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  • 1.
    Al-Salihi, Hayder
    et al.
    The Department of Informatics, King’s College London, UK.
    Van Chien, Trinh
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Le, Tuan Anh
    The Department of Design Engineering and Mathematics, Middlesex University, London, UK.
    Nakhai, Mohammad Reza
    The Department of Informatics, King’s College London, London, UK.
    A Successive Optimization Approach to Pilot Design for Multi-Cell Massive MIMO Systems2018In: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 22, no 5, p. 1086-1089Article in journal (Refereed)
    Abstract [en]

    In this letter, we introduce a novel pilot designapproach that minimizes the total mean square errors of theminimum mean square error estimators of all base stations (BSs)subject to the transmit power constraints of individual users inthe network, while tackling the pilot contamination in multicellmassive MIMO systems. First, we decompose the originalnon-convex problem into distributed optimization sub-problemsat individual BSs, where each BS can optimize its own pilotsignals given the knowledge of pilot signals from the remainingBSs. We then introduce a successive optimization approach totransform each optimization sub-problem into a linear matrixinequality form, which is convex and can be solved by availableoptimization packages. Simulation results confirm the fast convergenceof the proposed approach and prevails a benchmarkscheme in terms of providing higher accuracy.

  • 2.
    Le, Tuan Anh
    et al.
    Department of Design Engineering & Mathematics, Middlesex University, London.
    Van Chien, Trinh
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Nakhai, Mohammad Reza
    Department of Informatics, King’s College London, London.
    A Power Efficient Pilot Design for Multi-cell Massive MIMO Systems2018Conference paper (Refereed)
    Abstract [en]

    In this paper, we address the pilot contamination problem in multi-cell massive MIMO systems. Particularly, we propose a pilot design scheme that simultaneously minimizes the channel estimation errors of all base stations (BSs) and the total pilot power consumption of all users subject to the transmit power constraint for every user in the network. We decompose the proposed non-convex problem into distributed optimization problems to be solved at each BS, assuming the knowledge of pilot signals of the other BSs. Then, we introduce a successive optimization approach to cast each distributed optimization problem into a convex linear matrix inequality form. Simulation results confirm that the proposed approach significantly reduces pilot power while maintain the same level of channel estimation error as a recent work in [1].

  • 3.
    van Chien, Trinh
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Resource Allocation for Max-Min Fairness in Multi-Cell Massive MIMO2017Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Massive MIMO (multiple-input multiple-output) is considered as an heir of the multi-user MIMO technology and it has recently gained lots of attention from both academia and industry. By equipping base stations (BSs) with hundreds of antennas, this new technology can provide very large multiplexing gains by serving many users on the same time-frequency resources and thereby bring significant improvements in spectral efficiency (SE) and energy efficiency (EE) over the current wireless networks. The transmit power, pilot training, and spatial transmission resources need to be allocated properly to the users to achieve the highest possible performance. This is called resource allocation and can be formulated as design utility optimization problems. If the resource allocation in Massive MIMO is optimized, the technology can handle the exponential growth in both wireless data traffic and number of wireless devices, which cannot be done by the current cellular network technology.

    In this thesis, we focus on two resource allocation aspects in Massive MIMO: The first part of the thesis studies if power control and advanced coordinated multipoint (CoMP) techniques are able to bring substantial gains to multi-cell Massive MIMO systems compared to the systems without using CoMP. More specifically, we consider a network topology with no cell boundary where the BSs can collaborate to serve the users in the considered coverage area. We focus on a downlink (DL) scenario in which each BS transmits different data signals to each user. This scenario does not require phase synchronization between BSs and therefore has the same backhaul requirements as conventional Massive MIMO systems, where each user is preassigned to only one BS. The scenario where all BSs are phase synchronized to send the same data is also included for comparison. We solve a total transmit power minimization problem in order to observe how much power Massive MIMO BSs consume to provide the requested quality of service (QoS) of each user. A max-min fairness optimization is also solved to provide every user with the same maximum QoS regardless of the propagation conditions.

    The second part of the thesis considers a joint pilot design and uplink (UL) power control problem in multi-cell Massive MIMO. The main motivation for this work is that the pilot assignment and pilot power allocation is momentous in Massive MIMO since the BSs are supposed to construct linear detection and precoding vectors from the channel estimates. Pilot contamination between pilot-sharing users leads to more interference during data transmission. The pilot design is more difficult if the pilot signals are reused frequently in space, as in Massive MIMO, which leads to greater pilot contamination effects. Related works have only studied either the pilot assignment or the pilot power control, but not the joint optimization. Furthermore, the pilot assignment is usually formulated as a combinatorial problem leading to prohibitive computational complexity. Therefore, in the second part of this thesis, a new pilot design is proposed to overcome such challenges by treating the pilot signals as continuous optimization variables. We use those pilot signals to solve different max-min fairness optimization problems with either ideal hardware or hardware impairments.

    List of papers
    1. Joint Power Allocation and User Association Optimization for Massive MIMO Systems
    Open this publication in new window or tab >>Joint Power Allocation and User Association Optimization for Massive MIMO Systems
    2016 (English)In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 9, p. 6384-6399Article in journal (Refereed) Published
    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.

    Place, publisher, year, edition, pages
    Institute of Electrical and Electronics Engineers (IEEE), 2016
    Keywords
    Massive MIMO, user association, power allocation, load balancing, linear program
    National Category
    Communication Systems
    Identifiers
    urn:nbn:se:liu:diva-131129 (URN)10.1109/TWC.2016.2583436 (DOI)000384241400040 ()
    Funder
    ELLIIT - The Linköping‐Lund Initiative on IT and Mobile Communications
    Available from: 2016-09-11 Created: 2016-09-11 Last updated: 2019-06-28Bibliographically approved
  • 4.
    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.

  • 5.
    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.

  • 6.
    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.

  • 7.
    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.
    Sum Spectral Efficiency Maximization in Massive MIMO Systems: Benefits from Deep Learning2019In: ICC 2019 - 2019 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS (ICC), IEEE Communications Society, 2019Conference paper (Refereed)
    Abstract [en]

    This paper investigates the joint data and pilot power optimization for maximum sum spectral efficiency (SE) in multi-cell Massive MIMO systems, which is a non-convex problem. We first propose a new optimization algorithm, inspired by the weighted minimum mean square error (MMSE) approach, to obtain a stationary point in polynomial time. We then use this algorithm together with deep learning to train a convolutional neural network to perform the joint data and pilot power control in sub-millisecond runtime, making it suitable for online optimization in real multi-cell Massive MIMO systems. The numerical result demonstrates that the solution obtained by the neural network is 1% less than the stationary point for four-cell systems, while the sum SE loss is 2% in a nine-cell system.

  • 8.
    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.

  • 9.
    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.

  • 10.
    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 Correlation2019In: Proceedings of 2019 IEEE International Conference on Communications, ICC 2019, 2019, article id 8761502Conference 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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