Nuestros investigadores

Pedro Crespo Bofill

Departamento de Ingeniería Biomédica y Ciencias
Escuela de Ingenieros (TECNUN). Universidad de Navarra
Líneas de investigación
Digital Communications, Information Theory and Signal Processing
Índice H
19, (Google Scholar, 01/10/2018)

Publicaciones científicas más recientes (desde 2010)

Autores: Santamaria, I., (Autor de correspondencia); Crespo, Pedro M.; Lameiro, C.; et al.
Revista: ENTROPY
ISSN 1099-4300  Vol. 20  Nº 1  2018 
Non-circular or improper Gaussian signaling has proven beneficial in several interference-limited wireless networks. However, all implementable coding schemes are based on finite discrete constellations rather than Gaussian signals. In this paper, we propose a new family of improper constellations generated by widely linear processing of a square M-QAM (quadrature amplitude modulation) signal. This family of discrete constellations is parameterized by , the circularity coefficient and a phase phi. For uncoded communication systems, this phase should be optimized as phi * to maximize the minimum Euclidean distance between points of the improper constellation, therefore minimizing the bit error rate (BER). For the more relevant case of coded communications, where the coded symbols are constrained to be in this family of improper constellations using phi*, it is shown theoretically and further corroborated by simulations that, except for a shaping loss of 1.53 dB encountered at a high signal-to-noise ratio (snr), there is no rate loss with respect to the improper Gaussian capacity. In this sense, the proposed family of constellations can be viewed as the improper counterpart of the standard proper M-QAM constellations widely used in coded communication systems.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); de Zárraga, Marta; Crespo, Pedro M.; et al.
Revista: ENTROPY
ISSN 1099-4300  Vol. 20  Nº 9  2018  págs. 719
Autores: Yuanyuan Ma, (Autor de correspondencia); Matthias Pätzold; et al.
ISSN 1530-8669  2018 
This paper focuses on the modeling, simulation, and experimental verification of wideband single-input single-output (SISO) mobile fading channels for indoor propagation environments. The indoor reference channel model is derived from a geometrical rectangle scattering model, which consists of an infinite number of scatterers. It is assumed that the scatterers are exponentially distributed over the two-dimensional (2D) horizontal plane of a rectangular room. Analytical expressions are derived for the probability density function (PDF) of the angle of arrival (AOA), the PDF of the propagation path length, the power delay profile (PDP), and the frequency correlation function (FCF). An efficient sum-of-cisoids (SOC) channel simulator is derived from the nonrealizable reference model by employing the SOC principle. It is shown that the SOC channel simulator approximates closely the reference model with respect to the FCF. The SOC channel simulator enables the performance evaluation of wideband indoor wireless communication systems with reduced realization expenditure. Moreover, the rationality and usefulness of the derived indoor channel model is confirmed by various measurements at 2.4, 5, and 60¿GHz.
Autores: Insausti, Xabier; Crespo, Pedro M.; Gutiérrez-Gutiérrez, Jesús; et al.
ISSN 1089-7798  Vol. 22  Nº 9  2018  págs. 1754 - 1757
In this letter, we design a low-latency, low-complexity, and low-transmission power analog linear coding scheme to estimate the finite-length data blocks under a mean-square-error (distortion) criterion. The proposed scheme is based on the analog linear coding and the discrete Fourier transform. A remarkable feature of our scheme is that it does not require knowing the correlation matrix of the data blocks, and therefore, it can be used even if the correlation matrix changes slowly with time.
Autores: Insausti, Xabier; Saez, A.; Crespo, Pedro M.;
ISSN 1572-8196  2017  págs. 1 - 9
This paper proposes a novel scheme for the slow block fading Gaussian multiple access relay channel inspired by the compute-and-forward (CoF) relaying strategy. The CoF relaying strategy exploits interference to obtain significantly higher rates between users in a network by decoding linear functions of the transmitted messages. Unlike other approaches in the literature, our approach is valid for any number of transmitters and, most importantly, it only requires channel state information at the receiver side, while it still attains similar or higher rates than the other approaches found in the literature
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Crespo, Pedro M.; de Zárraga, Marta; et al.
ISSN 0018-9448  Vol. 63  Nº 9  2017  págs. 6000 - 6003
Using some recent results on asymptotically equivalent sequences of matrices, we present in this paper, a new derivation of the capacity formula given by Brandenburg and Wyner for a discrete-time Gaussian multiple-input-multiple-output channel with memory. In this paper, we tackle not only the case considered by them, where the number of channel inputs and the number of channel outputs are the same, but also when both numbers are different.
Autores: Insausti, Xabier, (Autor de correspondencia); Gutiérrez-Gutiérrez, Jesús; de Zárraga, Marta; et al.
Revista: SENSORS
ISSN 1424-8220  Vol. 17  Nº 1702  2017 
In a network, a distributed consensus algorithm is fully characterized by its weighting matrix. Although there exist numerical methods for obtaining the optimal weighting matrix, we have not found an in-network implementation of any of these methods that works for all network topologies. In this paper, we propose an in-network algorithm for finding such an optimal weighting matrix.
Autores: Bilbao, J.; Crespo, Pedro M.; Armendariz, I.; et al.
ISSN 0733-8716  Vol. 34  Nº 7  2016  págs. 1965 - 1977
The wide availability of power distribution cables provides an interesting no-new-wires communication channel. However, its electrical characteristics make it a harsh environment for the data transmission purpose and prevent the deployment of services with high reliability requirements. This paper proposes and implements an OSI-Layer2 network coding-based cooperative scheme with the aim of improving communication reliability in indoor narrowband powerline channels. The proposed scheme uses random linear network coding with a sliding window and relaying. We use network coding to replace the retransmissions triggered by legacy subsequent repeat request (ARQ) schemes. We evaluate the performance of our approach in terms of throughput and delay. Regarding the throughput achieved in harsh environments, we show that our scheme often more than doubles the throughput of existing legacy ARQ schemes. At the same time, and even under the large variation of traffic characteristics, it is shown that the delay is likely to be upper bounded by a few seconds, a bound that cannot be guaranteed in other existing transmission techniques.
Autores: Alustiza, I.; Hernaez, M.; Crespo, Pedro M.;
ISSN 1687-1499  2015 
This paper proposes a Decode-and-Forward (DF) relaying scheme for the multi-hop transmission in wireless networks, where the information generated by an independent source has to be sent to a far destination based on multiple-relay cooperation. The proposed DF scheme blends together convolutional channel coding with linear combination of blocks of data over a finite field using very short block lengths (K=13). We provide an extrinsic information transfer (EXIT) chart analysis to understand the good performance behavior of the proposed scheme when compared with other referenced schemes using much larger block lengths. This fact is corroborated by a set of Monte Carlo simulations. Moreover, the proposed DF scheme is suitable for large multi-hop networks since a negligible performance degradation is obtained when adding more hops.
Autores: Alustiza, I.; Crespo, Pedro M.; Beferull-Lozano, B.;
ISSN 1053-587X  Vol. 63  Nº 12  2015  págs. 3046 - 3061
Joint source-channel coding schemes based on analog mappings for point-to-point channels have recently gained attention for their simplicity and low delay. In this paper, these schemes are extended either to scenarios with or without side information at the decoders to transmit multiple descriptions of a Gaussian source over independent parallel channels. They are based on a lattice scaling approach together with bandwidth reduction analog mappings adapted for this multiple description scenario. The rationale behind lattice scaling is to improve performance through band-width expansion. Another important contribution of this paper is the proof of the separation theorem for the communication scenario of multiple description with side information at the decoders. This proof allows us to compare the performance of the proposed schemes with the theoretical limits when considering AWGN channels. Finally, when the channels are parallel slow-fading Rayleigh, the proposed schemes are optimal in terms of distortion exponent.
Autores: Insausti, Xabier; Camaro, F.; Crespo, Pedro M.; et al.
ISSN 1932-4553  Vol. 7  Nº 2  2013  págs. 163 - 174
In this paper, we design a practical power-efficient algorithm for Wireless Sensor Networks (WSN) in order to obtain, in a distributed manner, the projection of an observed sampled spatial field on a subspace of lower dimension. This is an important problem that is motivated in various applications where there are well defined subspaces of interest (e. g., spectral maps in cognitive radios). As opposed to traditional Gossip Algorithms used for subspace projection, where separation of channel coding and computation is assumed, our algorithm combines binary finite-length Computational Coding and a novel gossip-like protocol with certain communication rules, achieving important savings in convergence time and yielding a decrease in energy consumption as the density of the network increases, as compared to a separation scheme.
Autores: Hernaez, M.; Crespo, Pedro M.; Del Ser, J.;
ISSN 0733-8716  Vol. 31  Nº 8  2013  págs. 1368 - 1378
This paper proposes a novel joint non-binary network-channel code for the Time-Division Decode-and-Forward Multiple Access Relay Channel (TD-DF-MARC), where the relay linearly combines - over a non-binary finite field - the coded sequences from the source nodes. A method based on an EXIT chart analysis is derived for selecting the best coefficients of the linear combination. Moreover, it is shown that for different setups of the system, different coefficients should be chosen in order to improve the performance. This conclusion contrasts with previous works where a random selection was considered. Monte Carlo simulations show that the proposed scheme outperforms, in terms of its gap to the outage probabilities, the previously published joint network-channel coding approaches. Besides, this gain is achieved by using very short-length codewords, which makes the scheme particularly attractive for low-latency applications.
Autores: Gutierrez, C.A.; Patzold, M.; et al.
ISSN 1687-1499  Vol. 2013  Nº 125  2013  págs. 1 - 15
In this paper, we present a fundamental study on the stationarity and ergodicity of eight classes of sum-of-cisoids (SOC) processes for the modeling and simulation of frequency-nonselective mobile Rayleigh fading channels. The purpose of this study is to determine which classes of SOC models enable the design of channel simulators that accurately reproduce the channel's statistical properties without demanding information on the time origin or the time-consuming computation of an ensemble average. We investigate the wide-sense stationarity, first-order stationarity of the envelope, mean ergodicity, and autocorrelation ergodicity of the underlying random processes characterizing the different classes of stochastic SOC simulators. The obtained results demonstrate that only the class of SOC models comprising cisoids with constant gains, constant frequencies, and random phases is defined by a set of stationary and ergodic random processes. The analysis presented here can easily be extended with respect to the modeling and simulation of frequency-selective single-input single-output (SISO) and multiple-input multiple-output channels. For the case of frequency-selective SISO channels, we investigate the stationarity and ergodicity in both time and frequency of 16 different classes of SOC simulation models. The findings presented in this paper can be used in the laboratory as guidelines to design efficient simulation platforms for the performance evaluation of modern mobile communication systems.
Autores: Bilbao, J.; Calvo, A.; Armendariz, I.; et al.
ISSN 1509-4553  Vol. 2013  2013  págs. 23 - 40
One of the most challenging research fields in which research community has taken a very active role is focused on trying to bring the features of wireless networks into line with the traditional wired solutions. Given the noisy and lossy nature of the wireless medium, it is more difficult to provide a comparable Quality of Service (QoS) and Reliability over wireless networks. This lack of reliability avoids the use of wireless solution in scenarios under harsh environment and mission-critical applications. In this paper we propose an inter-node collaborative schema with the aim of improving the achievable QoS level for multicast streaming, through the use of Network Coding and the algebra it is based on. We also present an implementation of the described algorithm on the OPNET discrete event simulation tool. Experimental results highlighting the performance achieved by the proposed algorithm and its improved efficiency as compared to other solutions are described.
Autores: Crespo, Pedro M.; Beferull-Lozano, B.;
ISSN 1053-587X  Vol. 60  Nº 11  2012  págs. 5880 - 5892
The complexity and delay introduced by efficient digital coding strategies may be a barrier in some real-time communications. In this sense, these last years, joint source-channel coding schemes based on analog mappings have gained prominence precisely for their simplicity and their implicit low delay. In this work, analog mappings originally designed for point-to-point communications are adapted to the case of parallel channels by following the multiple description strategy traditionally used in source coding. In principle, the coding scheme is designed to transmit over parallel AWGN on-off channels, which are characterized by the possibility of having failures. We also show that our scheme performs satisfactorily over slow Rayleigh fading parallel channels.
Autores: Hernaez, M.; Crespo, Pedro M.;
ISSN 1089-7798  Vol. 16  Nº 9  2012  págs. 1508 - 1511
This letter introduces a channel coding design framework for short-length codewords which can achieve lower error floor than previous approaches. The proposed code is based on combining convolutional coding with a q-ary linear combination and unequal energy allocation. Simulation results suggest that for very low Bit Error Rates (BER) the proposed system will exhibit lower error floors than previous approaches, with a small performance penalty at mid-range BERs. On the other hand, when selecting an error floor higher than the previous approaches, the loss in performance at mid-range BERs is negligible.
Autores: Khodaian, M.; Perez, J.; Khalaj, B.; et al.
ISSN 1687-1499  2012 
In this article, we present a cross-layer adaptive algorithm that dynamically maximizes the average utility function. A per stage utility function is defined for each link of a carrier sense multiple access-based wireless network as a weighted concave function of energy consumption, smoothed rate, and smoothed queue size. Hence, by selecting weights we can control the trade-off among them. Using dynamic programming, the utility function is maximized by dynamically adapting channel access, modulation, and coding according to the queue size and quality of the time-varying channel. We show that the optimal transmission policy has a threshold structure versus the channel state where the optimal decision is to transmit when the wireless channel state is better than a threshold. We also provide a queue management scheme where arrival rate is controlled based on the link state. Numerical results show characteristics of the proposed adaptation scheme and highlight the trade-off among energy consumption, smoothed data rate, and link delay.
Autores: Crespo, Pedro M.;
ISSN 0165-1684  Vol. 91  Nº 8  2011  págs. 1709 - 1718
In the absence of observation noise, it is known that it is possible to develop exact sampling schemes for a large class of parametric non-bandlimited signals, namely, certain signals of finite rate of innovation (FRI signals), either periodic or aperiodic, such as streams of Diracs, nonuniform splines or piecewise polynomials. A common feature of such signals is that they have a finite number of degrees of freedom per unit of time and they can be reconstructed from a finite number of uniform samples of the filtered signal. Unfortunately, the accuracy of such reconstruction substantially degrades when the samples are distorted by noise. For the case of periodic FRI signals, good algorithms based on the state space method have been proposed which are robust against noise. However, in the case of aperiodic signals, these algorithms may still fail to accurately reconstruct the signals due to ill-conditioning problems that often arise in the matrices involved. This paper proposes a new reconstruction method for aperiodic FRI signals that is also based on the state space method but has a considerably better numerical conditioning than previous reconstruction algorithms. This advantage is achieved by using a frequency domain formulation. (C) 2011 Elsevier B.V. All rights reserved.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Crespo, Pedro M.;
ISSN 0018-9448  Vol. 57  Nº 8  2011  págs. 5444 - 5454
The present paper considers a special class of vector random processes that we call multivariate asymptotically wide sense stationary (WSS) processes. A multivariate random process is said to be asymptotically WSS if it has constant mean and the sequence of its autocorrelation matrices is asymptotically equivalent (a. e.) to the sequence of autocorrelation matrices of some multivariate WSS process. It is shown that this class of processes contains meaningful processes other than multivariate WSS processes. In particular, we give sufficient conditions for multivariate moving average (MA) processes, multivariate autoregressive (AR) processes and multivariate autoregressive moving average (ARMA) processes to be asymptotically WSS. Furthermore, in order to solve multiple-input-multiple-output (MIMO) problems in communications and signal processing involving this kind of processes, we extend the Gray definition of a. e. sequences of matrices and his main results on these sequences to non-square matrices. As an example, the derived results on a. e. sequences of non-square matrices are applied to compute the differential entropy rate and the minimum mean square error (MMSE) for a linear predictor of a multivariate asymptotically WSS process.
Autores: Manjarres, D.; Crespo, Pedro M.; et al.
ISSN 1687-1499  Vol. 2011  2011 
This paper focuses on the data fusion scenario where N nodes sense and transmit the data generated by a source S to a common destination, which estimates the original information from S more accurately than in the case of a single sensor. This work joins the upsurge of research interest in this topic by addressing the setup where the sensed information is transmitted over a Gaussian Multiple-Access Channel (MAC). We use Low Density Generator Matrix (LDGM) codes in order to keep the correlation between the transmitted codewords, which leads to an improved received Signal-to-Noise Ratio (SNR) thanks to the constructive signal addition at the receiver front-end. At reception, we propose a joint decoder and estimator that exchanges soft information between the N LDGM decoders and a data fusion stage. An error-correcting Bose, Ray-Chaudhuri, Hocquenghem (BCH) code is further applied suppress the error floor derived from the ambiguity of the MAC channel when dealing with correlated sources. Simulation results are presented for several values of N and diverse LDGM and BCH codes, based on which we conclude that the proposed scheme outperforms significantly (by up to 6.3 dB) the suboptimum limit assuming separation between Slepian-Wolf source coding and capacity-achieving channel coding.
Autores: Hernaez, M.; Crespo, Pedro M.; et al.
ISSN 1089-7798  Vol. 14  Nº 3  2010  págs. 235 - 235
Autores: Crespo, Pedro M.;
ISSN 0165-1684  Vol. 90  Nº 1  2010  págs. 134 - 144
In early 2000, it was shown that it is possible to develop exact sampling schemes for a large class of parametric non-bandlimited noiseless signals, namely certain signals of finite rate of innovation. In particular, signals x(t) that are linear combinations of a finite number of Diracs per unit of time can be acquired by linear filtering followed by uniform sampling. However, when noise is present, many of the early proposed schemes can become ill-conditioned. Recently, a novel stochastic algorithm based on Gibbs sampling was proposed by Tan & Goyal [IEEE Trans. Sign. Proc., 56 (10) 5135] to recover the filtered signal z(t) of x(t) by observing noisy samples of z(t). In the present paper, by blending together concepts of evolutionary algorithms with those of Gibbs sampling, a novel stochastic algorithm which substantially improves the results in the cited reference is proposed. (C) 2009 Elsevier B.V. All rights reserved.
Autores: Ochoa, I.; Crespo, Pedro M.; Hernaez, M.;
ISSN 1089-7798  Vol. 14  Nº 9  2010  págs. 794 - 796
In this paper, we design a new energy allocation strategy for non-uniform binary memoryless sources encoded by Low-Density Parity-Check (LDPC) codes and sent over Additive White Gaussian Noise (AWGN) channels. The new approach estimates the a priori probabilities of the encoded symbols, and uses this information to allocate more energy to the transmitted symbols that occur less likely. It can be applied to systematic and non-systematic LDPC codes, improving in both cases the performance of previous LDPC based schemes using binary signaling. The decoder introduces the source non-uniformity and estimates the source symbols by applying the SPA (Sum Product Algorithm) over the factor graph describing the code.
Autores: Del Ser, J.; Crespo, Pedro M.; Esnaola, I.; et al.
ISSN 0090-6778  Vol. 58  Nº 7  2010  págs. 1984 - 1992
The Burrows-Wheeler Transform (BWT) [1] is a block sorting algorithm which has been proven to be useful in compressing text data [2]. More recently, schemes based on the BWT have been proposed for lossless data compression using LDPC [3]-[5] and Fountain [6] codes, as well as for joint source-channel coding of sources with memory [7], [8]. In this paper we propose a source-controlled Turbo coding scheme for the transmission of sources with memory over AWGN channels also based on the Burrows-Wheeler Transform. Our approach combines the BWT with a Turbo code and employs different energy allocation techniques for the encoded symbols before their transmission. Simulation results show that the performance of the designed scheme is close (within 1.5 dB) to the theoretical Shannon limit.
Autores: Salavati, A.; Khalaj, B.; Crespo, Pedro M.; et al.
ISSN 1229-2370  Vol. 12  Nº 1  2010  págs. 86-94
In this paper, we present a decentralized algorithm to find minimum cost quality of service (QoS) flow subgraphs in network coded multicast schemes. The main objective is to find minimum cost subgraphs that also satisfy user-specified QoS constraints, specifically with respect to rate and delay demands. We consider networks with multiple multicast sessions. Although earlier network coding algorithms in this area have demonstrated performance improvements in terms of QoS parameters, the proposed QoS network coding approach provides a framework that guarantees QoS constraints are actually met over the network.
Autores: Ochoa, I.; Crespo, Pedro M.; et al.
ISSN 1089-7798  Vol. 14  Nº 4  2010  págs. 336 - 338
This letter proposes a novel one-layer coding/shaping scheme with single-level codes and sigma-mapping for the bandwidth-limited regime. Specifically, we consider non-uniform memoryless sources sent over AWGN channels. At the transmitter, binary data are encoded by a Turbo code composed of two identical RSC (Recursive Systematic Convolutional) encoders. The encoded bits are randomly interleaved and modulated before entering the sigma-mapper. The modulation employed in this system follows the unequal energy allocation scheme first introduced in [1]. The receiver consists of an iterative demapping/decoding algorithm, which incorporates the a priori probabilities of the source symbols. To the authors' knowledge, work in this area has only been done for the power-limited regime. In particular, the authors in [2] proposed a scheme based on a Turbo code with RSC encoders and unequal energy allocation. Therefore, it is reasonable to compare the performance - with respect to the Shannon limit - of our proposed bandwidth-limited regime scheme with this former power-limited regime scheme. Simulation results show that our performance is as good or slightly better than that of the system in [2].
Autores: Daniel Valderas; Crespo, Pedro M.; Ling, C.;
ISSN 0895-2477  Vol. 52  Nº 4  2010  págs. 889-895
Antenna arrays that incorporate MIMO technology for indoor-outdoor network interconnection on the same terminal, i.e., for DCS 1800. PCS 1900, WCDMA, 3G. 802.11a/b/g. Bluetooth (R). ZigBee (R), WiMAX (TM), and UWB standards, are proposed. Staircase profile printed circuit antenaas, monopoles (PCM). and slots (PCS) with VSWR < 2 bandwidth mainly from 1.12 to 10.1 GHz are previously designed, simulated. constructed, and measured as antenna elements for those arrays. For comparison. prototypes for two-element PCM and PCS MIMO arrays have been constructed and measured, The choice should be made according to the directivity required by the final application and portable device size. For the worst signal interference case, the operational bandwidth ranges from 1.5 to 9.9 GHz and from 1.7 to 11.4 GHz for the PCM and the PCS MIMO arrays, respectively. VSWR is basically below two, average capacity loss 0.32 bps/Hz with respect to the ideal uncorrelated (2,2) case and envelope correlation lower than 20 dB. (C) 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 889-895, 2010: Published online in Wiley InterScience ( DOI:10.1002/mop.25047
Autores: Peralta, G.; Cid-Fuentes, R.G.; Bilbao, J.; et al.
Libro:  Network Coding
2018  págs. 37 - 52
Industry 4.0 has become the main source of applications of the Internet of Things (IoT), which is generating new business opportunities. The use of cloud computing and artificial intelligence is also showing remarkable improvements in industrial operation, saving millions of dollars to manufacturers. The need for time-critical decision-making is evidencing a trade-off between latency and computation, urging Industrial IoT (IIoT) deployments to integrate fog nodes to perform early analytics. In this chapter, we review next-generation IIoT architectures, which aim to meet the requirements of industrial applications, such as low-latency and highly reliable communications. These architectures can be divided into IoT node, fog, and multicloud layers. We describe these three layers and compare their characteristics, providing also different use-cases of IIoT architectures. We introduce network coding (NC) as a solution to meet some of the requirements of next-generation communications. We review a variety of its approaches as well as different scenarios that improve their performance and reliability thanks to this technique. Then, we describe the communication process across the different levels of the architecture based on NC-based state-of-the-art works. Finally, we summarize the benefits and open challenges of combining IIoT architectures together with NC techniques.



Universidad de Navarra - Escuela de Ingenieros.

Comunicaciones digitales avanzadas (MIT). 
Universidad de Navarra - Escuela de Ingenieros.



Pedro M. Crespo is a Professor at TECNUN, the Technological Campus of University of Navarra, San Sebastian, Spain, and Head of the Mathematical Principles of Information and Communications Group. In 1978 he received the engineering degree in Telecommunications from Universidad Politécnica de Barcelona, Spain, in 1978, and the M. Sc. in Applied Mathematics and Ph.D. in Electrical Engineering from University of Southern California, CA USA, in 1983 and 1984, respectively. After finishing his Ph.D. degree, he joined the Signal Processing Research Group at Bell Communications Research (Bellcore), NJ, USA. At the time, Bellcore was the world¿s leading research Institution in Telecommunication, providing R&D to the Bell Operating Companies. As a member of the Technical Staff he worked as a researcher in the general area of data communication and signal processing. His research focused on various topics related to mobile communications, optical communications and digital subscriber line communications (ADSL). He actively contributed to the definition and development of the first ADSL prototypes. In 1992 Bellcore was one of the few USA Labs that had an ADSL working prototype. In May 1992 he joined as a Senior Researcher, the R&D center Telefónica Investigación y Desarrollo, Madrid, Spain. Among other responsibilities, he was in charge of the planning and technical management for the European Research projects (RACE, EURESCOM, ACTS) in which Telefonica participated. In particular, he was involved in the definition and implementation of the standard H.324 for video telephony for applications in mobile networks. During the period of 1999 to 2002, Dr. Crespo was the technical director of the Spanish telecommunication operator Jazztel, an alternative telecommunications access provider in the Iberian Peninsula. In September 1999, he joined the R&D center CEIT, San Sebastian, Spain, as the Head of the Mathematical Principles of Information and Communications Group. In 2003 he became a full Professor at University of Navarra, and from 2007 until 2016, he was the director of the Electronics and Communications department at CEIT. He combined his work at CEIT with his role as professor at the university, teaching courses in the area of Information Theory, Signal Processing and Data Communications. Pedro Crespo is a Senior Member of the Institute of Electrical and Electronic Engineers (IEEE) and he is a Recipient of Bell Communication Research¿s Award of Excellence. Professor Crespo holds seven patents in the areas of digital subscriber lines and wireless communications and is author of more than 160 international conference papers and journals.