Space-Time Signal Design for Multilevel Polar Coding in Slow Fading Broadcast Channels

Slow fading broadcast channels can model a wide range of applications in wireless networks. Due to delay requirements and the unavailability of the channel state information at the transmitter (CSIT), these channels for many applications are non-ergodic. The appropriate measure for designing signals in non-ergodic channels is the outage probability. In this paper, we provide a method to optimize STBCs based on the outage probability at moderate SNRs. Multilevel polar coded-modulation is a new class of coded-modulation techniques that benefits from low complexity decoders and simple rate matching. In this paper, we derive the outage optimality condition for multistage decoding and propose a rule for determining component code rates. We also derive an upper bound on the outage probability of STBCs for designing the set-partitioning-based labelling. Finally, due to the optimality of the outage-minimized STBCs for long codes, we introduce a novel method for the joint optimization of short-to-moderate length polar codes and STBCs

Design and Performance Analysis of Non-Coherent Detection Systems with Massive Receiver Arrays

Harvesting the gain of a large number of antennas in a mmWave band has mainly been relying on the costly operation of channel state information (CSI) acquisition and cumbersome phase shifters. Recent works have started to investigate the possibility to use receivers based on energy detection (ED), where a single data stream is decoded based on the channel and noise energy. The asymptotic features of the massive receiver array lead to a system where the impact of the noise becomes predictable due to a noise hardening effect. This in effect extends the communication range compared to the receiver with a small number of antennas, as the latter is limited by the unpredictability of the additive noise. When the channel has a large number of spatial degrees of freedom, the system becomes robust to imperfect channel knowledge due to channel hardening. We propose two detection methods based on the instantaneous and average channel energy, respectively. Meanwhile, we design the detection thresholds based on the asymptotic properties of the received energy. Differently from existing works, we analyze the scaling law behavior of the symbol-error-rate (SER). When the instantaneous channel energy is known, the performance of ED approaches that of the coherent detection in high SNR scenarios. When the receiver relies on the average channel energy, our performance analysis is based on the exact SER, rather than an approximation. It is shown that the logarithm of SER decreases linearly as a function of the number of antennas. Additionally, a saturation appears at high SNR for PAM constellations of order larger than two, due to the uncertainty on the channel energy. Simulation results show that ED, with a much lower complexity, achieves promising performance both in Rayleigh fading channels and in sparse channels

On the BICM Capacity

Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor

Study of phase noise in optical coherent systems

Le bruit de phase est un problème important dans la conception de systèmes cohérents optiques. Bien que le bruit de phase soit étudié énormément dans les communications sans fil, certains aspects de bruit de phase sont nouveaux dans des systèmes cohérents optiques. Dans cette thèse, nous explorons les statistiques de bruit de phase dans les systèmes optiques cohérentes et proposons une nouvelle technique pour améliorer la robustesse du système envers le bruit de phase. Notre première contribution traite de l’étude des statistiques de bruit de phase en présence de compensation électronique de la dispersion chromatique (CD) dans des systèmes cohérents. Nous montrons que le modèle proposé précédemment pour l’interaction de CD avec bruit de phase doit être modifié à cause d’un modèle trop simple pour la récupération de phase. Nous dérivons une expression plus précise pour le bruit de phase estimé par la récupération de phase avec décision dirigée (DD), et utilisons cette expression pour modifier les statistiques de décision pour les symboles reçus. Nous calculons le taux d’erreur binaire (BER) pour le format de transmission DQPSK semi-analytiquement en utilisant nos statistiques de décision modifiées et montrons que pour la récupération de phase idéale, le BER semi-analytique est bien assorti avec le BER simulé avec la technique Monte-Carlo (MC). Notre deuxième contribution est l’adaptation d’une technique de codage MLCM pour les systèmes cohérents limités par le bruit de phase et le bruit blanc additif Gaussien (AWGN). Nous montrons que la combinaison d’une constellation optimisée pour le bruit de phase avec MLCM offre un système robuste à complexité modérée. Nous vérifions que la performance de MLCM dans des systèmes cohérents avec constellations 16-aires se détériorés par le bruit de phase non-linéaire et de Wiener. Pour le bruit de phase non-linéaire, notre conception de MLCM démontre une performance supérieure par rapport àune conception de MLCM déjà présente dans la littérature. Pour le bruit de phase de Wiener, nous comparons deux format de transmission, constellations carrées et optimisée pour bruit de phase, et deux techniques de codage, MLCM et codage à débit uniforme. Nos résultats expérimentaux pour BER après codage suivent les mêmes tendances que le BER simulé et confirment notre conception.Phase noise is an important issue in designing today’s optical coherent systems. Although phase noise is studied heavily in wireless communications, some aspects of phase noise are novel in optical coherent systems. In this thesis we explore phase noise statistics in optical coherent systems and propose a novel technique to increase system robustness toward phase noise. Our first contribution deals with the study of phase noise statistics in the presence of electronic chromatic dispersion (CD) compensation in coherent systems. We show that previously proposed model for phase noise and CD interaction must be modified due to an overly simple model of carrier phase recovery. We derive a more accurate expression for the estimated phase noise of decision directed (DD) carrier phase recovery, and use this expression to modify the decision statistics of received symbols. We calculate bit error rate (BER) of a differential quadrature phase shift keying (DQPSK) system semi-analytically using our modified decision statistics and show that for ideal DD carrier phase recovery the semi-analytical BER matches the BER simulated via Monte-Carlo (MC) technique. We show that the semi-analytical BER is a lower bound of simulated BER from Viterbi-Viterbi (VV) carrier phase recovery for a wide range of practical system parameters. Our second contribution is concerned with adapting a multi-level coded modulation (MLCM) technique for phase noise and additive white Gaussian noise (AWGN) limited coherent system. We show that the combination of a phase noise optimized constellation with MLCM offers a phase-noise robust system at moderate complexity. We propose a numerical method to design set-partitioning (mapping bits to symbols) and optimizing code rates for minimum block error rate (BLER).We verify MLCM performance in coherent systems of 16-ary constellations impaired by nonlinear and Wiener phase noise. For nonlinear phase noise, superior performance of our MLCM design over a previously designed MLCM system is demonstrated in terms of BLER. For Wiener phase noise, we compare optimized and square 16-QAM constellations assuming either MLCM or uniform rate coding. We compare post forward error correction (FEC) BER in addition to BLER by both simulation and experiment and show that superior BLER performance is translated into post FEC BER. Our experimental post FEC BER results follow the same trends as simulated BER, validating our design

The Gaussian assumption in second-order estimation problems in digital communications

This paper deals with the goodness of the Gaussian assumption when designing second-order blind estimation methods in the context of digital communications. The low- and high-signal-to-noise ratio (SNR) asymptotic performance of the maximum likelihood estimator - derived assuming Gaussian transmitted symbols - is compared with the performance of the optimal second-order estimator, which exploits the actual distribution of the discrete constellation. The asymptotic study concludes that the Gaussian assumption leads to the optimal second-order solution if the SNR is very low or if the symbols belong to a multilevel constellation such as quadrature-amplitude modulation (QAM) or amplitude-phase-shift keying (APSK). On the other hand, the Gaussian assumption can yield important losses at high SNR if the transmitted symbols are drawn from a constant modulus constellation such as phase-shift keying (PSK) or continuous-phase modulations (CPM). These conclusions are illustrated for the problem of direction-of-arrival (DOA) estimation of multiple digitally-modulated signals.Peer ReviewedPostprint (published version

On the Impact of Phase Noise in Communication Systems –- Performance Analysis and Algorithms

The mobile industry is preparing to scale up the network capacity by a factor of 1000x in order to cope with the staggering growth in mobile traffic. As a consequence, there is a tremendous pressure on the network infrastructure, where more cost-effective, flexible, high speed connectivity solutions are being sought for. In this regard, massive multiple-input multiple-output (MIMO) systems, and millimeter-wave communication systems are new physical layer technologies, which promise to facilitate the 1000 fold increase in network capacity. However, these technologies are extremely prone to hardware impairments like phase noise caused by noisy oscillators. Furthermore, wireless backhaul networks are an effective solution to transport data by using high-order signal constellations, which are also susceptible to phase noise impairments. Analyzing the performance of wireless communication systems impaired by oscillator phase noise, and designing systems to operate efficiently in strong phase noise conditions are critical problems in communication theory. The criticality of these problems is accentuated with the growing interest in new physical layer technologies, and the deployment of wireless backhaul networks. This forms the main motivation for this thesis where we analyze the impact of phase noise on the system performance, and we also design algorithms in order to mitigate phase noise and its effects. First, we address the problem of maximum a posteriori (MAP) detection of data in the presence of strong phase noise in single-antenna systems. This is achieved by designing a low-complexity joint phase-estimator data-detector. We show that the proposed method outperforms existing detectors, especially when high order signal constellations are used. Then, in order to further improve system performance, we consider the problem of optimizing signal constellations for transmission over channels impaired by phase noise. Specifically, we design signal constellations such that the error rate performance of the system is minimized, and the information rate of the system is maximized. We observe that these optimized constellations significantly improve the system performance, when compared to conventional constellations, and those proposed in the literature. Next, we derive the MAP symbol detector for a MIMO system where each antenna at the transceiver has its own oscillator. We propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. We observe that the proposed techniques significantly outperform the other algorithms in prior works. Finally, we study the impact of phase noise on the performance of a massive MIMO system, where we analyze both uplink and downlink performances. Based on rigorous analyses of the achievable rates, we provide interesting insights for the following question: how should oscillators be connected to the antennas at a base station, which employs a large number of antennas

Voronoi Constellations for Coherent Fiber-Optic Communication Systems

The increasing demand for higher data rates is driving the adoption of high-spectral-efficiency (SE) transmission in communication systems. The well-known 1.53 dB gap between Shannon\u27s capacity and the mutual information (MI) of uniform quadrature amplitude modulation (QAM) formats indicates the importance of power efficiency, particularly in high-SE transmission scenarios, such as fiber-optic communication systems and wireless backhaul links. Shaping techniques are the only way to close this gap, by adapting the uniform input distribution to the capacity-achieving distribution. The two categories of shaping are probabilistic shaping (PS) and geometric shaping (GS). Various methods have been proposed for performing PS and GS, each with distinct implementation complexity and performance characteristics. In general, the complexity of these methods grows dramatically with the SE and number of dimensions.Among different methods, multidimensional Voronoi constellations (VCs) provide a good trade-off between high shaping gains and low-complexity encoding/decoding algorithms due to their nice geometric structures. However, VCs with high shaping gains are usually very large and the huge cardinality makes system analysis and design cumbersome, which motives this thesis.In this thesis, we develop a set of methods to make VCs applicable to communication systems with a low complexity. The encoding and decoding, labeling, and coded modulation schemes of VCs are investigated. Various system performance metrics including uncoded/coded bit error rate, MI, and generalized mutual information (GMI) are studied and compared with QAM formats for both the additive white Gaussian noise channel and nonlinear fiber channels. We show that the proposed methods preserve high shaping gains of VCs, enabling significant improvements on system performance for high-SE transmission in both the additive white Gaussian noise channel and nonlinear fiber channel. In addition, we propose general algorithms for estimating the MI and GMI, and approximating the log-likelihood ratios in soft-decision forward error correction codes for very large constellations

Multidimensional Optimized Optical Modulation Formats

This chapter overviews the relatively large body of work (experimental and theoretical) on modulation formats for optical coherent links. It first gives basic definitions and performance metrics for modulation formats that are common in the literature. Then, the chapter discusses optimization of modulation formats in coded systems. It distinguishes between three cases, depending on the type of decoder employed, which pose quite different requirements on the choice of modulation format. The three cases are soft-decision decoding, hard-decision decoding, and iterative decoding, which loosely correspond to weak, medium, and strong coding, respectively. The chapter also discusses the realizations of the transmitter and transmission link properties and the receiver algorithms, including DSP and decoding. It further explains how to simply determine the transmitted symbol from the received 4D vector, without resorting to a full search of the Euclidean distances to all points in the whole constellation

The Effect of Macrodiversity on the Performance of Maximal Ratio Combining in Flat Rayleigh Fading

The performance of maximal ratio combining (MRC) in Rayleigh channels with co-channel interference (CCI) is well-known for receive arrays which are co-located. Recent work in network MIMO, edge-excited cells and base station collaboration is increasing interest in macrodiversity systems. Hence, in this paper we consider the effect of macrodiversity on MRC performance in Rayleigh fading channels with CCI. We consider the uncoded symbol error rate (SER) as our performance measure of interest and investigate how different macrodiversity power profiles affect SER performance. This is the first analytical work in this area. We derive approximate and exact symbol error rate results for M-QAM/BPSK modulations and use the analysis to provide a simple power metric. Numerical results, verified by simulations, are used in conjunction with the analysis to gain insight into the effects of the link powers on performance.Comment: 10 pages, 5 figures; IEEE Transaction of Communication, 2012 Corrected typo