Fundamental limits of short-packet wireless communications

Mención Internacional en el título de doctorThis thesis concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an errorcorrecting code of a given blocklength with a block-error probability not exceeding a given value. This is an emerging problem originated by the next generation of wireless communications, where the understanding of the fundamental limits in the transmission of short packets is crucial. For this setting, traditional informationtheoretical metrics of performance that rely on the transmission of long packets, such as capacity or outage capacity, are not good benchmarks anymore, and the study of the maximum coding rate as a function of the blocklength is needed. For the noncoherent Rayleigh block-fading channel model, to study the maximum coding rate as a function of the blocklength, only nonasymptotic bounds that must be evaluated numerically were available in the literature. The principal drawback of the nonasymptotic bounds is their high computational cost, which increases linearly with the number of blocks (also called throughout this thesis coherence intervals) needed to transmit a given codeword. By means of different asymptotic expansions in the number of blocks, this thesis provides an alternative way of studying the maximum coding rate as a function of the blocklength for the noncoherent, single-antenna, Rayleigh block-fading channel. The first approximation on the maximum coding rate derived in this thesis is a high-SNR normal approximation. This central-limit-theorem-based approximation becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L of size T tend to infinity. We show that the high-SNR normal approximation is roughly equal to the normal approximation one obtains by transmitting one pilot symbol per coherence block to estimate the fading coefficient, and by then transmitting T−1 symbols per coherence block over a coherent fading channel. This suggests that, at high SNR, one pilot symbol per coherence block suffices to achieve both the capacity and the channel dispersion. While the approximation was derived under the assumption that the number of coherence intervals and the SNR tend to infinity, numerical analyses suggest that it becomes accurate already at SNR values of 15 dB, for 10 coherence intervals or more, and probabilities of error of 10−3 or more. The derived normal approximation is not only useful because it complements the nonasymptotic bounds available in the literature, but also because it lays the foundation for analytical studies that analyze the behavior of the maximum coding rate as a function of system parameters such as SNR, number of coherence intervals, or blocklength. An example of such a study concerns the optimal design of a simple slotted-ALOHA protocol, which is also given in this thesis. Since a big amount of services and applications in the next generation of wireless communication systems will require to operate at low SNRs and small probabilities of error (for instance, SNR values of 0 dB and probabilities of error of 10−6), the second half of this thesis presents saddlepoint approximations of upper and lower nonasymptotic bounds on the maximum coding rate that are accurate in that regime. Similar to the normal approximation, these approximations become accurate as the number of coherence intervals L increases, and they can be calculated efficiently. Indeed, compared to the nonasymptotic bounds, which require the evaluation of L-dimensional integrals, the saddlepoint approximations only require the evaluation of four one-dimensional integrals. Although developed under the assumption of large L, the saddlepoint approximations are shown to be accurate even for L = 1 and SNR values of 0 dB or more. The small computational cost of these approximations can be further avoided by performing high-SNR saddlepoint approximations that can be evaluated in closed form. These approximations can be applied when some conditions of convergence are satisfied and are shown to be accurate for 10 dB or more. In our analysis, the saddlepoint method is applied to the tail probabilities appearing in the nonasymptotic bounds. These probabilities often depend on a set of parameters, such as the SNR. Existing saddlepoint expansions do not consider such dependencies. Hence, they can only characterize the behavior of the expansion error in function of the number of coherence intervals L, but not in terms of the remaining parameters. In contrast, we derive a saddlepoint expansion for random variables whose distribution depends on an extra parameter, carefully analyze the error terms, and demonstrate that they are uniform in such an extra parameter. We then apply the expansion to the Rayleigh block-fading channel and obtain approximations in which the error terms depend only on the blocklength and are uniform in the remaining parameters. Furthermore, the proposed approximations are shown to recover the normal approximation and the reliability function of the channel, thus providing a unifying tool for the two regimes, which are usually considered separately in the literature. Specifically, we show that the high-SNR normal approximation can be recovered from the normal approximation derived from the saddlepoint approximations. By means of the error exponent analysis that recovers the reliability function of the channel, we also obtain easier-to-evaluate approximations of the saddlepoint approximations consisting of the error exponent of the channel multiplied by a subexponential factor. Numerical evidence suggests that these approximations are as accurate as the saddlepoint approximations. Finally, this thesis includes a practical case study where we analyze the benefit of cooperation in optical wireless communications, a promising technology that can play an important role in the next generation of wireless communications due to the high data rates it can achieve. Specifically, a cooperative multipoint transmission and reception scheme is evaluated for visible light communication (VLC) in an indoor scenario. The proposed scheme is shown to provide SNR improvements of 3 dB or more compared to a noncooperative scheme, especially when there is non-line-of-sight (NLOS) between the access point and the receiver.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Joerg Widmer.- Secretario: Matilde Pilar Sánchez Fernández.- Vocal: Petar Popovsk

Implementación de la señalización de una estación de base UMTS

Los principales objetivos buscados en la realización de este trabajo son los siguientes: - Iniciación a las comunicaciones móviles. Con este trabajo se pretende adquirir las bases que permitan iniciar una tarea investigadora relacionada con las comunicaciones móviles. - Conocimiento profundo de una de las tecnologías de comunicaciones móviles más usadas en la actualidad, como es UMTS. - Aprender a leer y usar la información proporcionada en un estándar. Generalmente, los estándares proporcionan una gran cantidad de información. En muchos casos, es mucho más amplia de lo que se necesita para realizar un estudio de algo concreto. Es muy importante saber interpretar y extraer lo que es necesario para realizar un trabajo determinado. - Implementación de la funcionalidad de la estación base de UMTS en un software completamente nuevo, de programación gráfica, como es NI Labview y que permite la conexión de hardware específico para poder realizar transmisiones de verdad. Con ello se pretendía además de aprender un lenguaje de programación nuevo, poder enfrentarse a los problemas reales que conlleva el trabajo con hardware y la propagación inalámbrica en un entorno real. - Familiarización con material del laboratorio de comunicaciones móviles. Para la realización de diversas pruebas, es necesario utilizar los distintos dispositivos de análisis disponibles en el laboratorio de comunicaciones móviles. - Implementación de una estación base con fines docentes. El contenido de este proyecto podrá ser usado en el futuro por los estudiantes que cursen la asignatura de Comunicaciones MóvilesIngeniería de Sistemas de Comunicacione

Sincronización y Estimación de canal eficiente y robusta en sistemas CoMP OFDM

Este trabajo fue presentado en el XXIX Simposium Nacional de la Unión Científica Internacional de Radio, celebrado los días 3-5 de septiembre de 2014 en la Universidad Politécnica de Valencia (España).In this paper, an efficient and robust simultaneous timing synchronization and channel estimation method for Cooperative MultiPoint Transmission and Reception (CoMP) is proposed. Efficiency is obtained by using the same two Orthogonal Frequency Division Multiplexing (OFDM) symbols for simultaneously transmitting preambles by all the base stations. Robustness is achieved by specially designed orthogonal sequences both in time and frequency domain. The proposed method is able to estimate the channels from several base stations without losing anything in performance with respect to the single transmission scenario. Furthermore, our proposed synchronization outperforms single transmitter methods and so, it could also be adapted for single base station OFDM systems.Este trabajo ha sido financiado parcialmente por los proyectos GRE3NSYST (TEC2011-29006-C03-03) y COMONSENS (CSD2008-00010).Publicad

Short-Packet Transmission over a Bidirectional Massive MIMO link

We consider the transmission of short packets over a bidirectional communication link where multiple devices, e.g., sensors and actuators, exchange small-data payloads with a base station equipped with a large antenna array. Using results from finite-blocklength information theory, we characterize the minimum SNR required to achieve a target error probability for a fixed packet length and a fixed payload size. Our nonasymptotic analysis, which applies to the scenario in which the bidirectional communication is device-initiated, and also to the more challenging case when it is base-station initiated, provides guidelines on the design of massive multiple-input multiple-output links that need to support sporadic ultra-reliable low-latency transmissions. Specifically, it allows us to determine the optimal amount of resources that need to be dedicated to the acquisition of channel state information

A high-SNR normal approximation for single-antenna Rayleigh block-fading channels

Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June, 2017This paper concerns the maximal achievable rate at which data can be transmitted over a non-coherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. In particular, a high-SNR normal approximation of the maximal achievable rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate already at SNR values of 15 dB.A. Lancho and T. Koch have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013-41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU), from an FPU fellowship from the Spanish Ministerio de Educación, Cultura y Deporte under Grant FPU14/01274 and from the Comunidad de Madrid under Grant S2103/ICE-2845. G. Durisi has been supported by the Swedish Research Council under Grants 2012-4571 and 2016-03293

Normal approximations for fading channels

Proceeding of: 52nd Annual Conference on Information Sciences and Systems (CISS 2018)Capacity and outage capacity characterize the maximum coding rate at which reliable communication is feasible when there are no constraints on the packet length. Evaluated for fading channels, they are important performance benchmarks for wireless communication systems. However, the latency of a communication system is proportional to the length of the packets it exchanges, so assuming that there are no constraints on the packet length may be overly optimistic for communication systems with stringent latency constraints. Recently, there has been great interest within the information theory community in characterizing the maximum coding rate for short packet lengths. Research on this topic is often concerned with asymptotic expansions of the coding rate with respect to the packet length, which then give rise to normal approximations. In this paper, we review existing normal approximations for single-antenna Rayleigh block-fading channels and compare them with the high-SNR normal approximation we presented at the 2017 IEEE International Symposium on Information Theory (Lancho, Koch, and Durisi, 2017). We further discuss how these normal approx- imations may help to assess the performance of communication protocols.A. Lancho and T. Koch have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 714161), from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013-41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU), from an FPU fellowship from the Spanish Ministerio de Educación, Cultura y Deporte under Grant FPU14/01274, and from the Comunidad de Madrid under Grant S2103/ICE-2845. G. Durisi has been supported by the Swedish Research Council under Grant and 2016-03293

On Single-Antenna Rayleigh Block-Fading Channels at Finite Blocklength

This article concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals $L$ over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10 or more.The work of A. Lancho and T. Koch was supported in part by the Spanish Ministerio de Economia y Competitividad under Grant TEC2013-41718-R and Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU), in part by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under Grant 714161, and in part by the Comunidad de Madrid under Grant S2103/ICE-2845. The work of A. Lancho further was supported by an FPU fellowship from the Spanish Ministerio de Educación, Cultura y Deporte under Grant FPU14/01274. The work of T. Koch further was supported in part by the Spanish Ministerio de Economía y Competitividad under Grant RYC-2014-16332 and in part by the 7th European Union Framework Programme under Grant 333680. The work of G. Durisi was supported by the Swedish Research Council under Grant 2012-4571 and Grant 2016-03293

URLLC with Massive MIMO: Analysis and Design at Finite Blocklength

The fast adoption of Massive MIMO for high-throughput communications was enabled by many research contributions mostly relying on infinite-blocklength information-theoretic bounds. This makes it hard to assess the suitability of Massive MIMO for ultra-reliable low-latency communications (URLLC) operating with short-blocklength codes. This paper provides a rigorous framework for the characterization and numerical evaluation (using the saddlepoint approximation) of the error probability achievable in the uplink and downlink of Massive MIMO at finite blocklength. The framework encompasses imperfect channel state information, pilot contamination, spatially correlated channels, and arbitrary linear spatial processing. In line with previous results based on infinite-blocklength bounds, we prove that, with minimum mean-square error (MMSE) processing and spatially correlated channels, the error probability at finite blocklength goes to zero as the number M of antennas grows to infinity, even under pilot contamination. However, numerical results for a practical URLLC network setup involving a base station with M-100 antennas, show that a target error probability of 10^¿5 can be achieved with MMSE processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. Maximum ratio processing does not suffice.The work of Johan Östman, Alejandro Lancho, and Giuseppe Durisi was supported in part by the Swedish Research Council under grant 2016-03293 and in part by the Wallenberg AI, Autonomous Systems, and Software Program. The work of Luca Sanguinetti was supported in part by the Italian Ministry of Education and Research (MIUR) in the framework of the CrossLab Project (Departments of Excellence)

Saddlepoint Approximations for Noncoherent Single-Antenna Rayleigh Block-Fading Channels

Proceeding of: 2019 IEEE International Symposium on Information Theory (ISIT), 7-12 July 2019, Paris, FranceThis paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB, blocklengths of 168 channel uses or more, and when the channel's coherence interval is not smaller than two. It is demonstrated that the derived approximations recover both the normal approximation and the reliability function of the channel.A. Lancho, G. Vázquez-Vilar and T. Koch have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (714161), the Spanish Ministerio de Economía y Competitividad (RYC-2014-16332, TEC2016-78434-C3-3-R (AEI/FEDER, EU) and IJCI2015-27020), the Spanish Ministerio de Educación, Cultura y Deporte (FPU014/01274), and the Comunidad de Madrid (S2103/ICE-2845). G. Durisi and J. Östman have been supported by the Swedish Research Council under Grants 2016-03293 and 2014-6066

Learning Mobile Communications Standards through Flexible Software Defined Radio Base Stations

Mobile communications are today widespread and contribute to the development of our society. Every day new devices include some means of wireless transmission, which is becoming ubiquitous with the Internet of Things. These systems are standardized by international organizations such as the IEEE, 3GPP, and ETSI, among others. Even though knowledge of wireless standards is key to the understanding of these systems, wireless communications are quite often taught in engineering degrees in a traditional way, without much emphasis on the standardization. Moreover, strong focus is often placed on the theoretical performance analysis rather than on practical implementation aspects. In contrast, most of the current applications make extensive use of mobile data, and the global users' satisfaction is highly correlated with the mobile data throughput. Thus, modern wireless engineers need to have deep insight on the standards that define the mobile transmission systems, and this knowledge is not acquired following the traditional theoretical teaching schemes. In this article, a new learning approach is described. This novel paradigm is based on a new flexible hardware/software platform (FRAMED-SOFT), which is also detailed. Although the article is focused on two wireless standards, GSM and UMTS, the work discussed in this article can easily be extended to other standards of interest, such as LTE and beyond, WiFi, and WiMAX