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  • 1.
    Björnson, Emil
    Lunds universitet.
    Beamforming Utilizing Channel Norm Feedback in Multiuser MIMO Systems2007Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Cellular wireless communication like GSM and WLAN has become an important part of the infrastructure. The next generation of wireless systems is believed to be based on multiple-input multiple-output (MIMO), where all units are equipped with multiple antennas. In contrast to the single antenna case, MIMO systems may exploit beamforming to concentrate the transmission in the direction of the receiver. The receiver may in turn use beamforming to maximize the received signal power and to suppress the interference from other transmissions. The capacity of a MIMO system has the potential of increasing linearly with the number of antennas, but the performance gain is limited in practice by the lack of channel information at the transmitter side.

    This thesis considers downlink strategies where the transmitter utilizes channel norm feedback to perform beamforming that maximizes the signal-to-noise ratio (SNR) for a single beam. Two optimal strategies with feedback of, either the channel squared norm to each receive antenna, or the maximum of them are introduced and analyzed in terms of conditional covariance, eigenbeamforming, minimum mean-square error (MMSE) estimation of the SNR and the corresponding estimation variance. These strategies are compared under fair conditions to the upper bound and strategies without feedback or with pure SNR feedback. Simulations show that both strategies perform well, even if spatial division multiple access (SDMA) is required to exploit the full potential.

    The beamforming strategies are generalized to the multiuser case where a scheduler schedule users in time slots in which their channel realization seems to be strong and thereby support high data rates. The gain of exploiting multiuser diversity is shown in simulations.

    The thesis is concluded by a generalization to a multi-cell environment with intercell interference. Optimal and suboptimal receive beamforming is analyzed and used to propose approximate beamforming strategies based on channel norm feedback.

  • 2.
    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.

  • 3.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. Dept. of Electrical Engineering, Linkoping University, Sweden.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Optimal Multiuser Transmit Beamforming: A Difficult Problem with a Simple Solution Structure2014In: IEEE signal processing magazine (Print), ISSN 1053-5888, E-ISSN 1558-0792, Vol. 31, no 4, p. 142-148Article in journal (Refereed)
    Abstract [en]

    Transmit beamforming is a versatile technique for signal transmission from an array of antennas to one or multiple users [1]. In wireless communications, the goal is to increase the signal power at the intended user and reduce interference to nonintended users. A high signal power is achieved by transmitting the same data signal from all antennas but with different amplitudes and phases, such that the signal components add coherently at the user. Low interference is accomplished by making the signal components add destructively at nonintended users. This corresponds mathematically to designing beamforming vectors (that describe the amplitudes and phases) to have large inner products with the vectors describing the intended channels and small inner products with nonintended user channels.

  • 4.
    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.

  • 5.
    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).

  • 6.
    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.

  • 7.
    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.

  • 8.
    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.

  • 9.
    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.

  • 10.
    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.

  • 11.
    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.

  • 12.
    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.

  • 13.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. Linköping University, Sweden.
    Hoydis, Jakob
    Kountouris, Marios
    Debbah, Merouane
    Massive MIMO Systems With Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 11, p. 7112-7139Article in journal (Refereed)
    Abstract [en]

    The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.

  • 14.
    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.

  • 15.
    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

  • 16.
    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.

  • 17.
    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.

  • 18.
    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.

  • 19.
    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.

  • 20.
    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.

  • 21.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Larsson, E. G.
    Debbah, Méroúane
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Optimizing multi-cell massive MIMO for spectral efficiency: How Many users should be scheduled?2014In: 2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014, IEEE conference proceedings, 2014, p. 612-616Conference paper (Refereed)
    Abstract [en]

    Massive MIMO is a promising technique to increase the spectral efficiency of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent beamforming. A common rule-of-thumb is that these systems should have an order of magnitude more antennas, N, than scheduled users, K, because the users' channels are then likely to be quasi-orthogonal. However, it has not been proved that this rule-of-thumb actually maximizes the spectral efficiency. In this paper, we analyze how the optimal number of scheduled users, K, depends on N and other system parameters. The value of K in the large-N regime is derived in closed form, while simulations are used to show what happens at finite N, in different interference scenarios, and for different beamforming.

  • 22.
    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.

  • 23.
    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.

  • 24.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. Supélec, France; Linköping University, Sweden.
    Matthaiou, Michail
    Debbah, Merouane
    Massive MIMO with Non-Ideal Arbitrary Arrays: Hardware Scaling Laws and Circuit-Aware Design2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 8, p. 4353-4368Article in journal (Refereed)
    Abstract [en]

    Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas N. Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today's conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phase-drifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with N while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as root N, instead of linearly, by careful circuit-aware system design.

  • 25.
    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.

  • 26.
    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.

  • 27.
    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.

  • 28.
    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.

  • 29.
    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.

  • 30.
    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.

  • 31.
    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.

  • 32.
    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.

  • 33.
    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.

  • 34.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Papadogiannis, A.
    Matthaiou, M.
    Debbah, M.
    On the impact of transceiver impairments on af relaying2013In: ICASSP IEEE Int Conf Acoust Speech Signal Process Proc, 2013, p. 4948-4952Conference paper (Refereed)
    Abstract [en]

    Recently, it was shown that transceiver hardware impairments have a detrimental impact on the performance of communication systems, especially for high-rate systems. The vast majority of technical contributions in the area of relaying assume ideal transceiver hardware. This paper quantifies the impact of transceiver hardware impairments in dual-hop Amplify-and-Forward (AF) relaying, both for fixed and variable gain relays. The outage probability (OP) in this practical scenario is a function of the instantaneous end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives closed-form expressions for the exact and asymptotic OPs under Rayleigh fading, accounting for hardware impairments at both the transmitter and the relay. The performance loss is small at low spectral efficiency, but can otherwise be very substantial. In particular, it turns out that for high signal-to-noise ratio (SNR), the instantaneous end-to-end SNDR converges to a deterministic constant, called the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in stark contrast to the ideal hardware case for which the end-to-end SNDR grows without bound in the high SNR regime.

  • 35.
    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.

  • 36. Björnson, Emil
    et al.
    Sanguinetti, Luca
    Hoydis, Jakob
    Debbah, Merouane
    Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 6, p. 3059-3075Article in journal (Refereed)
    Abstract [en]

    Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.

  • 37.
    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.

  • 38.
    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.

  • 39.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zetterberg, Per
    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.
    Optimal Coordinated Beamforming in the Multicell Downlink with Transceiver Impairments2012In: 2012 IEEE Global Telecommunications Conference (GLOBECOM), New York: IEEE conference proceedings, 2012, p. 4775-4780Conference paper (Refereed)
    Abstract [en]

    Physical wireless transceivers suffer from a variety of impairments that distort the transmitted and received signals. Their degrading impact is particularly evident in modern systems with multiuser transmission, high transmit power, and low-cost devices, but their existence is routinely ignored in the optimization literature for multicell transmission. This paper provides a detailed analysis of coordinated beamforming in the multicell downlink. We solve two optimization problems under a transceiver impairment model and derive the structure of the optimal solutions. We show numerically that these solutions greatly reduce the impact of impairments, compared with beamforming developed for ideal transceivers. Although the so-called multiplexing gain is zero under transceiver impairments, we show that the gain of multiplexing can be large at practical SNRs.

  • 40.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Zetterberg, Per
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Bengtsson, Mats
    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.
    Capacity Limits and Multiplexing Gains of MIMO Channels with Transceiver Impairments2013In: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 17, no 1, p. 91-94Article in journal (Refereed)
    Abstract [en]

    The capacity of ideal MIMO channels has a high-SNR slope that equals the minimum of the number of transmit and receive antennas. This letter analyzes if this result holds when there are distortions from physical transceiver impairments. We prove analytically that such physical MIMO channels have a finite upper capacity limit, for any channel distribution and SNR. The high-SNR slope thus collapses to zero. This appears discouraging, but we prove the encouraging result that the relative capacity gain of employing MIMO is at least as large as with ideal transceivers.

  • 41.
    Björnson, Emil
    et al.
    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.
    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.
    Robust Monotonic Optimization Framework for Multicell MISO Systems2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 5, p. 2508-2523Article in journal (Refereed)
    Abstract [en]

    The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are nonconvex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robustness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasiconvex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem.

  • 42.
    Brandt, Rasmus
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Björnson, Emil
    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.
    Weighted Sum Rate Optimization for Multicell MIMO Systems with Hardware-Impaired Transceivers2014Conference paper (Refereed)
    Abstract [en]

    Physical transceivers exhibit distortions from hardware impairments, of which traces remain even after compensation and calibration. Multicell MIMO coordinated beamforming methods that ignore these residual impairments may suffer from severely degraded performance. In this work, we consider a general model for the aggregate effect of the residual hardware impairments, and propose an iterative algorithm for finding locally optimal points to a weighted sum rate optimization problem. The importance of accounting for the residual hardware impairments is verified by numerical simulation, and a substantial gain over traditional time-division multiple access with impairments-aware resource allocation is observed.

  • 43. Flåm, John
    et al.
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Pilot design for MIMO channel estimation: An alternative to the Kronecker structure assumption2013In: ICASSP IEEE Int Conf Acoust Speech Signal Process Proc, IEEE conference proceedings, 2013, p. 5061-5064Conference paper (Refereed)
    Abstract [en]

    This work seeks to design a pilot signal, under a power constraint, such that the channel can be estimated with minimum mean square error. The procedure we derive does not assume Kronecker structure on the underlying covariance matrices, and the pilot signal is obtained in three main steps. Firstly, we solve a relaxed convex version of the original minimization problem. Secondly, its solution is projected onto the feasible set. Thirdly we use the projected solution as starting point for an augmented Lagrangian method. Numerical experiments indicate that this procedure may produce pilot signals that are far better than those obtained under the Kronecker structure assumption.

  • 44.
    Hou, Xueying
    et al.
    Beihang University (BUAA).
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Yang, Chenyang
    Beihang University (BUAA).
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cell-Grouping Based Distributed Beamforming and Scheduling for Multi-cell Cooperative Transmission2011In: Proceedings 22nd IEEE Symposium on Personal, Indoor, Mobile and Radio Communications (PIMRC), IEEE conference proceedings, 2011, p. 1929-1933Conference paper (Refereed)
    Abstract [en]

    Base station cooperative transmission is an effective strategy to mitigate inter-cell interference. Centralized multicell transmission provides considerable performance gains but is impractical in large cellular systems, due to its prohibitive complexity and large amount of overhead. Dividing cells into small clusters enables practical channel acquisition and coordination within each cluster but still suffers from out-of-cluster interference. In this paper, we propose a dynamic cooperative framework for large cellular systems, which divides cells into groups such that neighboring cells belong to different groups. Based on the cell-grouping, a distributed scheduling strategy is proposed which can effectively coordinate the interference between cell-groups. With limited signalling among BSs and lower complexity, the cell-grouping based distributed scheduling and beamforming shows performance advantages over the fixed clustering based centralized scheduling and beamforming.

  • 45. Kammoun, A.
    et al.
    Müller, A.
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing. Alcatel-Lucent, France .
    Debbah, M.
    Low-complexity linear precoding for multi-cell massive MIMO systems2014Conference paper (Refereed)
    Abstract [en]

    Massive MIMO (multiple-input multiple-output) has been recognized as an efficient solution to improve the spectral efficiency of future communication systems. However, increasing the number of antennas and users goes hand-in-hand with increasing computational complexity. In particular, the precoding design becomes involved since near-optimal precoding, such as regularized-zero forcing (RZF), requires the inversion of a large matrix. In our previous work [1] we proposed to solve this issue in the single-cell case by approximating the matrix inverse by a truncated polynomial expansion (TPE), where the polynomial coefficients are selected for optimal system performance. In this paper, we generalize this technique to multi-cell scenarios. While the optimization of the RZF precoding has, thus far, not been feasible in multi-cell systems, we show that the proposed TPE precoding can be optimized to maximize the weighted max-min fairness. Using simulations, we compare the proposed TPE precoding with RZF and show that our scheme can achieve higher throughput using a TPE order of only 3.

  • 46. Kammoun, Abla
    et al.
    Mueller, Axel
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Alcatel-Lucent Department of Flexible Radio, France.
    Debbah, Merouane
    Linear Precoding Based on Polynomial Expansion: Large-Scale Multi-Cell MIMO Systems2014In: IEEE Journal on Selected Topics in Signal Processing, ISSN 1932-4553, E-ISSN 1941-0484, Vol. 8, no 5, p. 861-875Article in journal (Refereed)
    Abstract [en]

    Large-scale MIMO systems can yield a substantial improvements in spectral efficiency for future communication systems. Due to the finer spatial resolution and array gain achieved by a massive number of antennas at the base station, these systems have shown to be robust to inter-user interference and the use of linear precoding appears to be asymptotically optimal. However, from a practical point of view, most precoding schemes exhibit prohibitively high computational complexity as the system dimensions increase. For example, the near-optimal regularized zero forcing (RZF) precoding requires the inversion of a large matrix. To solve this issue, we propose in this paper to approximate the matrix inverse by a truncated polynomial expansion (TPE), where the polynomial coefficients are optimized to maximize the system performance. This technique has been recently applied in single cell scenarios and it was shown that a small number of coefficients is sufficient to reach performance similar to that of RZF, while it was not possible to surpass RZF. In a realistic multi-cell scenario involving large-scale multi-user MIMO systems, the optimization of RZF precoding has, thus far, not been feasible. This is mainly attributed to the high complexity of the scenario and the non-linear impact of the necessary regularizing parameters. On the other hand, the scalar coefficients in TPE precoding give hope for possible throughput optimization. To this end, we exploit random matrix theory to derive a deterministic expression of the asymptotic signal-to-interference-and-noise ratio for each user based on channel statistics. We also provide an optimization algorithm to approximate the coefficients that maximize the network-wide weighted max-min fairness. The optimization weights can be used to mimic the user throughput distribution of RZF precoding. Using simulations, we compare the network throughput of the proposed TPE precoding with that of the suboptimal RZF scheme and show that our scheme can achieve higher throughput using a TPE order of only 5.

  • 47.
    Katselis, Dimitrios
    et al.
    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.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bombois, Xavier
    Delft University of Technology.
    Shariati, Nafiseh
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Training sequence design for MIMO channels: an application-oriented approach2013In: EURASIP Journal on Wireless Communications and Networking, ISSN 1687-1472, E-ISSN 1687-1499, Vol. 2013, p. 245-Article in journal (Refereed)
    Abstract [en]

    In this paper, the problem of training optimization for estimating a multiple-input multiple-output (MIMO) flat fading channel in the presence of spatially and temporally correlated Gaussian noise is studied in an application-oriented setup. So far, the problem of MIMO channel estimation has mostly been treated within the context of minimizing the mean square error (MSE) of the channel estimate subject to various constraints, such as an upper bound on the available training energy. We introduce a more general framework for the task of training sequence design in MIMO systems, which can treat not only the minimization of channel estimator's MSE but also the optimization of a final performance metric of interest related to the use of the channel estimate in the communication system. First, we show that the proposed framework can be used to minimize the training energy budget subject to a quality constraint on the MSE of the channel estimator. A deterministic version of the 'dual' problem is also provided. We then focus on four specific applications, where the training sequence can be optimized with respect to the classical channel estimation MSE, a weighted channel estimation MSE and the MSE of the equalization error due to the use of an equalizer at the receiver or an appropriate linear precoder at the transmitter. In this way, the intended use of the channel estimate is explicitly accounted for. The superiority of the proposed designs over existing methods is demonstrated via numerical simulations.

  • 48.
    Komulainen, Petri
    et al.
    Centre for Wireless Communications, University of Oulu.
    Tölli, Antti
    Centre for Wireless Communications, University of Oulu.
    Song, Bin
    Ilmenau University of Technology.
    Roemer, Florian
    Ilmenau University of Technology.
    Björnson, Emil
    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.
    CSI acquisition concepts for advanced antenna schemes in the WINNER+ project2010In: Future Network and MobileSummit 2010 Conference Proceedings / [ed] Paul Cunningham and Miriam Cunningham, IIMC International Information Management Corporation , 2010, p. 5722348-Conference paper (Refereed)
    Abstract [en]

    This paper summarizes four novel advanced antenna concepts explored in the framework of the WINNER+ project. The concepts are related to multiuser MIMO communication in cellular networks, focusing on the acquisition and application of channel state information (CSI) at the transmitter in time-division-duplex (TDD) mode. The concepts include new ideas for CSI modeling and sounding for the purposes of multiuser precoding, and methods for pilot signal design with the aim to support the estimation of different CSI quantities. Furthermore, a new relaying strategy for terminal-to-terminal communication is described. All the ideas are feasible for adoption into practical upcoming communication systems such as LTE-Advanced, and most of the proposed concepts have only a minor impact on standards.

    Our study indicates that the CSI at its best is not only about estimating the channel responses between different antenna pairs. What counts is the nature of the intended communication link as well as the form in which CSI is applied.

  • 49. Li, Jingya
    et al.
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing. Supelec.
    Svensson, Tommy
    Eriksson, Thomas
    Debbah, Merouane
    Joint Precoding and Load Balancing Optimization for Energy-Efficient Heterogeneous Networks2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 10, p. 5810-5822Article in journal (Refereed)
    Abstract [en]

    This paper considers a downlink heterogeneous network, where different types of multiantenna base stations (BSs) communicate with a number of single-antenna users. Multiple BSs can serve the users by spatial multiflow transmission techniques. Assuming imperfect channel state information at both BSs and users, the precoding, load balancing, and BS operation mode are jointly optimized for improving the network energy efficiency. We minimize the weighted total power consumption while satisfying quality-of-service constraints at the users. This problem is nonconvex, but we prove that for each BS mode combination, the considered problem has a hidden convexity structure. Thus, the optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the nonconvex objective function, a heuristic algorithm is proposed to obtain a suboptimal solution of low complexity. We show that although multicell joint transmission is allowed, in most cases, it is optimal for each user to be served by a single BS. The optimal BS association condition is parameterized, which reveals how it is impacted by different system parameters. Simulation results indicate that putting a BS into sleep mode by proper load balancing is an important solution for energy savings.

  • 50. Matthaiou, Michail
    et al.
    Papadogiannis, Agisilaos
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Debbah, Merouane
    Two-Way Relaying Under the Presence of Relay Transceiver Hardware Impairments2013In: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 17, no 6, p. 1136-1139Article in journal (Refereed)
    Abstract [en]

    Hardware impairments in physical transceivers are known to have a deleterious effect on communication systems; however, very few contributions have investigated their impact on relaying. This paper quantifies the impact of transceiver impairments in a two-way amplify-and-forward configuration. More specifically, the effective signal-to-noise-and-distortion ratios at both transmitter nodes are obtained. These are used to deduce exact and asymptotic closed-form expressions for the outage probabilities (OPs), as well as tractable formulations for the symbol error rates (SERs). It is explicitly shown that non-zero lower bounds on the OP and SER exist in the high-power regime-this stands in contrast to the special case of ideal hardware, where the OP and SER go asymptotically to zero.

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