## 2015 |

## Inproceedings |

Valera, Isabel ; Ruiz, Francisco J R; Svensson, Lennart ; Perez-Cruz, Fernando A Bayesian Nonparametric Approach for Blind Multiuser Channel Estimation Inproceedings 2015 23rd European Signal Processing Conference (EUSIPCO), pp. 2766–2770, IEEE, Nice, 2015, ISBN: 978-0-9928-6263-3. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian nonparametric, communication systems, factorial HMM, Hidden Markov models, machine-to-machine, multiuser communication, Receiving antennas, Signal to noise ratio, Transmitters @inproceedings{Valera2015, title = {A Bayesian Nonparametric Approach for Blind Multiuser Channel Estimation}, author = {Valera, Isabel and Ruiz, Francisco J. R. and Svensson, Lennart and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7362888 http://www.eurasip.org/Proceedings/Eusipco/Eusipco2015/papers/1570096659.pdf}, doi = {10.1109/EUSIPCO.2015.7362888}, isbn = {978-0-9928-6263-3}, year = {2015}, date = {2015-08-01}, booktitle = {2015 23rd European Signal Processing Conference (EUSIPCO)}, pages = {2766--2770}, publisher = {IEEE}, address = {Nice}, abstract = {In many modern multiuser communication systems, users are allowed to enter and leave the system at any given time. Thus, the number of active users is an unknown and time-varying parameter, and the performance of the system depends on how accurately this parameter is estimated over time. We address the problem of blind joint channel parameter and data estimation in a multiuser communication channel in which the number of transmitters is not known. For that purpose, we develop a Bayesian nonparametric model based on the Markov Indian buffet process and an inference algorithm that makes use of slice sampling and particle Gibbs with ancestor sampling. Our experimental results show that the proposed approach can effectively recover the data-generating process for a wide range of scenarios.}, keywords = {Bayes methods, Bayesian nonparametric, communication systems, factorial HMM, Hidden Markov models, machine-to-machine, multiuser communication, Receiving antennas, Signal to noise ratio, Transmitters}, pubstate = {published}, tppubtype = {inproceedings} } In many modern multiuser communication systems, users are allowed to enter and leave the system at any given time. Thus, the number of active users is an unknown and time-varying parameter, and the performance of the system depends on how accurately this parameter is estimated over time. We address the problem of blind joint channel parameter and data estimation in a multiuser communication channel in which the number of transmitters is not known. For that purpose, we develop a Bayesian nonparametric model based on the Markov Indian buffet process and an inference algorithm that makes use of slice sampling and particle Gibbs with ancestor sampling. Our experimental results show that the proposed approach can effectively recover the data-generating process for a wide range of scenarios. |

## 2014 |

## Journal Articles |

Alvarado, Alex ; Brannstrom, Fredrik ; Agrell, Erik ; Koch, Tobias High-SNR Asymptotics of Mutual Information for Discrete Constellations With Applications to BICM Journal Article IEEE Transactions on Information Theory, 60 (2), pp. 1061–1076, 2014, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: additive white Gaussian noise channel, Anti-Gray code, bit-interleaved coded modulation, discrete constellations, Entropy, Gray code, high-SNR asymptotics, IP networks, Labeling, minimum-mean square error, Modulation, Mutual information, Signal to noise ratio, Vectors @article{Alvarado2014, title = {High-SNR Asymptotics of Mutual Information for Discrete Constellations With Applications to BICM}, author = {Alvarado, Alex and Brannstrom, Fredrik and Agrell, Erik and Koch, Tobias}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6671479 http://www.tsc.uc3m.es/~koch/files/IEEE_TIT_60%282%29.pdf}, issn = {0018-9448}, year = {2014}, date = {2014-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {60}, number = {2}, pages = {1061--1076}, abstract = {Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR.}, keywords = {additive white Gaussian noise channel, Anti-Gray code, bit-interleaved coded modulation, discrete constellations, Entropy, Gray code, high-SNR asymptotics, IP networks, Labeling, minimum-mean square error, Modulation, Mutual information, Signal to noise ratio, Vectors}, pubstate = {published}, tppubtype = {article} } Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR. |

Pastore A, ; Koch, Tobias ; Fonollosa, Javier Rodriguez A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information Journal Article IEEE Transactions on Information Theory, 60 (7), pp. 4266–4285, 2014, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: channel capacity, COMONSENS, DEIPRO, Entropy, Fading, fading channels, flat fading, imperfect channel-state information, MobileNET, Mutual information, OTOSiS, Random variables, Receivers, Signal to noise ratio, Upper bound @article{Pastore2014a, title = {A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information}, author = {Pastore, A, and Koch, Tobias and Fonollosa, Javier Rodriguez}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6832779 http://www.tsc.uc3m.es/~koch/files/IEEE_TIT_60(7).pdf http://arxiv.org/pdf/1301.6120.pdf}, issn = {0018-9448}, year = {2014}, date = {2014-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {60}, number = {7}, pages = {4266--4285}, publisher = {IEEE}, abstract = {As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input (X) with power (P) and by upper-bounding the conditional entropy (h(X|Y,hat Ħ)) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating (X) from ((Y,hat Ħ)) . We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input (X) as the sum of two independent Gaussian variables (X_1) and (X_2) and by applying Médard\'s lower bound first to bound the mutual information between (X_1) and (Y) while treating (X_2) as noise, and by applying it a second time to the mutual information between (X_2) and (Y) while assuming (X_1) to be known, we obtain a capacity lower bound that is strictly larger than Médard\'s lower bound. We then generalize this approach to an arbi- rary number (L) of layers, where (X) is expressed as the sum of (L) independent Gaussian random variables of respective variances (P_ell ) , (ell = 1,dotsc ,L) summing up to (P) . Among all such rate-splitting bounds, we determine the supremum over power allocations (P_ell ) and total number of layers (L) . This supremum is achieved for (L rightarrow infty ) and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error (H-hat Ħ) tends to zero as the SNR tends to infinity.}, keywords = {channel capacity, COMONSENS, DEIPRO, Entropy, Fading, fading channels, flat fading, imperfect channel-state information, MobileNET, Mutual information, OTOSiS, Random variables, Receivers, Signal to noise ratio, Upper bound}, pubstate = {published}, tppubtype = {article} } As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input (X) with power (P) and by upper-bounding the conditional entropy (h(X|Y,hat Ħ)) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating (X) from ((Y,hat Ħ)) . We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input (X) as the sum of two independent Gaussian variables (X_1) and (X_2) and by applying Médard's lower bound first to bound the mutual information between (X_1) and (Y) while treating (X_2) as noise, and by applying it a second time to the mutual information between (X_2) and (Y) while assuming (X_1) to be known, we obtain a capacity lower bound that is strictly larger than Médard's lower bound. We then generalize this approach to an arbi- rary number (L) of layers, where (X) is expressed as the sum of (L) independent Gaussian random variables of respective variances (P_ell ) , (ell = 1,dotsc ,L) summing up to (P) . Among all such rate-splitting bounds, we determine the supremum over power allocations (P_ell ) and total number of layers (L) . This supremum is achieved for (L rightarrow infty ) and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error (H-hat Ħ) tends to zero as the SNR tends to infinity. |

Cespedes, Javier ; Olmos, Pablo M; 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 |

Djuric, Petar M; Bravo-Santos, Ángel M Cooperative Mesh Networks with EGC Detectors Inproceedings 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp. 225–228, IEEE, A Coruña, 2014, ISBN: 978-1-4799-1481-4. Abstract | Links | BibTeX | Tags: binary modulations, cooperative communications, cooperative mesh networks, decode and forward communication, decode and forward relays, Detectors, EGC detectors, Gaussian processes, Joints, Manganese, Mesh networks, multihop multibranch networks, Nakagami channels, Nakagami distribution, Nakagami distributions, relay networks (telecommunication), Signal to noise ratio, zero mean Gaussian @inproceedings{Djuric2014, title = {Cooperative Mesh Networks with EGC Detectors}, author = {Djuric, Petar M. and Bravo-Santos, Ángel M.}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6882381}, isbn = {978-1-4799-1481-4}, year = {2014}, date = {2014-01-01}, booktitle = {2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM)}, pages = {225--228}, publisher = {IEEE}, address = {A Coruña}, abstract = {We address mesh networks with decode and forward relays that use binary modulations. For detection, the nodes employ equal gain combining, which is appealing because it is very easy to implement. We study the performance of these networks and compare it to that of multihop multi-branch networks. We also examine the performance of the networks when both the number of groups and total number of nodes are fixed but the topology of the network varies. We demonstrate the performance of these networks where the channels are modeled with Nakagami distributions and the noise is zero mean Gaussian}, keywords = {binary modulations, cooperative communications, cooperative mesh networks, decode and forward communication, decode and forward relays, Detectors, EGC detectors, Gaussian processes, Joints, Manganese, Mesh networks, multihop multibranch networks, Nakagami channels, Nakagami distribution, Nakagami distributions, relay networks (telecommunication), Signal to noise ratio, zero mean Gaussian}, pubstate = {published}, tppubtype = {inproceedings} } We address mesh networks with decode and forward relays that use binary modulations. For detection, the nodes employ equal gain combining, which is appealing because it is very easy to implement. We study the performance of these networks and compare it to that of multihop multi-branch networks. We also examine the performance of the networks when both the number of groups and total number of nodes are fixed but the topology of the network varies. We demonstrate the performance of these networks where the channels are modeled with Nakagami distributions and the noise is zero mean Gaussian |

Koch, Tobias On the Dither-Quantized Gaussian Channel at Low SNR Inproceedings 2014 IEEE International Symposium on Information Theory, pp. 186–190, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4. Abstract | Links | BibTeX | Tags: Additive noise, channel capacity, dither quantized Gaussian channel, Entropy, Gaussian channels, low signal-to-noise-ratio, low-SNR asymptotic capacity, peak power constraint, peak-and-average-power-limited Gaussian channel, Quantization (signal), Signal to noise ratio @inproceedings{Koch2014, title = {On the Dither-Quantized Gaussian Channel at Low SNR}, author = {Koch, Tobias}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6874820}, isbn = {978-1-4799-5186-4}, year = {2014}, date = {2014-01-01}, booktitle = {2014 IEEE International Symposium on Information Theory}, pages = {186--190}, publisher = {IEEE}, address = {Honolulu}, abstract = {We study the capacity of the peak-and-average-power-limited Gaussian channel when its output is quantized using a dithered, infinite-level, uniform quantizer of step size $Delta$. We focus on the low signal-to-noise-ratio (SNR) regime, where communication at low spectral efficiencies takes place. We show that, when the peak-power constraint is absent, the low-SNR asymptotic capacity is equal to that of the unquantized channel irrespective of $Delta$. We further derive an expression for the low-SNR asymptotic capacity for finite peak-to-average-power ratios and evaluate it in the low- and high-resolution limit. We demonstrate that, in this case, the low-SNR asymptotic capacity converges to that of the unquantized channel when $Delta$ tends to zero, and it tends to zero when $Delta$ tends to infinity.}, keywords = {Additive noise, channel capacity, dither quantized Gaussian channel, Entropy, Gaussian channels, low signal-to-noise-ratio, low-SNR asymptotic capacity, peak power constraint, peak-and-average-power-limited Gaussian channel, Quantization (signal), Signal to noise ratio}, pubstate = {published}, tppubtype = {inproceedings} } We study the capacity of the peak-and-average-power-limited Gaussian channel when its output is quantized using a dithered, infinite-level, uniform quantizer of step size $Delta$. We focus on the low signal-to-noise-ratio (SNR) regime, where communication at low spectral efficiencies takes place. We show that, when the peak-power constraint is absent, the low-SNR asymptotic capacity is equal to that of the unquantized channel irrespective of $Delta$. We further derive an expression for the low-SNR asymptotic capacity for finite peak-to-average-power ratios and evaluate it in the low- and high-resolution limit. We demonstrate that, in this case, the low-SNR asymptotic capacity converges to that of the unquantized channel when $Delta$ tends to zero, and it tends to zero when $Delta$ tends to infinity. |

Valera, Isabel ; Ruiz, Francisco J R; Perez-Cruz, Fernando Infinite Factorial Unbounded Hidden Markov Model for Blind Multiuser Channel Estimation Inproceedings 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. |

## 2013 |

## Journal Articles |

Koch, Tobias ; Kramer, Gerhard On Noncoherent Fading Relay Channels at High Signal-to-Noise Ratio Journal Article IEEE Transactions on Information Theory, 59 (4), pp. 2221–2241, 2013, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: channel capacity, Channel models, Fading, fading channels, MIMO communication, multiple-input single-output fading channel statis, noncoherent, noncoherent fading relay channel capacity, radio receiver, radio receivers, radio transmitter, radio transmitters, Receivers, relay channels, relay networks (telecommunication), Relays, Signal to noise ratio, signal-to-noise ratio, SNR, statistics, time selective, Transmitters, Upper bound @article{Koch2013a, title = {On Noncoherent Fading Relay Channels at High Signal-to-Noise Ratio}, author = {Koch, Tobias and Kramer, Gerhard}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6378474}, issn = {0018-9448}, year = {2013}, date = {2013-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {59}, number = {4}, pages = {2221--2241}, abstract = {The capacity of noncoherent regular-fading relay channels is studied where all terminals are aware of the fading statistics but not of their realizations. It is shown that if the fading coefficient of the channel between the transmitter and the receiver can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high signal-to-noise ratio (SNR), the relay does not increase capacity. It is further shown that if the fading coefficient of the channel between the transmitter and the relay can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high SNR, one can achieve communication rates that are within one bit of the capacity of the multiple-input single-output fading channel that results when the transmitter and the relay can cooperate.}, keywords = {channel capacity, Channel models, Fading, fading channels, MIMO communication, multiple-input single-output fading channel statis, noncoherent, noncoherent fading relay channel capacity, radio receiver, radio receivers, radio transmitter, radio transmitters, Receivers, relay channels, relay networks (telecommunication), Relays, Signal to noise ratio, signal-to-noise ratio, SNR, statistics, time selective, Transmitters, Upper bound}, pubstate = {published}, tppubtype = {article} } The capacity of noncoherent regular-fading relay channels is studied where all terminals are aware of the fading statistics but not of their realizations. It is shown that if the fading coefficient of the channel between the transmitter and the receiver can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high signal-to-noise ratio (SNR), the relay does not increase capacity. It is further shown that if the fading coefficient of the channel between the transmitter and the relay can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high SNR, one can achieve communication rates that are within one bit of the capacity of the multiple-input single-output fading channel that results when the transmitter and the relay can cooperate. |

## Inproceedings |

Alvarado, Alex ; Brannstrom, Fredrik ; Agrell, Erik ; Koch, Tobias High-SNR Asymptotics of Mutual Information for Discrete Constellations Inproceedings 2013 IEEE International Symposium on Information Theory, pp. 2274–2278, IEEE, Istanbul, 2013, ISSN: 2157-8095. Abstract | Links | BibTeX | Tags: AWGN channels, discrete constellations, Entropy, Fading, Gaussian Q-function, high-SNR asymptotics, IP networks, least mean squares methods, minimum mean-square error, MMSE, Mutual information, scalar additive white Gaussian noise channel, Signal to noise ratio, signal-to-noise ratio, Upper bound @inproceedings{Alvarado2013b, title = {High-SNR Asymptotics of Mutual Information for Discrete Constellations}, author = {Alvarado, Alex and Brannstrom, Fredrik and Agrell, Erik and Koch, Tobias}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6620631}, issn = {2157-8095}, year = {2013}, date = {2013-01-01}, booktitle = {2013 IEEE International Symposium on Information Theory}, pages = {2274--2278}, publisher = {IEEE}, address = {Istanbul}, abstract = {The asymptotic behavior of the mutual information (MI) at high signal-to-noise ratio (SNR) for discrete constellations over the scalar additive white Gaussian noise channel is studied. Exact asymptotic expressions for the MI for arbitrary one-dimensional constellations and input distributions are presented in the limit as the SNR tends to infinity. Asymptotics of the minimum mean-square error (MMSE) are also developed. It is shown that for any input distribution, the MI and the MMSE have an asymptotic behavior proportional to a Gaussian Q-function, whose argument depends on the minimum Euclidean distance of the constellation and the SNR. Closed-form expressions for the coefficients of these Q-functions are calculated.}, keywords = {AWGN channels, discrete constellations, Entropy, Fading, Gaussian Q-function, high-SNR asymptotics, IP networks, least mean squares methods, minimum mean-square error, MMSE, Mutual information, scalar additive white Gaussian noise channel, Signal to noise ratio, signal-to-noise ratio, Upper bound}, pubstate = {published}, tppubtype = {inproceedings} } The asymptotic behavior of the mutual information (MI) at high signal-to-noise ratio (SNR) for discrete constellations over the scalar additive white Gaussian noise channel is studied. Exact asymptotic expressions for the MI for arbitrary one-dimensional constellations and input distributions are presented in the limit as the SNR tends to infinity. Asymptotics of the minimum mean-square error (MMSE) are also developed. It is shown that for any input distribution, the MI and the MMSE have an asymptotic behavior proportional to a Gaussian Q-function, whose argument depends on the minimum Euclidean distance of the constellation and the SNR. Closed-form expressions for the coefficients of these Q-functions are calculated. |

Durisi, Giuseppe ; Tarable, Alberto ; Koch, Tobias On the Multiplexing Gain of MIMO Microwave Backhaul Links Affected by Phase Noise Inproceedings 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. |

## 2012 |

## Inproceedings |

Koch, Tobias ; Martinez, Alfonso ; Guillen i Fabregas, Albert The Capacity Loss of Dense Constellations Inproceedings 2012 IEEE International Symposium on Information Theory Proceedings, pp. 572–576, IEEE, Cambridge, MA, 2012, ISSN: 2157-8095. Abstract | Links | BibTeX | Tags: capacity loss, channel capacity, Constellation diagram, dense constellations, Entropy, general complex-valued additive-noise channels, high signal-to-noise ratio, loss 1.53 dB, power loss, Quadrature amplitude modulation, Random variables, signal constellations, Signal processing, Signal to noise ratio, square signal constellations, Upper bound @inproceedings{Koch2012, title = {The Capacity Loss of Dense Constellations}, author = {Koch, Tobias and Martinez, Alfonso and Guillen i Fabregas, Albert}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6283482}, issn = {2157-8095}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE International Symposium on Information Theory Proceedings}, pages = {572--576}, publisher = {IEEE}, address = {Cambridge, MA}, abstract = {We determine the loss in capacity incurred by using signal constellations with a bounded support over general complex-valued additive-noise channels for suitably high signal-to-noise ratio. Our expression for the capacity loss recovers the power loss of 1.53 dB for square signal constellations.}, keywords = {capacity loss, channel capacity, Constellation diagram, dense constellations, Entropy, general complex-valued additive-noise channels, high signal-to-noise ratio, loss 1.53 dB, power loss, Quadrature amplitude modulation, Random variables, signal constellations, Signal processing, Signal to noise ratio, square signal constellations, Upper bound}, pubstate = {published}, tppubtype = {inproceedings} } We determine the loss in capacity incurred by using signal constellations with a bounded support over general complex-valued additive-noise channels for suitably high signal-to-noise ratio. Our expression for the capacity loss recovers the power loss of 1.53 dB for square signal constellations. |

Durisi, Giuseppe ; Koch, Tobias ; Polyanskiy, Yury Diversity Versus Channel Knowledge at Finite Block-Length Inproceedings 2012 IEEE Information Theory Workshop, pp. 572–576, IEEE, Lausanne, 2012, ISBN: 978-1-4673-0223-4. Abstract | Links | BibTeX | Tags: Approximation methods, block error probability, channel coherence time, Channel estimation, channel knowledge, Coherence, diversity, diversity reception, error statistics, Fading, finite block-length, maximal achievable rate, noncoherent setting, Rayleigh block-fading channels, Rayleigh channels, Receivers, Signal to noise ratio, Upper bound @inproceedings{Durisi2012, title = {Diversity Versus Channel Knowledge at Finite Block-Length}, author = {Durisi, Giuseppe and Koch, Tobias and Polyanskiy, Yury}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6404740}, isbn = {978-1-4673-0223-4}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE Information Theory Workshop}, pages = {572--576}, publisher = {IEEE}, address = {Lausanne}, abstract = {We study the maximal achievable rate R*(n, ∈) for a given block-length n and block error probability o over Rayleigh block-fading channels in the noncoherent setting and in the finite block-length regime. Our results show that for a given block-length and error probability, R*(n, ∈) is not monotonic in the channel's coherence time, but there exists a rate maximizing coherence time that optimally trades between diversity and cost of estimating the channel.}, keywords = {Approximation methods, block error probability, channel coherence time, Channel estimation, channel knowledge, Coherence, diversity, diversity reception, error statistics, Fading, finite block-length, maximal achievable rate, noncoherent setting, Rayleigh block-fading channels, Rayleigh channels, Receivers, Signal to noise ratio, Upper bound}, pubstate = {published}, tppubtype = {inproceedings} } We study the maximal achievable rate R*(n, ∈) for a given block-length n and block error probability o over Rayleigh block-fading channels in the noncoherent setting and in the finite block-length regime. Our results show that for a given block-length and error probability, R*(n, ∈) is not monotonic in the channel's coherence time, but there exists a rate maximizing coherence time that optimally trades between diversity and cost of estimating the channel. |

## 2011 |

## Inproceedings |

Koch, Tobias ; Lapidoth, Amos Asymmetric Quantizers are Better at Low SNR Inproceedings 2011 IEEE International Symposium on Information Theory Proceedings, pp. 2592–2596, IEEE, St. Petersburg, 2011, ISSN: 2157-8095. Abstract | Links | BibTeX | Tags: asymmetric one-bit quantizer, asymmetric signal constellations, channel capacity, Channel Coding, Constellation diagram, Decoding, discrete-time average-power-limited Gaussian chann, Gaussian channels, quantization, Signal to noise ratio, signal-to-noise ratio, SNR, spread spectrum communication, spread-spectrum communications, ultra wideband communication, ultrawideband communications, Upper bound @inproceedings{Koch2011, title = {Asymmetric Quantizers are Better at Low SNR}, author = {Koch, Tobias and Lapidoth, Amos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6034037}, issn = {2157-8095}, year = {2011}, date = {2011-01-01}, booktitle = {2011 IEEE International Symposium on Information Theory Proceedings}, pages = {2592--2596}, publisher = {IEEE}, address = {St. Petersburg}, abstract = {We study the behavior of channel capacity when a one-bit quantizer is employed at the output of the discrete-time average-power-limited Gaussian channel. We focus on the low signal-to-noise ratio regime, where communication at very low spectral efficiencies takes place, as in Spread-Spectrum and Ultra-Wideband communications. It is well known that, in this regime, a symmetric one-bit quantizer reduces capacity by 2/$pi$, which translates to a power loss of approximately two decibels. Here we show that if an asymmetric one-bit quantizer is employed, and if asymmetric signal constellations are used, then these two decibels can be recovered in full.}, keywords = {asymmetric one-bit quantizer, asymmetric signal constellations, channel capacity, Channel Coding, Constellation diagram, Decoding, discrete-time average-power-limited Gaussian chann, Gaussian channels, quantization, Signal to noise ratio, signal-to-noise ratio, SNR, spread spectrum communication, spread-spectrum communications, ultra wideband communication, ultrawideband communications, Upper bound}, pubstate = {published}, tppubtype = {inproceedings} } We study the behavior of channel capacity when a one-bit quantizer is employed at the output of the discrete-time average-power-limited Gaussian channel. We focus on the low signal-to-noise ratio regime, where communication at very low spectral efficiencies takes place, as in Spread-Spectrum and Ultra-Wideband communications. It is well known that, in this regime, a symmetric one-bit quantizer reduces capacity by 2/$pi$, which translates to a power loss of approximately two decibels. Here we show that if an asymmetric one-bit quantizer is employed, and if asymmetric signal constellations are used, then these two decibels can be recovered in full. |

Goparaju, S; Calderbank, A R; Carson, W R; Rodrigues, Miguel R D; Perez-Cruz, Fernando When to Add Another Dimension when Communicating over MIMO Channels Inproceedings 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 A; Koch, Tobias ; Guillén i Fàbregas, Albert Nearest Neighbour Decoding and Pilot-Aided Channel Estimation in Stationary Gaussian Flat-Fading Channels Inproceedings 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 Guillén i Fàbregas, Albert}, 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 A; Koch, Tobias ; Guillen i Fabregas, Albert Nearest Neighbour Decoding with Pilot-Assisted Channel Estimation for Fading Multiple-Access Channels Inproceedings 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 Guillen i Fabregas, Albert}, 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 |

Koch, Tobias ; Lapidoth, Amos Gaussian Fading Is the Worst Fading Journal Article IEEE Transactions on Information Theory, 56 (3), pp. 1158–1165, 2010, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: Additive noise, channel capacity, channels with memory, Distribution functions, ergodic fading processes, Fading, fading channels, flat fading, flat-fading channel capacity, Gaussian channels, Gaussian fading, Gaussian processes, H infinity control, high signal-to-noise ratio (SNR), Information technology, information theory, multiple-input single-output fading channels, multiplexing gain, noncoherent, noncoherent channel capacity, peak-power limited channel capacity, Signal to noise ratio, signal-to-noise ratio, single-antenna channel capacity, spectral distribution function, time-selective, Transmitters @article{Koch2010a, title = {Gaussian Fading Is the Worst Fading}, author = {Koch, Tobias and Lapidoth, Amos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5429105}, issn = {0018-9448}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {56}, number = {3}, pages = {1158--1165}, abstract = {The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented.}, keywords = {Additive noise, channel capacity, channels with memory, Distribution functions, ergodic fading processes, Fading, fading channels, flat fading, flat-fading channel capacity, Gaussian channels, Gaussian fading, Gaussian processes, H infinity control, high signal-to-noise ratio (SNR), Information technology, information theory, multiple-input single-output fading channels, multiplexing gain, noncoherent, noncoherent channel capacity, peak-power limited channel capacity, Signal to noise ratio, signal-to-noise ratio, single-antenna channel capacity, spectral distribution function, time-selective, Transmitters}, pubstate = {published}, tppubtype = {article} } The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented. |

Koch, Tobias ; Lapidoth, Amos On Multipath Fading Channels at High SNR Journal Article IEEE Transactions on Information Theory, 56 (12), pp. 5945–5957, 2010, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: approximation theory, capacity pre-loglog, capacity to loglog, channel capacity, channels with memory, Delay, Fading, fading channels, frequency-selective fading, high signal-to-noise ratio, high SNR, Limiting, multipath, multipath channels, noncoherent, noncoherent multipath fading channel, Receivers, Signal to noise ratio, signal-to-noise ratio, Transmitters @article{Koch2010b, title = {On Multipath Fading Channels at High SNR}, author = {Koch, Tobias and Lapidoth, Amos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5625630}, issn = {0018-9448}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {56}, number = {12}, pages = {5945--5957}, abstract = {A noncoherent multipath fading channel is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog-defined as the limiting ratio of capacity to loglog(SNR) as the SNR tends to infinity-is 1 irrespective of the number of paths. The results demonstrate that at high SNR multipath fading channels with an infinite number of paths cannot be approximated by multipath fading channels with only a finite number of paths. The number of paths that are needed to approximate a multipath fading channel typically depends on the SNR and may grow to infinity as the SNR tends to infinity.}, keywords = {approximation theory, capacity pre-loglog, capacity to loglog, channel capacity, channels with memory, Delay, Fading, fading channels, frequency-selective fading, high signal-to-noise ratio, high SNR, Limiting, multipath, multipath channels, noncoherent, noncoherent multipath fading channel, Receivers, Signal to noise ratio, signal-to-noise ratio, Transmitters}, pubstate = {published}, tppubtype = {article} } A noncoherent multipath fading channel is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog-defined as the limiting ratio of capacity to loglog(SNR) as the SNR tends to infinity-is 1 irrespective of the number of paths. The results demonstrate that at high SNR multipath fading channels with an infinite number of paths cannot be approximated by multipath fading channels with only a finite number of paths. The number of paths that are needed to approximate a multipath fading channel typically depends on the SNR and may grow to infinity as the SNR tends to infinity. |

## Inproceedings |

Vazquez, Manuel A; Miguez, Joaquin Adaptive MLSD for MIMO Transmission Systems with Unknown Subchannel Orders Inproceedings 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 |

Koch, Tobias ; Lapidoth, Amos On Multipath Fading Channels at High SNR Inproceedings 2008 IEEE International Symposium on Information Theory, pp. 1572–1576, IEEE, Toronto, 2008, ISBN: 978-1-4244-2256-2. Abstract | Links | BibTeX | Tags: channel capacity, Delay, discrete time systems, discrete-time channels, Entropy, Fading, fading channels, Frequency, Mathematical model, multipath channels, multipath fading channels, noncoherent channel model, Random variables, Signal to noise ratio, signal-to-noise ratios, SNR, statistics, Transmitters @inproceedings{Koch2008, title = {On Multipath Fading Channels at High SNR}, author = {Koch, Tobias and Lapidoth, Amos}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=4595252}, isbn = {978-1-4244-2256-2}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE International Symposium on Information Theory}, pages = {1572--1576}, publisher = {IEEE}, address = {Toronto}, abstract = {This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog-defined as the limiting ratio of the capacity to loglog(SNR) as SNR tends to infinity-is studied. It is shown that, irrespective of the number of paths L, the capacity pre-loglog is 1.}, keywords = {channel capacity, Delay, discrete time systems, discrete-time channels, Entropy, Fading, fading channels, Frequency, Mathematical model, multipath channels, multipath fading channels, noncoherent channel model, Random variables, Signal to noise ratio, signal-to-noise ratios, SNR, statistics, Transmitters}, pubstate = {published}, tppubtype = {inproceedings} } This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog-defined as the limiting ratio of the capacity to loglog(SNR) as SNR tends to infinity-is studied. It is shown that, irrespective of the number of paths L, the capacity pre-loglog is 1. |

Koch, Tobias ; Lapidoth, Amos Multipath Channels of Unbounded Capacity Inproceedings 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, pp. 640–644, IEEE, Eilat, 2008, ISBN: 978-1-4244-2481-8. Abstract | Links | BibTeX | Tags: channel capacity, discrete-time capacity, Entropy, Fading, fading channels, Frequency, H infinity control, Information rates, multipath channels, multipath fading channels, noncoherent, noncoherent capacity, path gains decay, Signal to noise ratio, statistics, Transmitters, unbounded capacity @inproceedings{Koch2008b, title = {Multipath Channels of Unbounded Capacity}, author = {Koch, Tobias and Lapidoth, Amos}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=4736611}, isbn = {978-1-4244-2481-8}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel}, pages = {640--644}, publisher = {IEEE}, address = {Eilat}, abstract = {The capacity of discrete-time, noncoherent, multipath fading channels is considered. It is shown that if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the transmit power.}, keywords = {channel capacity, discrete-time capacity, Entropy, Fading, fading channels, Frequency, H infinity control, Information rates, multipath channels, multipath fading channels, noncoherent, noncoherent capacity, path gains decay, Signal to noise ratio, statistics, Transmitters, unbounded capacity}, pubstate = {published}, tppubtype = {inproceedings} } The capacity of discrete-time, noncoherent, multipath fading channels is considered. It is shown that if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the transmit power. |