Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective

The signal processing community currently witnesses the emergence of sensor array processing and Direction-of-Arrival (DoA) estimation in various modern applications, such as automotive radar, mobile user and millimeter wave indoor localization, drone surveillance, as well as in new paradigms, such as joint sensing and communication in future wireless systems. This trend is further enhanced by technology leaps and availability of powerful and affordable multi-antenna hardware platforms. The history of advances in super resolution DoA estimation techniques is long, starting from the early parametric multi-source methods such as the computationally expensive maximum likelihood (ML) techniques to the early subspace-based techniques such as Pisarenko and MUSIC. Inspired by the seminal review paper Two Decades of Array Signal Processing Research: The Parametric Approach by Krim and Viberg published in the IEEE Signal Processing Magazine, we are looking back at another three decades in Array Signal Processing Research under the classical narrowband array processing model based on second order statistics. We revisit major trends in the field and retell the story of array signal processing from a modern optimization and structure exploitation perspective. In our overview, through prominent examples, we illustrate how different DoA estimation methods can be cast as optimization problems with side constraints originating from prior knowledge regarding the structure of the measurement system. Due to space limitations, our review of the DoA estimation research in the past three decades is by no means complete. For didactic reasons, we mainly focus on developments in the field that easily relate the traditional multi-source estimation criteria and choose simple illustrative examples.Comment: 16 pages, 8 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Downlink Achievable Rate Analysis for FDD Massive MIMO Systems

Multiple-Input Multiple-Output (MIMO) systems with large-scale transmit antenna arrays, often called massive MIMO, are a very promising direction for 5G due to their ability to increase capacity and enhance both spectrum and energy efficiency. To get the benefit of massive MIMO systems, accurate downlink channel state information at the transmitter (CSIT) is essential for downlink beamforming and resource allocation. Conventional approaches to obtain CSIT for FDD massive MIMO systems require downlink training and CSI feedback. However, such training will cause a large overhead for massive MIMO systems because of the large dimensionality of the channel matrix. In this dissertation, we improve the performance of FDD massive MIMO networks in terms of downlink training overhead reduction, by designing an efficient downlink beamforming method and developing a new algorithm to estimate the channel state information based on compressive sensing techniques. First, we design an efficient downlink beamforming method based on partial CSI. By exploiting the relationship between uplink direction of arrivals (DoAs) and downlink direction of departures (DoDs), we derive an expression for estimated downlink DoDs, which will be used for downlink beamforming. Second, By exploiting the sparsity structure of downlink channel matrix, we develop an algorithm that selects the best features from the measurement matrix to obtain efficient CSIT acquisition that can reduce the downlink training overhead compared with conventional LS/MMSE estimators. In both cases, we compare the performance of our proposed beamforming method with traditional methods in terms of downlink achievable rate and simulation results show that our proposed method outperform the traditional beamforming methods

Fast converging robust beamforming for downlink massive MIMO systems in heterogenous networks

Massive multiple-input multiple-output (MIMO) is an emerging technology, which is an enabler for future broadband wireless networks that support high speed connection of densely populated areas. Application of massive MIMO at the macrocell base stations in heterogeneous networks (HetNets) offers an increase in throughput without increasing the bandwidth, but with reduced power consumption. This research investigated the optimisation problem of signal-to-interference-plus-noise ratio (SINR) balancing for macrocell users in a typical HetNet scenario with massive MIMO at the base station. The aim was to present an efficient beamforming solution that would enhance inter-tier interference mitigation in heterogeneous networks. The system model considered the case of perfect channel state information (CSI) acquisition at the transmitter, as well as the case of imperfect CSI at the transmitter. A fast converging beamforming solution, which is applicable to both channel models, is presented. The proposed beamforming solution method applies the matrix stuffing technique and the alternative direction method of multipliers, in a two-stage fashion, to give a modestly accurate and efficient solution. In the first stage, the original optimisation problem is transformed into standard second-order conic program (SOCP) form using the Smith form reformulation and applying the matrix stuffing technique for fast transformation. The second stage uses the alternative direction method of multipliers to solve the SOCP-based optimisation problem. Simulations to evaluate the SINR performance of the proposed solution method were carried out with supporting software-based simulations using relevant MATLAB toolboxes. The simulation results of a typical single cell in a HetNet show that the proposed solution gives performance with modest accuracy, while converging in an efficient manner, compared to optimal solutions achieved by state-of-the-art modelling languages and interior-point solvers. This is particularly for cases when the number of antennas at the base station increases to large values, for both models of perfect CSI and imperfect CSI. This makes the solution method attractive for practical implementation in heterogeneous networks with large scale antenna arrays at the macrocell base station.Dissertation (MEng)--University of Pretoria, 2018.Electrical, Electronic and Computer EngineeringMEngUnrestricte

A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data: With applications in machine learning and signal processing

This article presents a powerful algorithmic framework for big data optimization, called the block successive upper-bound minimization (BSUM). The BSUM includes as special cases many well-known methods for analyzing massive data sets, such as the block coordinate descent (BCD) method, the convex-concave procedure (CCCP) method, the block coordinate proximal gradient (BCPG) method, the nonnegative matrix factorization (NMF) method, the expectation maximization (EM) method, etc. In this article, various features and properties of the BSUM are discussed from the viewpoint of design flexibility, computational efficiency, parallel/distributed implementation, and the required communication overhead. Illustrative examples from networking, signal processing, and machine learning are presented to demonstrate the practical performance of the BSUM framework

Retournement temporel : application aux réseaux mobiles

This thesis studies the time reversal technique to improve the energy efficiency of future mobile networks and reduce the cost of future mobile devices. Time reversal technique consists in using the time inverse of the propagation channel impulse response (between a transceiver and a receiver) as a prefilter. Such pre-filtered signal is received with a stronger power (this is spatial focusing) and with a strong main echo, relatively to secondary echoes (this is time compression). During a previous learning phase, the transceiver estimates the channel by measuring the pilot signal emitted by the receiver. Space-time focusing is obtained only at the condition that the propagation remains identical between the learning phase and the data transmission phase: this is the ‘channel reciprocity’ condition. Numerous works show that spatial focusing allows for the reduction of the required transmit power for a given target received power, on the one hand, and that time compression allow for the reduction of the required complexity at the receiver side to handle multiple echoes, on the other hand. However, studies on complexity reduction are limited to ultra wideband. Some works of this thesis (based on simulations and experimental measurements) show that, for bands which are more typical for future networks (a carrier frequency of 1GHz and a spectrum of 30 MHz to 100 MHz), thanks to time reversal, a simple receiver and a mono-carrier signal are sufficient to reach high data rates. Moreover, the channel reciprocity condition is not verified in two scenarios which are typical from mobile networks. Firstly, in most European mobile networks, the frequency division duplex mode is used. This mode implies that the transceiver and the receiver communicate on distinct carriers, and therefore through different propagation channels. Secondly, when considering a receiver on a moving connected vehicle, the transceiver and the receiver communicate one with each other at distinct instants, corresponding to distinct positions of the vehicles, and therefore through different propagation channels. Some works of this thesis propose solutions to obtain space-time focusing for these two scenarios. Finally, some works of this thesis explore the combination of time reversal with other recent signal processing techniques (spatial modulation, on the one hand, a new multi-carrier waveform, on the other hand), or new deployment scenarios (millimeter waves and large antenna arrays to interconnect the nodes of an ultra dense network) or new applications (guidance and navigation) which can be envisaged for future mobile networks.Cette thèse étudie la technique dite de ‘Retournement Temporel’ afin d’améliorer l’efficacité énergétique des futurs réseaux mobiles d’une part, et réduire le coût des futurs terminaux mobiles, d’autre part. Le retournement temporel consiste à utiliser l’inverse temporel de la réponse impulsionnelle du canal de propagation entre un émetteur et un récepteur pour préfiltrer l’émission d’un signal de données. Avantageusement, le signal ainsi préfiltré est reçu avec une puissance renforcée (c’est la focalisation spatiale) et un écho principal qui est renforcé par rapport aux échos secondaires (c’est la compression temporelle). Lors d’une étape préalable d’apprentissage, l’émetteur estime le canal en mesurant un signal pilote provenant du récepteur. La focalisation spatiotemporelle n’est obtenue qu’à condition que la propagation demeure identique entre la phase d’apprentissage et la phase de transmission de données : c’est la condition de ‘réciprocité du canal’. De nombreux travaux montrent que la focalisation spatiale permet de réduire la puissance émise nécessaire pour atteindre une puissance cible au récepteur d’une part, et que la compression temporelle permet de réduire la complexité du récepteur nécessaire pour gérer l’effet des échos multiples, d’autre part. Cependant, les études sur la réduction de la complexité du récepteur se limitent à l’ultra large bande. Des travaux de cette thèse (basés sur des simulations et des mesures expérimentales) montrent que pour des bandes de fréquences plus typiques des futurs réseaux mobiles (fréquence porteuse à 1GHz et spectre de 30 MHz à 100 MHz), grâce au retournement temporel, un récepteur simple et un signal monoporteuse suffisent pour atteindre de hauts débits. En outre, la condition de réciprocité du canal n’est pas vérifiée dans deux scénarios typiques des réseaux mobiles. Tout d’abord, dans la plupart des réseaux mobiles européens, le mode de duplex en fréquence est utilisé. Ce mode implique que l’émetteur et le récepteur communiquent l’un avec l’autre sur des fréquences porteuses distinctes, et donc à travers des canaux de propagations différents. De plus, lorsqu’on considère un récepteur sur un véhicule connecté en mouvement, l’émetteur et le récepteur communiquent l’un avec l’autre à des instants distincts, correspondants à des positions distinctes du véhicule, et donc à travers des canaux de propagations différents. Des travaux de cette thèse proposent des solutions pour obtenir la focalisation spatio-temporelle dans ces deux scenarios. Enfin, des travaux de la thèse explorent la combinaison du retournement temporel avec d’autres techniques de traitement de signal récentes (la modulation spatiale, d’une part, et une nouvelle forme d’onde multiporteuse, d’autre part), ou des scenarios de déploiement nouveaux (ondes millimétriques et très grands réseaux d’antennes pour inter-connecter les noeuds d’un réseau ultra dense) ou de nouvelles applications (guidage et navigation) envisageables pour les futurs réseaux mobiles

Bayesian Beamforming for Mobile Millimeter Wave Channel Tracking in the Presence of DOA Uncertainty

This paper proposes a Bayesian approach for angle-based hybrid beamforming and tracking that is robust to uncertain or erroneous direction-of-arrival (DOA) estimation in millimeter wave (mmWave) multiple input multiple output (MIMO) systems. Because the resolution of the phase shifters is finite and typically adjustable through a digital control, the DOA can be modeled as a discrete random variable with a prior distribution defined over a discrete set of candidate DOAs, and the variance of this distribution can be introduced to describe the level of uncertainty. The estimation problem of DOA is thereby formulated as a weighted sum of previously observed DOA values, where the weights are chosen according to a posteriori probability density function (pdf) of the DOA. To alleviate the computational complexity and cost, we present a motion trajectory-constrained a priori probability approximation method. It suggests that within a specific spatial region, a directional estimate can be close to true DOA with a high probability and sufficient to ensure trustworthiness. We show that the proposed approach has the advantage of robustness to uncertain DOA, and the beam tracking problem can be solved by incorporating the Bayesian approach with an expectation-maximization (EM) algorithm. Simulation results validate the theoretical analysis and demonstrate that the proposed solution outperforms a number of state-of-the-art benchmarks.This work was in part supported by the State Key Laboratory of Rail Traffic Control and Safety (Contract No. RCS2020ZT012), Beijing Jiaotong University and China Railway Corporation (Contract No. N2019G028). This article was presented in part at the 2019 IEEE GLOBECOM’19. The associate editor coordinating the review of this article and approving it for publication was O. Oyman. (Corresponding author: Yan Yang.) Yan Yang is with the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, Chin

Non-convex Quadratically Constrained Quadratic Programming: Hidden Convexity, Scalable Approximation and Applications

University of Minnesota Ph.D. dissertation. September 2017. Major: Electrical Engineering. Advisor: Nicholas Sidiropoulos. 1 computer file (PDF); viii, 85 pages.Quadratically Constrained Quadratic Programming (QCQP) constitutes a class of computationally hard optimization problems that have a broad spectrum of applications in wireless communications, networking, signal processing, power systems, and other areas. The QCQP problem is known to be NP–hard in its general form; only in certain special cases can it be solved to global optimality in polynomial-time. Such cases are said to be convex in a hidden way, and the task of identifying them remains an active area of research. Meanwhile, relatively few methods are known to be effective for general QCQP problems. The prevailing approach of Semidefinite Relaxation (SDR) is computationally expensive, and often fails to work for general non-convex QCQP problems. Other methods based on Successive Convex Approximation (SCA) require initialization from a feasible point, which is NP-hard to compute in general. This dissertation focuses on both of the above mentioned aspects of non-convex QCQP. In the first part of this work, we consider the special case of QCQP with Toeplitz-Hermitian quadratic forms and establish that it possesses hidden convexity, which makes it possible to obtain globally optimal solutions in polynomial-time. The second part of this dissertation introduces a framework for efficiently computing feasible solutions of general quadratic feasibility problems. While an approximation framework known as Feasible Point Pursuit-Successive Convex Approximation (FPP-SCA) was recently proposed for this task, with considerable empirical success, it remains unsuitable for application on large-scale problems. This work is primarily focused on speeding and scaling up these approximation schemes to enable dealing with large-scale problems. For this purpose, we reformulate the feasibility criteria employed by FPP-SCA for minimizing constraint violations in the form of non-smooth, non-convex penalty functions. We demonstrate that by employing judicious approximation of the penalty functions, we obtain problem formulations which are well suited for the application of first-order methods (FOMs). The appeal of using FOMs lies in the fact that they are capable of efficiently exploiting various forms of problem structure while being computationally lightweight. This endows our approximation algorithms the ability to scale well with problem dimension. Specific applications in wireless communications and power grid system optimization considered to illustrate the efficacy of our FOM based approximation schemes. Our experimental results reveal the surprising effectiveness of FOMs for this class of hard optimization problems

Single-anchor two-way localization bounds for 5G mmWave systems

Recently, millimeter-wave (mmWave) 5G localization has been shown to be to provide centimeter-level accuracy, lending itself to many location-aware applications, e.g., connected autonomous vehicles (CAVs). One assumption usually made in the investigation of localization methods is that the user equipment (UE), i.e., a CAV, and the base station (BS) are time synchronized. In this paper, we remove this assumption and investigate two two-way localization protocols: (i) a round-trip localization protocol (RLP), whereby the BS and UE exchange signals in two rounds of transmission and then localization is achieved using the signal received in the second round; (ii) a collaborative localization protocol (CLP), whereby localization is achieved using the signals received in the two rounds. We derive the position and orientation error bounds applying beamforming at both ends and compare them to the traditional one-way localization. Our results show that mmWave localization is mainly limited by the angular rather than the temporal estimation and that CLP significantly outperforms RLP. Our simulations also show that it is more beneficial to have more antennas at the BS than at the UE