Algorithms for Joint Phase Estimation and Decoding for MIMO Systems in the Presence of Phase Noise and Quasi-Static Fading Channels

In this work, we derive the maximum a posteriori (MAP) symbol detector for a multiple-input multiple-output system in the presence of Wiener phase noise due to noisy local oscillators. As in single-antenna systems, the computation of the optimum receiver is an analytically intractable problem and is unimplementable in practice. In this purview, we propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. Our first algorithm is obtained by means of the sum-product algorithm, where we use the multivariate Tikhonov canonical distribution approach. In our next algorithm, we derive an approximate MAP symbol detector based on the smoother-detector framework, wherein the detector is properly designed by incorporating the phase noise statistics from the smoother. The third algorithm is derived based on the variational Bayesian framework. By simulations, we evaluate the performance of the proposed algorithms for both uncoded and coded data transmissions, and we observe that the proposed techniques significantly outperform the other important algorithms from prior works, which are considered in this work. Index Terms – Maximum a posteriori (MAP) detection, phase noise, sum-product algorithm (SPA), variational Bayesian (VB) framework, extended Kalman smoother (EKS), MIMO

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

Receiver Algorithm based on Differential Signaling for SIMO Phase Noise Channels with Common and Separate Oscillator Configurations

In this paper, a receiver algorithm consisting of differential transmission and a two-stage detection for a single-input multiple-output (SIMO) phase-noise channels is studied. Specifically, the phases of the QAM modulated data symbols are manipulated before transmission in order to make them more immune to the random rotational effects of phase noise. At the receiver, a two-stage detector is implemented, which first detects the amplitude of the transmitted symbols from a nonlinear combination of the received signal amplitudes. Then in the second stage, the detector performs phase detection. The studied signaling method does not require transmission of any known symbols that act as pilots. Furthermore, no phase noise estimator (or a tracker) is needed at the receiver to compensate the effect of phase noise. This considerably reduces the complexity of the receiver structure. Moreover, it is observed that the studied algorithm can be used for the setups where a common local oscillator or separate independent oscillators drive the radio-frequency circuitries connected to each antenna. Due to the differential encoding/decoding of the phase, weighted averaging can be employed at a multi-antenna receiver, allowing for phase noise suppression to leverage the large number of antennas. Hence, we observe that the performance improves by increasing the number of antennas, especially in the separate oscillator case. Further increasing the number of receive antennas results in a performance error floor, which is a function of the quality of the oscillator at the transmitter.Comment: IEEE GLOBECOM 201

ML Detection in Phase Noise Impaired SIMO Channels with Uplink Training

The problem of maximum likelihood (ML) detection in training-assisted single-input multiple-output (SIMO) systems with phase noise impairments is studied for two different scenarios, i.e. the case when the channel is deterministic and known (constant channel) and the case when the channel is stochastic and unknown (fading channel). Further, two different operations with respect to the phase noise sources are considered, namely, the case of identical phase noise sources and the case of independent phase noise sources over the antennas. In all scenarios the optimal detector is derived for a very general parametrization of the phase noise distribution. Further, a high signal-to-noise-ratio (SNR) analysis is performed to show that symbol-error-rate (SER) floors appear in all cases. The SER floor in the case of identical phase noise sources (for both constant and fading channels) is independent of the number of antenna elements. In contrast, the SER floor in the case of independent phase noise sources is reduced when increasing the number of antenna elements (for both constant and fading channels). Finally, the system model is extended to multiple data channel uses and it is shown that the conclusions are valid for these setups, as well.Comment: (To appear in IEEE Transactions on Communications, 2015), Contains additional material (Appendix B. T-slot Detectors

Phase-Noise Compensation for Space-Division Multiplexed Multicore Fiber Transmission

The advancements of popular Internet-based services such as social media, virtual reality, and cloud computing constantly drive vendors and operators to increase the throughput of the Internet backbone formed by fiber-optic communication systems. Due to this, space-division multiplexing (SDM) has surfaced as an appealing technology that presents an opportunity to upscale optical networks in a cost-efficient manner. It entails the sharing of various system components, such as hardware, power, and processing resources, as well as the use of SDM fibers, e.g., multicore fibers (MCFs) or multimode fibers, which are able to carry multiple independent signals at the same wavelength in parallel.Higher-order modulation formats have also garnered attention in recent years as they allow for a higher spectral efficiency, an important parameter that relates to the throughput of communication systems. However, a drawback with increasing the order of modulation formats is the added sensitivity to phase noise, which calls for effective phase-noise compensation (PNC). This thesis studies the idea of sharing processing resources to increase the performance of PNC in SDM systems using a particular type of fiber, namely uncoupled, homogeneous, single-mode MCF.Phase noise can be highly correlated across channels in various multichannel transmission scenarios, e.g., SDM systems utilizing MCFs with all cores sharing the same light source and local oscillator, and wavelength-division multiplexed systems using frequency combs. However, the nature of the correlation in the phase noise depends on the system in question. Based on this, a phase-noise model is introduced to describe arbitrarily correlated phase noise in multichannel transmission. Using this model, two pilot-aided algorithms are developed using i) the sum–product algorithm operating in a factor graph and ii) variational Bayesian inference. The algorithms carry out joint-channel PNC and data detection for coded multichannel transmission in the presence of phase noise. Simulation results show that in the case of partially-correlated phase noise, they outperform the typical PNC approach by a wide margin. Moreover, it is shown that the placement of pilot symbols across the channels has a considerable effect on the resulting performance.Focusing on SDM transmission through an uncoupled, homogeneous, single-mode MCF with shared light source and local oscillator lasers, the performance benefits of joint-channel PNC are investigated. A significant gain in transmission reach is experimentally demonstrated, and the results are shown to agree strongly with simulations based on the introduced phase-noise model. In addition, the simulations show that dramatic improvements can be made for phase-noise limited systems in terms of power efficiency, spectral efficiency, and hardware requirements

Practical methods for Gaussian mixture filtering and smoothing

In many applications, there is an interest in systematically and sequentially estimating quantities of interest in a dynamical system, using indirect and inaccurate sensor observations. There are three important sub-problems of sequential estimation: prediction, filtering and smoothing. The objective in the prediction problem is to estimate the future states of the system, using the observations until the current point in time. In the filtering problem, we seek to estimate the current state of the system, using the same information and in the smoothing problem, the aim is to estimate a past state. The smoothing estimate has the advantage that it offers the best performance on average compared to filtering and prediction estimates. Often, the uncertainties regarding the system and the observations are modeled using Gaussian mixtures (GMs). The smoothing solutions to GMs are usually based on pruning approximations, which suffer from the degeneracy problem, resulting in inconsistent estimates. Solutions based on merging have not been explored well in the literature. We address the problem of GM smoothing using both pruning and merging approximations. We consider the two main smoothing strategies of forward-backward smoothing (FBS) and two-filter smoothing (TFS), and develop novel algorithms for GM smoothing which are specifically tailored for the two principles. The FBS strategy involves forward filtering followed by backward smoothing. The existing literature provides pruning-based solutions to the forward filtering and the backward smoothing steps involved. In this thesis, we present a novel solution to the backward smoothing step of FBS, when the forward filtering uses merging methods. The TFS method works by running two filtering steps: forward filtering and backward filtering. It is not possible to apply the pruning or merging strategies to the backward filtering, as it is not a density function. To the best of our knowledge, there does not exist practical approximation techniques to reduce the complexity of the backward filtering. Therefore, in this thesis we propose two novel techniques to approximate the output of the backward filtering, which we call intragroup approximation and smoothed posterior pruning. We also show that the smoothed posterior pruning technique is applicable to forward filtering as well. The FBS and TFS solutions based on the proposed ideas are implemented for a single target tracking scenario and are shown to have similar performance with respect to root mean squared error, normalized estimation error squared, computational complexity and track loss. Compared to the FBS based on N-scan pruning, both these algorithms provide estimates with high consistency and low complexity