MIMO), multiple-input multiple-output communication syste, receiver performance, Receivers, Signal to noise ratio, Transmitters, unbounded channel length, unbounded number, user detection}, pubstate = {published}, tppubtype = {inproceedings} } Bayesian nonparametric models allow solving estimation and detection problems with an unbounded number of degrees of freedom. In multiuser multiple-input multiple-output (MIMO) communication systems we might not know the number of active users and the channel they face, and assuming maximal scenarios (maximum number of transmitters and maximum channel length) might degrade the receiver performance. In this paper, we propose a Bayesian nonparametric prior and its associated inference algorithm, which is able to detect an unbounded number of users with an unbounded channel length. This generative model provides the dispersive channel model for each user and a probabilistic estimate for each transmitted symbol in a fully blind manner, i.e., without the need of pilot (training) symbols. |

Cespedes, Javier; Olmos, Pablo; Sanchez-Fernandez, Matilde; Perez-Cruz, Fernando Improved Performance of LDPC-Coded MIMO Systems with EP-based Soft-Decisions (Inproceeding) 2014 IEEE International Symposium on Information Theory, pp. 1997–2001, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4. (Abstract | Links | BibTeX | Tags: Approximation algorithms, Approximation methods, approximation theory, Channel Coding, channel decoder, communication complexity, complexity, Complexity theory, Detectors, encoding scheme, EP soft bit probability, EP-based soft decision, error statistics, expectation propagation, expectation-maximisation algorithm, expectation-propagation algorithm, Gaussian approximation, Gaussian channels, LDPC, LDPC coded MIMO system, Low Complexity receiver, MIMO, MIMO communication, MIMO communication systems, MIMO receiver, modern communication system, multiple input multiple output, parity check codes, per-antenna soft bit probability, posterior marginalization problem, posterior probability computation, QAM constellation, Quadrature amplitude modulation, radio receivers, signaling, spectral analysis, spectral efficiency maximization, symbol detection, telecommunication signalling, Vectors) @inproceedings{Cespedes2014b, title = {Improved Performance of LDPC-Coded MIMO Systems with EP-based Soft-Decisions}, author = {Cespedes, Javier and Olmos, Pablo M. and Sanchez-Fernandez, Matilde and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6875183}, isbn = {978-1-4799-5186-4}, year = {2014}, date = {2014-01-01}, booktitle = {2014 IEEE International Symposium on Information Theory}, pages = {1997--2001}, publisher = {IEEE}, address = {Honolulu}, abstract = {Modern communications systems use efficient encoding schemes, multiple-input multiple-output (MIMO) and high-order QAM constellations for maximizing spectral efficiency. However, as the dimensions of the system grow, the design of efficient and low-complexity MIMO receivers possesses technical challenges. Symbol detection can no longer rely on conventional approaches for posterior probability computation due to complexity. Marginalization of this posterior to obtain per-antenna soft-bit probabilities to be fed to a channel decoder is computationally challenging when realistic signaling is used. In this work, we propose to use Expectation Propagation (EP) algorithm to provide an accurate low-complexity Gaussian approximation to the posterior, easily solving the posterior marginalization problem. EP soft-bit probabilities are used in an LDPC-coded MIMO system, achieving outstanding performance improvement compared to similar approaches in the literature for low-complexity LDPC MIMO decoding.}, keywords = {Approximation algorithms, Approximation methods, approximation theory, Channel Coding, channel decoder, communication complexity, complexity, Complexity theory, Detectors, encoding scheme, EP soft bit probability, EP-based soft decision, error statistics, expectation propagation, expectation-maximisation algorithm, expectation-propagation algorithm, Gaussian approximation, Gaussian channels, LDPC, LDPC coded MIMO system, Low Complexity receiver, MIMO, MIMO communication, MIMO communication systems, MIMO receiver, modern communication system, multiple input multiple output, parity check codes, per-antenna soft bit probability, posterior marginalization problem, posterior probability computation, QAM constellation, Quadrature amplitude modulation, radio receivers, signaling, spectral analysis, spectral efficiency maximization, symbol detection, telecommunication signalling, Vectors}, pubstate = {published}, tppubtype = {inproceedings} } Modern communications systems use efficient encoding schemes, multiple-input multiple-output (MIMO) and high-order QAM constellations for maximizing spectral efficiency. However, as the dimensions of the system grow, the design of efficient and low-complexity MIMO receivers possesses technical challenges. Symbol detection can no longer rely on conventional approaches for posterior probability computation due to complexity. Marginalization of this posterior to obtain per-antenna soft-bit probabilities to be fed to a channel decoder is computationally challenging when realistic signaling is used. In this work, we propose to use Expectation Propagation (EP) algorithm to provide an accurate low-complexity Gaussian approximation to the posterior, easily solving the posterior marginalization problem. EP soft-bit probabilities are used in an LDPC-coded MIMO system, achieving outstanding performance improvement compared to similar approaches in the literature for low-complexity LDPC MIMO decoding. |

## 2013 |

## Inproceedings |

Durisi, Giuseppe; Tarable, Alberto; Koch, Tobias On the Multiplexing Gain of MIMO Microwave Backhaul Links Affected by Phase Noise (Inproceeding) 2013 IEEE International Conference on Communications (ICC), pp. 3209–3214, IEEE, Budapest, 2013, ISSN: 1550-3607. (Abstract | Links | BibTeX | Tags: AWGN channels, marginal distribution, Microwave antennas, microwave links, MIMO, MIMO AWGN channel, MIMO communication, MIMO microwave backhaul links, MIMO multiplexing gain, multiple-input multiple-output AWGN channel, Multiplexing, Phase noise, phase-noise processes, Receivers, Signal to noise ratio, strong phase noise, transmit signal, Transmitters) @inproceedings{Durisi2013, title = {On the Multiplexing Gain of MIMO Microwave Backhaul Links Affected by Phase Noise}, author = {Durisi, Giuseppe and Tarable, Alberto and Koch, Tobias}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6655038}, issn = {1550-3607}, year = {2013}, date = {2013-01-01}, booktitle = {2013 IEEE International Conference on Communications (ICC)}, pages = {3209--3214}, publisher = {IEEE}, address = {Budapest}, abstract = {We consider a multiple-input multiple-output (MIMO) AWGN channel affected by phase noise. Focusing on the 2 × 2 case, we show that no MIMO multiplexing gain is to be expected when the phase-noise processes at each antenna are independent, memoryless in time, and with uniform marginal distribution over [0, 2$pi$] (strong phase noise), and when the transmit signal is isotropically distributed on the real plane. The scenario of independent phase-noise processes across antennas is relevant for microwave backhaul links operating in the 20-40 GHz range.}, keywords = {AWGN channels, marginal distribution, Microwave antennas, microwave links, MIMO, MIMO AWGN channel, MIMO communication, MIMO microwave backhaul links, MIMO multiplexing gain, multiple-input multiple-output AWGN channel, Multiplexing, Phase noise, phase-noise processes, Receivers, Signal to noise ratio, strong phase noise, transmit signal, Transmitters}, pubstate = {published}, tppubtype = {inproceedings} } We consider a multiple-input multiple-output (MIMO) AWGN channel affected by phase noise. Focusing on the 2 × 2 case, we show that no MIMO multiplexing gain is to be expected when the phase-noise processes at each antenna are independent, memoryless in time, and with uniform marginal distribution over [0, 2$pi$] (strong phase noise), and when the transmit signal is isotropically distributed on the real plane. The scenario of independent phase-noise processes across antennas is relevant for microwave backhaul links operating in the 20-40 GHz range. |

## 2011 |

## Journal Articles |

Vazquez, Manuel; Miguez, Joaquin A Per-Survivor Processing Receiver for MIMO Transmission Systems With One Unknown Channel Order Per Output (Journal Article) IEEE Transactions on Vehicular Technology, 60 (9), pp. 4415–4426, 2011, ISSN: 0018-9545. (Abstract | Links | BibTeX | Tags: Channel estimation, communication channel, Complexity theory, dynamic programming, frequency-selective MIMO channel, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channel impulse response coefficient, MIMO communication, MIMO transmission system, multipath channels, mutiple-input–multiple-output (MIMO), per-survivor processing receiver, Receiving antennas, Signal processing algorithms, time-selective MIMO channel, Transmitting antennas, Viterbi algorithm) @article{Vazquez2011, title = {A Per-Survivor Processing Receiver for MIMO Transmission Systems With One Unknown Channel Order Per Output}, author = {Vazquez, Manuel A. and Miguez, Joaquin}, url = {http://www.tsc.uc3m.es/~jmiguez/papers/P31_2011_A Per-Survivor Processing Receiver for MIMO Transmission Systems With One Unknown Channel Order Per Output.pdf http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6032763}, issn = {0018-9545}, year = {2011}, date = {2011-01-01}, journal = {IEEE Transactions on Vehicular Technology}, volume = {60}, number = {9}, pages = {4415--4426}, abstract = {The order of a communications channel is the length of its impulse response. Recently, several works have tackled the problem of estimating the order of a frequency-selective multiple-input-multiple-output (MIMO) channel. However, all of them consider a single order, despite the fact that a MIMO channel comprises several subchannels (specifically, as many as the number of inputs times the number of outputs), each one possibly with its own order. In this paper, we introduce an algorithm for maximum-likelihood sequence detection (MLSD) in frequency- and time-selective MIMO channels that incorporates full estimation of the MIMO channel impulse response (CIR) coefficients, including one channel order per output. Simulation results following the analytical derivation of the algorithm suggest that the proposed receiver can achieve significant improvements in performance when transmitting through a MIMO channel that effectively comprises subchannels of different lengths.}, keywords = {Channel estimation, communication channel, Complexity theory, dynamic programming, frequency-selective MIMO channel, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channel impulse response coefficient, MIMO communication, MIMO transmission system, multipath channels, mutiple-input–multiple-output (MIMO), per-survivor processing receiver, Receiving antennas, Signal processing algorithms, time-selective MIMO channel, Transmitting antennas, Viterbi algorithm}, pubstate = {published}, tppubtype = {article} } The order of a communications channel is the length of its impulse response. Recently, several works have tackled the problem of estimating the order of a frequency-selective multiple-input-multiple-output (MIMO) channel. However, all of them consider a single order, despite the fact that a MIMO channel comprises several subchannels (specifically, as many as the number of inputs times the number of outputs), each one possibly with its own order. In this paper, we introduce an algorithm for maximum-likelihood sequence detection (MLSD) in frequency- and time-selective MIMO channels that incorporates full estimation of the MIMO channel impulse response (CIR) coefficients, including one channel order per output. Simulation results following the analytical derivation of the algorithm suggest that the proposed receiver can achieve significant improvements in performance when transmitting through a MIMO channel that effectively comprises subchannels of different lengths. |

## Inproceedings |

Goparaju,; Calderbank,; Carson,; Rodrigues, Miguel; Perez-Cruz, Fernando When to Add Another Dimension when Communicating over MIMO Channels (Inproceeding) 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3100–3103, IEEE, Prague, 2011, ISSN: 1520-6149. (Abstract | Links | BibTeX | Tags: divide and conquer approach, divide and conquer methods, error probability, error rate, error statistics, Gaussian channels, Lattices, Manganese, MIMO, MIMO channel, MIMO communication, multiple input multiple output Gaussian channel, Mutual information, optimal power allocation, power allocation, power constraint, receive filter, Resource management, Signal to noise ratio, signal-to-noise ratio, transmit filter, Upper bound) @inproceedings{Goparaju2011, title = {When to Add Another Dimension when Communicating over MIMO Channels}, author = {Goparaju, S. and Calderbank, A. R. and Carson, W. R. and Rodrigues, Miguel R. D. and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5946351}, issn = {1520-6149}, year = {2011}, date = {2011-01-01}, booktitle = {2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pages = {3100--3103}, publisher = {IEEE}, address = {Prague}, abstract = {This paper introduces a divide and conquer approach to the design of transmit and receive filters for communication over a Multiple Input Multiple Output (MIMO) Gaussian channel subject to an average power constraint. It involves conversion to a set of parallel scalar channels, possibly with very different gains, followed by coding per sub-channel (i.e. over time) rather than coding across sub-channels (i.e. over time and space). The loss in performance is negligible at high signal-to-noise ratio (SNR) and not significant at medium SNR. The advantages are reduction in signal processing complexity and greater insight into the SNR thresholds at which a channel is first allocated power. This insight is a consequence of formulating the optimal power allocation in terms of an upper bound on error rate that is determined by parameters of the input lattice such as the minimum distance and kissing number. The resulting thresholds are given explicitly in terms of these lattice parameters. By contrast, when the optimization problem is phrased in terms of maximizing mutual information, the solution is mercury waterfilling, and the thresholds are implicit.}, keywords = {divide and conquer approach, divide and conquer methods, error probability, error rate, error statistics, Gaussian channels, Lattices, Manganese, MIMO, MIMO channel, MIMO communication, multiple input multiple output Gaussian channel, Mutual information, optimal power allocation, power allocation, power constraint, receive filter, Resource management, Signal to noise ratio, signal-to-noise ratio, transmit filter, Upper bound}, pubstate = {published}, tppubtype = {inproceedings} } This paper introduces a divide and conquer approach to the design of transmit and receive filters for communication over a Multiple Input Multiple Output (MIMO) Gaussian channel subject to an average power constraint. It involves conversion to a set of parallel scalar channels, possibly with very different gains, followed by coding per sub-channel (i.e. over time) rather than coding across sub-channels (i.e. over time and space). The loss in performance is negligible at high signal-to-noise ratio (SNR) and not significant at medium SNR. The advantages are reduction in signal processing complexity and greater insight into the SNR thresholds at which a channel is first allocated power. This insight is a consequence of formulating the optimal power allocation in terms of an upper bound on error rate that is determined by parameters of the input lattice such as the minimum distance and kissing number. The resulting thresholds are given explicitly in terms of these lattice parameters. By contrast, when the optimization problem is phrased in terms of maximizing mutual information, the solution is mercury waterfilling, and the thresholds are implicit. |

Asyhari, Taufiq; Koch, Tobias; i Fabregas, Albert Guillen Nearest Neighbour Decoding and Pilot-Aided Channel Estimation in Stationary Gaussian Flat-Fading Channels (Inproceeding) 2011 IEEE International Symposium on Information Theory Proceedings, pp. 2786–2790, IEEE, St. Petersburg, 2011, ISSN: 2157-8095. (Abstract | Links | BibTeX | Tags: Channel estimation, Decoding, Fading, fading channels, Gaussian channels, MIMO, MIMO communication, MISO, multiple-input multiple-output, nearest neighbour decoding, noncoherent multiple-input single-output, pilot-aided channel estimation, Receiving antennas, Signal to noise ratio, signal-to-noise ratio, SNR, stationary Gaussian flat-fading channels, Wireless communication) @inproceedings{Asyhari2011, title = {Nearest Neighbour Decoding and Pilot-Aided Channel Estimation in Stationary Gaussian Flat-Fading Channels}, author = {Asyhari, A. Taufiq and Koch, Tobias and Fabregas, Albert Guillen i}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6034081}, issn = {2157-8095}, year = {2011}, date = {2011-01-01}, booktitle = {2011 IEEE International Symposium on Information Theory Proceedings}, pages = {2786--2790}, publisher = {IEEE}, address = {St. Petersburg}, abstract = {We study the information rates of non-coherent, stationary, Gaussian, multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbour decoding and pilot-aided channel estimation. In particular, we analyse the behaviour of these achievable rates in the limit as the signal-to-noise ratio (SNR) tends to infinity. We demonstrate that nearest neighbour decoding and pilot-aided channel estimation achieves the capacity pre-log-which is defined as the limiting ratio of the capacity to the logarithm of SNR as the SNR tends to infinity-of non-coherent multiple-input single-output (MISO) flat-fading channels, and it achieves the best so far known lower bound on the capacity pre-log of non-coherent MIMO flat-fading channels.}, keywords = {Channel estimation, Decoding, Fading, fading channels, Gaussian channels, MIMO, MIMO communication, MISO, multiple-input multiple-output, nearest neighbour decoding, noncoherent multiple-input single-output, pilot-aided channel estimation, Receiving antennas, Signal to noise ratio, signal-to-noise ratio, SNR, stationary Gaussian flat-fading channels, Wireless communication}, pubstate = {published}, tppubtype = {inproceedings} } We study the information rates of non-coherent, stationary, Gaussian, multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbour decoding and pilot-aided channel estimation. In particular, we analyse the behaviour of these achievable rates in the limit as the signal-to-noise ratio (SNR) tends to infinity. We demonstrate that nearest neighbour decoding and pilot-aided channel estimation achieves the capacity pre-log-which is defined as the limiting ratio of the capacity to the logarithm of SNR as the SNR tends to infinity-of non-coherent multiple-input single-output (MISO) flat-fading channels, and it achieves the best so far known lower bound on the capacity pre-log of non-coherent MIMO flat-fading channels. |

Asyhari, Taufiq; Koch, Tobias; i Fabregas, Albert Guillen Nearest Neighbour Decoding with Pilot-Assisted Channel Estimation for Fading Multiple-Access Channels (Inproceeding) 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 1686–1693, IEEE, Allerton, 2011, ISBN: 978-1-4577-1818-2. (Abstract | Links | BibTeX | Tags: Channel estimation, Decoding, Fading, fading channels, fading multiple-access channels, MIMO, MIMO communication, multi-access systems, multiple-input multiple-output channel, nearest-neighbour decoding, noncoherent MIMO fading MAC channel, pilot-assisted channel estimation, Receiving antennas, Signal to noise ratio, signal-to-noise ratio, Time division multiple access, Vectors) @inproceedings{Asyhari2011a, title = {Nearest Neighbour Decoding with Pilot-Assisted Channel Estimation for Fading Multiple-Access Channels}, author = {Asyhari, A. Taufiq and Koch, Tobias and i Fabregas, Albert Guillen}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6120371}, isbn = {978-1-4577-1818-2}, year = {2011}, date = {2011-01-01}, booktitle = {2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)}, pages = {1686--1693}, publisher = {IEEE}, address = {Allerton}, abstract = {This paper studies a noncoherent multiple-input multiple-output (MIMO) fading multiple-access channel (MAC). The rate region that is achievable with nearest neighbour decoding and pilot-assisted channel estimation is analysed and the corresponding pre-log region, defined as the limiting ratio of the rate region to the logarithm of the signal-to-noise ratio (SNR) as the SNR tends to infinity, is determined.}, keywords = {Channel estimation, Decoding, Fading, fading channels, fading multiple-access channels, MIMO, MIMO communication, multi-access systems, multiple-input multiple-output channel, nearest-neighbour decoding, noncoherent MIMO fading MAC channel, pilot-assisted channel estimation, Receiving antennas, Signal to noise ratio, signal-to-noise ratio, Time division multiple access, Vectors}, pubstate = {published}, tppubtype = {inproceedings} } This paper studies a noncoherent multiple-input multiple-output (MIMO) fading multiple-access channel (MAC). The rate region that is achievable with nearest neighbour decoding and pilot-assisted channel estimation is analysed and the corresponding pre-log region, defined as the limiting ratio of the rate region to the logarithm of the signal-to-noise ratio (SNR) as the SNR tends to infinity, is determined. |

## 2010 |

## Journal Articles |

Perez-Cruz, Fernando; Rodrigues, Miguel; Verdu, Sergio MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation (Journal Article) IEEE Transactions on Information Theory, 56 (3), pp. 1070–1084, 2010, ISSN: 0018-9448. (Abstract | Links | BibTeX | Tags: Collaborative work, Equations, fixed-point equation, Gaussian channels, Gaussian noise channels, Gaussian processes, Government, Interference, linear precoding, matrix algebra, mean square error methods, mercury-waterfilling algorithm, MIMO, MIMO communication, MIMO Gaussian channel, minimum mean-square error, minimum mean-square error (MMSE), multiple-input-multiple-output channel, multiple-input–multiple-output (MIMO) systems, Mutual information, nondiagonal precoding matrix, optimal linear precoder, optimal power allocation policy, optimal precoding, optimum power allocation, Phase shift keying, precoding, Quadrature amplitude modulation, Telecommunications, waterfilling) @article{Perez-Cruz2010a, title = {MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation}, author = {Perez-Cruz, Fernando and Rodrigues, Miguel R. D. and Verdu, Sergio}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5429131}, issn = {0018-9448}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {56}, number = {3}, pages = {1070--1084}, abstract = {In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input-multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean-square error (MMSE). The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For non-Gaussian inputs, a nondiagonal precoding matrix in general increases the information transmission rate, even for parallel noninteracting channels. Whenever precoding is precluded, the optimal power allocation policy also satisfies a fixed-point equation; we put forth a generalization of the mercury/waterfilling algorithm, previously proposed for parallel noninterfering channels, in which the mercury level accounts not only for the non-Gaussian input distributions, but also for the interference among inputs.}, keywords = {Collaborative work, Equations, fixed-point equation, Gaussian channels, Gaussian noise channels, Gaussian processes, Government, Interference, linear precoding, matrix algebra, mean square error methods, mercury-waterfilling algorithm, MIMO, MIMO communication, MIMO Gaussian channel, minimum mean-square error, minimum mean-square error (MMSE), multiple-input-multiple-output channel, multiple-input–multiple-output (MIMO) systems, Mutual information, nondiagonal precoding matrix, optimal linear precoder, optimal power allocation policy, optimal precoding, optimum power allocation, Phase shift keying, precoding, Quadrature amplitude modulation, Telecommunications, waterfilling}, pubstate = {published}, tppubtype = {article} } In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input-multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean-square error (MMSE). The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For non-Gaussian inputs, a nondiagonal precoding matrix in general increases the information transmission rate, even for parallel noninteracting channels. Whenever precoding is precluded, the optimal power allocation policy also satisfies a fixed-point equation; we put forth a generalization of the mercury/waterfilling algorithm, previously proposed for parallel noninterfering channels, in which the mercury level accounts not only for the non-Gaussian input distributions, but also for the interference among inputs. |

## Inproceedings |

Vazquez, Manuel; Miguez, Joaquin Adaptive MLSD for MIMO Transmission Systems with Unknown Subchannel Orders (Inproceeding) 2010 7th International Symposium on Wireless Communication Systems, pp. 451–455, IEEE, York, 2010, ISSN: 2154-0217. (Abstract | Links | BibTeX | Tags: Bit error rate, Channel estimation, channel impulse response, computational complexity, Estimation, frequency-selective multiple-input multiple-output, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO communication, MIMO transmission systems, multiple subchannels, per survivor processing methodology, pilot data, Receivers, Signal to noise ratio, Time frequency analysis, time selective MIMO channel) @inproceedings{Vazquez2010, title = {Adaptive MLSD for MIMO Transmission Systems with Unknown Subchannel Orders}, author = {Vazquez, Manuel A. and Miguez, Joaquin}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5624335}, issn = {2154-0217}, year = {2010}, date = {2010-01-01}, booktitle = {2010 7th International Symposium on Wireless Communication Systems}, pages = {451--455}, publisher = {IEEE}, address = {York}, abstract = {In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This very frequently leads to overestimating the channel order, which increases the computational complexity of any maximum likelihood sequence detection (MLSD) algorithm, while degrading its performance at the same time. The problem of estimating a single channel order for a time and frequency selective MIMO channel has recently been tackled. However, this is an idealized approach, since a MIMO channel comprises multiple subchannels (as many as the number of inputs times that of the outputs), each of them possibly with its own order. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including one channel order per output. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and it is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver.}, keywords = {Bit error rate, Channel estimation, channel impulse response, computational complexity, Estimation, frequency-selective multiple-input multiple-output, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO communication, MIMO transmission systems, multiple subchannels, per survivor processing methodology, pilot data, Receivers, Signal to noise ratio, Time frequency analysis, time selective MIMO channel}, pubstate = {published}, tppubtype = {inproceedings} } In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This very frequently leads to overestimating the channel order, which increases the computational complexity of any maximum likelihood sequence detection (MLSD) algorithm, while degrading its performance at the same time. The problem of estimating a single channel order for a time and frequency selective MIMO channel has recently been tackled. However, this is an idealized approach, since a MIMO channel comprises multiple subchannels (as many as the number of inputs times that of the outputs), each of them possibly with its own order. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including one channel order per output. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and it is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver. |

## 2008 |

## Inproceedings |

Vazquez, Manuel; Miguez, Joaquin A Per-Survivor Processing Algorithm for Maximum Likelihood Equalization of MIMO Channels with Unknown Order (Inproceeding) 2008 International ITG Workshop on Smart Antennas, pp. 387–391, IEEE, Vienna, 2008, ISBN: 978-1-4244-1756-8. (Abstract | Links | BibTeX | Tags: Channel estimation, channel impulse response, computational complexity, Computer science education, Computer Simulation, Degradation, Frequency, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood equalization, maximum likelihood estimation, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channels, MIMO communication, per-survivor processing algorithm, time-selective channels, Transmitting antennas) @inproceedings{Vazquez2008, title = {A Per-Survivor Processing Algorithm for Maximum Likelihood Equalization of MIMO Channels with Unknown Order}, author = {Vazquez, Manuel A. and Miguez, Joaquin}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=4475587}, isbn = {978-1-4244-1756-8}, year = {2008}, date = {2008-01-01}, booktitle = {2008 International ITG Workshop on Smart Antennas}, pages = {387--391}, publisher = {IEEE}, address = {Vienna}, abstract = {In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This possibly means overestimating the channel order, and is not desirable since the computational complexity of maximum likelihood sequence detection (MLSD) in frequency-selective channels grows exponentially with the channel order. In addition to that, the higher the channel order considered, the more the number of channel coefficients that need to be estimated from the same set of observations. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including its order. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver}, keywords = {Channel estimation, channel impulse response, computational complexity, Computer science education, Computer Simulation, Degradation, Frequency, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood equalization, maximum likelihood estimation, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channels, MIMO communication, per-survivor processing algorithm, time-selective channels, Transmitting antennas}, pubstate = {published}, tppubtype = {inproceedings} } In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This possibly means overestimating the channel order, and is not desirable since the computational complexity of maximum likelihood sequence detection (MLSD) in frequency-selective channels grows exponentially with the channel order. In addition to that, the higher the channel order considered, the more the number of channel coefficients that need to be estimated from the same set of observations. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including its order. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver |

Perez-Cruz, Fernando; Rodrigues, Miguel; Verdu, Sergio Optimal Precoding for Digital Subscriber Lines (Inproceeding) 2008 IEEE International Conference on Communications, pp. 1200–1204, IEEE, Beijing, 2008, ISBN: 978-1-4244-2075-9. (Abstract | Links | BibTeX | Tags: Bit error rate, channel matrix diagonalization, Communications Society, Computer science, digital subscriber lines, DSL, Equations, fixed-point equation, Gaussian channels, least mean squares methods, linear codes, matrix algebra, MIMO, MIMO communication, MIMO Gaussian channel, minimum mean squared error method, MMSE, multiple-input multiple-output communication, Mutual information, optimal linear precoder, precoding, Telecommunications, Telephony) @inproceedings{Perez-Cruz2008a, title = {Optimal Precoding for Digital Subscriber Lines}, author = {Perez-Cruz, Fernando and Rodrigues, Miguel R. D. and Verdu, Sergio}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4533270}, isbn = {978-1-4244-2075-9}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE International Conference on Communications}, pages = {1200--1204}, publisher = {IEEE}, address = {Beijing}, abstract = {We determine the linear precoding policy that maximizes the mutual information for general multiple-input multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean squared error (MMSE). The optimal linear precoder can be computed by means of a fixed- point equation as a function of the channel and the input constellation. We show that diagonalizing the channel matrix does not maximize the information transmission rate for nonGaussian inputs. A full precoding matrix may significantly increase the information transmission rate, even for parallel non-interacting channels. We illustrate the application of our results to typical Gigabit DSL systems.}, keywords = {Bit error rate, channel matrix diagonalization, Communications Society, Computer science, digital subscriber lines, DSL, Equations, fixed-point equation, Gaussian channels, least mean squares methods, linear codes, matrix algebra, MIMO, MIMO communication, MIMO Gaussian channel, minimum mean squared error method, MMSE, multiple-input multiple-output communication, Mutual information, optimal linear precoder, precoding, Telecommunications, Telephony}, pubstate = {published}, tppubtype = {inproceedings} } We determine the linear precoding policy that maximizes the mutual information for general multiple-input multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean squared error (MMSE). The optimal linear precoder can be computed by means of a fixed- point equation as a function of the channel and the input constellation. We show that diagonalizing the channel matrix does not maximize the information transmission rate for nonGaussian inputs. A full precoding matrix may significantly increase the information transmission rate, even for parallel non-interacting channels. We illustrate the application of our results to typical Gigabit DSL systems. |

Rodrigues, Miguel; Perez-Cruz, Fernando; Verdu, Sergio Multiple-Input Multiple-Output Gaussian Channels: Optimal Covariance for Non-Gaussian Inputs (Inproceeding) 2008 IEEE Information Theory Workshop, pp. 445–449, IEEE, Porto, 2008, ISBN: 978-1-4244-2269-2. (Abstract | Links | BibTeX | Tags: Binary phase shift keying, covariance matrices, Covariance matrix, deterministic MIMO Gaussian channel, fixed-point equation, Gaussian channels, Gaussian noise, Information rates, intersymbol interference, least mean squares methods, Magnetic recording, mercury-waterfilling power allocation policy, MIMO, MIMO communication, minimum mean-squared error, MMSE, MMSE matrix, multiple-input multiple-output system, Multiple-Input Multiple-Output Systems, Mutual information, Optimal Input Covariance, Optimization, Telecommunications) @inproceedings{Rodrigues2008, title = {Multiple-Input Multiple-Output Gaussian Channels: Optimal Covariance for Non-Gaussian Inputs}, author = {Rodrigues, Miguel R. D. and Perez-Cruz, Fernando and Verdu, Sergio}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4578704}, isbn = {978-1-4244-2269-2}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE Information Theory Workshop}, pages = {445--449}, publisher = {IEEE}, address = {Porto}, abstract = {We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleo-utput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr.}, keywords = {Binary phase shift keying, covariance matrices, Covariance matrix, deterministic MIMO Gaussian channel, fixed-point equation, Gaussian channels, Gaussian noise, Information rates, intersymbol interference, least mean squares methods, Magnetic recording, mercury-waterfilling power allocation policy, MIMO, MIMO communication, minimum mean-squared error, MMSE, MMSE matrix, multiple-input multiple-output system, Multiple-Input Multiple-Output Systems, Mutual information, Optimal Input Covariance, Optimization, Telecommunications}, pubstate = {published}, tppubtype = {inproceedings} } We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleo-utput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr. |

Vazquez, Manuel; Miguez, Joaquin A Per-Survivor Processing Algorithm for Maximum Likelihood Equalization of MIMO Channels with Unknown Order (Inproceeding) 2008 International ITG Workshop on Smart Antennas, pp. 387–391, IEEE, Vienna, 2008, ISBN: 978-1-4244-1756-8. (Abstract | Links | BibTeX | Tags: Channel estimation, channel impulse response, computational complexity, Computer science education, Computer Simulation, Degradation, Frequency, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood equalization, maximum likelihood estimation, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channels, MIMO communication, per-survivor processing algorithm, time-selective channels, Transmitting antennas) @inproceedings{Vazquez2008a, title = {A Per-Survivor Processing Algorithm for Maximum Likelihood Equalization of MIMO Channels with Unknown Order}, author = {Vazquez, Manuel A. and Miguez, Joaquin}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4475587}, isbn = {978-1-4244-1756-8}, year = {2008}, date = {2008-01-01}, booktitle = {2008 International ITG Workshop on Smart Antennas}, pages = {387--391}, publisher = {IEEE}, address = {Vienna}, abstract = {In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This possibly means overestimating the channel order, and is not desirable since the computational complexity of maximum likelihood sequence detection (MLSD) in frequency-selective channels grows exponentially with the channel order. In addition to that, the higher the channel order considered, the more the number of channel coefficients that need to be estimated from the same set of observations. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including its order. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver.}, keywords = {Channel estimation, channel impulse response, computational complexity, Computer science education, Computer Simulation, Degradation, Frequency, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood equalization, maximum likelihood estimation, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channels, MIMO communication, per-survivor processing algorithm, time-selective channels, Transmitting antennas}, pubstate = {published}, tppubtype = {inproceedings} } In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This possibly means overestimating the channel order, and is not desirable since the computational complexity of maximum likelihood sequence detection (MLSD) in frequency-selective channels grows exponentially with the channel order. In addition to that, the higher the channel order considered, the more the number of channel coefficients that need to be estimated from the same set of observations. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including its order. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver. |