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

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

Multiple-symbol differential sphere detection and decision-feedback differential detection conceived for differential QAM

Multiple-Symbol Differential Sphere Detection (MSDSD) relies on the knowledge of channel correlation. More explicitly, for Differential PSK (DPSK), the transmitted symbols’ phases form a unitary matrix, which can be separated from the channel’s correlation matrix by the classic Multiple-Symbol Differential Detection (MSDD), so that a lower triangular matrix extracted from the inverted channel correlation matrix is utilized for the MSDSD’s sphere decoding. However, for Differential QAM (DQAM), the transmitted symbols’ amplitudes cannot form a unitary matrix, which implies that the MSDD’s channel correlation matrix becomes amplitude-dependent and remains unknown, unless all the data-carrying symbol amplitudes are detected. In order to tackle this open problem, in this paper, we propose to determine the MSDD’s non-constant amplitudedependent channel correlation matrix with the aid of a sphere decoder, so that the classic MSDSD algorithms that were originally conceived for DPSK may also be invoked for DQAM detection. As a result, our simulation results demonstrate that the MSDSD aided DQAM schemes substantially outperform their DPSK counterparts. However, the price paid is that the detection complexity of MSDSD is also significantly increased. In order to mitigate this, we then propose a reduced-complexity MSDSD search strategy specifically conceived for DQAM constellations, which separately map bits to their ring-amplitude index and phase index. Furthermore, the classic Decision-Feedback Differential Detection (DFDD) conceived for DQAM relies on a constant channel correlation matrix, which implies that these DFDD solutions are sub-optimal and they are not equivalent to the optimum MSDD operating in decision-feedback mode. With the advent for solving the open problem of MSDSD aided DQAM, we further propose to improve the conventional DFDD aided DQAM solutions in this paper

Electronic processing for optical communication systems

I sistemi di comunicazione in fibra ottica risentono di diversi tipi di disturbi, quali ad esempio la dispersione cromatica e la dispersione dei modi di polarizzazione. La compensazione ottica di tali disturbi è possibile ma complessa e costosa, mentre le tecniche di elaborazione elettronica del segnale presentano diversi vantaggi, semplicità, costo, adattabilità. L'equalizzazione elettronica e la strategia di rivelazione di sequenza a massima verosimiglianza rappresentano soluzioni efficaci e realizzabili con semplici modulazioni di ampiezza e anche con più avanzate modulazioni di fase e fase-ampiezza.Optical communication systems are suffering from several typical impairments, chromatic dispersion and polarization mode dispersion. Optical compensation of such impairments is possible but it is technological demanding and expensive, whereas electronic signal processing presents many advantages, implementation ease, cost-efficiency, adaptability. Electronic equalization and maximum likelihood sequence detection represent effective and feasible solutions for simple amplitude modulation formats as well as for more advanced phase and phase-amplitude modulation formats

Carrier Synchronization in High Bit-Rate Optical Transmission Systems

In this dissertation, design of optical transmission systems with differential detection and coherent detection is briefly described. More over, algorithms for carrier synchronization and phase estimation with their implementation in high bit-rate optical transmission systems are proposed