## 2016 |

## Journal Articles |

Durisi, Giuseppe; Koch, Tobias; Ostman, Johan; Polyanskiy, Yury; Yang, Wei Short-Packet Communications Over Multiple-Antenna Rayleigh-Fading Channels Journal Article IEEE Transactions on Communications, 64 (2), pp. 618–629, 2016, ISSN: 0090-6778. Abstract | Links | BibTeX | Tags: diversity branches, Encoding, ergodic capacity, Fading, fading channels, finite-blocklength information theory, finiteblocklength information theory, infinite-blocklength performance metrics, Journal, machine-type communication systems, maximum coding rate, Mission critical systems, mission-critical machine-type communications, multiple antennas, multiple-antenna Rayleigh block-fading channels, Multiplexing, optimal number, outage capacity, rate gain, Rayleigh channels, Receivers, Reliability, short-packet communications, spatial multiplexing, Throughput, Time-frequency analysis, time-frequency-spatial degrees of freedom, transmit antennas, transmit diversity, Transmitting antennas, Ultra-reliable low-latency communications @article{Durisi2016b, title = {Short-Packet Communications Over Multiple-Antenna Rayleigh-Fading Channels}, author = {Giuseppe Durisi and Tobias Koch and Johan Ostman and Yury Polyanskiy and Wei Yang}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7362178}, doi = {10.1109/TCOMM.2015.2511087}, issn = {0090-6778}, year = {2016}, date = {2016-02-01}, journal = {IEEE Transactions on Communications}, volume = {64}, number = {2}, pages = {618--629}, publisher = {IEEE}, abstract = {Motivated by the current interest in ultra-reliable, low-latency, machine-type communication systems, we investigate the tradeoff between reliability, throughput, and latency in the transmission of information over multiple-antenna Rayleigh block-fading channels. Specifically, we obtain finite-blocklength, finite-SNR upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability. Numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths (packets of about 100 symbols). Furthermore, our bounds reveal the existence of a tradeoff between the rate gain obtainable by spreading each codeword over all available time-frequency-spatial degrees of freedom, and the rate loss caused by the need of estimating the fading coefficients over these degrees of freedom. In particular, our bounds allow us to determine the optimal number of transmit antennas and the optimal number of time-frequency diversity branches that maximize the rate. Finally, we show that infinite-blocklength performance metrics such as the ergodic capacity and the outage capacity yield inaccurate throughput estimates}, keywords = {diversity branches, Encoding, ergodic capacity, Fading, fading channels, finite-blocklength information theory, finiteblocklength information theory, infinite-blocklength performance metrics, Journal, machine-type communication systems, maximum coding rate, Mission critical systems, mission-critical machine-type communications, multiple antennas, multiple-antenna Rayleigh block-fading channels, Multiplexing, optimal number, outage capacity, rate gain, Rayleigh channels, Receivers, Reliability, short-packet communications, spatial multiplexing, Throughput, Time-frequency analysis, time-frequency-spatial degrees of freedom, transmit antennas, transmit diversity, Transmitting antennas, Ultra-reliable low-latency communications}, pubstate = {published}, tppubtype = {article} } Motivated by the current interest in ultra-reliable, low-latency, machine-type communication systems, we investigate the tradeoff between reliability, throughput, and latency in the transmission of information over multiple-antenna Rayleigh block-fading channels. Specifically, we obtain finite-blocklength, finite-SNR upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability. Numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths (packets of about 100 symbols). Furthermore, our bounds reveal the existence of a tradeoff between the rate gain obtainable by spreading each codeword over all available time-frequency-spatial degrees of freedom, and the rate loss caused by the need of estimating the fading coefficients over these degrees of freedom. In particular, our bounds allow us to determine the optimal number of transmit antennas and the optimal number of time-frequency diversity branches that maximize the rate. Finally, we show that infinite-blocklength performance metrics such as the ergodic capacity and the outage capacity yield inaccurate throughput estimates |

## 2014 |

## Journal Articles |

Yang, Wei; 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{Yang2014b, title = {Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength}, author = {Wei Yang and Giuseppe Durisi and Tobias Koch and Yury Polyanskiy}, 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. |

A, Pastore; 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 Tobias Koch and Javier Rodriguez Fonollosa}, 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. |

## Inproceedings |

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 = {Isabel Valera and Francisco J R Ruiz and Fernando Perez-Cruz}, 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 |

Vazquez, Manuel A; Miguez, Joaquin User Activity Tracking in DS-CDMA Systems Journal Article IEEE Transactions on Vehicular Technology, 62 (7), pp. 3188–3203, 2013, ISSN: 0018-9545. Abstract | Links | BibTeX | Tags: Activity detection, activity tracking, Bayes methods, Bayesian framework, Channel estimation, code division multiple access, code-division multiple access (CDMA), computer simulations, data detection, direct sequence code division multiple-access, DS-CDMA systems, Equations, joint channel and data estimation, joint channel estimation, Joints, MAP equalizers, Mathematical model, maximum a posteriori, MIMO communication, Multiaccess communication, multiple-input-multiple-output communication chann, multiuser communication systems, per-survivor processing (PSP), radio receivers, Receivers, sequential Monte Carlo (SMC) methods, time-varying number, time-varying parameter, Vectors, wireless channels @article{Vazquez2013a, title = {User Activity Tracking in DS-CDMA Systems}, author = {Manuel A Vazquez and Joaquin Miguez}, url = {http://www.tsc.uc3m.es/~jmiguez/papers/P39_2013_User Activity Tracking in DS-CDMA Systems.pdf http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6473922}, issn = {0018-9545}, year = {2013}, date = {2013-01-01}, journal = {IEEE Transactions on Vehicular Technology}, volume = {62}, number = {7}, pages = {3188--3203}, abstract = {In modern multiuser communication systems, users are allowed to enter or 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. The so-called problem of user identification, which consists of determining the number and identities of users transmitting in a communication system, is usually solved prior to, and hence independently of, that posed by the detection of the transmitted data. Since both problems are tightly connected, a joint solution is desirable. In this paper, we focus on direct-sequence (DS) code-division multiple-access (CDMA) systems and derive, within a Bayesian framework, different receivers that cope with an unknown and time-varying number of users while performing joint channel estimation and data detection. The main feature of these receivers, compared with other recently proposed schemes for user activity detection, is that they are natural extensions of existing maximum a posteriori (MAP) equalizers for multiple-input-multiple-output communication channels. We assess the validity of the proposed receivers, including their reliability in detecting the number and identities of active users, by way of computer simulations.}, keywords = {Activity detection, activity tracking, Bayes methods, Bayesian framework, Channel estimation, code division multiple access, code-division multiple access (CDMA), computer simulations, data detection, direct sequence code division multiple-access, DS-CDMA systems, Equations, joint channel and data estimation, joint channel estimation, Joints, MAP equalizers, Mathematical model, maximum a posteriori, MIMO communication, Multiaccess communication, multiple-input-multiple-output communication chann, multiuser communication systems, per-survivor processing (PSP), radio receivers, Receivers, sequential Monte Carlo (SMC) methods, time-varying number, time-varying parameter, Vectors, wireless channels}, pubstate = {published}, tppubtype = {article} } In modern multiuser communication systems, users are allowed to enter or 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. The so-called problem of user identification, which consists of determining the number and identities of users transmitting in a communication system, is usually solved prior to, and hence independently of, that posed by the detection of the transmitted data. Since both problems are tightly connected, a joint solution is desirable. In this paper, we focus on direct-sequence (DS) code-division multiple-access (CDMA) systems and derive, within a Bayesian framework, different receivers that cope with an unknown and time-varying number of users while performing joint channel estimation and data detection. The main feature of these receivers, compared with other recently proposed schemes for user activity detection, is that they are natural extensions of existing maximum a posteriori (MAP) equalizers for multiple-input-multiple-output communication channels. We assess the validity of the proposed receivers, including their reliability in detecting the number and identities of active users, by way of computer simulations. |

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 = {Tobias Koch and Gerhard Kramer}, 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 |

Yang, Wei; Durisi, Giuseppe; Koch, Tobias; Polyanskiy, Yury Quasi-Static SIMO Fading Channels at Finite Blocklength Inproceedings 2013 IEEE International Symposium on Information Theory, pp. 1531–1535, IEEE, Istanbul, 2013, ISSN: 2157-8095. Abstract | Links | BibTeX | Tags: achievability bounds, AWGN channel, AWGN channels, channel capacity, channel dispersion, channel gains, Dispersion, error probability, error statistics, Fading, fading channels, fading realizations, fast convergence, finite blocklength, maximal achievable rate, numerical evaluation, outage capacity, quasistatic SIMO fading channels, Random variables, Receivers, SIMO Rician channel, single-input multiple-output, Transmitters, zero dispersion @inproceedings{Yang2013a, title = {Quasi-Static SIMO Fading Channels at Finite Blocklength}, author = {Wei Yang and Giuseppe Durisi and Tobias Koch and Yury Polyanskiy}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6620483}, issn = {2157-8095}, year = {2013}, date = {2013-01-01}, booktitle = {2013 IEEE International Symposium on Information Theory}, pages = {1531--1535}, publisher = {IEEE}, address = {Istanbul}, abstract = {We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The result follows from computationally and analytically tractable converse and achievability bounds. Through numerical evaluation, we verify that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blocklength increases. In the example of a particular 1×2 SIMO Rician channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity.}, keywords = {achievability bounds, AWGN channel, AWGN channels, channel capacity, channel dispersion, channel gains, Dispersion, error probability, error statistics, Fading, fading channels, fading realizations, fast convergence, finite blocklength, maximal achievable rate, numerical evaluation, outage capacity, quasistatic SIMO fading channels, Random variables, Receivers, SIMO Rician channel, single-input multiple-output, Transmitters, zero dispersion}, pubstate = {published}, tppubtype = {inproceedings} } We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The result follows from computationally and analytically tractable converse and achievability bounds. Through numerical evaluation, we verify that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blocklength increases. In the example of a particular 1×2 SIMO Rician channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity. |

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 = {Giuseppe Durisi and Alberto Tarable and Tobias Koch}, 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 |

## Journal Articles |

Cruz-Roldan, Fernando; Dominguez-Jimenez, María Elena; Vidal, Gabriela Sansigre; Amo-Lopez, Pedro; Blanco-Velasco, Manuel; Bravo-Santos, Ángel M On the Use of Discrete Cosine Transforms for Multicarrier Communications Journal Article IEEE Transactions on Signal Processing, 60 (11), pp. 6085–6090, 2012, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: broadband networks, carrier frequency offset, Carrier-frequency offset (CFO), CFO, channel equalization, computer simulations, Convolution, Data communication, data symbol, DCT, DFT, discrete cosine transform (DCT), discrete cosine transform domain, Discrete cosine transforms, discrete Fourier transforms, discrete multitone modulation (DMT), discrete trigonometric domain, element-by-element multiplication, equalisers, equivalent channel impulse response, linear convolution, mobile broadband wireless communication, mobile radio, Modulation, multicarrier communications, multicarrier data transmission, multicarrier modulation (MCM), multicarrier transceiver, OFDM, orthogonal frequency-division multiplexing (OFDM), Receivers, Redundancy, subcarrier equalizers, symmetric convolution-multiplication property, symmetric redundancy, time-domain analysis, transient response, transmission channel @article{Cruz-Roldan2012, title = {On the Use of Discrete Cosine Transforms for Multicarrier Communications}, author = {Fernando Cruz-Roldan and María Elena Dominguez-Jimenez and Gabriela Sansigre Vidal and Pedro Amo-Lopez and Manuel Blanco-Velasco and Ángel M Bravo-Santos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6252068}, issn = {1053-587X}, year = {2012}, date = {2012-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {60}, number = {11}, pages = {6085--6090}, abstract = {In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redundancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT.}, keywords = {broadband networks, carrier frequency offset, Carrier-frequency offset (CFO), CFO, channel equalization, computer simulations, Convolution, Data communication, data symbol, DCT, DFT, discrete cosine transform (DCT), discrete cosine transform domain, Discrete cosine transforms, discrete Fourier transforms, discrete multitone modulation (DMT), discrete trigonometric domain, element-by-element multiplication, equalisers, equivalent channel impulse response, linear convolution, mobile broadband wireless communication, mobile radio, Modulation, multicarrier communications, multicarrier data transmission, multicarrier modulation (MCM), multicarrier transceiver, OFDM, orthogonal frequency-division multiplexing (OFDM), Receivers, Redundancy, subcarrier equalizers, symmetric convolution-multiplication property, symmetric redundancy, time-domain analysis, transient response, transmission channel}, pubstate = {published}, tppubtype = {article} } In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redundancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT. |

## Inproceedings |

O'Mahony, Niamh; Perez-Cruz, Fernando A novel Sequential Bayesian Approach to GPS Acquisition Inproceedings 2012 3rd International Workshop on Cognitive Information Processing (CIP), pp. 1–6, IEEE, Baiona, 2012, ISBN: 978-1-4673-1878-5. Abstract | Links | BibTeX | Tags: Bayes methods, coarse synchronization, Correlators, data acquisition, Delay, Doppler effect, Global Positioning System, GPS acquisition, GPS signal parameters, learning (artificial intelligence), online learning algorithm, Receivers, Satellites, sequential Bayesian approach, signal acquisition, signal detection, Synchronization @inproceedings{O'Mahony2012, title = {A novel Sequential Bayesian Approach to GPS Acquisition}, author = {Niamh O'Mahony and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6232921}, isbn = {978-1-4673-1878-5}, year = {2012}, date = {2012-01-01}, booktitle = {2012 3rd International Workshop on Cognitive Information Processing (CIP)}, pages = {1--6}, publisher = {IEEE}, address = {Baiona}, abstract = {In this work, a novel online learning algorithm is presented for the synchronization of Global Positioning System (GPS) signal parameters at the acquisition, or coarse synchronization, stage. The algorithm is based on a Bayesian approach, which has, to date, not been exploited for the acquisition problem. Simulated results are presented to illustrate the algorithm performance, in terms of accuracy and acquisition time, along with results from the acquisition of signals from live GPS satellites using both the new algorithm and a state-of-the-art approach for comparison.}, keywords = {Bayes methods, coarse synchronization, Correlators, data acquisition, Delay, Doppler effect, Global Positioning System, GPS acquisition, GPS signal parameters, learning (artificial intelligence), online learning algorithm, Receivers, Satellites, sequential Bayesian approach, signal acquisition, signal detection, Synchronization}, pubstate = {published}, tppubtype = {inproceedings} } In this work, a novel online learning algorithm is presented for the synchronization of Global Positioning System (GPS) signal parameters at the acquisition, or coarse synchronization, stage. The algorithm is based on a Bayesian approach, which has, to date, not been exploited for the acquisition problem. Simulated results are presented to illustrate the algorithm performance, in terms of accuracy and acquisition time, along with results from the acquisition of signals from live GPS satellites using both the new algorithm and a state-of-the-art approach for comparison. |

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 = {Giuseppe Durisi and Tobias Koch and Yury Polyanskiy}, 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. |

## 2010 |

## Journal Articles |

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 = {Tobias Koch and Amos Lapidoth}, 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 = {Manuel A Vazquez and Joaquin Miguez}, 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. |

## 2009 |

## Journal Articles |

Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Gaussian Process Regressors for Multiuser Detection in DS-CDMA Systems Journal Article IEEE Transactions on Communications, 57 (8), pp. 2339–2347, 2009, ISSN: 0090-6778. Abstract | Links | BibTeX | Tags: analytical nonlinear multiuser detectors, code division multiple access, communication systems, Detectors, digital communication, digital communications, DS-CDMA systems, Gaussian process for regressi, Gaussian process regressors, Gaussian processes, GPR, Ground penetrating radar, least mean squares methods, maximum likelihood, maximum likelihood detection, maximum likelihood estimation, mean square error methods, minimum mean square error, MMSE, Multiaccess communication, Multiuser detection, nonlinear estimator, nonlinear state-ofthe- art solutions, radio receivers, Receivers, regression analysis, Support vector machines @article{Murillo-Fuentes2009, title = {Gaussian Process Regressors for Multiuser Detection in DS-CDMA Systems}, author = {Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5201027}, issn = {0090-6778}, year = {2009}, date = {2009-01-01}, journal = {IEEE Transactions on Communications}, volume = {57}, number = {8}, pages = {2339--2347}, abstract = {In this paper we present Gaussian processes for Regression (GPR) as a novel detector for CDMA digital communications. Particularly, we propose GPR for constructing analytical nonlinear multiuser detectors in CDMA communication systems. GPR can easily compute the parameters that describe its nonlinearities by maximum likelihood. Thereby, no cross-validation is needed, as it is typically used in nonlinear estimation procedures. The GPR solution is analytical, given its parameters, and it does not need to solve an optimization problem for building the nonlinear estimator. These properties provide fast and accurate learning, two major issues in digital communications. The GPR with a linear decision function can be understood as a regularized MMSE detector, in which the regularization parameter is optimally set. We also show the GPR receiver to be a straightforward nonlinear extension of the linear minimum mean square error (MMSE) criterion, widely used in the design of these receivers. We argue the benefits of this new approach in short codes CDMA systems where little information on the users' codes, users' amplitudes or the channel is available. The paper includes some experiments to show that GPR outperforms linear (MMSE) and nonlinear (SVM) state-ofthe- art solutions.}, keywords = {analytical nonlinear multiuser detectors, code division multiple access, communication systems, Detectors, digital communication, digital communications, DS-CDMA systems, Gaussian process for regressi, Gaussian process regressors, Gaussian processes, GPR, Ground penetrating radar, least mean squares methods, maximum likelihood, maximum likelihood detection, maximum likelihood estimation, mean square error methods, minimum mean square error, MMSE, Multiaccess communication, Multiuser detection, nonlinear estimator, nonlinear state-ofthe- art solutions, radio receivers, Receivers, regression analysis, Support vector machines}, pubstate = {published}, tppubtype = {article} } In this paper we present Gaussian processes for Regression (GPR) as a novel detector for CDMA digital communications. Particularly, we propose GPR for constructing analytical nonlinear multiuser detectors in CDMA communication systems. GPR can easily compute the parameters that describe its nonlinearities by maximum likelihood. Thereby, no cross-validation is needed, as it is typically used in nonlinear estimation procedures. The GPR solution is analytical, given its parameters, and it does not need to solve an optimization problem for building the nonlinear estimator. These properties provide fast and accurate learning, two major issues in digital communications. The GPR with a linear decision function can be understood as a regularized MMSE detector, in which the regularization parameter is optimally set. We also show the GPR receiver to be a straightforward nonlinear extension of the linear minimum mean square error (MMSE) criterion, widely used in the design of these receivers. We argue the benefits of this new approach in short codes CDMA systems where little information on the users' codes, users' amplitudes or the channel is available. The paper includes some experiments to show that GPR outperforms linear (MMSE) and nonlinear (SVM) state-ofthe- art solutions. |