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  • 1.
    Björnson, Emil
    KTH Royal Institute Technology, Sweden; Supelec, France.
    Kountouris, Marios
    CentraleSupelec, France.
    Debbah, Merouane
    CentraleSupelec, France.
    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 hardwareimpairments 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 hardwareimpairments 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.

  • 2.
    Björnson, Emil
    KTH Royal Institute Technology, Sweden; Supelec, France.
    Debbah, Merouane
    CentraleSupelec, France.
    Ottersten, Björn
    KTH Royal Institute of Technology.
    Multi-Objective 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.

  • 3.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Bengtsson, Mats
    KTH Royal Institute of Technology, Stockholm, Sweden .
    Ottersten, Björn
    KTH Royal Institute of Technology, Stockholm, Sweden; University of Luxembourg.
    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.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Hoydis, Jakob
    Nokia Bell Labs, France.
    Sanguinetti, Luca
    University of Pisa, Italy / CentraleSupelec, France.
    Massive MIMO Networks: spectral, energy, and hardware efficiency2018Book (Refereed)
    Abstract [en]

    Massive multiple-input multiple-output (Massive MIMO) is the latest technology that will improve the speed and throughput of wireless communication systems for years to come. Whilst there may be some debate over the origins of the term Massive MIMO and what it precisely means, this monograph describes in detail how the research conducted in the past decades lead to a scalable multiantenna technology that offers great throughput and energy efficiency under practical conditions. Written for students, practicing engineers and researchers who want to learn the conceptual and analytical foundations of Massive MIMO, in terms of spectral, energy, and/or hardware efficiency, as well as channel estimation and practical considerations, it provides a clear and tutorial like exposition of all the major topics. It also connects the dots of the research literature covering numerous topics not easily found therein. Massive MIMO Networks is the first monograph on the subject to cover the spatial chan el correlation and consider rigorous signal processing design essential for the complete understanding by its target audience.

  • 5.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Three Practical Aspects of Massive MIMO: Intermittent User Activity, Pilot Synchronism, and Asymmetric Deployment2015In: 2015 IEEE Globecom Workshops (GC Wkshps), Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 1-6Conference paper (Refereed)
    Abstract [en]

    This paper considers three aspects of Massive MIMO (multiple- input multiple-output) communication networks that have received little attention in previous works, but are important to understand when designing and implementing this promising wireless technology. First, we analyze how bursty data traffic behaviors affect the system. Using a probabilistic model for intermittent user activity, we show that the spectral efficiency (SE) scales gracefully with reduced user activity. Then, we make an analytic comparison between synchronous and asynchronous pilot signaling, and prove that the choice between these has no impact on the SE. Finally, we provide an analytical and numerical study of the SE achieved with random network deployment.

  • 6.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Debbah, Merouane
    CentraleSupelec, France; Huawei, France.
    Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated?2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 2, p. 1293-1308Article in journal (Refereed)
    Abstract [en]

    Massive MIMO is a promising technique for increasing the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas M than scheduled users K because the users channels are likely to be near-orthogonal when M/K > 10. However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users K-star depends on M and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of K-star in the large-M regime is derived in closed form, while simulations are used to show what happens at finite M, in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal M/K is less than 10 in many cases of practical relevance. Interestingly, K-star depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same K.

  • 7.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Debbah, Merouane
    CentraleSupelec, France.
    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, Institute of Electrical and Electronics Engineers (IEEE), 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.

  • 8.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Marzetta, Thomas L.
    Nokia, France.
    Massive MIMO: Ten Myths and One Critical Question2016In: IEEE Communications Magazine, ISSN 0163-6804, E-ISSN 1558-1896, Vol. 54, no 2, p. 114-123Article in journal (Refereed)
    Abstract [en]

    Wireless communications is one of the most successful technologies in modern years, given that an exponential growth rate in wireless traffic has been sustained for over a century (known as Coopers law). This trend will certainly continue, driven by new innovative applications; for example, augmented reality and the Internet of Things. Massive MIMO has been identified as a key technology to handle orders of magnitude more data traffic. Despite the attention it is receiving from the communication community, we have personally witnessed that Massive MIMO is subject to several widespread misunderstandings, as epitomized by following (fictional) abstract: "The Massive MIMO technology uses a nearly infinite number of high-quality antennas at the base stations. By having at least an order of magnitude more antennas than active terminals, one can exploit asymptotic behaviors that some special kinds of wireless channels have. This technology looks great at first sight, but unfortunately the signal processing complexity is off the charts and the antenna arrays would be so huge that it can only be implemented in millimeter-wave bands." These statements are, in fact, completely false. In this overview article, we identify 10 myths and explain why they are not true. We also ask a question that is critical for the practical adoption of the technology and which will require intense future research activities to answer properly. We provide references to key technical papers that support our claims, while a further list of related overview and technical papers can be found at the Massive MIMO Info Point: http://massivemimo.eu

  • 9.
    Björnson, Emil
    et al.
    KTH Royal Institute Technology, Sweden; Supelec, France.
    Matthaiou, Michail
    Chalmers, Sweden; Queens University of Belfast, North Ireland.
    Debbah, Merouane
    CentraleSupelec, France.
    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 N − −  √   , instead of linearly, by careful circuit-aware system design

  • 10.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Matthaiou, Michail
    Chalmers, Sweden; Queens University of Belfast, North Ireland.
    Pitarokoilis, Antonios
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Distributed Massive MIMO in Cellular Networks: Impact of Imperfect Hardware and Number of Oscillators2015In: 23rd European Signal Processing Conference, EUSIPCO 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 2436-2440Conference paper (Refereed)
    Abstract [en]

    Distributed massive multiple-input multiple-output (MIMO) combines the array gain of coherent MIMO processing with the proximity gains of distributed antenna setups. In this paper, we analyze how transceiver hardware impairments affect the downlink with maximum ratio transmission. We derive closed-form spectral efficiencies expressions and study their asymptotic behavior as the number of the antennas increases. We prove a scaling law on the hardware quality, which reveals that massive MIMO is resilient to additive distortions, while multiplicative phase noise is a limiting factor. It is also better to have separate oscillators at each antenna than one per BS

  • 11.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. KTH Royal Institute Technology, Sweden; Supelec, France.
    Sanguinetti, Luca
    University of Pisa, Italy; CentraleSupelec, France.
    Hoydis, Jakob
    Bell Labs, Germany.
    Debbah, Merouane
    CentraleSupelec, France.
    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.

  • 12.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Sanguinetti, Luca
    University of Pisa, Italy; University of Paris Saclay, France.
    Kountouris, Marios
    Huawei Technology Co Ltd, France.
    Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO2016In: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 34, no 4, p. 832-847Article in journal (Refereed)
    Abstract [en]

    What would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a "massive MIMO" fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.

  • 13.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Sanguinetti, Luca
    University of Pisa, Italy; CentraleSupelec, France.
    Kountouris, Marios
    CentraleSupelec, France.
    Designing Wireless Broadband Access for Energy Efficiency: Are Small Cells the Only Answer?2015In: 2015 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATION WORKSHOP, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 136-141Conference paper (Refereed)
  • 14.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Van der Perre, Liesbet
    Katholieke Univ Leuven, Belgium; Lund Univ, Sweden.
    Buzzi, Stefano
    Univ Cassino and Lazio Merid, Italy; CNIT, Italy.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Massive MIMO in Sub-6 GHz and mmWave: Physical, Practical, and Use-Case Differences2019In: IEEE wireless communications, ISSN 1536-1284, E-ISSN 1558-0687, Vol. 26, no 2, p. 100-108Article in journal (Refereed)
    Abstract [en]

    The use of base stations (BSs) and access points (APs) with a large number of antennas, called Massive MIMO (multiple-input multiple-output), is a key technology for increasing the capacity of 5G networks and beyond. While originally conceived for conventional sub-6 GHz frequencies, Massive MIMO (mMIMO) is also ideal for frequency bands in the range 30-300 GHz, known as millimeter wave (mmWave). Despite conceptual similarities, the way in which mMIMO can be exploited in these bands is radically different, due to their specific propagation behaviors and hardware characteristics. This article reviews these differences and their implications, while dispelling common misunderstandings. Building on this foundation, we suggest appropriate signal processing schemes and use cases to efficiently exploit mMIMO in both frequency bands.

  • 15.
    Cheng, Hei Victor
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Uplink pilot and data power control for single cell massive MIMO systems with MRC2015In: International Symposium on Wireless Communication Systems (ISWCS), 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 396-400Conference paper (Refereed)
    Abstract [en]

    This paper considers the jointly optimal pilot and data power allocation in single cell uplink massive MIMO systems. A closed form solution for the optimal length of the training interval is derived. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per coherence interval the power control is formulated as optimization problems for two different objective functions: the minimum SE among the users and the sum SE. The optimal power control policy is found for the case of maximizing the minimum SE by converting it to a geometric program (GP). Since maximizing the sum SE is an NP-hard problem, an efficient algorithm is developed for finding KKT (local maximum) points. Simulation results show the advantage of optimizing the power control over both pilot and data power, as compared to heuristic power control policies.

  • 16.
    Cheng, Hei Victor
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Persson, Daniel
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Massive MIMO at Night: On the Operation of Massive MIMO in Low Traffic Scenarios2015In: 2015 IEEE International Conference on Communications (ICC), IEEE , 2015, p. 1697-1702Conference paper (Refereed)
    Abstract [en]

    For both maximum ratio transmission (MRT) and zero forcing (ZF) precoding schemes and given any specific rate requirement the optimal transmit power, number of antennas to be used, number of users to be served and number of pilots spent on channel training are found with the objective to minimize the total consumed power at the base station. The optimization problem is solved by finding closed form expressions of the optimal transmit power and then search over the remaining discrete variables. The analysis consists of two parts, the first part investigates the situation when only power consumed in the RF amplifiers is considered. The second part includes both the power consumed in the RF amplifiers and in other transceiver circuits. In the former case having all antennas active while reducing the transmit power is optimal. Adaptive scheme to switch off some of the antennas at the base stations is found to be optimal in the latter case.

  • 17.
    Do, Tan Tai
    et al.
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    JAMMING RESISTANT RECEIVERS FOR MASSIVE MIMO2017In: 2017 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 3619-3623Conference paper (Refereed)
    Abstract [en]

    We design jamming resistant receivers to enhance the robustness of a massive MIMO uplink channel against jamming. In the pilot phase, we estimate not only the desired channel, but also the jamming channel by exploiting purposely unused pilot sequences. The jamming channel estimate is used to construct the linear receive filter to reduce impact that jamming has on the achievable rates. The performance of the proposed scheme is analytically and numerically evaluated. These results show that the proposed scheme greatly improves the rates, as compared to conventional receivers. Moreover, the proposed schemes still work well with stronger jamming power.

  • 18.
    Do, Tan Tai
    et al.
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Mohammad Razavizadeh, S.
    Iran University of Science and Technology, Iran.
    Jamming-Resistant Receivers for the Massive MIMO Uplink2018In: IEEE Transactions on Information Forensics and Security, ISSN 1556-6013, E-ISSN 1556-6021, Vol. 13, no 1, p. 210-223Article in journal (Refereed)
    Abstract [en]

    We design a jamming-resistant receiver scheme to enhance the robustness of a massive MIMO uplink system against jamming. We assume that a jammer attacks the system both in the pilot and data transmission phases. The key feature of the proposed scheme is that, in the pilot phase, the base station estimates not only the legitimate channel, but also the jamming channel by exploiting a purposely unused pilot sequence. The jamming channel estimate is used to construct linear receiver filters that reject the impact of the jamming signal. The performance of the proposed scheme is analytically evaluated using the asymptotic properties of massive MIMO. The best regularized zero-forcing receiver and the optimal power allocations for the legitimate system and the jammer are also studied. Numerical results are provided to verify our analysis and show that the proposed scheme greatly improves the achievable rates, as compared with conventional receivers. Interestingly, the proposed scheme works particularly well under strong jamming attacks, since the improved estimate of the jamming channel outweighs the extra jamming power.

  • 19.
    Fozooni, Milad
    et al.
    Queen's University of Belfast, North Ireland, UK.
    Matthaiou, Michail
    Queen's University of Belfast, North Ireland, UK.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Duong, Trung Q.
    Queen's University of Belfast, North Ireland, UK.
    Performance Limits of MIMO Systems with Nonlinear Power Amplifiers2015In: 2015 IEEE GLOBAL COMMUNICATIONS CONFERENCE (GLOBECOM), Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)
  • 20.
    Ghazanfar, Amin
    et al.
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Linköping University, The Institute of Technology.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Linköping University, The Institute of Technology.
    Power Control for D2D Underlay in Multi-cell Massive MIMO Networks2018In: ITG-Fb. 276: WSA 2018: 22nd International ITG Workshop on Smart Antennas March 14-16, 2018, Bochum, Germany (CD-ROM), Berlin, Offenbach: VDE Verlag , 2018Conference paper (Refereed)
    Abstract [en]

    This paper proposes a new power control and pilot allocation scheme for device-to-device (D2D) communication underlaying a multi-cell massive MIMO system. In this scheme, the cellular users in each cell get orthogonal pilots which are reused with reuse factor one across cells, while the D2D pairs share another set of orthogonal pilots. We derive a closed-form capacity lower bound for the cellular users with different receive processing schemes. In addition, we derive a capacity lower bound for the D2D receivers and a closed-form approximation of it. Then we provide a power control algorithm that maximizes the minimum spectral efficiency (SE) of the users in the network. Finally, we provide a numerical evaluation where we compare our proposed power control algorithm with the maximum transmit power case and the case of conventional multi-cell massive MIMO without D2D communication. Based on the provided results, we conclude that our proposed scheme increases the sum spectral efficiency of multi-cell massive MIMO networks.

  • 21.
    Hossain, M. M. Aftab
    et al.
    Aalto University, Finland.
    Cavdar, Cicek
    KTH Royal Institute of Technology, Sweden.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Jäntti, Riku
    Aalto University, Finland.
    Energy-Efficient Load-Adaptive Massive MIMO2015In: 2015 IEEE GLOBECOM WORKSHOPS (GC WKSHPS), 2015Conference paper (Refereed)
  • 22.
    Interdonato, Giovanni
    et al.
    Ericsson Research, Linköping, 581 12, Sweden.
    Karlsson, Marcus
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Downlink Spectral Efficiency of Cell-Free Massive MIMO with Full-Pilot Zero-Forcing2018In: 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2018, p. 1003-1007Conference paper (Refereed)
    Abstract [en]

    Cell-free Massive multiple-input multiple-output (MIMO) ensures ubiquitous communication at high spectral efficiency (SE) thanks to increased macro-diversity as compared cellular communications. However, system scalability and performance are limited by fronthauling traffic and interference. Unlike conventional precoding schemes that only suppress intra-cell interference, full-pilot zero-forcing (fpZF), introduced in [1], actively suppresses also inter-cell interference, without sharing channel state information (CSI) among the access points (APs). In this study, we derive a new closed-form expression for the downlink (DL) SE of a cell-free Massive MIMO system with multi-antenna APs and fpZF precoding, under imperfect CSI and pilot contamination. The analysis also includes max-min fairness DL power optimization. Numerical results show that fpZF significantly outperforms maximum ratio transmission scheme, without increasing the fronthauling overhead, as long as the system is sufficiently distributed.

  • 23.
    Jingya, Li
    et al.
    Chalmers University of Technology,Gothenburg, Sweden.
    Björnson, Emil
    KTH Royal Institute of Technology, Sweden; Supelec, France.
    Svensson, Tommy
    Chalmers University of Technology,Gothenburg, Sweden.
    Eriksson, Thomas
    Chalmers University of Technology,Gothenburg, Sweden,.
    Debbah, Merouane
    CentraleSupelec, France.
    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.

  • 24.
    Kammoun, A.
    et al.
    Alcatel-Lucent Department of Flexible Radio, SUPELECGif-sur-Yvette, France.
    Muller, A.
    Alcatel-Lucent Department of Flexible Radio, SUPELECGif-sur-Yvette, France.
    Björnson, Emil
    Alcatel-Lucent Department of Flexible Radio, SUPELECGif-sur-Yvette, France; Signal Processing Lab, ACCESS Linnaeus Centre, KTH Royal Institute of TechnologyStockholm, Sweden.
    Debbah, M.
    Alcatel-Lucent Department of Flexible Radio, SUPELECGif-sur-Yvette, France.
    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.

  • 25.
    Karlsson, Marcus
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Broadcasting in Massive MIMO Using OSTBC with Reduced Dimension2015Conference paper (Refereed)
    Abstract [en]

    Abstract—An analysis of broadcasting in massive MIMO (multiple-input and multiple-output) systems with a limited coherence interval is presented. When broadcasting common information, such as control signals, the base station does not have channel state information to the terminals. We propose that the base station broadcasts this common information using a low dimensional orthogonal space-time block code (OSTBC). This code is mapped onto the large antenna array with the use of a dimension reducing matrix, effectively “shrinking” the channel. The terminal can estimate the effective channel and decode the information, even when the coherence interval is short compared to the number of base station antennas. Different OSTBCs are compared in terms of outage capacity in practical scenarios using estimated CSI. In particular, the trade-off between diversity and rate, when little or no time/frequency diversity is available, is investigated.

  • 26.
    Kashyap, Salil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Can wireless power transfer benefit from large transmitter arrays?2015In: Proceedings of IEEE Wireless Power Transfer Conference (WPTC), Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 1-3Conference paper (Refereed)
    Abstract [en]

    In this paper, we illustrate the potential benefits of using large transmitter arrays for wireless power transfer. Specifically, we analyze the probability of outage in energy transfer over fading channels when the base station (BS) with multiple antennas beamforms energy to a wireless sensor node. Our analytical and numerical results show that by using large transmitter arrays, the range of wireless power transfer can be increased while maintaining a target outage probability. We also observe and quantify that by using multi-antenna arrays at the BS, a lower downlink energy is required to get the same outage performance

  • 27.
    Kashyap, Salil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    On the Feasibility of Wireless Energy Transfer Using Massive Antenna Arrays2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 5, p. 3466-3480Article in journal (Refereed)
    Abstract [en]

    We illustrate potential benefits of using massive antenna arrays for wireless energy transfer (WET). Specifically, we analyze probability of outage in WET over fading channels when a base station (BS) with multiple antennas beamforms energy to a wireless sensor node (WSN). Our analytical results show that by using massive antenna arrays, the range of WET can be increased for a given target outage probability. We prove that by using multiple-antenna arrays at the BS, a lower downlink energy is required to get the same outage performance, resulting in savings of radiated energy. We show that for energy levels used in WET, the outage performance with least-squares or minimum mean-square-error channel estimates is the same as that obtained based on perfect channel estimates. We observe that a strong line-of-sight component between the BS and WSN lowers outage probability. Furthermore, by deploying more antennas at the BS, a larger energy can be transferred reliably to the WSN at a given target outage performance for the sensor to be able to perform its main tasks. In our numerical examples, the RF power received at the input of the sensor is assumed to be on the order of a mW, such that the rectenna operates at an efficiency in the order of 50%.

  • 28.
    Kashyap, Salil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    On the feasibility of wireless energy transfer using massive antenna arrays in Rician channels2015In: 16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 46-50Conference paper (Refereed)
    Abstract [en]

    In this paper, we examine the feasibility of wireless energy transfer (WET) using arrays with multiple antennas. Specifically, we compute the probability of outage in energy transfer over a Rician fading channel when the base station (BS) with multiple antennas transfers energy to a wireless sensor node (WSN). Through our analytical and numerical results, we prove that by deploying more antennas at the BS, the range of WET can be increased while maintaining a target outage probability. We observe that the use of massive antenna arrays at the BS results into huge savings of radiated energy. We show that for typical energy levels used in WET, the outage performance with imperfect channel state information (CSI) is essentially the same as that obtained based on perfect CSI. We also observe that a strong line-of-sight component between the BS and the WSN lowers the probability of outage in energy transfer.

  • 29.
    Li, Jingya
    et al.
    Chalmers, Sweden; Ericsson AB, Sweden.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Svensson, Tommy
    Chalmers, Sweden.
    Eriksson, Thomas
    Chalmers, Sweden.
    Debbah, Merouane
    Supelec, France.
    Optimal Design of Energy-Efficient HetNets: Joint Precoding and Load Balancing2015In: 2015 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS (ICC), IEEE , 2015, p. 4664-4669Conference paper (Refereed)
    Abstract [en]

    This paper considers the downlink of a heterogeneous network, where multiple base stations (BSs) can serve the users by non-coherent multiflow beamforming. We assume imperfect channel state information at both BSs and users. The objective is to jointly optimize the precoding, load balancing, and BS operation mode (active or sleep) for improving the energy efficiency of the network. The considered problem is to minimize the weighted total power consumption (both circuit power and dynamic transmit power), while satisfying per-user quality of service constraints and per-BS transmit power constraints. This problem is non-convex, but we prove that for each combination of BS modes, the considered problem has a hidden convexity structure. Thus, the global optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the non-convex power consumption functions, a heuristic algorithm is proposed to obtain a local optimal solution with low complexity. Simulation results illustrate that our proposed algorithms significantly reduce the total power consumption, compared to the scheme where all BSs are continuously active. This implies that putting a BS into sleep mode by proper load balancing is an important solution for energy savings in heterogeneous networks.

  • 30.
    Li, Xueru
    et al.
    Tsinghua University, Beijing, China.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Zhou, Shidong
    Tsinghua University, Beijing, China.
    Wang, Jing
    Tsinghua University, Beijing, China.
    A Multi-cell MMSE Detector for Massive MIMO Systems and New Large System Analysis2015In: 2015 IEEE Global Communications Conference, GLOBECOM 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 1-6Conference paper (Refereed)
    Abstract [en]

    In this paper, a new multi-cell MMSE detector is proposed for massive MIMO systems. Let K and B denote the number of users in each cell and the number of available pilot sequences in the network, respectively, with B = βK, where β ≥ 1 is called the pilot reuse factor. The novelty of the multi-cell MMSE detector is that it utilizes all B channel directions that can be estimated locally at a base station, so that intra-cell interference, parts of the inter-cell interference and the noise can all be actively suppressed, while conventional detectors only use the K intra-cell channels. Furthermore, in the large- system limit, a deterministic equivalent expression of the uplink SINR for the proposed multi-cell MMSE is derived. The expression is easy to compute and accounts for power control for the pilot and payload, imperfect channel estimation and arbitrary pilot allocation. Numerical results show that significant sum spectral efficiency gains can be obtained by the multi-cell MMSE over the conventional single-cell MMSE and the recent multi-cell ZF, and the gains become more significant as β and/or K increases. Furthermore, the deterministic equivalent is shown to be very accurate even for relatively small system dimensions.

  • 31.
    Li, Xueru
    et al.
    Tsinghua University, Beijing, China.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Zhou, Shidong
    Tsinghua University, Beijing, China.
    Wang, Jing
    Tsinghua University, Beijing, China.
    A Multi-cell MMSE Precoder for Massive MIMO Systems and New Large System Analysis2015In: 2015 IEEE Global Communications Conference, GLOBECOM 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 1-6Conference paper (Refereed)
    Abstract [en]

    In this paper, a new multi-cell MMSE precoder is proposed for massive MIMO systems. We consider a multi-cell network where each cell has K users and B orthogonal pilot sequences are available, with B = βK and β ≥ 1 being the pilot reuse factor over the network. In comparison with conventional single-cell precoding which only uses the K intra-cell channel estimates, the proposed multi-cell MMSE precoder utilizes all B channel directions that can be estimated locally at a base station, so that the transmission is designed spatially to suppress both parts of the inter-cell and intra-cell interference. To evaluate the performance, a large-scale approximation of the downlink SINR for the proposed multi-cell MMSE precoder is derived and the approximation is tight in the large-system limit. Power control for the pilot and payload, imperfect channel estimation and arbitrary pilot allocation are accounted for in our precoder. Numerical results show that the proposed multi-cell MMSE precoder achieves a significant sum spectral efficiency gain over the classical single-cell MMSE precoder and the gain increases as K or β grows. Compared with the recent M-ZF precoder, whose performance degrades drastically for a large K, our M-MMSE can always guarantee a high and stable performance. Moreover, the large-scale approximation is easy to compute and shown to be accurate even for small system dimensions. 

  • 32.
    Li, Xueru
    et al.
    Tsinghua University, Peoples R China.
    Zhou, Shidong
    Tsinghua University, Peoples R China.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Wang, Jing
    Tsinghua University, Peoples R China.
    Capacity Analysis for Spatially Non-Wide Sense Stationary Uplink Massive MIMO Systems2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 12, p. 7044-7056Article in journal (Refereed)
    Abstract [en]

    Channel measurements show that significant spatially non-wide-sense-stationary characteristics rise in massive MIMO channels. Notable parameter variations are experienced along the base station array, such as the average received energy at each antenna, and the directions of arrival of signals impinging on different parts of the array. In this paper, a new channel model is proposed to describe this spatial non-stationarity in massive MIMO channels by incorporating the concepts of partially visible clusters and wholly visible clusters. Furthermore, a closed-form expression of an upper bound on the ergodic sum capacity is derived for the new model, and the influence of the spatial non-stationarity on the sum capacity is analyzed. Analysis shows that for non-identically-and-independent-distributed (i.i.d.) Rayleigh fading channels, the non-stationarity benefits the sum capacity by bringing a more even spread of channel eigenvalues. Specifically, more partially visible clusters, smaller cluster visibility regions, and a larger antenna array can all help to yield a well-conditioned channel, and benefit the sum capacity. This shows the advantage of using a large antenna array in a non-i.i.d. channel: the sum capacity benefits not only from a higher array gain, but also from a more spatially non-stationary channel. Numerical results demonstrate our analysis and the tightness of the upper bound.

  • 33.
    Mochaourab, Rami
    et al.
    KTH Royal Institute of Technology, Sweden.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Bengtsson, Mats
    KTH Royal Institute of Technology, Sweden.
    Pilot Clustering in Asymmetric Massive MIMO Networks2015In: 2015 IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 231-235Conference paper (Refereed)
  • 34.
    Mueller, Axel
    et al.
    Huawei Technology Co Ltd, France; SUPELEC, France.
    Kammoun, Abla
    SUPELEC, France; King Abdullah University of Science and Technology, Saudi Arabia.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. SUPELEC, France.
    Debbah, Merouane
    Huawei Technology Co Ltd, France; SUPELEC, France.
    Linear precoding based on polynomial expansion: reducing complexity in massive MIMO2016In: EURASIP Journal on Wireless Communications and Networking, ISSN 1687-1472, E-ISSN 1687-1499, no 63Article in journal (Refereed)
    Abstract [en]

    Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively "antenna-efficient" regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.

  • 35.
    Müller, Axel
    et al.
    CentraleSupelec, France.
    Couillet, Romain
    CentraleSupelec, France.
    Björnson, Emil
    KTH Royal Institute Technology, Sweden; Supelec, France.
    Wagner, Sebastian
    Universität Dresden, Germany.
    Debbah, Merouane
    CentraleSupelec, France.
    Interference-Aware RZF Precoding for Multi-Cell Downlink Systems2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 15, p. 3959-3973Article in journal (Refereed)
    Abstract [en]

    Recently, a structure of an optimal linear precoder for multi cell downlink systems has been described, and many other references have used simplified versions of this precoder to obtain promising performance gains. These gains have been hypothesized to stem from the additional degrees of freedom that allow for interference mitigation through interference relegation to orthogonal subspaces. However, no conclusive or rigorous understanding has yet been developed. In this paper, we build on an intuitive interference induction trade-off and the aforementioned preceding structure to propose an interference aware RZF (iaRZF) precoding scheme for multi celldownlink systems, and we analyze its rate performance. Special emphasis is placed on the induced interference mitigation mechanism of iaRZF. For example, we will verify the intuitive expectation that the precoder structure can either completely remove induced inter-cell or intra-cell interference. We state new results from large-scale random matrix theory that make it possible to give more intuitive and insightful explanations of the precoder behavior, also for cases involving imperfect channel state information (CSI). We remark especially that the interference-aware precoder makes use of all available information about interfering channels to improve performance. Even very poor CSI allows for significant sum-rate gains. Our obtained insights are then used to propose heuristic precoder parameters for arbitrary systems, whose effectiveness are shown in more involved system scenarios. Furthermore, calculation and implementation of these parameters does not require explicit inter base station cooperation.

  • 36.
    Pirzadeh, Hessam
    et al.
    IUST, Sch Elect Engn, Tehran 1684613114, Iran.
    Razavizadeh, S. Mohammad
    IUST, Sch Elect Engn, Tehran 1684613114, Iran.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Subverting Massive MIMO by Smart Jamming2016In: IEEE Wireless Communications Letters, ISSN 2162-2337, E-ISSN 2162-2345, Vol. 5, no 1, p. 20-23Article in journal (Refereed)
    Abstract [en]

    We consider uplink transmission of a massive multiuser multiple-input multiple-output (MU-MIMO) system in the presence of a smart jammer. The jammer aims to degrade the sum spectral efficiency of the legitimate system by attacking both the training and data transmission phases. First, we derive a closed-form expression for the sum spectral efficiency by taking into account the presence of a smart jammer. Then, we determine how a jammer with a given energy budget should attack the training and data transmission phases to induce the maximum loss to the sum spectral efficiency. Numerical results illustrate the impact of optimal jamming specifically in the large limit of the number of base station (BS) antennas.

  • 37.
    Pitarokoilis, Antonios
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    ML Detection in Phase Noise Impaired SIMO Channels with Uplink Training2016In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 64, no 1, p. 223-235Article in journal (Refereed)
    Abstract [en]

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

  • 38.
    Pitarokoilis, Antonios
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Optimal Detection in Training Assisted SIMO Systems with Phase Noise Impairments2015In: 2015 IEEE International Conference on Communications (ICC), IEEE Press, 2015, p. 2597-2602Conference paper (Refereed)
    Abstract [en]

    Abstract—In this paper, the problem of optimal maximum likelihood detection in a single user single-input multiple-output (SIMO) channel with phase noise at the receiver is considered. The optimal detection rules under training are derived for two operation modes, namely when the phase increments are fully correlated among the M receiver antennas (synchronous operation) and when they are independent (non-synchronous operation). The phase noise increments are parameterized by a very general distribution, which includes the Wiener phase noise model as a special case. It is proven that phase noise creates a symbol-error-rate (SER) floor for both operation modes. Inthe synchronous operation this error floor is independent of M, while it goes to zero exponentially withM in the non-synchronous operation.

  • 39.
    Pitarokoilis, Antonios
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Performance of the Massive MIMO Uplink with OFDM and Phase Noise2016In: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 20, no 8, p. 1595-1598Article in journal (Refereed)
    Abstract [en]

    The performance of multi-userMassiveMIMO-OFDMuplink systems in the presence of base station (BS) phase noise impairments is investigated. Closed-form achievable rate expressions are rigorously derived under two different operations, namely the case of a common oscillator (synchronous operation) at the BS and the case of independent oscillators at each BS antenna (non-synchronous operation). It is observed that the non-synchronous operation exhibits superior performance due to the averaging of intercarrier interference. Further, radiated power scaling lawsare derived, which are identical to the phase-noise-free case.

  • 40.
    Sadeghi, Meysam
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Yuen, Chau
    Singapore University of Technology and Design, Singapore.
    Marzetta, Thomas L.
    Department of Electrical and Computer Engineering, New York University, New York, USA.
    Joint Unicast and Multi-group Multicast Transmission in Massive MIMO Systems2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 10, p. 6375-6388Article in journal (Refereed)
    Abstract [en]

    We study the joint unicast and multi-group multicast transmission in massive multiple-input-multiple-output (MIMO) systems. We consider a system model that accounts for channel estimation and pilot contamination, and derive achievable spectral efficiencies (SEs) for unicast and multicast user terminals (UTs), under maximum ratio transmission and zero-forcing precoding. For unicast transmission, our objective is to maximize the weighted sum SE of the unicast UTs, and for the multicast transmission, our objective is to maximize the minimum SE of the multicast UTs. These two objectives are coupled in a conflicting manner, due to their shared power resource. Therefore, we formulate a multiobjective optimization problem (MOOP) for the two conflicting objectives. We derive the Pareto boundary of the MOOP analytically. As each Pareto optimal point describes a particular efficient trade-off between the two objectives of the system, we determine the values of the system parameters (uplink training powers, downlink transmission powers, etc.) to achieve any desired Pareto optimal point. Moreover, we prove that the Pareto region is convex, hence the system should serve the unicast and multicast UTs at the same time-frequency resource. Finally, we validate our results using numerical simulations.

  • 41.
    Sanguinetti, L.
    et al.
    Dipartimento di Ingegneria dellInformazione, University of of PisaPisa, Italy; Alcatel-Lucent, Ecole Supérieure dÉlectricité (Supélec)Gif-sur-Yvette, France.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Alcatel-Lucent, Ecole Supérieure dÉlectricité (Supélec)Gif-sur-Yvette, France; Dept. of Signal Processing, KTH, Stockholm, Sweden.
    Debbah, M.
    Alcatel-Lucent, Ecole Supérieure dÉlectricité (Supélec)Gif-sur-Yvette, France.
    Moustakas, A.L.
    Alcatel-Lucent, Ecole Supérieure dÉlectricité (Supélec)Gif-sur-Yvette, France; Department of Physics, National and Capodistrian University of of AthensAthens, Greece.
    Optimal linear precoding in multi-user MIMO systems: A large system analysis2014In: 2014 IEEE Global Communications Conference, GLOBECOM 2014, Institute of Electrical and Electronics Engineers Inc. , 2014, no 7037420, p. 3922-3927Conference paper (Refereed)
    Abstract [en]

    We consider the downlink of a single-cell multi-user MIMO system in which the base station makes use of N antennas to communicate with K single-antenna user equipments (UEs) randomly positioned in the coverage area. In particular, we focus on the problem of designing the optimal linear precoding for minimizing the total power consumption while satisfying a set of target signal-to-interference-plus-noise ratios (SINRs). To gain insights into the structure of the optimal solution and reduce the computational complexity for its evaluation, we analyze the asymptotic regime where N and K grow large with a given ratio and make use of recent results from large system analysis to compute the asymptotic solution. Then, we concentrate on the asymptotically design of heuristic linear precoding techniques. Interestingly, it turns out that the regularized zero-forcing (RZF) precoder is equivalent to the optimal one when the ratio between the SINR requirement and the average channel attenuation is the same for all UEs. If this condition does not hold true but only the same SINR constraint is imposed for all UEs, then the RZF can be modified to still achieve optimality if statistical information of the UE positions is available at the BS. Numerical results are used to evaluate the performance gap in the finite system regime and to make comparisons among the precoding techniques.

  • 42.
    Sanguinetti, Luca
    et al.
    University of Pisa, Italy; CentraleSupelec, France.
    Moustakas, Aris L.
    National and Capodistrian University of Athens, Greece.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Debbah, Merouane
    CentraleSupelec, France.
    Large System Analysis of the Energy Consumption Distribution in Multi-User MIMO Systems With Mobility2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 3, p. 1730-1745Article in journal (Refereed)
    Abstract [en]

    In this work, we consider the downlink of a single-cell multi-user MIMO system in which the base station (BS) makes use of N antennas to communicate with K single-antenna user equipments (UEs). The UEs move around in the cell according to a random walk mobility model. We aim at determining the energy consumption distribution when different linear precoding techniques are used at the BS to guarantee target rates within a finite time interval T. The analysis is conducted in the asymptotic regime where N and K grow large with fixed ratio under the assumption of perfect channel state information (CSI). Both recent and standard results from large system analysis are used to provide concise formulae for the asymptotic transmit powers and beamforming vectors for all considered schemes. These results are eventually used to provide a deterministic approximation of the energy consumption and to study its fluctuations around this value in the form of a central limit theorem. Closed-form expressions for the asymptotic means and variances are given. Numerical results are used to validate the accuracy of the theoretical analysis and to make comparisons. We show how the results can be used to approximate the probability that a battery-powered BS runs out of energy and also to design the cell radius for minimizing the energy consumption per unit area. The imperfect CSI case is also briefly considered.

  • 43.
    Shalmashi, Serveh
    et al.
    KTH Royal Institute of Technology, Sweden.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Kountouris, Marios
    CentraleSupelec, France.
    Sung, Ki Won
    KTH Royal Institute of Technology, Sweden.
    Debbah, Merouane
    CentraleSupelec, France.
    Energy Efficiency and Sum Rate when Massive MIMO meets Device-to-Device Communication2015Conference paper (Refereed)
    Abstract [en]

    This paper considers a scenario of short-range communication, known as device-to-device (D2D) communication, where D2D users reuse the downlink resources of a cellular network to transmit directly to their corresponding receivers. In addition, multiple antennas at the base station (BS) are used in order to simultaneously support multiple cellular users using multiuser or massive MIMO. The network model considers a fixed number of cellular users and that D2D users are distributed according to a homogeneous Poisson point process (PPP). Two metrics are studied, namely, average sum rate (ASR) and energy efficiency (EE). We derive tractable expressions and study the tradeoffs between the ASR and EE as functions of the number of BS antennas and density of D2D users for a given coverage area.

  • 44.
    Shariati, N.
    et al.
    Department of Signal Processing, KTH Royal Institute of TechnologyStockholm, Sweden.
    Björnson, Emil
    Alcatel-Lucent Department on Flexible Radio, SupélecGif-sur-Yvette, France.
    Bengtsson, M.
    Department of Signal Processing, KTH Royal Institute of TechnologyStockholm, Sweden.
    Debbah, M.
    Alcatel-Lucent Department on Flexible Radio, SupélecGif-sur-Yvette, France.
    Low-complexity polynomial channel estimation in large-scale MIMO with arbitrary statistics2014In: IEEE Journal on Selected Topics in Signal Processing, ISSN 1932-4553, E-ISSN 1941-0484, Vol. 8, no 5, p. 815-830Article in journal (Refereed)
    Abstract [en]

    This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as massive MIMO, where there are hundreds of antennas at one side of the link. Motivated by the fact that computational complexity is one of the main challenges in such systems, a set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced for arbitrary channel and interference statistics. While the conventional minimum mean square error (MMSE) estimator has cubic complexity in the dimension of the covariance matrices, due to an inversion operation, our proposed estimators significantly reduce this to square complexity by approximating the inverse by a $L$-degree matrix polynomial. The coefficients of the polynomial are optimized to minimize the mean square error (MSE) of the estimate. We show numerically that near-optimal MSEs are achieved with low polynomial degrees. We also derive the exact computational complexity of the proposed estimators, in terms of the floating-point operations (FLOPs), by which we prove that the proposed estimators outperform the conventional estimators in large-scale MIMO systems of practical dimensions while providing a reasonable MSEs. Moreover, we show that $L$ needs not scale with the system dimensions to maintain a certain normalized MSE. By analyzing different interference scenarios, we observe that the relative MSE loss of using the low-complexity PEACH estimators is smaller in realistic scenarios with pilot contamination. On the other hand, PEACH estimators are not well suited for noise-limited scenarios with high pilot power; therefore, we also introduce the low-complexity diagonalized estimator that performs well in this regime. Finally, we also investigate numerically how the estimation performance is affected by having imperfect statistical knowledge. High robustness is achieved for large-dimensional matrices by using a new covariance estimate which is an affine function of the sample covariance matrix and a regularization term.

  • 45.
    Van Chien, Trinh
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Downlink Power Control for Massive MIMO Cellular Systems with Optimal User Association2016In: IEEE International Conference on Communications, Malaysia, May 23-27, 2016: proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016Conference paper (Refereed)
    Abstract [en]

    This paper aims to minimize the total transmit power consumption for Massive MIMO (multiple-input multiple-output) downlink cellular systems when each user is served by the optimized subset of the base stations (BSs). We derive a lower bound on the ergodic spectral efficiency (SE) for Rayleigh fading channels and maximum ratio transmission (MRT) when the BSs cooperate using non-coherent joint transmission. We solve the joint user association and downlink transmit power minimization problem optimally under fixed SE constraints. Furthermore, we solve a max-min fairness problem with user specific weights that maximizes the worst SE among the users. The optimal BS-user association rule is derived, which is different from maximum signal-to-noise-ratio (max-SNR) association. Simulation results manifest that the proposed methods can provide good SE for the users using less transmit power than in small-scale systems and that the optimal user association can effectively balance the load between BSs when needed.

  • 46.
    Van Chien, Trinh
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Joint Pilot Design and Uplink Power Allocation in Multi-Cell Massive MIMO Systems2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 3, p. 2000-2015Article in journal (Refereed)
    Abstract [en]

    This paper considers pilot design to mitigate pilot contamination and provide good service for everyone in multi-cell Massive multiple input multiple output (MIMO) systems. Instead of modeling the pilot design as a combinatorial assignment problem, as in prior works, we express the pilot signals using a pilot basis and treat the associated power coefficients as continuous optimization variables. We compute a lower bound on the uplink capacity for Rayleigh fading channels with maximum ratio detection that applies with arbitrary pilot signals. We further formulate the max-min fairness problem under power budget constraints, with the pilot signals and data powers as optimization variables. Because this optimization problem is non-deterministic polynomial-time hard due to signomial constraints, we then propose an algorithm to obtain a local optimum with polynomial complexity. Our framework serves as a benchmark for pilot design in scenarios with either ideal or non-ideal hardware. Numerical results manifest that the proposed optimization algorithms are close to the optimal solution obtained by exhaustive search for different pilot assignments and the new pilot structure and optimization bring large gains over the state-of-the-art suboptimal pilot design.

  • 47.
    Van Chien, Trinh
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Joint Power Allocation and User Association Optimization for Massive MIMO Systems2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 9, p. 6384-6399Article in journal (Refereed)
    Abstract [en]

    This paper investigates the joint power allocationand user association problem in multi-cell Massive MIMO(multiple-input multiple-output) downlink (DL) systems. Thetarget is to minimize the total transmit power consumptionwhen each user is served by an optimized subset of the basestations (BSs), using non-coherent joint transmission. We firstderive a lower bound on the ergodic spectral efficiency (SE),which is applicable for any channel distribution and precodingscheme. Closed-form expressions are obtained for Rayleigh fadingchannels with either maximum ratio transmission (MRT) or zeroforcing (ZF) precoding. From these bounds, we further formulatethe DL power minimization problems with fixed SE constraintsfor the users. These problems are proved to be solvable aslinear programs, giving the optimal power allocation and BS-user association with low complexity. Furthermore, we formulatea max-min fairness problem which maximizes the worst SEamong the users, and we show that it can be solved as aquasi-linear program. Simulations manifest that the proposedmethods provide good SE for the users using less transmit powerthan in small-scale systems and the optimal user associationcan effectively balance the load between BSs when needed.Even though our framework allows the joint transmission frommultiple BSs, there is an overwhelming probability that only oneBS is associated with each user at the optimal solution.

  • 48.
    Van Chien, Trinh
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Le, Tuan Anh
    Department of Design Engineering & Maths, Middlesex University London, United Kingdom.
    Distributed Power Control in Downlink Cellular Massive MIMO Systems2018In: WSA 2018: 22nd International ITG Workshop on Smart Antennas, VDE Verlag GmbH, 2018, p. 1-7Conference paper (Refereed)
    Abstract [en]

    This paper compares centralized and distributed methods to solve the power minimization problem with quality-of-service (QoS) constraints in the downlink (DL) of multi-cell Massive multiple-input multiple-output (MIMO) systems. In particular, we study the computational complexity, number of parameters that need to be exchanged between base stations (BSs), and the convergence of iterative implementations. Although a distributed implementation based on dual decomposition (which only requires statistical channel knowledge at each BS) typically converges to the global optimum after a few iterations, many parameters need to be exchanged to reach convergence.

  • 49.
    Van Chien, Trinh
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Mollén, Christopher
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Large-scale-fading decoding in cellular Massive MIMO systems with spatially correlated channels2019In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 67, no 4, p. 2746-2762Article in journal (Refereed)
    Abstract [en]

    Massive multiple-input–multiple-output (MIMO) systems can suffer from coherent intercell interference due to the phenomenon of pilot contamination. This paper investigates a two-layer decoding method that mitigates both coherent and non-coherent interference in multi-cell Massive MIMO. To this end, each base station (BS) first estimates the channels to intra-cell users using either minimum mean-squared error (MMSE) or element-wise MMSE estimation based on uplink pilots. The estimates are used for local decoding on each BS followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An uplink achievable spectral efficiency (SE) expression is computed for arbitrary two-layer decoding schemes. A closed form expression is then obtained for correlated Rayleigh fading, maximum-ratio combining, and the proposed large-scale fading decoding (LSFD) in the second layer. We also formulate a sum SE maximization problem with both the data power and LSFD vectors as optimization variables. Since this is an NP-hard problem, we develop a low-complexity algorithm based on the weighted MMSE approach to obtain a local optimum. The numerical results show that both data power control and LSFD improve the sum SE performance over single-layer decoding multi-cell Massive MIMO systems.

  • 50.
    Van Chien, Trinh
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Mollén, Christopher
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Two-Layer Decoding in Cellular Massive MIMO Systems with Spatial Channel Correlation2019Conference paper (Refereed)
    Abstract [en]

    This paper studies a two-layer decoding method that mitigates inter-cell interference in multi-cell Massive MIMO systems. In layer one, each base station (BS) estimates the channels to intra-cell users and uses the estimates for local decoding on each BS, followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An uplink achievable spectral efficiency (SE) expression is computed for arbitrary two-layer decoding schemes, while a closed-form expression is obtained for correlated Rayleigh fading channels, maximum-ratio combining (MRC), and large-scale fading decoding (LSFD) in the second layer. We formulate a non-convex sum SE maximization problem with both the data power and LSFD vectors as optimization variables and develop an algorithm based on the weighted MMSE (minimum mean square error) approach to obtain a stationary point with low computational complexity.

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