Channel Estimation in Multi-user Massive MIMO Systems by Expectation Propagation based Algorithms

Massive multiple input multiple output (MIMO) technology uses large antenna arrays with tens or hundreds of antennas at the base station (BS) to achieve high spectral efficiency, high diversity, and high capacity. These benefits, however, rely on obtaining accurate channel state information (CSI) at the receiver for both uplink and downlink channels. Traditionally, pilot sequences are transmitted and used at the receiver to estimate the CSI. Since the length of the pilot sequences scale with the number of transmit antennas, for massive MIMO systems downlink channel estimation requires long pilot sequences resulting in reduced spectral efficiency and the so-called pilot contamination due to sharing of the pilots in adjacent cells. In this dissertation we first review the problem of channel estimation in massive MIMO systems. Next, we study the problem of semi-blind channel estimation in the uplink in the case of spatially correlated time-varying channels. The proposed method uses the transmitted data symbols as virtual pilots to enhance channel estimation. An expectation propagation (EP) algorithm is developed to iteratively approximate the joint a posterior distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. The distribution is then used for direct estimation of the channel matrix and detection of the data symbols. A modified version of Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize our algorithm. Simulation results demonstrate that channel estimation error and the symbol error rate of the proposed algorithm improve with the increase in the number of BS antennas or the number of data symbols in the transmitted frame. Moreover, the proposed algorithms can mitigate the effects of pilot contamination as well as time-variations of the channel. Next, we study the problem of downlink channel estimation in multi-user massive MIMO systems. Our approach is based on Bayesian compressive sensing in which the clustered sparse structure of the channel in the angular domain is exploited to reduce the pilot overhead. To capture the clustered structure, we employ a conditionally independent identically distributed Bernoulli-Gaussian prior on the sparse vector representing the channel, and a Markov prior on its support vector. An EP algorithm is developed to approximate the intractable joint distribution on the sparse vector and its support with a distribution from an exponential family. This distribution is then used for direct estimation of the channel. The EP algorithm requires the model parameters which are unknown. We estimate these parameters using the expectation maximization (EM) algorithm. Simulation results show that the proposed combination of EM and EP referred to as EM-EP algorithm outperforms several recently-proposed algorithms in the literature

Semi-blind Channel Estimation and Data Detection for Multi-cell Massive MIMO Systems on Time-Varying Channels

We study the problem of semi-blind channel estimation and symbol detection in the uplink of multi-cell massive MIMO systems with spatially correlated time-varying channels. An algorithm based on expectation propagation (EP) is developed to iteratively approximate the joint a posteriori distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. This distribution is then used for direct estimation of the channel matrix and detection of data symbols. A modified version of the popular Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize the EP-based algorithm. Performance of the Kalman smoothing algorithm followed by KF-M is also examined. Simulation results demonstrate that channel estimation error and the symbol error rate (SER) of the semi-blind KF-M, KS-M, and EP-based algorithms improve with the increase in the number of base station antennas and the length of the transmitted frame. It is shown that the EP-based algorithm significantly outperforms KF-M and KS-M algorithms in channel estimation and symbol detection. Finally, our results show that when applied to time-varying channels, these algorithms outperform the algorithms that are developed for block-fading channel models.Comment: 28 pages, 13 figures, Submitted to IEEE Trans. on Vehicular Technolog

Digital Signal Processing Research Program

Contains table of contents for Section 2, an introduction, reports on twenty research projects and a list of publications.Lockheed Sanders, Inc. Contract BZ4962U.S. Army Research Laboratory Grant QK-8819U.S. Navy - Office of Naval Research Grant N00014-93-1-0686National Science Foundation Grant MIP 95-02885U.S. Navy - Office of Naval Research Grant N00014-95-1-0834U.S. Navy - Office of Naval Research Grant N00014-96-1-0930U.S. Navy - Office of Naval Research Grant N00014-95-1-0362National Defense Science and Engineering FellowshipU.S. Air Force - Office of Scientific Research Grant F49620-96-1-0072National Science Foundation Graduate Research Fellowship Grant MIP 95-02885Lockheed Sanders, Inc. Grant N00014-93-1-0686National Science Foundation Graduate FellowshipU.S. Army Research Laboratory/ARL Advanced Sensors Federated Lab Program Contract DAAL01-96-2-000

Cooperative transmission for the downlink of multiuser mimo cellular networks

Ankara : The Department of Electrical and Electronics Engineering and The Institute of Engineering and Science of Bilkent University, 2007.Thesis (Master's) -- Bilkent University, 2007.Includes bibliographical references leaves 58-60.In this thesis, we propose a distributed transmission scheme for the downlink of a multiuser system. The base-stations (BSs) cooperate with each other with limited, local message-passing to find the optimum beamforming vectors, where there are individual signal-to-interference-plus-noise-ratio (SINR) targets for each user. Majority of the previous work on this problem assumed a total power constraint on the BSs. However, since each transmit antenna is limited by the amount of power it can transmit due to the limited linear region of the power amplifiers, a more realistic constraint is to place a limit on the per-antenna power. In a recent work, Yu and Lan proposed an iterative algorithm for computing the optimum beamforming vectors minimizing the power margin over all antennas under individual SINR and per-antenna power constraints. However, from a system designer point of view, it may be more desirable to minimize the total transmit power rather than minimizing the power margin, especially when the system is not symmetric. Reformulating the transmitter optimization problem to minimize the total transmit power subject to individual SINR constraints on the users and per-antenna power constraints on the base stations, the algorithm proposed by Yu and Lan is modified. Performance of the modified algorithm is compared with the existing methods for various cellular array scenarios. The modified algorithm requires inversion of a matrix, which cannot be implemented fully distributively using limited information exchange between BSs. By approximating the matrix as tridiagonal, a suboptimal distributed algorithm for computing the beamforming vectors in a cooperative system is obtained. The proposed distributed algorithm is shown to achieve near optimal performance when the target SINRs and the size of the array are small.Yazarel, Yakup KadriM.S

Contribution à la mise en oeuvre de récepteurs et de techniques d'estimation de canal pour les systèmes mobiles de DS-CDMA multi-porteuse

Ce mémoire traite du développement de récepteurs et de techniques déstimation de canal pour les systèmes mobiles sans fil de type DS-CDMA multi-porteuse. Deux problèmes principaux doivent être pris en compte dans ce cas. Premièrement, l'Interférence d'Accès Multiple (IAM) causée par d'autres utilisateurs. Deuxièmement, les propriétés des canaux de propagation dans les systèmes radio mobiles. Ainsi, dans la première partie du manuscrit, nous proposons deux structures adaptatives (dites détection séparée et détection jointe) pour la mise en oeuvre de récepteurs minimisant lérreur quadratique moyenne (MMSE), fondés sur un Algorithme de Projection Affine (APA). Ces récepteurs permettent de supprimer les IAM, notamment lorsque le canal d'évanouissement est invariant dans le temps. Cependant, comme ces récepteurs nécessitent les séquences d'apprentissage de chaque utilisateur actif, nous développons ensuite deux récepteurs adaptatifs dits aveugles, fondés sur un algorithme de type projection affine. Dans ce cas, seule la séquence d'étalement de l'utilisateur désiré est nécessaire. Quand les séquences d'étalement de tous les utilisateurs sont disponibles, un récepteur reposant sur le décorrélateur est aussi proposé et permet d'éliminer les IAM, sans qu'une période pour l'adaptation soit nécessaire. Dans la seconde partie, comme la mise en oeuvre de récepteurs exige léstimation du canal, nous proposons plusieurs algorithmes pour léstimation des canaux d'évanouissement de Rayleigh, variables dans le temps et produits dans les systèmes multi-porteuses. A cette fin, les canaux sont approximés par des processus autorégressifs (AR) d'ordre supérieur à deux. Le premier algorithme repose sur deux filtres de Kalman interactifs pour léstimation conjointe du canal et de ses paramètres AR. Puis, pour nous affranchir des hypothèses de gaussianité nécessaires à la mise en oeuvre d'un filtre optimal de Kalman, nous étudions la pertinence d'une structure fondée sur deux filtres H1 interactifs. Enfin, léstimation de canal peut ^etre vue telle un problème déstimation fondée sur un modèle à erreur- sur-les-variables (EIV). Les paramètres AR du canal et les variances de processus générateur et du bruit d'observation dans la représentation de léspace d'état du système sont dans ce cas estimés conjointement à partir du noyau des matrices d'autocorrélation appropriées.This dissertation deals with the development of receivers and channel estimation techniques for multi-carrier DS- CDMA mobile wireless systems. Two major problems should be taken into account in that case. Firstly, the Multiple Access Interference (MAI) caused by other users. Secondly, the multi-path fading of mobile wireless channels. In the first part of the dissertation, we propose two adaptive structures (called separate and joint detection) to design Minimum Mean Square Error (MMSE) receivers, based on the Affine Projection Algorithm (APA). These receivers are able to suppress the MAI, particularly when the fading channel is time-invariant. However, as they require a training sequence for every active user, we then propose two blind adaptive multiuser receiver structures based on a blind APA-like multiuser detector. In that case, only the knowledge of the spreading code of the desired user is required. When the spreading codes of all users are available, a decorrelating detector based receiver is proposed and is able to completely eliminate the MAI without any training. In the second part, as receiver design usually requires the estimation of the channel, we propose several training-based algorithms for the estimation of time-varying Rayleigh fading channels in multi-carrier systems. For this purpose, the fading channels are approximated by autoregressive (AR) processes whose order is higher than two. The first algorithm makes it possible to jointly estimate the channel and its AR parameters based on two-cross-coupled Kalman filters. Nevertheless, this filtering is based on restrictive Gaussian assumptions. To relax them, we investigate the relevance of a structure based on two-cross-coupled H1 filters. This method consists in minimizing the influence of the disturbances such as the additive noise on the estimation error. Finally, we propose to view the channel estimation as an Errors-In-Variables (EIV) issue. In that case, the channel AR parameters and the variances of both the driving process and the measurement noise in the state-space representation of the system are estimated from the null space of suitable correlation matrices

Adaptive Spatial Intercell Interference Cancellation in Multicell Wireless Networks

Downlink spatial intercell interference cancellation (ICIC) is considered for mitigating other-cell interference using multiple transmit antennas. A principle question we explore is whether it is better to do ICIC or simply standard single-cell beamforming. We explore this question analytically and show that beamforming is preferred for all users when the edge SNR (signal-to-noise ratio) is low ($<0$ dB), and ICIC is preferred when the edge SNR is high ($>10$ dB), for example in an urban setting. At medium SNR, a proposed adaptive strategy, where multiple base stations jointly select transmission strategies based on the user location, outperforms both while requiring a lower feedback rate than the pure ICIC approach. The employed metric is sum rate, which is normally a dubious metric for cellular systems, but surprisingly we show that even with this reward function the adaptive strategy also improves fairness. When the channel information is provided by limited feedback, the impact of the induced quantization error is also investigated. It is shown that ICIC with well-designed feedback strategies still provides significant throughput gain.Comment: 26 pages, submitted to IEEE J. Select. Areas Commun. special issue on Cooperative Communications in MIMO Cellular Networks, Sept. 200

Multilane traffic density estimation with KDE and nonlinear LS and tracking with Scalar Kalman filtering

Tezin basılısı, İstanbul Şehir Üniversitesi Kütüphanesi'ndedir.With increasing population, the determination of traffic density becomes very critical in managing the urban city roads for safer driving and low carbon emission. In this study, Kernel Density Estimation is utilized in order to estimate the traffic density more accurately when the speeds of the vehicles are available for a given region. For the proposed approach, as a first step, the probability density function of the speed data is modeled by Kernel Density Estimation. Then, the speed centers from the density function are modeled as clusters. The cumulative distribution function of the speed data is then determined by Kolmogorov-Smirnov Test, whose complexity is less when compared to the other techniques and whose robustness is high when outliers exist. Then, the mean values of clusters are estimated from the smoothed density function of the distribution function, followed by a peak detection algorithm. The estimation of variance values and kernel weights, on the other hand, are found by a nonlinear Least Square approach. As the estimation problem has linear and non-linear components, the nonlinear Least Square with separation of parameters approach is adopted, instead of dealing with a high complexity nonlinear equation. Finally, the tracking of former and latter estimations of a road is calculated by using Scalar Kalman Filtering with scalar state - scalar observation generality level. Simulations are carried out in order to assess theperformanceoftheproposedapproach. Forallexampledatasets, theminimummean square error of kernel weights is found to be less than 0.002 while error of mean values is found to be less than 0.261. The proposed approach was also applied to real data from sample road traffic, and the speed center and the variance was accurately estimated. By using the proposed approach, accurate traffic density estimation is realized, providing extra information to the municipalities for better planning of their cities.Declaration of Authorship ii Abstract iii Öz iv Acknowledgments vi List of Figures ix List of Tables x Abbreviations xi 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Methods to Find Probability Density Function and Cumulative Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3 Traffic Density Estimation with Kernel Density Estimation . . . . . . . . 4 1.4 The Approaches for Determination of Key Parameters of Traffic Density Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.5 Tracking between Estimated Data and New Data . . . . . . . . . . . . . . 6 1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Literature Review 7 2.1 Methodologies Used for Estimation of Traffic Density . . . . . . . . . . . . 7 2.2 An Example Study of Traffic Density Estimation with KDE and CvM . . 9 2.3 Three Complementary Studies for Traffic Density Estimation and Tracking 9 2.4 Comparison of Three Different Nonlinear Estimation Techniques on the Same Problem . . . . . . . . . . . . . . . . . . . . . . . . .10 2.4.1 A Maximum Likelihood Approach for Estimating DS-CDMA Multipath Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.2 Channel Estimation for the Uplink of a DS-CDMA System . . . . 12 2.4.3 A Robust Method for Estimating Multipath Channel Parameters in the Uplink of a DS-CDMA System. . . . . . . . . . . . . . .13 3 The Model 16 3.1 Finding Density Distribution with KDE . . . . . . . . . . . . . . . . . . . 16 3.2 Finding Empirical CDF with KS Test . . . . . . . . . . . . . . . . . . . . 18 3.3 Determination of Speed Centers via PDA . . . . . . . . . . . . . . . . . . 20 3.4 Estimation of Variance and Kernel Weights with Nonlinear LS Method . . 21 3.5 Tracking of Traffic Density Estimation with Scalar Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4 Numerical Calculations for Traffic Density Estimation 26 4.1 An Example Traffic Scenario with Five Speed Centers . . . . . . . . . . . 26 4.2 The Estimation of A Real Time Data . . . . . . . . . . . . . . . . . . . . . 29 4.3 Traffic Density Estimation with Different Kernel Numbers . . . . . . . . . 29 5 Examples to Test Tracking Part of the Model 31 5.1 Tracking with the Change only in Mean Values . . . . . . . . . . . . . . . 32 5.2 Tracking with the Change only in Kernel Weights . . . . . . . . . . . . . . 35 5.3 Tracking with the Change in All Three Parameters . . . . . . . . . . . . . 36 6 Assesment 38 7 Conclusion 41 A Derivation of Newton-Raphson Method for the Estimation of Variance Values and Kernel Weights 43 Bibliography 4