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  • 151.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Control of platoons of heavy-duty vehicles using a delay-based spacing policy2015Conference paper (Refereed)
  • 152.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Clustering-based model reduction of networked passive systems2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 61, no 10, p. 2958-2973, article id 7350110Article in journal (Refereed)
    Abstract [en]

    The model reduction problem for networks of interconnected dynamical systems is studied in this paper. In particular, networks of identical passive subsystems, which are coupled according to a tree topology, are considered. For such networked systems, reduction is performed by clustering subsystems that show similar behavior and subsequently aggregating their states, leading to a reduced-order networked system that allows for an insightful physical interpretation. The clusters are chosen on the basis of the analysis of controllability and observability properties of associated edge systems, representing the importance of the couplings and providing ameasure of the similarity of the behavior of neighboring subsystems. This reduction procedure is shown to preserve synchronization properties (i.e., the convergence of the subsystem trajectories to each other) and allows for the a priori computation of a bound on the reduction error with respect to external inputs and outputs. The method is illustrated by means of an example of a thermal model of a building.

  • 153.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Model reduction of networked passive systems through clustering2014In: 2014 European Control Conference, ECC 2014, IEEE , 2014, p. 1069-1074Conference paper (Refereed)
    Abstract [en]

    In this paper, a model reduction procedure for a network of interconnected identical passive subsystems is presented. Here, rather than performing model reduction on the subsystems, adjacent subsystems are clustered, leading to a reduced-order networked system that allows for a convenient physical interpretation. The identification of the subsystems to be clustered is performed through controllability and observability analysis of an associated edge system and it is shown that the property of synchronization (i.e., the convergence of trajectories of the subsystems to each other) is preserved during reduction. The results are illustrated by means of an example.

  • 154.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Imura, Jun-ichi
    Tokyo Institute of Technology.
    Controllability of a class of networked passive linear systems2013In: Proceedings of the 52nd IEEE Conference on Decision and Control, Florence, Italy, IEEE conference proceedings, 2013, p. 4901-4906Conference paper (Refereed)
    Abstract [en]

    In this paper, controllability properties of networks of diffusively coupled linear systems are considered through the controllability Gramian. For a class of passive linear systems, it is shown that the controllability Gramian can be decomposed into two parts. The first part is related to the dynamics of the individual systems whereas the second part is dependent only on the interconnection topology, allowing for a clear interpretation and efficient computation of controllability properties for a class of networked systems. Moreover, a relation between symmetries in the interconnection topology and controllability is given. The results are illustrated by an example.

  • 155.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Tabak, U.
    Lutowska, A.
    van de Wouw, N.
    Nijmeijer, H.
    Rixen, D. J.
    Hochstenbach, M. E.
    Schilders, W. H. A.
    A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control2013In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 332, no 19, p. 4403-4422Article, review/survey (Refereed)
    Abstract [en]

    In this paper, popular model reduction techniques from the fields of structural dynamics, numerical mathematics and systems and control are reviewed and compared. The motivation for such a comparison stems from the fact that the model reduction techniques in these fields have been developed fairly independently. In addition, the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique, on the basis of the desired objectives and properties of the model reduction problem. In particular, a detailed review is given on mode displacement techniques, moment matching methods and balanced truncation, whereas important extensions are outlined briefly. In addition, a qualitative comparison of these methods is presented, hereby focusing both on theoretical and computational aspects. Finally, the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example.

  • 156.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Turri, Valerio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Van De Hoef, Sebastian Hendrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Liang, Kuo-Yun
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Scania CV AB, Sweden.
    Alam, A.
    Mårtensson, Jonas
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cyber-Physical Control of Road Freight Transport2016In: Proceedings of the IEEE, ISSN 0018-9219, E-ISSN 1558-2256, Vol. 104, no 5, p. 1128-1141, article id 7437386Article in journal (Refereed)
    Abstract [en]

    Freight transportation is of outmost importance in our society and is continuously increasing. At the same time, transporting goods on roads accounts for about 26% of the total energy consumption and 18% of all greenhouse gas emissions in the European Union. Despite the influence the transportation system has on our energy consumption and the environment, road transportation is mainly done by individual long-haulage trucks with no real-time coordination or global optimization. In this paper, we review how modern information and communication technology supports a cyber-physical transportation system architecture with an integrated logistic system coordinating fleets of trucks traveling together in vehicle platoons. From the reduced air drag, platooning trucks traveling close together can save about 10% of their fuel consumption. Utilizing road grade information and vehicle-to-vehicle communication, a safe and fuel-optimized cooperative look-ahead control strategy is implemented on top of the existing cruise controller. By optimizing the interaction between vehicles and platoons of vehicles, it is shown that significant improvements can be achieved. An integrated transport planning and vehicle routing in the fleet management system allows both small and large fleet owners to benefit from the collaboration. A realistic case study with 200 heavy-duty vehicles performing transportation tasks in Sweden is described. Simulations show overall fuel savings at more than 5% thanks to coordinated platoon planning. It is also illustrated how well the proposed cooperative look-ahead controller for heavy-duty vehicle platoons manages to optimize the velocity profiles of the vehicles over a hilly segment of the considered road network.

  • 157.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Van De Wouw, N.
    Scherpen, J. M. A.
    Nijmeijer, H.
    Generalized incremental balanced truncation for nonlinear systems2013In: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2013, p. 5552-5557Conference paper (Refereed)
    Abstract [en]

    The method of generalized incremental balanced truncation is introduced in this paper, providing a technique for model reduction of nonlinear systems in which the autonomous part of the vector field is anti-symmetric. This approach differs from existing balancing-like reduction techniques in the definition of two novel, incremental energy functions, which provides several advantages. First, stability properties of the reduced-order model can be guaranteed, hereby considering the stability of trajectories for both zero and nonzero input. Second, a computable bound on the reduction error is derived. The reduction technique is illustrated by means of application to an example of a nonlinear electronic circuit.

  • 158.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    van de Wouw, Nathan
    Scherpen, Jacquelien M. A.
    Nijmeijer, Henk
    Model Reduction for Nonlinear Systems by Incremental Balanced Truncation2014In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 10, p. 2739-2753Article in journal (Refereed)
    Abstract [en]

    In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing techniques in the definition of two novel energy functions. These incremental observability and incremental controllability functions form the basis for a model reduction procedure in which the preservation of stability properties is guaranteed. In particular, the property of incremental stability, which provides a notion of stability for systems with nonzero inputs, is preserved. Moreover, a computable error bound is given. Next, an extension towards so-called generalized incremental balanced truncation is proposed, which provides a reduction technique with increased computational feasibility at the cost of a (potentially) larger error bound. The proposed reduction technique is illustrated by means of application to an example of an electronic circuit with nonlinear elements.

  • 159.
    Besselink, Bart
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Vromen, Thijs
    Kremers, Niek
    van de Wouw, Nathan
    Analysis and Control of Stick-Slip Oscillations in Drilling Systems2016In: IEEE Transactions on Control Systems Technology, ISSN 1063-6536, E-ISSN 1558-0865, Vol. 24, no 5, p. 1582-1593Article in journal (Refereed)
    Abstract [en]

    This paper proposes feedback control strategies for the mitigation of torsional stick-slip oscillations in drilling systems using drag bits. Herein, we employ a model for the coupled axial-torsional drill-string dynamics in combination with a rate-independent bit-rock interaction law including both cutting and frictional effects. Using a singular perturbation and averaging approach, we show that the dynamics of this model generate an apparent velocity-weakening effect in the torque-on-bit, explaining the onset of torsional stick-slip vibrations. Based on this dynamic analysis, the (decoupled) torsional dynamics can be described by a delay-differential equation with a state-dependent delay. Using this model, we propose both state-and output-feedback control strategies for the mitigation of torsional stick-slip oscillations, where the latter strategy uses surface measurements only. The effectiveness of the proposed approaches is shown in a simulation study.

  • 160.
    Biel, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Farokhi, Farhad
    Sandberg, Henrik
    SiMpLIfy: A toolbox for structured model reduction2015In: 2015 European Control Conference, ECC 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 1159-1164Conference paper (Refereed)
    Abstract [en]

    In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured model reduction using a subgradient optimization algorithm. We briefly present the syntax for the toolbox and its features. Finally, we demonstrate the applicability of various model reduction methods in the toolbox on a structured mass-spring mechanical system.

  • 161.
    Bilal, Ibrahim
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zaidi, Ali Abbas
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Oechtering, Tobias J.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Feedback stabilization over a Gaussian interference relay channel2013In: 2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications, SPAWC, IEEE , 2013, p. 560-564Conference paper (Refereed)
    Abstract [en]

    A transmission scheme for mean square stabilization of two linear systems over a Gaussian interference relay channel is studied. A delay-free linear sensing and control strategy is proposed and an achievable stability region is derived. It shows that the stability region can be significantly enlarged by deploying a relay node in such a multi-user Gaussian channels. Furthermore we observe that the separation structure between estimation and control is inadequate in high interference regime.

  • 162.
    Bilal, Ibrahim
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zaidi, Ali Abbas
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Oechtering, Tobias J.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Managing interference for stabilization over wireless channels2012In: Intelligent Control (ISIC), 2012 IEEE International Symposium on, IEEE , 2012, p. 933-938Conference paper (Refereed)
    Abstract [en]

    The remote stabilization of a first order linear plant over a wireless channel is studied. The plant is assumed to have an arbitrary distributed initial state and the wireless channel between the plant's sensor and the controller is modeled as a white Gaussian channel subject to an external interference signal. In order to combat the interference a dedicated sensor (relay) node is deployed adjacent to the interferer, which relays the interference information to both the plant's sensor and the controller. The sensor and the controller utilize this information to mitigate interference. We use delay-free linear sensing and control scheme in order to derive sufficient conditions for mean square stability. The achievable stability region significantly enlarges with the relay assisted interference cancelation scheme. Moreover the effect of interference can be completely eliminated if the encoder knows all the future values of the interference.

  • 163. Bishop, A. N.
    et al.
    Shames, Iman
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Noisy network localization via optimal measurement refinement part 1: Bearing-only orientation registration and localization2011In: IFAC Proc. Vol. (IFAC-PapersOnline), 2011, no PART 1, p. 8842-8847Conference paper (Refereed)
    Abstract [en]

    The problem of localizing or tracking a number of targets using a network of bearing-only sensors is considered. To solve such a high-level problem, each sensor report must be successfully recorded in a common spatial reference frame and the position of the sensors must be determined. In practice, however, the reports from individual sensors are characterized by both random (called noise) and systematic errors (called biases). Typical bias errors are axis misalignments (due to azimuth and elevation biases) and range offset errors. Conditions under which the systematic errors can be removed given noisy measurements are examined in this work. In addition, certain conditions are identified which lend themselves naturally to the design of algorithms for network registration, localization and subsequently target localization. These conditions are feasible from a computational complexity point of view. This work provides a comprehensive solution to the problem of sensor network-based target localization with bearing measurements as very little a prior information is assumed known and, if certain sensing conditions are met, efficient algorithms are provided.

  • 164.
    Bishop, Adrian
    et al.
    Australian National University.
    Shames, Iman
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Link Operations for Slowing the Spread of Disease in Complex Networks2011In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 95, no 1, p. 18005-Article in journal (Refereed)
    Abstract [en]

    A variety of social, biological and communication networks can be modelled using graph theoretical tools. Similar graphical tools can be used to model the topology by which disease, errors, and/or other undesired phenomenon etc. is spread and propagated through such networks. Certain network operations are proposed in this work that can be used to slow the spread of diseases in complex network topologies. The approach considered in this work differs from existing techniques in that it is based on optimally removing (or immunizing) individual links in the network as opposed to individual nodes. A systematic algorithm is outlined to achieve this edgewise immunization via a relaxed convex optimization protocol.

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    fulltext
  • 165. Bjorsell, Niclas
    et al.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Post-correction of under-sampled analog to digital converters2007In: 2007 IEEE INSTRUMENTATION & MEASUREMENT TECHNOLOGY CONFERENCE, 2007, p. 58-62Conference paper (Refereed)
    Abstract [en]

    Applications with wide bandwidth and high center frequencies force the analog to digital converter (ADC) to be active in a working range with less dynamic performance in relation to lower frequency bands. However using under-sampling techniques in combination with post-correction methods enable a combination of high sampling rate, wide bandwidth and low distortion. In this paper the employed dynamic post-correction is a combination of look-up tables and model based correction. The results are mainly based on measurements on a 12-bit 210 MSPS ADC. The improvement in total harmonic distortion and spurious free dynamic range are acceptable over a wide frequency range and it is robust to variations in amplitude.

  • 166. Bjorsell, Niclas
    et al.
    Ronnow, Daniel
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Measuring Volterra kernels of analog to digital converters using a stepped three-tone scan2006In: 2006 IEEE INSTRUMENTATION AND MEASUREMENT TECHNOLOGY CONFERENCE PROCEEDINGS, 2006, p. 1047-1050Conference paper (Other academic)
    Abstract [en]

    Volterra theory can be used to mathematically model nonlinear dynamic components such as analog-to-digital converter (ADC). This paper describes how frequency domain Volterra kernels of an ADC are determined from measurements. The elements of Volterra theory are given and practical issues are considered, such as methods for signal conditioning, finding the appropriate test signals scenario and suitable sampling frequency. The results show that for the used pipeline ADC, the frequency dependence is significantly stronger for second order difference products than for sum products and the linear frequency dependence was not as pronounced as that of the second order Volterra kernel.

  • 167.
    Bjurgert, Johan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Valenzuela, Patricio E.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Adaptive Boosting for System Identification2018In: IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, E-ISSN 2162-2388, Vol. 29, no 9, p. 4510-4514Article in journal (Refereed)
    Abstract [en]

    In the field of machine learning, the algorithm Adaptive Boosting has been successfully applied to a wide range of regression and classification problems. However, to the best of the authors' knowledge, the use of this algorithm to estimate dynamical systems has not been exploited. In this brief, we explore the connection between Adaptive Boosting and system identification, and give examples of an identification method that makes use of this connection. We prove that the resulting estimate converges to the true underlying system for an output-error model structure under reasonable assumptions in the large sample limit and derive a bound of the model mismatch for the noise-free case.

  • 168.
    Björk, Marcus
    et al.
    Dept. of IT, Uppsala University.
    Gudmundson, Erik
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Barral, Joelle K.
    Stanford University.
    Stoica, Petre
    Dept. of IT, Uppsala University.
    Signal processing algorithms for removing banding artifacts in MRI2011In: 19th European Signal Processing Conference (EUSIPCO), 2011, p. 1000-1004Conference paper (Refereed)
    Abstract [en]

    In magnetic resonance imaging (MRI), the balanced steady- state free precession (bSSFP) pulse sequence has shown to be of great interest, due to its relatively high signal-to-noise ratio in a short scan time. However, images acquired with this pulse sequence suffer from banding artifacts due to off- resonance effects. These artifacts typically appear as black bands covering parts of the image and they severely degrade the image quality. In this paper, we present a fast two-step algorithm for estimating the unknowns in the signal model and removing the banding artifacts. The first step consists of rewriting the model in such a way that it becomes linear in the unknowns (this step is named Linearization for Off- Resonance Estimation, or LORE). In the second step, we use a Gauss-Newton iterative optimization with the parameters obtained by LORE as initial guesses. We name the full al- gorithm LORE-GN. Using both simulated and in vivo data, we show the performance gain associated with using LORE- GN as compared to general methods commonly employed in similar cases.

  • 169.
    Björk, Marcus
    et al.
    Dept. of IT, Uppsala University.
    Ingle, R. Reeve
    Stanford University.
    Barral, Joelle K.
    Stanford University.
    Erik, Gudmundson
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Nishimura, Dwight G.
    Stanford University.
    Stoica, Petre
    Dept. of IT, Uppsala University.
    Optimality of Equally-Spaced Phase Increments for Banding Removal in bSSFP2012In: Proceedings 20th Scientific Meeting, International Society for Magnetic Resonance in Medicine (2012), 2012, p. 3380-3380Conference paper (Refereed)
  • 170.
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Multiantenna Cellular Communications: Channel Estimation, Feedback, and Resource Allocation2011Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The use of multiple antennas at base stations and user devices is a key component in the design of cellular communication systems that can meet the capacity demands of tomorrow. The downlink transmission from base stations to users is particularly limiting, both from a theoretical and a practical perspective, since user devices should be simple and power-efficient, and because many applications primarily create downlink traffic (e.g., video streaming). The potential gain of employing multiple antennas for downlink transmission is well recognized: the total data throughput increases linearly with the number of transmit antennas if the spatial dimension is exploited for simultaneous transmission to multiple users. In the design of practical cellular systems, the actual benefit of multiuser multiantenna transmission is limited by a variety of factors, including acquisition and accuracy of channel information, transmit power, channel conditions, cell density, user mobility, computational complexity, and the level of cooperation between base stations in the transmission design.

    The thesis considers three main components of downlink communications: 1) estimation of current channel conditions using training signaling; 2) efficient feedback of channel estimates; and 3) allocation of transmit resources (e.g., power, time and spatial dimensions) to users. In each area, the thesis seeks to provide a greater understanding of the interplay between different system properties. This is achieved by generalizing the underlying assumptions in prior work and providing both extensions of previous outcomes and entirely new mathematical results, along with supporting numerical examples. Some of the main thesis contributions can be summarized as follows.

    A framework is proposed for estimation of different channel quantities using a common optimized training sequence. Furthermore, it is proved that each user should only be allocated one data stream and utilize its antennas for receive combining and interference rejection, instead of using the antennas for reception of multiple data streams. This fundamental result is proved under both exact channel acquisition and under imperfections from channel estimation and limited feedback. This also has positive implications on the hardware and system design.

    Next, a general mathematical model is proposed for joint analysis of cellular systems with different levels of base station cooperation. The optimal multicell resource allocation can in general only be found with exponential computational complexity, but a systematic algorithm is proposed to find the optimal solution for the purpose of offline benchmarking. A parametrization of the optimal solution is also derived, creating a foundation for heuristic low-complexity algorithms that can provide close-to-optimal performance. This is exemplified by proposing centralized and distributed multicell transmission strategies and by evaluating these using multicell channel measurements.

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    doctoral_thesis_emil_bjornson
  • 171.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimality Properties and Low-Complexity Solutions to Coordinated Multicell Transmission2010In: 2010 IEEE GLOBAL TELECOMMUNICATIONS CONFERENCE GLOBECOM 2010, IEEE , 2010, p. 1-6Conference paper (Refereed)
    Abstract [en]

    Base station cooperation can theoretically improve the throughput of multicell systems by coordinating interference and serving cell edge terminals through multiple base stations. In practice, the extent of cooperation is limited by the increase in backhaul signaling and computational demands. To address these concerns, we propose a novel distributed cooperation structure where each base station has responsibility for the interference towards a set of terminals, while only serving a subset of them with data. Weighted sum rate maximization is considered, and conditions for beamforming optimality and the optimal transmission structure are derived using Lagrange duality theory. This leads to distributed low-complexity transmission strategies, which are evaluated on measured multiantenna channels in a typical urban multicell environment.

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    globecom2010
  • 172.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pareto characterization of the multicell MIMO performance region with simple receivers2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 8, p. 4464-4469Article in journal (Refereed)
    Abstract [en]

    We study the performance region of a general multicell downlink scenario with multiantenna transmitters, hardware impairments, and low-complexity receivers that treat interference as noise. The Pareto boundary of this region describes all efficient resource allocations, but is generally hard to compute. We propose a novel explicit characterization that gives Pareto optimal transmit strategies using a set of positive parameters-fewer than in prior work. We also propose an implicit characterization that requires even fewer parameters and guarantees to find the Pareto boundary for every choice of parameters, but at the expense of solving quasi-convex optimization problems. The merits of the two characterizations are illustrated for interference channels and ideal network multiple-input multiple-output (MIMO).

    Download full text (pdf)
    fulltext
  • 173.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Receive combining vs. multistream multiplexing in multiuser MIMO systems2011In: Communication Technologies Workshop (Swe-CTW), 2011 IEEE Swedish, IEEE Communications Society, 2011, p. 103-108Conference paper (Refereed)
    Abstract [en]

    In single-user transmission, the receive antennas should preferably be used to enable multiplexing. The situation is different under multiuser transmission, where only the number of transmit antennas limits the multiplexing gain. The system therefore has the choice between sending one stream per scheduled user (i.e., combining receive antennas for diversity) or selecting a smaller number of users and multiplex multiple streams to each of them. This tradeoff is investigated herein, based on zero-forcing (with receive antenna combining) and block-diagonalization precoding which represents the two extremes. Based on asymptotic analysis and numerical examples, the unexpected conclusion is that each user only should receive one stream and use its antennas to achieve a receive combining gain. This is explained by zero-forcing having a stronger resilience towards spatial correlation and larger benefit from multiuser diversity. This fundamental result has positive implications for the design of multiuser systems as it reduces the hardware constraints at the user devices.

    Download full text (pdf)
    swectw2011
  • 174.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zheng, Gan
    Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg.
    Computational Framework for Optimal Robust Beamforming in Coordinated Multicell Systems2011In: Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), IEEE Signal Processing Society, 2011, p. 245-248Conference paper (Refereed)
    Abstract [en]

    Coordinated beamforming can significantly improvethe performance of cellular systems through joint interferencemanagement. Unfortunately, such beamforming optimization problems are typically NP-hard in multicell scenarios, making heuristic beamforming the only feasible choice in practice. Thispaper proposes a new branch-reduce-and-bound algorithm thatsolves such optimization problems globally, with a complexitysuitable for benchmarking and analysis. Compared to priorwork, the framework handles robustness to uncertain intercell interference and numerical analysis shows higher efficiency.

    Download full text (pdf)
    CAMSAP2011
  • 175.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Devarakota, Pandu Ranga Rao
    IEE S.A., Zone Industrielle, 2b, Route de Tr`eves L-2632 Findel, Luxembourg.
    Medawar, Samer
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Schur-convexity of the Symbol Error Rate in Correlated MIMO Systems with Precoding and Space-time Coding2008In: Proceedings of the twentieth Nordic Conference on Radio Science and Communications, 2008Conference paper (Other academic)
    Abstract [en]

    This paper analyzes the symbol error rate (SER) of spatially correlated multiple-input multiple-output (MIMO) systems with linear precoding, space-time block codes, and long-term statistical channel state information at the transmitter. Majorization theory and the notion of Schur-convexity is used to show how the SER depends on the signal-to-noise ratio (SNR), on the transmit and receive correlation, and on the choice of precoder. Depending on these conditions, the Chernoff bound on the SER is shown to be Schur- convex (i.e., increasing with the amount of correlation) with respect to the receive correlation, while it is Schur-convex at high SNR and Schur-concave (i.e., decreasing with increasing amount of correlation) at low SNR with respect to the transmit correlation. These properties are inherited by the exact SER, as shown analytically and illustrated numerically.

    Download full text (pdf)
    rvk08_majorization
  • 176.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hammarwall, David
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Beamforming utilizing channel norm feedback in multiuser MIMO systems2007In: IEEE Workshop on Signal Processing Advances in Wireless Communications, IEEE , 2007, Vol. SPAWC, p. 1-5Conference paper (Refereed)
    Abstract [en]

    The problem of beamforming and rate estimation in a multi-user downlink multiple-input multiple-output (MIMO) system with limited feedback and statistical channel information at the transmitter is considered. In order to exploit the spatial properties of the channel, the norm of the channel to each receive antenna is computed. We propose to feed back the largest norm to the transmitter and derive the conditional second and fourth order channel moments in order to design the downlink beamforming weights. Similar approaches have previously been presented for multi-user multiple-input single-output (MISO) systems. Herein, these techniques are generalized to MIMO systems, by either antenna selection or receive beamforming at the receiver. Two eigenbeamforming strategies are proposed and shown to outperform opportunistic beamforming, based on similar feedback information.

    Download full text (pdf)
    spawc2007
  • 177.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hammarwall, David
    Ericsson Research, Stockholm, Sweden.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Exploiting Quantized Channel Norm Feedback Through Conditional Statistics in Arbitrarily Correlated MIMO Systems2009In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 57, no 10, p. 4027-4041Article in journal (Refereed)
    Abstract [en]

    In the design of narrowband multi-antenna systems, a limiting factor is the amount of channel state information (CSI) available at the transmitter. This is especially evident in multi-user systems, where the spatial user separability determines the multi-plexing gain, but it is also important for transmission-rate adaptation in single-user systems. To limit the feedback load, the unknown and multi-dimensional channel needs to be represented by a limited number of bits. When combined with long-term channel statistics, the norm of the channel matrix has been shown to provide substantial CSI that permits efficient user selection, linear precoder design, and rate adaptation. Herein, we consider quantized feedback of the squared Frobenius norm in a Rayleigh fading environment with arbitrary spatial correlation. The conditional channel statistics are characterized and their moments are derived for both identical, distinct, and sets of repeated eigenvalues. These results are applied for minimum mean square error (MMSE) estimation of signal and interference powers in single- and multi-user systems, for the purpose of reliable rate adaptation and resource allocation. The problem of efficient feedback quantization is discussed and an entropy-maximizing framework is developed where the post-user-selection distribution can be taken into account in the design of the quantization levels. The analytic results of this paper are directly applicable in many widely used communication techniques, such as space-time block codes, linear precoding, space division multiple access (SDMA), and scheduling.

    Download full text (pdf)
    fulltext
  • 178.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hammarwall, David
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zakhour, Randa
    Institut Eurécom, 2229 route des crêtes, BP 193, F-06560, Sophia Antipolis, France.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Gesbert, David
    Institut Eurécom, 2229 route des crêtes, BP 193, F-06560, Sophia Antipolis, France.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Feedback design in multiuser MIMO systems using quantization splitting and hybrid instantaneous/statistical channel information2008In: ICT-MobileSummit 2008 Conference Proceedings / [ed] Paul Cunningham and Miriam Cunningham, IIMC International Information Management Corporation , 2008, , p. 8Conference paper (Refereed)
    Abstract [en]

    In the design of next generation multiuser communication systems, multiple antenna transmission is an essential part providing spatial multiplexing gain and allowing efficient use of resources. A major limiting factor in the resource allocation is the amount of channel state information (CSI) available at the transmitter, particularly in multiuser systems where the feedback from each user terminal must be limited. To this effect we propose two independent approaches for an efficient representation of the channel in multiuser MIMO systems. In the first approach, channel quantization is considered where the total number of feedback bits is limited. A resource allocation scheme is proposed where the available rate is split between the scheduling phase, where all users feed back a coarse CSI quantization, and the precoding phase where the selected receivers refine their CSI. The optimum splitting of the available feedback rate provides a large increase in performance and even simple heuristic splitting gives a noticeable advantage. In the second approach, we exploit a combination of instantaneous and statistical channel information. For spatially correlated Rayleigh and Ricean channels, it is shown that the CSI to large extent can be represented by the channel norm when the long-term channel statistics are known. Within a minimum mean square error (MMSE) estimation framework, feedback of a few bits of the quantized channel norm is sufficient to perform efficient resource allocation and achieve performance close to that of full CSI.

    Download full text (pdf)
    fulltext
  • 179.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hoydis, J.
    Kountouris, M.
    Debbah, M.
    Hardware impairments in large-scale MISO systems: Energy efficiency, estimation, and capacity limits2013In: 2013 18th International Conference on Digital Signal Processing, DSP 2013, IEEE conference proceedings, 2013, p. -6Conference paper (Refereed)
    Abstract [en]

    The use of large-scale antenna arrays has the potential to bring substantial improvements in energy efficiency and/or spectral efficiency to future wireless systems, due to the greatly improved spatial beamforming resolution. Recent asymptotic results show that by increasing the number of antennas one can achieve a large array gain and at the same time naturally decorrelate the user channels; thus, the available energy can be focused very accurately at the intended destinations without causing much inter-user interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are still reasonable in the asymptotic regimes. This paper analyzes the fundamental limits of large-scale multiple-input single-output (MISO) communication systems using a generalized system model that accounts for transceiver hardware impairments. As opposed to the case of ideal hardware, we show that these practical impairments create finite ceilings on the estimation accuracy and capacity of large-scale MISO systems. Surprisingly, the performance is only limited by the hardware at the single-antenna user terminal, while the impact of impairments at the large-scale array vanishes asymptotically. Furthermore, we show that an arbitrarily high energy efficiency can be achieved by reducing the power while increasing the number of antennas.

    Download full text (pdf)
    fulltext
  • 180.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jaldén, Niklas
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimality Properties, Distributed Strategies, and Measurement-Based Evaluation of Coordinated Multicell OFDMA Transmission2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 12, p. 6086-6101Article in journal (Refereed)
    Abstract [en]

    The throughput of multicell systems is inherently limited by interference andthe available communication resources. Coordinated resource allocation is the key to efficient performance, but the demand on backhaul signaling andcomputational resources grows rapidly with number of cells, terminals, andsubcarriers. To handle this, we propose a novel multicell framework with dynamic cooperation clusters where each terminal is jointly served by a small set of base stations. Each base station coordinates interference to neighboring terminals only, thus limiting backhaul signalling and making the framework scalable. This framework can describe anything from interference channels to ideal joint multicell transmission. The resource allocation (i.e., precoding and scheduling) is formulated as an optimization problem (P1) with performance described by arbitrary monotonic functions of the signal-to-interference-and-noise ratios (SINRs) and arbitrary linear power constraints. Although (P1) is nonconvex and difficult to solve optimally, we are able to prove: 1) optimalityof single-stream beamforming; 2) conditions for full power usage; and 3) a precoding parametrization based on a few parameters between zero and one. These optimality properties are used to propose low-complexity strategies: both a centralized scheme and a distributed version that only requires local channel knowledge and processing. We evaluate the performance on measuredmulticell channels and observe that the proposed strategies achieve close-to-optimal performance among centralized and distributed solutions, respectively. In addition, we show that multicell interference coordination can give substantial improvements in sum performance, but that joint transmission is very sensitive to synchronization errors and that some terminals can experience performance degradations.

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    tsp2011
  • 181.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    Dresden University of Technology, Communications Theory, Communications Laboratory, Dresden, Germany.
    Optimal Resource Allocation in Coordinated Multi-Cell Systems2013Book (Refereed)
    Abstract [en]

    The use of multiple antennas at base stations is a key component in the design of cellular communication systems that can meet high-capacity demands in the downlink. Under ideal conditions, the gain of employing multiple antennas is well-recognized: the data throughput increases linearly with the number of transmit antennas if the spatial dimension is utilized to serve many users in parallel. The practical performance of multi-cell systems is, however, limited by a variety of nonidealities, such as insufficient channel knowledge, high computational complexity, heterogeneous user conditions, limited backhaul capacity, transceiver impairments, and the constrained level of coordination between base stations.

    This tutorial presents a general framework for modeling different multi-cell scenarios, including clustered joint transmission, coordinated beamforming, interference channels, cognitive radio, and spectrum sharing between operators. The framework enables joint analysis and insights that are both scenario independent and dependent.

    The performance of multi-cell systems depends on the resource allocation; that is, how the time, power, frequency, and spatial resources are divided among users. A comprehensive characterization of resource allocation problem categories is provided, along with the signal processing algorithms that solve them. The inherent difficulties are revealed: (a) the overwhelming spatial degrees-of-freedom created by the multitude of transmit antennas; and (b) the fundamental tradeoff between maximizing aggregate system throughput and maintaining user fairness. The tutorial provides a pragmatic foundation for resource allocation where the system utility metric can be selected to achieve practical feasibility. The structure of optimal resource allocation is also derived, in terms of beamforming parameterizations and optimal operating points.

    This tutorial provides a solid ground and understanding for optimization of practical multi-cell systems, including the impact of the nonidealities mentioned above. The Matlab code is available online for some of the examples and algorithms in this tutorial.

    Note: The supplementary Matlab Code is available at http://dx.doi.org/10.1561/0100000069_supp

    Download full text (pdf)
    bjornson_jorswieck_cit2013
  • 182.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Alcatel-Lucent Chair on Flexible Radio, Supélec, France.
    Jorswieck, Eduard
    Dresden University of Technology, Communications Theory, Communications Laboratory, Dresden, Germany.
    Optimal Resource Allocation in Coordinated Multi-Cell Systems: Matlab Code2013Report (Other academic)
    Abstract [en]

    This is the documentation of the Matlab code supplement to the monograph "Optimal Resource Allocation in Coordinated Multi-Cell Systems" by Emil Björnson and Eduard Jorswieck; see [1] for the full publication details.

    This documentation is distributed along with the code package mentioned above. The package contains Matlab implementations of many of the algorithms described in [1]. The use of these algorithms is exemplified by Matlab scripts (m-files) that generate some of the figures shown in the monograph. The algorithms are briefly described in Section 5 and the selected example figures are described and shown in Section 6. Please note that the all channel vectors are generated randomly as Rayleigh fading in these examples, thus this code package is not able to reproduce exactly the same curves as was shown in the monograph.

  • 183.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard A.
    Dresden University of Technology (TUD), Germany.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Impact of Spatial Correlation and Precoding Design in OSTBC MIMO Systems2010In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 9, no 11, p. 3578-3589Article in journal (Refereed)
    Abstract [en]

    The impact of transmission design and spatial correlation on the symbol error rate (SER) is analyzed for multi-antenna communication links. The receiver has perfect channel state information (CSI), while the transmitter has either statistical or no CSI. The transmission is based on orthogonal space-time block codes (OSTBCs) and linear precoding. The precoding strategy that minimizes the worst-case SER is derived for the case when the transmitter has no CSI. Based on this strategy, the intuitive result that spatial correlation degrades the SER performance is proved mathematically. In the case when the transmitter knows the channel statistics, the correlation matrix is assumed to be jointly-correlated (a generalization of the Kronecker model). The eigenvectors of the SER-optimal precoding matrix are shown to originate from the correlation matrix and the remaining power allocation is a convex problem. Equal power allocation is SER-optimal at high SNR. Beamforming is SER-optimal at low SNR, or for increasing constellation sizes, and its optimality range is characterized. A heuristic low-complexity power allocation is proposed and evaluated numerically. Finally, it is proved analytically that receive-side correlation always degrades the SER. Transmit-side correlation will however improve the SER at low to medium SNR, while its impact is negligible at high SNR.

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    twcom2010
  • 184.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    Dresden University of Technology, Germany.
    Debbah, Merouane
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Multiobjective Signal Processing Optimization: The way to balance conflicting metrics in 5G systems2014In: IEEE signal processing magazine (Print), ISSN 1053-5888, E-ISSN 1558-0792, Vol. 31, no 6, p. 14-23Article in journal (Refereed)
    Abstract [en]

    The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: any data service is instantly accessible everywhere. With each generation of cellular networks, we have moved closer to this wireless dream; first by delivering wireless access to voice communications, then by providing wireless data services, and recently by delivering a Wi-Fi-like experience with wide-area coverage and user mobility management. The support for high data rates has been the main objective in recent years [1], as seen from the academic focus on sum-rate optimization and the efforts from standardization bodies to meet the peak rate requirements specified in IMT-Advanced. In contrast, a variety of metrics/objectives are put forward in the technological preparations for fifth-generation (5G) networks: higher peak rates, improved coverage with uniform user experience, higher reliability and lower latency, better energy efficiency (EE), lower-cost user devices and services, better scalability with number of devices, etc. These multiple objectives are coupled, often in a conflicting manner such that improvements in one objective lead to degradation in the other objectives. Hence, the design of future networks calls for new optimization tools that properly handle the existence of multiple objectives and tradeoffs between them.

  • 185.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Alcatel-Lucent Department on Flexible Radio, SUPELEC, Gif-sur-Yvette, France .
    Kountouris, M.
    Debbah, M.
    Massive MIMO and small cells: Improving energy efficiency by optimal soft-cell coordination2013In: 2013 20th International Conference on Telecommunications, ICT 2013, IEEE Computer Society, 2013, p. 6632074-Conference paper (Refereed)
    Abstract [en]

    To improve the cellular energy efficiency, without sacrificing quality-of-service (QoS) at the users, the network topology must be densified to enable higher spatial reuse. We analyze a combination of two densification approaches, namely "massive" multiple-input multiple-output (MIMO) base stations and small-cell access points. If the latter are operator-deployed, a spatial soft-cell approach can be taken where the multiple transmitters serve the users by joint non-coherent multiflow beamforming. We minimize the total power consumption (both dynamic emitted power and static hardware power) while satisfying QoS constraints. This problem is proved to have a hidden convexity that enables efficient solution algorithms. Interestingly, the optimal solution promotes exclusive assignment of users to transmitters. Furthermore, we provide promising simulation results showing how the total power consumption can be greatly improved by combining massive MIMO and small cells; this is possible with both optimal and low-complexity beamforming.

  • 186.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kountouris, Marios
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems With Multi-Antenna Users2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 13, p. 3431-3446Article in journal (Refereed)
    Abstract [en]

    In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are near-orthogonal, for multi-stream multiplexing to users with well-conditioned channels, and/or to enable interference-aware receive combining. In this paper, we try to answer the question if the data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user-the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multi-user diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization.

    Download full text (pdf)
    tsp2013
  • 187.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Matthaiou, M.
    Debbah, M.
    A New Look at Dual-Hop Relaying: Performance Limits with Hardware Impairments2013In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 61, no 11, p. 4512-4525Article in journal (Refereed)
    Abstract [en]

    Physical transceivers have hardware impairments that create distortions which degrade the performance of communication systems. The vast majority of technical contributions in the area of relaying neglect hardware impairments and, thus, assume ideal hardware. Such approximations make sense in low-rate systems, but can lead to very misleading results when analyzing future high-rate systems. This paper quantifies the impact of hardware impairments on dual-hop relaying, for both amplify-and-forward and decode-and-forward protocols. The outage probability (OP) in these practical scenarios is a function of the effective end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives new closed-form expressions for the exact and asymptotic OPs, accounting for hardware impairments at the source, relay, and destination. A similar analysis for the ergodic capacity is also pursued, resulting in new upper bounds. We assume that both hops are subject to independent but non-identically distributed Nakagami-m fading. This paper validates that the performance loss is small at low rates, but otherwise can be very substantial. In particular, it is proved that for high signal-to-noise ratio (SNR), the end-to-end SNDR converges to a deterministic constant, coined the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in contrast to the ideal hardware case in which the end-to-end SNDR grows without bound in the high-SNR regime. Finally, we provide fundamental design guidelines for selecting hardware that satisfies the requirements of a practical relaying system.

    Download full text (pdf)
    fulltext
  • 188.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. SUPELEC, France .
    Matthaiou, M.
    Debbah, M.
    Massive MIMO systems with hardware-constrained base stations2014Conference paper (Refereed)
    Abstract [en]

    Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas. Such large antenna arrays offer huge spatial degrees-of-freedom for transmission optimization; in particular, great signal gains, resilience to imperfect channel knowledge, and small inter-user interference are all achievable without extensive inter-cell coordination. The key to cost-efficient deployment of large arrays is the use of hardware-constrained base stations with low-cost antenna elements, as compared to today's expensive and power-hungry BSs. Low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the excessive degrees-of-freedom of massive MIMO would bring robustness to such imperfections. We herein prove this claim for an uplink channel with multiplicative phase-drift, additive distortion noise, and noise amplification. Specifically, we derive a closed-form scaling law that shows how fast the imperfections increase with the number of antennas.

  • 189.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. SUPELEC, France.
    Matthaiou, Michail
    Debbah, Mérouane
    Circuit-aware design of energy-efficient massive MIMO systems2014In: ISCCSP 2014 - 2014 6th International Symposium on Communications, Control and Signal Processing, Proceedings, 2014, p. 101-104Conference paper (Refereed)
    Abstract [en]

    Densification is a key to greater throughput in cellular networks. The full potential of coordinated multipoint (CoMP) can be realized by massive multiple-input multiple-output (MIMO) systems, where each base station (BS) has very many antennas. However, the improved throughput comes at the price of more infrastructure; hardware cost and circuit power consumption scale linearly/affinely with the number of antennas. In this paper, we show that one can make the circuit power increase with only the square root of the number of antennas by circuit-aware system design. To this end, we derive achievable user rates for a system model with hardware imperfections and show how the level of imperfections can be gradually increased while maintaining high throughput. The connection between this scaling law and the circuit power consumption is established for different circuits at the BS.

  • 190.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ntontin, Konstantinos
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Channel quantization design in multiuser MIMO systems: Asymptotic versus practical conclusions2011In: Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, IEEE Signal Processing Society, 2011, p. 3072-3075Conference paper (Refereed)
    Abstract [en]

    Feedback of channel state information (CSI) is necessary to achieve high throughput and low outage probability in multiuser multi antenna systems. There are two types of CSI: directional and quality information. Many papers have analyzed the importance of these in asymptotic regimes. However, we show that such results should be handled with care, as very different conclusions can be drawn depending on the spatial correlation and number of users. There fore, we propose a quantization framework and evaluate the tradeoff between directional and quality feedback under practical conditions.

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    icassp2011
  • 191.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels With Rician Disturbance2010In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 58, no 3, p. 1807-1820Article in journal (Refereed)
    Abstract [en]

    In this paper, we create a framework for training-based channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation in Rician fading multi-antenna systems is analyzed, and especially the design of mean square error (MSE) minimizing training sequences. By considering Kronecker-structured systems with a combination of noise and interference and arbitrary training sequence length, we collect and generalize several previous results in the framework. We clarify the conditions for achieving the optimal training sequence structure and show when the spatial training power allocation can be solved explicitly. We also prove that spatial correlation improves the estimation performance and establish how it determines the optimal training sequence length. The analytic results for Kronecker-structured systems are used to derive a heuristic training sequence under general unstructured statistics. The MMSE estimator of the squared Frobenius norm of the channel matrix is also derived and shown to provide far better gain estimates than other approaches. It is shown under which conditions training sequences that minimize the non-convex MSE can be derived explicitly or with low complexity. Numerical examples are used to evaluate the performance of the two estimators for different training sequences and system statistics. We also illustrate how the optimal length of the training sequence often can be shorter than the number of transmit antennas.

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    tsp2010
  • 192.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Exploiting long-term statistics in spatially correlated multi-user MIMO systems with quantized channel norm feedback2008In: 2008 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, IEEE , 2008, p. 3117-3120Conference paper (Refereed)
    Abstract [en]

    In wireless multiple antenna and multi-user systems, the spatial dimensions may be exploited to increase the performance by means of antenna gain, spatial diversity, and multi-user diversity. A limiting factor in such systems is the channel information required by the transmitter to control the intra-cell interference. Herein, the properties of spatially correlated channels with long-term statistical information at the transmitter and fixed-rate feedback of the quantized Euclidean channel norm are analyzed using a spectral subspace decomposition framework. A spatial division multiple access scheme is proposed with interference suppression at the receiver and joint scheduling and zero-forcing beamforming at the transmitter. Closed-form expressions for first and second order moments of the feedback conditional channel statistics are derived. It is shown that only a few bits of feedback are required to achieve reliable rate estimation and weighted sum-rate maximization.

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    icassp2008
  • 193.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the Principles of Multicell Precoding with Centralized and Distributed Cooperation2009In: 2009 INTERNATIONAL CONFERENCE ON WIRELESS COMMUNICATIONS AND SIGNAL PROCESSING (WCSP 2009), NEW YORK: IEEE , 2009, p. 1644-1648Conference paper (Refereed)
    Abstract [en]

    Cooperative precoding is an attractive way of improving the performance in multicell downlink scenarios. By serving each terminal through multiple surrounding base stations, inter-cell interference can be coordinated and higher spectral efficiency achieved, especially for terminals at cell edges. The optimal performance of multicell precoding is well-known as it can be treated as a single cell with distributed antennas. However, the requirements on backhaul signaling and computational power scales rapidly in large and dense networks, which often makes such fully centralized approaches impractical. In this paper, we review and generalize some recent work on multicell precoding with both centralized and distributed cooperation. We propose practical precoding strategies under Rician channel conditions, and illustrate how the major gain of multicell precoding originates from having good base station synchronization and not from making centralized precoding decisions.

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    wcsp2009
  • 194.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pilot-based Bayesian Channel Norm Estimation in Rayleigh Fading Multi-antenna Systems2008In: Proceedings of the twentieth Nordic Conference on Radio Science and Communications, Växjö, Sweden, 2008Conference paper (Other academic)
    Abstract [en]

    Pilot-based estimation of the squared Euclidean norm of the channel vector of a Rayleigh fading system is considered. Unlike most previous work in the area of estimation of multiple antenna channels, we consider Bayesian estimation where the long-term channel statistics are known a priori. Closed-form expressions of the minimum mean square error (MMSE) estimator and its mean squared error (MSE) are derived for the cases of either an unweighted or a weighted unitary pilot matrix. The problem of finding the optimal pilot weighting, in the sense of minimizing the average MSE, is solved and a simple algorithm is proposed to achieve this power allocation numerically. The numerical evaluation shows that an optimal weighting can significantly improve the estimation quality in spatially correlated environments.

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    rvk08_estimation
  • 195.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Post-User-Selection Quantization and Estimation of Correlated Frobenius and Spectral Channel Norms2008In: 2008 IEEE 19TH INTERNATIONAL SYMPOSIUM ON PERSONAL, INDOOR AND MOBILE RADIO COMMUNICATIONS, NEW YORK: IEEE , 2008, p. 2751-2756Conference paper (Refereed)
    Abstract [en]

    This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented.

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    pimrc2008
  • 196.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Training-based Bayesian MIMO channel and channel norm estimation2009In: 2009 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1- 8, PROCEEDINGS, IEEE , 2009, p. 2701-2704Conference paper (Refereed)
    Abstract [en]

    Training-based estimation of channel state information in multi-antenna systems is analyzed herein. Closed-form expressions for the general Bayesian minimum mean square error (MMSE) estimators of the channel matrix and the squared channel norm are derived in a Rayleigh fading environment with known statistics at the receiver side. When the second-order channel statistics are available also at the transmitter, this information can be exploited in the training sequence design to improve the performance. Herein, mean square error (MSE) minimizing training sequences are considered. The structure of the general solution is developed, with explicit expressions at high and low SNRs and in the special case of uncorrelated receive antennas. The optimal length of the training sequence is equal or smaller than the number of transmit antennas.

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    icassp2009b
  • 197.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    Communication Theory, Communications Laboratory, Dresden University of Technology, D-01062 Dresden, Germany.
    On the impact of spatial correlation and precoder design on the performance of MIMO systems with space-time coding2009In: 2009 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1- 8, PROCEEDINGS, IEEE , 2009, p. 2741-2744Conference paper (Refereed)
    Abstract [en]

    The symbol error performance of spatially correlated multi-antenna systems is analyzed herein. When the transmitter only has statistical channel information, the use of space-time block codes still permits spatial multiplexing and mitigation of fading. The statistical information can be used for precoding to optimize some quality measure. Herein, we analyze the performance in terms of the symbol error rate (SER). It is shown analytically that spatial correlation at the receiver decreases the performance both without precoding and with an SER minimizing precoder. Without precoding, correlation should also be avoided at the transmitter side, but with an SER minimizing precoder the performance is actually improved by increasing spatial correlation at the transmitter. The structure of the optimized precoder is analyzed and the asymptotic properties at high and low SNRs are characterized and illustrated numerically.

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    icassp2009a
  • 198.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sanguinetti, L.
    Hoydis, J.
    Debbah, M.
    Designing multi-user MIMO for energy efficiency: When is massive MIMO the answer?2014In: IEEE Wireless Communications and Networking Conference, WCNC, 2014, p. 242-247Conference paper (Refereed)
    Abstract [en]

    Assume that a multi-user multiple-input multiple-output (MIMO) communication system must be designed to cover a given area with maximal energy efficiency (bits/Joule). What are the optimal values for the number of antennas, active users, and transmit power? By using a new model that describes how these three parameters affect the total energy efficiency of the system, this work provides closed-form expressions for their optimal values and interactions. In sharp contrast to common belief, the transmit power is found to increase (not decrease) with the number of antennas. This implies that energy efficient systems can operate at high signal-to-noise ratio (SNR) regimes in which the use of interference-suppressing precoding schemes is essential. Numerical results show that the maximal energy efficiency is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve relatively many users using interference-suppressing regularized zero-forcing precoding.

  • 199.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zakhour, Randa
    Mobile Communications Department, EURECOM.
    Gesbert, David
    Mobile Communications Department, EURECOM.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cooperative Multicell Precoding: Rate Region Characterization and Distributed Strategies With Instantaneous and Statistical CSI2010In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 58, no 8, p. 4298-4310Article in journal (Refereed)
    Abstract [en]

    Base station cooperation is an attractive way of increasing the spectral efficiency in multiantenna communication. By serving each terminal through several base stations in a given area, intercell interference can be coordinated and higher performance achieved, especially for terminals at cell edges. Most previous work in the area has assumed that base stations have common knowledge of both data dedicated to all terminals and full or partial channel state information (CSI) of all links. Herein, we analyze the case of distributed cooperation where each base station has only local CSI, either instantaneous or statistical. In the case of instantaneous CSI, the beamforming vectors that can attain the outer boundary of the achievable rate region are characterized for an arbitrary number of multiantenna transmitters and single-antenna receivers. This characterization only requires local CSI and justifies distributed precoding design based on a novel virtual signal-to-interference noise ratio (SINR) framework, which can handle an arbitrary SNR and achieves the optimal multiplexing gain. The local power allocation between terminals is solved heuristically. Conceptually, analogous results for the achievable rate region characterization and precoding design are derived in the case of local statistical CSI. The benefits of distributed cooperative transmission are illustrated numerically, and it is shown that most of the performance with centralized cooperation can be obtained using only local CSI.

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    tsp2010
  • 200.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zakhour, Randa
    Mobile Communications Department EURECOM 06560 Sophia Antipolis, France.
    Gesbert, David
    Mobile Communications Department EURECOM 06560 Sophia Antipolis, France.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Distributed Multicell and Multiantenna Precoding: Characterization and Performance Evaluation2009In: GLOBECOM 2009: 2009 IEEE GLOBAL TELECOMMUNICATIONS CONFERENCE, VOLS 1-8 / [ed] Ulema M, IEEE , 2009, p. 1-6Conference paper (Refereed)
    Abstract [en]

    This paper considers downlink multiantenna communication with base stations that perform cooperative precoding in a distributed fashion. Most previous work in the area has assumed that transmitters have common knowledge of both data symbols of all users and full or partial channel state information (CSI). Herein, we assume that each base station only has local CSI, either instantaneous or statistical. For the case of instantaneous CSI, a parametrization of the beamforming vectors used to achieve the outer boundary of the achievable rate region is obtained for two multi-antenna transmitters and two single-antenna receivers. Distributed generalizations of classical beamforming approaches that satisfy this parametrization are provided, and it is shown how the distributed precoding design can be improved using the so-called virtual SINR framework [1]. Conceptually analog results for both the parametrization and the beamforming design are derived in the case of local statistical CSI. Heuristics on the distributed power allocation are provided in both cases, and the performance is illustrated numerically.

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    globecom2009
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