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  • 1.
    Abd-Elmagid, Mohamed A.
    et al.
    Virginia Tech, VA 24061 USA.
    Dhillon, Harpreet S.
    Virginia Tech, VA 24061 USA.
    Pappas, Nikolaos
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    A Reinforcement Learning Framework for Optimizing Age of Information in RF-Powered Communication Systems2020In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 68, no 8, p. 4747-4760Article in journal (Refereed)
    Abstract [en]

    In this paper, we study a real-time monitoring system in which multiple source nodes are responsible for sending update packets to a common destination node in order to maintain the freshness of information at the destination. Since it may not always be feasible to replace or recharge batteries in all source nodes, we consider that the nodes are powered through wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy (referred to as the age-optimal policy) that jointly optimizes WET and scheduling of update packet transmissions with the objective of minimizing the long-term average weighted sum of Age of Information (AoI) values for different physical processes (observed by the source nodes) at the destination node, referred to as the sum-AoI. To solve this optimization problem, we first model this setup as an average cost Markov decision process (MDP) with finite state and action spaces. Due to the extreme curse of dimensionality in the state space of the formulated MDP, classical reinforcement learning algorithms are no longer applicable to our problem even for reasonable-scale settings. Motivated by this, we propose a deep reinforcement learning (DRL) algorithm that can learn the age-optimal policy in a computationally-efficient manner. We further characterize the structural properties of the age-optimal policy analytically, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the age-optimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average weighted sum-AoI.

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  • 2.
    Akbar, Noman
    et al.
    Australian Natl Univ, Australia.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Yang, Nan
    Australian Natl Univ, Australia.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Max-Min Power Control in Downlink Massive MIMO With Distributed Antenna Arrays2021In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 69, no 2, p. 740-751Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate optimal downlink power allocation in massive multiple-input multiple-output (MIMO) networks with distributed antenna arrays (DAAs) under correlated and uncorrelated channel fading. In DAA massive MIMO, a base station (BS) consists of multiple antenna sub-arrays. Notably, the antenna sub-arrays are deployed in arbitrary locations within a DAA massive MIMO cell. Consequently, the distance-dependent large-scale propagation coefficients are different from a user to these different antenna sub-arrays, which makes power control a challenging problem. We assume that the network operates in time-division duplex mode, where each BS obtains the channel estimates via uplink pilots. Based on the channel estimates, the BSs perform maximum-ratio transmission in the downlink. We then derive a closed-form signal-to-interference-plus-noise ratio (SINR) expression, where the channels are subject to correlated fading. Based on the SINR expression, we propose a network-wide max-min power control algorithm to ensure that each user in the network receives a uniform quality of service. Numerical results demonstrate the performance advantages offered by DAA massive MIMO. For some specific scenarios, DAA massive MIMO can improve the average per-user throughput up to 55%. Furthermore, we demonstrate that channel fading covariance is an important factor in determining the performance of DAA massive MIMO.

  • 3.
    Akhlaghpasand, Hossein
    et al.
    Iran Univ Sci and Technol, Iran.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Razavizadeh, S. Mohammad
    Iran Univ Sci and Technol, Iran.
    Jamming-Robust Uplink Transmission for Spatially Correlated Massive MIMO Systems2020In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 68, no 6, p. 3495-3504Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider how the uplink transmission of a spatially correlated massive multiple-input multiple-output (MIMO) system can be protected from a jamming attack. To suppress the jamming, we propose a novel framework including a new optimal linear estimator in the training phase and a bilinear equalizer in the data phase. The proposed estimator is optimal in the sense of maximizing the spectral efficiency of the legitimate system attacked by a jammer, and its implementation needs the statistical knowledge about the jammers channel. We derive an efficient algorithm to estimate the jamming information needed for implementation of the proposed framework. Furthermore, we demonstrate that optimized power allocation at the legitimate users can improve the performance of the proposed framework regardless of the jamming power optimization. Our proposed framework can be exploited to combat jamming in scenarios with either ideal or non-ideal hardware at the legitimate users and the jammer. Numerical results reveal that using the proposed framework, the jammer cannot dramatically affect the performance of the legitimate system.

  • 4. Ayanoglu, Ender
    et al.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Karipidis, Eleftherios
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Computational Complexity of Decoding Orthogonal Space-Time Block Codes2011In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 59, no 4, p. 936-941Article in journal (Refereed)
    Abstract [en]

    The computational complexity of optimum decoding for an orthogonal space-time block code {cal G}_N satisfying {cal G}_N^H{cal G}_N=c(∑_{k=1}^Kos_ko^2)I_N where c is a positive integer is quantified. Four equivalent techniques of optimum decoding which have the same computational complexity are specified. Modifications to the basic formulation in special cases are calculated and illustrated by means of examples. This paper corrects and extends and unifies them with the results from the literature. In addition, a number of results from the literature are extended to the case c>1.

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  • 5.
    Bashar, Manijeh
    et al.
    Univ Surrey, England.
    Ngo, Hien Quoc
    Queens Univ Belfast, North Ireland.
    Cumanan, Kanapathippillai
    Univ York, England.
    Burr, Alister G.
    Univ York, England.
    Xiao, Pei
    Univ Surrey, England.
    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 Spectral and Energy Efficiency of Cell-Free Massive MIMO With Optimal Uniform Quantization2021In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 69, no 1, p. 223-245Article in journal (Refereed)
    Abstract [en]

    This paper investigates the performance of limited-fronthaul cell-free massive multiple-input multiple-output (MIMO) taking account the fronthaul quantization and imperfect channel acquisition. Three cases are studied, which we refer to as Estimate&Quantize, Quantize&Estimate, and Decentralized, according to where channel estimation is performed and exploited. Maximum-ratio combining (MRC), zero-forcing (ZF), and minimum mean-square error (MMSE) receivers are considered. The Max algorithm and the Bussgang decomposition are exploited to model optimum uniform quantization. Exploiting the optimal step size of the quantizer, analytical expressions for spectral and energy efficiencies are presented. Finally, an access point (AP) assignment algorithm is proposed to improve the performance of the decentralized scheme. Numerical results investigate the performance gap between limited fronthaul and perfect fronthaul cases, and demonstrate that exploiting relatively few quantization bits, the performance of limited-fronthaul cell-free massive MIMO closely approaches the perfect-fronthaul performance.

  • 6.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Sanguinetti, Luca
    Univ Pisa, Italy.
    Scalable Cell-Free Massive MIMO Systems2020In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 68, no 7, p. 4247-4261Article in journal (Refereed)
    Abstract [en]

    Imagine a coverage area with many wireless access points that cooperate to jointly serve the users, instead of creating autonomous cells. Such a cell-free network operation can potentially resolve many of the interference issues that appear in current cellular networks. This ambition was previously called Network MIMO (multiple-input multiple-output) and has recently reappeared under the name Cell-Free Massive MIMO. The main challenge is to achieve the benefits of cell-free operation in a practically feasible way, with computational complexity and fronthaul requirements that are scalable to large networks with many users. We propose a new framework for scalable Cell-Free Massive MIMO systems by exploiting the dynamic cooperation cluster concept from the Network MIMO literature. We provide a novel algorithm for joint initial access, pilot assignment, and cluster formation that is proved to be scalable. Moreover, we adapt the standard channel estimation, precoding, and combining methods to become scalable. A new uplink and downlink duality is proved and used to heuristically design the precoding vectors on the basis of the combining vectors. Interestingly, the proposed scalable precoding and combining outperform conventional maximum ratio (MR) processing and also performs closely to the best unscalable alternatives.

  • 7.
    Björnson, Emil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Sanguinetti, Luca
    Univ Pisa, Italy.
    Hoydis, Jakob
    Paris Saclay, France.
    Hardware Distortion Correlation Has Negligible Impact on UL Massive MIMO Spectral Efficiency2019In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 67, no 2, p. 1085-1098Article in journal (Refereed)
    Abstract [en]

    This paper analyzes how the distortion created by hardware impairments in a multiple-antenna base station affects the uplink spectral efficiency (SE), with a focus on massive multiple input multiple output (MIMO). This distortion is correlated across the antennas but has been often approximated as uncorrelated to facilitate (tractable) SE analysis. To determine when this approximation is accurate, basic properties of distortion correlation are first uncovered. Then, we separately analyze the distortion correlation caused by third-order non-linearities and by quantization. Finally, we study the SE numerically and show that the distortion correlation can be safely neglected in massive MIMO when there are sufficiently many users. Under independent identically distributed Rayleigh fading and equal signal-to-noise ratios (SNRs), this occurs for more than five transmitting users. Other channel models and SNR variations have only minor impact on the accuracy. We also demonstrate the importance of taking the distortion characteristics into account in the receive combining.

  • 8.
    Chen, Zheng
    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.
    Channel Hardening and Favorable Propagation in Cell-Free Massive MIMO With Stochastic Geometry2018In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 66, no 11, p. 5205-5219Article in journal (Refereed)
    Abstract [en]

    Cell-free (CF) massive multiple-input multiple-output (MIMO) is an alternative topology for future wireless networks, where a large number of single-antenna access points (APs) are distributed over the coverage area. There are no cells but all users are jointly served by the APs using network MIMO methods. Prior works have claimed that the CF massive MIMO inherits the basic properties of cellular massive MIMO, namely, channel hardening and favorable propagation. In this paper, we evaluate if one can rely on these properties when having a realistic stochastic AP deployment. Our results show that channel hardening only appears in special cases, for example, when the pathloss exponent is small. However, by using 5-10 antennas per AP, instead of one, we can substantially improve the hardening. Only spatially well-separated users will exhibit favorable propagation, but when adding more antennas and/or reducing the pathloss exponent, it becomes more likely for favorable propagation to occur. The conclusion is that we cannot rely on the channel hardening and the favorable propagation when analyzing and designing the CF massive MIMO networks, but we need to use achievable rate expressions and resource allocation schemes that work well also in the absence of these properties. Some options are reviewed in this paper.

  • 9.
    Chen, Zheng
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Kountouris, Marios
    Huawei Technol Co Ltd, France.
    Decentralized Opportunistic Access for D2D Underlaid Cellular Networks2018In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 66, no 10, p. 4842-4853Article in journal (Refereed)
    Abstract [en]

    In this paper, we propose a decentralized access control scheme for interference management in device-to-device (D2D) underlaid cellular networks. Our method combines signal-to-interference ratio (SIR)-aware link activation with cellular guard zones in a system, where D2D links opportunistically access the licensed cellular spectrum when the activation conditions are satisfied. Analytical expressions for the success/coverage probability of both cellular and D2D links are derived. We characterize the impact of the guard zone radius and the SIR threshold on the D2D potential throughput and cellular coverage. A tractable approach is proposed to find the SIR threshold and guard zone radius that maximize the potential throughput of the D2D communication while ensuring sufficient coverage probability for the cellular uplink users. Simulations validate the accuracy of our analytical results and show the performance gain of the proposed scheme compared to prior state-of-the-art solutions.

  • 10.
    Cheng, Jing
    et al.
    Beijing Jiaotong Univ, Peoples R China.
    Shen, Chao
    Beijing Jiaotong Univ, Peoples R China; Shenzhen Res Inst Big Data, Peoples R China.
    Chen, Zheng
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Pappas, Nikolaos
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Robust Beamforming Design for IRS-Aided URLLC in D2D Networks2022In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 70, no 9, p. 6035-6049Article in journal (Refereed)
    Abstract [en]

    Intelligent reflecting surface (IRS) and device-to-device (D2D) communication are two promising technologies for improving transmission reliability between transceivers in communication systems. In this paper, we consider the design of reliable communication between the access point (AP) and actuators for a downlink multiuser multiple-input single-output (MISO) system in the industrial IoT (IIoT) scenario. We propose a two-stage protocol combining IRS with D2D communication so that all actuators can successfully receive the message from AP within a given delay. The superiority of the protocol is that the communication reliability between AP and actuators is doubly augmented by the IRS-aided first-stage transmission and the second-stage D2D transmission. A joint optimization problem of active and passive beamforming is formulated, which aims to maximize the number of actuators with successful decoding. We study the joint beamforming problem for cases where the channel state information (CSI) is perfect and imperfect. For each case, we develop efficient algorithms that include convergence and complexity analysis. Simulation results demonstrate the necessity and role of IRS with a well-optimized reflection matrix, and the D2D network in promoting reliable communication. Moreover, the proposed protocol can enable reliable communication even in the presence of stringent latency requirements and CSI estimation errors.

  • 11.
    Cheng, Victor
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Persson, Daniel
    Qamcom Res and Technol AB, Sweden.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Optimal MIMO Precoding Under a Constraint on the Amplifier Power Consumption2019In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 67, no 1, p. 218-229Article in journal (Refereed)
    Abstract [en]

    The capacity of the MIMO channel taking into account both a limitation on total consumed power, and per-antenna radiated power constraints is considered. The total consumed power takes into account the traditionally used sum radiated power, and also the power dissipation in the amplifiers. For a fixed channel with full CSI at both the transmitter and the receiver, maximization of the mutual information is formulated as an optimization problem. Lower and upper bounds on the capacity are provided by numerical algorithms based on partitioning of the feasible region. Both bounds are shown to converge and give the exact capacity when number of regions increases. The bounds are also used to construct a monotonic optimization algorithm based on the branch-and-bound approach. An efficient suboptimal algorithm based on successive convex approximation performing close to the capacity is also presented. Numerical results show that the performance of the solution obtained from the suboptimal algorithm is close to that of the global optimal solution. Simulation results also show that in the low SNR regime, antenna selection provides performance that is close to the optimal scheme while at high SNR, uniform power allocation performs close to the optimal scheme.

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  • 12.
    Du, Jinfeng
    et al.
    KTH.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Xiao, Ming
    KTH.
    Skoglund, Mikael
    KTH.
    Optimal Symbol-by-Symbol Costa Precoding for a Relay-aided Downlink Channel2011In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 59, no 8, p. 2274-2284Article in journal (Refereed)
    Abstract [en]

    In this article, we consider practical approaches to Costa precoding (also known as dirty paper coding). Specifically, we propose a symbol-by-symbol scheme for cancellation of interference known at the transmitter in a relay-aided downlink channel. For finite-alphabet signaling and interference, we derive the optimal (in terms of maximum mutual information) modulator under a given power constraint. A sub-optimal modulator is also proposed by formulating an optimization problem that maximizes the minimum distance of the signal constellation, and this non-convex optimization problem is approximately solved by semi-definite relaxation. For the case of binary signaling with binary interference, we obtain a closed-form solution for the sub-optimal modulator, which only suffers little performance degradation compared to the optimal modulator in the region of interest. For more general signal constellations and more general interference distributions, we propose an optimized Tomlinson-Harashima precoder (THP), which uniformly outperforms conventional THP with heuristic parameters. Bit-level simulation shows that the optimal and sub-optimal modulators can achieve significant gains over the THP benchmark as well as over non-Costa reference schemes, especially when the power of the interference is larger than the power of the noise.

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  • 13.
    Fountoulakis, Emmanouil
    et al.
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Ericsson AB, Sweden.
    Charalambous, Themistoklis
    Univ Cyprus, Cyprus.
    Ephremides, Anthony
    Univ Maryland, MD 20742 USA.
    Pappas, Nikolaos
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Scheduling Policies for AoI Minimization With Timely Throughput Constraints2023In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 71, no 7, p. 3905-3917Article in journal (Refereed)
    Abstract [en]

    In 5G and beyond communication systems, the notion of latency gets great momentum in wireless connectivity as a metric for serving real-time communications requirements. However, in many applications, research has pointed out that latency could be inefficient to handle applications with data freshness requirements. Recently, Age of Information (AoI) metric, which can capture the freshness of the data, has attracted a lot of attention. In this work, we consider mixed traffic with time-sensitive users; a deadline-constrained user, and an AoI-oriented user. To develop an efficient scheduling policy, we cast a novel optimization problem formulation for minimizing the average AoI while satisfying the timely throughput constraints. The formulated problem is cast as a Constrained Markov Decision Process (CMDP). We relax the constrained problem to an unconstrained Markov Decision Process (MDP) problem by utilizing the Lyapunov optimization theory and it can be proved that it is solved per frame by applying backward dynamic programming algorithms with optimality guarantees. In addition, we provide a low-complexity algorithm guaranteeing that the timely-throughput constraint is satisfied. Simulation results show that the timely throughput constraints are satisfied while minimizing the average AoI. Simulation results show the convergence of the algorithms for different values of the weighted factor and the trade-off between the AoI and the timely throughput.

  • 14.
    Gao, Xiang
    et al.
    Lund University, Sweden.
    Edfors, Ove
    Lund University, Sweden.
    Tufvesson, Fredrik
    Lund University, Sweden.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Massive MIMO in Real Propagation Environments: Do All Antennas Contribute Equally?2015In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 63, no 11, p. 3917-3928Article in journal (Refereed)
    Abstract [en]

    Massive MIMO can greatly increase both spectral and transmit-energy efficiency. This is achieved by allowing the number of antennas and RF chains to grow very large. However, the challenges include high system complexity and hardware energy consumption. Here we investigate the possibilities to reduce the required number of RF chains, by performing antenna selection. While this approach is not a very effective strategy for theoretical independent Rayleigh fading channels, a substantial reduction in the number of RF chains can be achieved for real massive MIMO channels, without significant performance loss. We evaluate antenna selection performance on measured channels at 2.6 GHz, using a linear and a cylindrical array, both having 128 elements. Sum-rate maximization is used as the criterion for antenna selection. A selection scheme based on convex optimization is nearly optimal and used as a benchmark. The achieved sum-rate is compared with that of a very simple scheme that selects the antennas with the highest received power. The power-based scheme gives performance close to the convex optimization scheme, for the measured channels. This observation indicates a potential for significant reductions of massive MIMO implementation complexity, by reducing the number of RF chains and performing antenna selection using simple algorithms.

  • 15.
    Ghazanfari, Amin
    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.
    Optimized Power Control for Massive MIMO With Underlaid D2D Communications2019In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 67, no 4, p. 2763-2778Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider device-to-device (D2D) communication that is underlaid in a multi-cell massive multiple-input multiple-output (MIMO) system and proposes a new framework for power control and pilot allocation. In this scheme, the cellular users (CUs) in each cell get orthogonal pilots which are reused with reuse factor one across cells, while all the D2D pairs share another set of orthogonal pilots. We derive a closed-form capacity lower bound for the CUs with different receive processing schemes. In addition, we derive a capacity lower bound for the D2D receivers and a closed-form approximation of it. We provide power control algorithms to maximize the minimum spectral efficiency (SE) and to maximize the product of the signal-to-interference-plus-noise ratios in the network. Different from prior works, in our proposed power control schemes, we consider joint pilot and data transmission optimization. Finally, we provide a numerical evaluation, where we compare our proposed power control schemes 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 SE of multi-cell massive MIMO networks.

  • 16.
    Ghazanfari, Amin
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Cheng, Hei Victor
    Univ Toronto, Canada.
    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.
    Enhanced Fairness and Scalability of Power Control Schemes in Multi-Cell Massive MIMO2020In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 68, no 5, p. 2878-2890Article in journal (Refereed)
    Abstract [en]

    This paper studies the transmit power optimization in multi-cell Massive multiple-input multiple-output (MIMO) systems. Network-wide max-min fairness (NW-MMF) and network-wide proportional fairness (NW-PF) are two well-known power control schemes in the literature. The NW-MMF focus on maximizing the fairness among users at the cost of penalizing users with good channel conditions. On the other hand, the NW-PF focuses on maximizing the sum SE, thereby ignoring fairness, but gives some extra attention to the weakest users. However, both of these schemes suffer from a scalability issue which means that for large networks, it is highly probable that one user has a very poor channel condition, pushing the spectral efficiency (SE) of all users towards zero. To overcome the scalability issue of NW-MMF and NW-PF, we propose a novel power control scheme that is provably scalable. This scheme maximizes the geometric mean (GM) of the per-cell max-min SE. To solve this new optimization problem, we prove that it can be rewritten in a convex optimization form and then solved using standard tools. The simulation results highlight the benefits of our model which is balancing between NW-PF and NW-MMF.

  • 17.
    Ghazanfari, Amin
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Huawei Gotherburg Res Ctr, Sweden.
    Trinh Van, Chien
    Univ Luxembourg, Luxembourg.
    Björnson, Emil
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. KTH Royal Inst Technol, Sweden.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Model-Based and Data-Driven Approaches for Downlink Massive MIMO Channel Estimation2022In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 70, no 3, p. 2085-2101Article in journal (Refereed)
    Abstract [en]

    We study downlink channel estimation in a multi-cell Massive multiple-input multiple-output (MIMO) system operating in time-division duplex. The users must know their effective channel gains to decode their received downlink data. Previous works have used the mean value as the estimate, motivated by channel hardening. However, this is associated with a performance loss in non-isotropic scattering environments. We propose two novel estimation methods that can be applied without downlink pilots. The first method is model-based and asymptotic arguments are utilized to identify a connection between the effective channel gain and the average received power during a coherence interval. The second method is data-driven and trains a neural network to identify a mapping between the available information and the effective channel gain. Both methods can be utilized for any channel distribution and precoding. For the model-aided method, we derive all expressions in closed form for the case when maximum ratio or zero-forcing precoding is used. We compare the proposed methods with the state-of-the-art using the normalized mean-squared error and spectral efficiency (SE). The results suggest that the two proposed methods provide better SE than the state-of-the-art when there is a low level of channel hardening, while the performance difference is relatively small with the uncorrelated channel model.

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  • 18.
    Gupta, Nishant
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Agarwal, Satyam
    Indian Inst Technol IIT Ropar, India.
    Mishra, Deepak
    Univ New South Wales UNSW Sydney, Australia.
    Kumbhani, Brijesh
    Indian Inst Technol IIT Ropar, India.
    Trajectory and Resource Allocation for UAV Replacement to Provide Uninterrupted Service2023In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 71, no 12, p. 7288-7302Article in journal (Refereed)
    Abstract [en]

    Unmanned aerial vehicles (UAVs) have emerged as a specular technology that can assist the terrestrial base stations. However, the battery limitation of UAV inhibits the system performance by decreasing the overall lifespan of coverage provided by the UAV, driving the necessity of replacement and recharging. Thus, the energy-depleted UAV must be returned to a charging station and be replaced by a fully charged UAV to increase the service span. Therefore, this paper presents a novel framework of UAV replacement to maintain coverage continuity in a UAV-assisted wireless communication system when a serving UAV runs out of energy. Our objective during this replacement process is to maximize the minimum achievable throughput to the UAV-served ground users by jointly optimizing the three-dimensional (3D) multi-UAV trajectory and resources allocated to the users from the individual UAVs. The formulated problem is non-convex for which an efficient algorithm based on successive convex approximation and alternating optimization is proposed. Numerical results provide insights into the UAV trajectories and the effectiveness of the proposed scheme compared to the existing benchmark schemes.

  • 19.
    Gustafsson, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wahlberg, Bo
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Blind Equalization by Direct Examination of the Input Sequences1995In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 43, no 7, p. 2213-2222Article in journal (Refereed)
    Abstract [en]

    This paper presents a novel approach to blind equalization (deconvolution), which is based on direct examination of possible input sequences. In contrast to many other approaches, it does not rely on a model of the approximative inverse of the channel dynamics. To start with, the blind equalization identifiability problem for a noise-free finite impulse response channel model is investigated. A necessary condition for the input, which is algorithm independent, for blind deconvolution is derived. This condition is expressed in an information measure of the input sequence. A sufficient condition for identifiability is also inferred, which imposes a constraint on the true channel dynamics. The analysis motivates a recursive algorithm where all permissible input sequences are examined. The exact solution is guaranteed to be found as soon as it is possible. An upper bound on the computational complexity of the algorithm is given. This algorithm is then generalized to cope with time-varying infinite impulse response channel models with additive noise. The estimated sequence is an arbitrary good approximation of the maximum a posteriori estimate. The proposed method is evaluated on a Rayleigh fading communication channel. The simulation results indicate fast convergence properties and good tracking abilities.

  • 20.
    Gülgün, Ziya
    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.
    Is Massive MIMO Robust Against Distributed Jammers?2021In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 69, no 1, p. 457-469Article in journal (Refereed)
    Abstract [en]

    In this paper, we evaluate the uplink spectral efficiency (SE) of a single-cell massive multiple-input-multiple-output (MIMO) system with distributed jammers. We define four different attack scenarios and compare their impact on the massive MIMO system as well as on a conventional single-input-multiple-output (SIMO) system. More specifically, the jammers attack the base station (BS) during both the uplink training phase and data phase. The BS uses either least squares (LS) or linear minimum mean square error (LMMSE) estimators for channel estimation and utilizes either maximum-ratio-combining (MRC) or zero-forcing (ZF) decoding vectors. We show that ZF gives higher SE than MRC but, interestingly, the performance is unaffected by the choice of the estimators. The simulation results show that the performance loss percentage of massive MIMO is less than that of the SIMO system. Moreover, we consider two types of power control algorithms: jamming-aware and jamming-ignorant. In both cases, we consider the max-min and proportional fairness criteria to increase the uplink SE of massive MIMO systems. We notice numerically that max-min fairness is not a good option because if one user is strongly affected by the jamming, it will degrade the other users’ SE as well. On the other hand, proportional fairness improves the sum SE of the system compared with the full power transmission scenario.

  • 21.
    Gülgün, Ziya
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Yılmaz, Ali Özgür
    Middle East Technical University (METU), Ankara, Turkey.
    Detection Schemes for High Order M-Ary QAM Under Transmit Nonlinearities2019In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 67, no 7, p. 4825-4834Article in journal (Refereed)
    Abstract [en]

    Nonlinearities in various stages of a transmitter may hinder and restrict the transmission rate. As observed in many studies, outermost constellation points are usually more adversely affected by these impairments. To observe these effects, we utilize two power amplifier models that have different effects on transmitted signals. The Rapp model considers only amplitude deformation and the resultant in-phase and quadrature errors can be assumed to be independent on the receiver side. Unlike the Rapp model, the Saleh model exerts both amplitude and phase deformations and the phase deformation introduces correlation between the in-phase and quadrature errors according to our observations. In addition to the correlation, the variances of in-phase and quadrature errors may not be equal to each other. In this paper, we propose receivers that consider error variances of each quadrature amplitude modulation (QAM) symbol. We compare the performances of the receivers with those of other receivers that take average error variances into account for decoding. Furthermore, we propose a practical receiver that directly works on digitized observations based on a look-up table that keeps log-likelihood ratios of the quantized regions in order to reduce computational complexity.

  • 22.
    Handel, Peter
    et al.
    KTH Royal Inst Technol, Sweden.
    Tugfe Demir, Özlem Tugfe
    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.
    Ronnow, Daniel
    Univ Gavle, Sweden.
    Impact of Backward Crosstalk in 2 x 2 MIMO Transmitters on NMSE and Spectral Efficiency2020In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 68, no 7, p. 4277-4292Article in journal (Refereed)
    Abstract [en]

    We consider backward crosstalk in 2 x 2 transmitters, which is caused by crosstalk from the outputs of the transmitter to the inputs or by the combination of output crosstalk and impedance mismatch. We analyze its impact via feedback networks together with third-order power amplifier non-linearities. We utilize the Bussgang decomposition to express the distorted output signals of the transmitter as a linear transformation of the input plus uncorrelated distortion. The normalized mean-square errors (NMSEs) between the distorted and desired amplified signals are expressed analytically and the optimal closed-form power back-off that minimizes the worst NMSE of the two branches is derived. In the second part of the paper, an achievable spectral efficiency (SE) is presented for the communication from this "dirty" transmitter to another single-antenna receiver. The SE-maximizing precoder is optimally found by exploiting the hardware characteristics. Furthermore, the optimal power back-off is analyzed for two sub-optimal precoders, which either do not exploit any hardware knowledge or only partial knowledge. The simulation results show that the performance of these sub-optimal precoders is close-to-optimal. We also discuss how the analysis in this paper can be extended to transmitters with an arbitrary number of antenna branches.

  • 23.
    Hatami, Mohammad
    et al.
    Univ Oulu, Finland.
    Leinonen, Markus
    Univ Oulu, Finland.
    Chen, Zheng
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Pappas, Nikolaos
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Codreanu, Marian
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    On-Demand AoI Minimization in Resource-Constrained Cache-Enabled IoT Networks With Energy Harvesting Sensors2022In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 70, no 11, p. 7446-7463Article in journal (Refereed)
    Abstract [en]

    We consider a resource-constrained IoT network, where multiple users make on-demand requests to a cache-enabled edge node to send status updates about various random processes, each monitored by an energy harvesting sensor. The edge node serves users requests by deciding whether to command the corresponding sensor to send a fresh status update or retrieve the most recently received measurement from the cache. Our objective is to find the best actions of the edge node to minimize the average age of information (AoI) of the received measurements upon request, i.e., average on-demand AoI, subject to per-slot transmission and energy constraints. First, we derive a Markov decision process model and propose an iterative algorithm that obtains an optimal policy. Then, we develop an asymptotically optimal low-complexity algorithm - termed relax-then-truncate - and prove that it is optimal as the number of sensors goes to infinity. Simulation results illustrate that the proposed relax-then-truncate approach significantly reduces the average on-demand AoI compared to a request-aware greedy policy and a weighted AoI policy, and also depict that it performs close to the optimal solution even for moderate numbers of sensors.

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  • 24.
    Hatami, Mohammad
    et al.
    Univ Oulu, Finland.
    Leinonen, Markus
    Univ Oulu, Finland.
    Codreanu, Marian
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    AoI Minimization in Status Update Control With Energy Harvesting Sensors2021In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 69, no 12, p. 8335-8351Article in journal (Refereed)
    Abstract [en]

    Information freshness is crucial for time-critical IoT applications, e.g., monitoring and control. We consider an IoT status update system with users, energy harvesting sensors, and a cache-enabled edge node. The users receive time-sensitive information about physical quantities, each measured by a sensor. Users demand for the information from the edge node whose cache stores the most recently received measurements from each sensor. To serve a request, the edge node either commands the sensor to send an update or retrieves the aged measurement from the cache. We aim at finding the best actions of the edge node to minimize the average AoI of the served measurements at the users, termed on-demand AoI. We model this problem as a Markov decision process and develop reinforcement learning (RL) algorithms: model-based value iteration and model-free Q-learning. We also propose a Q-learning method for the realistic case where the edge node is informed about the sensors battery levels only via the status updates. The case under transmission limitations is also addressed. Furthermore, properties of an optimal policy are characterized. Simulation results show that an optimal policy is a threshold-based policy and that the proposed RL methods significantly reduce the average cost compared to several baselines.

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  • 25.
    Huang, Dawei
    et al.
    Queensland University of Technology, Australia.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sufficient Output Conditions for Identifiability in Blind Equalization1999In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 47, no 2, p. 191-194Article in journal (Refereed)
    Abstract [en]

    The problem of input identifiability in blind deconvolution is considered where the input belongs to a known discrete alphabet. Input identifiability is an algorithm independent property, which does not necessarily imply channel identifiability. Sufficient conditions for input identifiability are derived in terms of algebraic relations on the observed output. It is shown how these new results relate to and unify other known sufficient conditions.

  • 26.
    Interdonato, Giovanni
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Univ Cassino & Southern Lazio, Italy.
    Ngo, Hien Quoc
    Queens Univ Belfast, North Ireland.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Enhanced Normalized Conjugate Beamforming for Cell-Free Massive MIMO2021In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 69, no 5, p. 2863-2877Article in journal (Refereed)
    Abstract [en]

    In cell-free massive multiple-input multiple-output (MIMO) the fluctuations of the channel gain from the access points to a user are large due to the distributed topology of the system. Because of these fluctuations, data decoding schemes that treat the channel as deterministic perform inefficiently. A way to reduce the channel fluctuations is to design a precoding scheme that equalizes the effective channel gain seen by the users. Conjugate beamforming (CB) poorly contributes to harden the effective channel at the users. In this work, we propose a variant of CB dubbed enhanced normalized CB (ECB), in that the precoding vector consists of the conjugate of the channel estimate normalized by its squared norm. For this scheme, we derive an exact closed-form expression for an achievable downlink spectral efficiency (SE), accounting for channel estimation errors, pilot reuse and users lack of channel state information (CSI), assuming independent Rayleigh fading channels. We also devise an optimal max-min fairness power allocation based only on large-scale fading quantities. ECB greatly boosts the channel hardening enabling the users to reliably decode data relying only on statistical CSI. As the provided effective channel is nearly deterministic, acquiring CSI at the users does not yield a significant gain.

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  • 27.
    Jayachandran, Jinu
    et al.
    Indian Institute of Technology (I.I.T.), New Delhi, India.
    Biswas, Kamal
    Indian Institute of Technology (I.I.T.), New Delhi, India.
    Mohammed, Saif Khan
    Indian Institute of Technology (I.I.T.), New Delhi, India.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Efficient Techniques for In-Band System Information Broadcast in Multi-cell Massive MIMO2020In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 68, no 10, p. 6157-6173Article in journal (Refereed)
    Abstract [en]

    We consider joint beamforming of data to scheduled terminals (STs) and broadcast of system information (SI) to idle terminals (ITs) on the same time-frequency resource in multi-cell multi-user massive MIMO systems. We consider two different types of SI broadcast, i) synchronous broadcast of common (i.e., same) SI symbols from all cells, and ii) synchronous broadcast of cell-specific SI symbols from each cell. Through analysis we derive expressions for the achievable sum rate to STs in each cell and the rate of SI transmission to an IT for both these types of SI broadcast. We also derive expressions for the sum rate to STs and the rate to an IT for traditional orthogonal access (OA) where a fraction of physical resource is reserved for broadcast of SI. Simulations reveal that, just as in the single-cell scenario, for the multi-cell scenario also, joint beamforming and broadcasting (JBB) is more energy efficient than OA.

  • 28.
    Jorswieck, Eduard A.
    et al.
    Dresden University of Technology.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Monotonic Optimization Framework for theTwo-User MISO Interference Channel2010In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 58, no 7, p. 2159-2169Article in journal (Refereed)
    Abstract [en]

    Resource allocation and transmit optimization for the multiple-antenna Gaussian interference channel are important but difficult problems. The spatial degrees of freedom can be exploited to avoid, align, or utilize the interference. In recent literature, the upper boundary of the achievable rate region has been characterized. However, the resulting programming problems for finding the sum-rate, proportional fair, and minimax (egalitarian) operating points are non-linear and non-convex. In this paper, we develop a non-convex optimization framework based on monotonic optimization by outer polyblock approximation. First, the objective functions are represented in terms of differences of monotonic increasing functions. Next, the problems are reformulated as maximization of increasing functions over normal constraint sets. Finally, the idea to approximate the constraint set by outer polyblocks is explained and the corresponding algorithm is derived. Numerical examples illustrate the advantages of the proposed framework compared to an exhaustive grid search approach.

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  • 29.
    Karipidis, Eleftherios
    et al.
    Technical University of Crete, Chania, Greece.
    Sidiropoulos, Nicholas
    Technical University of Crete, Chania, Greece.
    Leshem, Amir
    Bar-Ilan University, Ramat-Gan, Israel.
    Youming, Li
    Bar-Ilan University, Ramat-Gan, Israel.
    Experimental Evaluation of Capacity Statistics for Short VDSL Loops2005In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 53, no 7, p. 1119-1122Article in journal (Refereed)
    Abstract [en]

    We assess the capacity potential of very short very-high data-rate digital subscriber line loops using full-binder channel measurements collected by France Telecom R&D. Key statistics are provided for both uncoordinated and vectored systems employing coordinated transmitters and coordinated receivers. The vectoring benefit is evaluated under the assumption of transmit precompensation for the elimination of self-far-end crosstalk, and echo cancellation of self-near-end crosstalk. The results provide useful bounds for developers and providers alike.

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  • 30.
    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.
    Techniques for System Information Broadcast in Cell-Free Massive MIMO2019In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 67, no 1, p. 244-257Article in journal (Refereed)
    Abstract [en]

    We consider transmission of system information in a cell-free massive MIMO system, when the transmitting access points do not have any channel state information and the receiving terminal has to estimate the channel based on downlink pilots. We analyze the system performance in terms of outage rate and coverage probability and use space-time block codes to increase performance. We propose a heuristic method for pilot/data power optimization that can be applied without any channel state information at the access points. We also analyze the problem of grouping the access points, which is needed when the single-antenna access points jointly transmit a space-time block code.

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  • 31.
    Kashyap, Salil
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Indian Institute Science, India.
    Mehta, Neelesh B.
    Indian Institute Science, India.
    Optimal Binary Power Control for Underlay CR With Different Interference Constraints and Impact of Channel Estimation Errors2014In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 62, no 11, p. 3753-3764Article in journal (Refereed)
    Abstract [en]

    Adapting the power of secondary users (SUs) while adhering to constraints on the interference caused to primary receivers (PRxs) is a critical issue in underlay cognitive radio (CR). This adaptation is driven by the interference and transmit power constraints imposed on the secondary transmitter (STx). Its performance also depends on the quality of channel state information (CSI) available at the STx of the links from the STx to the secondary receiver and to the PRxs. For a system in which an STx is subject to an average interference constraint or an interference outage probability constraint at each of the PRxs, we derive novel symbol error probability (SEP)-optimal, practically motivated binary transmit power control policies. As a reference, we also present the corresponding SEP-optimal continuous transmit power control policies for one PRx. We then analyze the robustness of the optimal policies when the STx knows noisy channel estimates of the links between the SU and the PRxs. Altogether, our work develops a holistic understanding of the critical role played by different transmit and interference constraints in driving power control in underlay CR and the impact of CSI on its performance.

  • 32.
    Khan Mohammed, Saif
    et al.
    Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Per-Antenna Constant Envelope Precoding for Large Multi-User MIMO Systems2013In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 61, no 3, p. 1059-1071Article in journal (Refereed)
    Abstract [en]

    We consider the multi-user MIMO broadcast channel with M single-antenna users and N transmit antennas under the constraint that each antenna emits signals having constant envelope (CE). The motivation for this is that CE signals facilitate the use of power-efficient RF power amplifiers. Analytical and numerical results show that, under certain mild conditions on the channel gains, for a fixed M, an array gain is achievable even under the stringent per-antenna CE constraint. Essentially, for a fixed M, at sufficiently large N the total transmitted power can be reduced with increasing N while maintaining a fixed information rate to each user. Simulations for the i.i.d. Rayleigh fading channel show that the total transmit power can be reduced linearly with increasing N (i.e., an O(N) array gain). We also propose a precoding scheme which finds near-optimal CE signals to be transmitted, and has O(MN) complexity. Also, in terms of the total transmit power required to achieve a fixed desired information sum-rate, despite the stringent per-antenna CE constraint, the proposed CE precoding scheme performs close to the sum-capacity achieving scheme for an average-only total transmit power constrained channel.

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  • 33.
    Knutsson, Hans
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Wilson, Roland
    University of Aston.
    Granlund, Gösta H.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Anisotropic Non-Stationary Image Estimation and its Applications: Part I. Restoration of Noisy Images1983In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. COM--31, no 3, p. 388-397Article in journal (Refereed)
    Abstract [en]

    A new form of image estimator, which takes account of linear features, is derived using a signal equivalent formulation. The estimator is shown to be a nonstationary linear combination of three stationary estimators. The relation of the estimator to human visual physiology is discussed. A method for estimating the nonstationary control information is described and shown to be effective when the estimation is made from noisy data. A suboptimal approach which is computationally less demanding is presented and used in the restoration of a variety of images corrupted by additive white noise. The results show that the method can improve the quality of noisy images even when the signal-to-noise ratio is very low.

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  • 34.
    Kosta, Antzela
    et al.
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Pappas, Nikolaos
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Ephremides, Anthony
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Univ Maryland, MD 20740 USA; Univ Maryland, MD 20740 USA.
    Angelakis, Vangelis
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    The Cost of Delay in Status Updates and Their Value: Non-Linear Ageing2020In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 68, no 8, p. 4905-4918Article in journal (Refereed)
    Abstract [en]

    We consider a status update communication system consisting of a source-destination link. A stochastic process is observed at the source, where samples are extracted at random time instances, and delivered to the destination, thus, providing status updates for the source. In this paper, we expand the concept of information ageing by introducing the cost of update delay (CoUD) metric to characterize the cost of having stale information at the destination. The CoUD captures the freshness of the information at the destination and can be used to reflect the information structure of the source. Moreover, we introduce the value of information of update (VoIU) metric that captures the reduction of CoUD upon reception of an update. Using the CoUD, its by-product metric called peak cost of update delay (PCoUD), and the VoIU, we evaluate the performance of an M/M/1 system in various settings that consider exact expressions and bounds. The optimal server utilization policy is to minimize the time average CoUD and maximize the time average VoIU. Our results indicate that the performance of CoUD differs depending on the cost assigned per time unit, however the optimal policy remains the same for linear ageing and varies for non-linear ageing. When it comes to the VoIU the performance difference appears only when the cost increases non-linearly with time. The study illustrates the importance of the newly introduced variants of age, furthermore supported in the case of VoIU by its tractability.

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  • 35.
    Kunnath Ganesan, Unnikrishnan
    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. KTH Royal Institute of Technology, Sweden..
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Clustering-Based Activity Detection Algorithms for Grant-Free Random Access in Cell-Free Massive MIMO2021In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 69, no 11, p. 7520-7530Article in journal (Refereed)
    Abstract [en]

    Future wireless networks need to support massive machine type communication (mMTC) where a massive number of devices accesses the network and massive MIMO is a promising enabling technology. Massive access schemes have been studied for co-located massive MIMO arrays. In this paper, we investigate the activity detection in grant-free random access for mMTC in cell-free massive MIMO networks using distributed arrays. Each active device transmits a non-orthogonal pilot sequence to the access points (APs) and the APs send the received signals to a central processing unit (CPU) for joint activity detection. The maximum likelihood device activity detection problem is formulated and algorithms for activity detection in cell-free massive MIMO are provided to solve it. The simulation results show that the macro diversity gain provided by the cell-free architecture improves the activity detection performance compared to co-located architecture when the coverage area is large.

  • 36.
    Larsson, Erik G.
    Department of Electrical and Computer Engineering, George Washington University, USA.
    Diversity and Channel Estimation Errors2004In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 52, no 2, p. 205-208Article in journal (Refereed)
    Abstract [en]

    We study the relation between a training-based detector and a coherent maximum-likelihood detector. We prove that under quite general conditions, the diversity gains associated with these two receivers are equal. Finally, we discuss the relation between our analysis and a related result in the literature.

  • 37.
    Larsson, Erik G.
    Royal Institute of Technology.
    Model-Averaged Interference Rejection Combining2007In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 55, no 2, p. 271-274Article in journal (Refereed)
    Abstract [en]

    We present a novel algorithm for interference suppression when the number of interferers is unknown. The key idea is to parameterize the second-order statistics of the interference via a mixture of several low-rank models. Numerical examples illustrate the performance of the method.

  • 38.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Optimal OFDMA Downlink Scheduling Under a Control Signaling Cost Constraint2010In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 58, no 10, p. 2776-2781Article in journal (Refereed)
    Abstract [en]

    This paper proposes a new algorithm for downlink scheduling in OFDMA systems. The method maximizes the throughput, taking into account the amount of signaling needed to transmit scheduling maps to the users. A combinatorial problem is formulated and solved via a dynamic programming approach reminiscent of the Viterbi algorithm. The total computational complexity of the algorithm is upper boundedby O(K^4N) where K is the number of users that are being considered for scheduling in a frame and N is the number of resource blocks per frame.

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  • 39.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Falconer, David
    Bell Telephone Laboratories, NJ, USA.
    Application of Fast Kalman Estimation to Adaptive Equalization1978In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 26, no 10, p. 1439-1446Article in journal (Refereed)
    Abstract [en]

    Very rapid initial convergence of the equalizer tap coefficients is a requirement of many data communication systems which employ adaptive equalizers to minimize intersymbol interference. As shown in recent papers by Godard, and by Gitlin and Magee, a recursive least squares estimation algorithm, which is a special case of the Kalman estimation algorithm, is applicable to the estimation of the optimal (minimum MSE) set of tap coefficients. It was furthermore shown to yield much faster equalizer convergence than that achieved by the simple estimated gradient algorithm, especially for severely distorted channels. We show how certain "fast recursive estimation" techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number of equalizer taps). These fast algorithms, applicable to both linear and decision feedback equalizers, exploit a certain shift-invariance property of successive equalizer contents. The rapid convergence properties of the "fast Kalman" adaptation algorithm are confirmed by simulation.

  • 40.
    Matthaiou, Michail
    et al.
    Chalmers University of Technology, Gothenburg, Sweden.
    Alexandropoulos, George C.
    Athens Information Technology (AIT), Greece.
    Ngo, Hien Quoc
    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, The Institute of Technology.
    Analytic framework for the effective rate of MISO fading channels2012In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 60, no 6, p. 1741-1751Article in journal (Refereed)
    Abstract [en]

    The delay constraints imposed by future wireless applications require a suitable metricfor assessing their impact on the overall system performance. Since the classical Shannon's ergodic capacityfails to do so, the so-called effective rate was recently established as a rigorous alternative. While prior relevant works have improved our knowledge on the effective rate characterization of communication systems, an analytical framework encompassing several fading models of interest isnot yet available. In this paper, we pursue a detailed effective rate analysis of Nakagami-m, Ricianand generalized-K multiple-input single-output (MISO) fading channels by deriving new, analytical expressions for their exact effective rate. Moreover, we consider the asymptotically low and high signal-to-noise (SNR) regimes, for which tractable, closed-form effective rate expressions are presented. These results enable us to draw useful conclusions about the impact of system parameters on the effective rate of different MISO fading channels. All the theoretical expressions are validated via Monte-Carlo simulations.

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  • 41.
    Mishra, Deepak
    et al.
    Department of Electrical Engineering and Bharti School of Telecommunication, IIT Delhi, New Delhi, India.
    De, Swades
    Department of Electrical Engineering and Bharti School of Telecommunication, IIT Delhi, New Delhi, India.
    i2RES: Integrated information relay and energy supply assisted RF harvesting communication2017In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 65, no 3, p. 1274-1288Article in journal (Refereed)
    Abstract [en]

    To overcome finite lifetime bottleneck in the ubiquitous deployment of low-power wireless devices in Internet-of-Things, we propose a novel integrated information relay and energy supply (i2RES)-assisted RF harvesting co-operative communication model. i2RES aids the communication between two distant energy-constrained wireless nodes by: 1) RF energy transfer to the source and 2) relaying source data along with supplying energy to the destination. To enable efficient i2RES-powered information transfer to the destination, we first derive and then maximize the delay-limited achievable throughput over Rician channels by jointly optimizing time allocation for information and energy transfer along with relative position of i2RES between source and destination. Although the throughput maximization problem is nonconvex and highly nonlinear, we prove its generalized-convexity and obtain the global-optimal numerical solutions. To gain analytical insights, we also derive tight closed-form approximation for the optimized solutions. Numerical results validate the analysis and demonstrate significant gain in throughput performance via our proposed optimization schemes under practical hardware constraints. Finally, we discuss how the analysis and optimization results can be extended to general RF-EH system settings with relaxed constraints.

  • 42.
    Mishra, Deepak
    et al.
    Department of Electrical Engineering, IIT Delhi, India.
    De, Swades
    Department of Electrical Engineering, IIT Delhi, India.
    Optimal relay placement in two-hop RF energy transfer2015In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 63, no 5, p. 1635-1647Article in journal (Refereed)
    Abstract [en]

    Recently, wireless radio frequency energy transfer (RFET) has emerged as an effective technology for prolonging lifetime of the energy-limited wireless sensor networks. However, low RFET efficiency is still a fundamental bottleneck in its widespread usage. Multi-hop RF energy transfer (MHET) can improve the RFET efficiency by deploying relay nodes that scavenge the dispersed energy and transfer it to the nearby sensor node. The efficiency of MHET is strongly influenced by the relay node’s placement. To maximize the RFET efficiency for a two-hop scenario, in this paper a novel optimization model is proposed to determine the optimal relay placement (ORP) on an Euclidean x-y plane. Nontrivial tradeoff between the energy scavenged at the relay versus the effective energy delivered by the relay to the target node is investigated. Due to the nonconvex and highly nonlinear nature of the optimization problem, an α-based branch and bound algorithm has been used. The proposed optimization model is further extended by incorporating distributed beamforming to enhance the RFET efficiency. Numerical results illustrate that the proposed algorithm provides convergence to the ∈-global optimal solution in a few iterations, and ORP provides significant energy saving over arbitrary relay positions for commercial RF energy harvesting systems.

  • 43.
    Mishra, Deepak
    et al.
    Department of Electrical Engineering and Bharti School of Telecommunication, Indian Institute of Technology Delhi, New Delhi, India.
    De, Swades
    Department of Electrical Engineering and Bharti School of Telecommunication, Indian Institute of Technology Delhi, New Delhi, India.
    Chiasserini, Carla-Fabiana
    Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy.
    Joint Optimization Schemes for Cooperative Wireless Information and Power Transfer Over Rician Channels2016In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 64, no 2, p. 554-571Article in journal (Refereed)
    Abstract [en]

    Simultaneous wireless information and power transfer (SWIPT) can lead to uninterrupted network operation by integrating radio frequency (RF) energy harvesting with data communication. In this paper, we consider a two-hop source-relay-destination network and investigate the efficient usage of a decode-and-forward (DF) relay for SWIPT toward the energy-constrained destination. In particular, by assuming a Rician fading environment, we jointly optimize power allocation (PA), relay placement (RP), and power splitting (PS) so as to minimize outage probability under the harvested power constraint at the destination node. We consider the two possible cases of source-to-destination distance: (1) small distance with direct information transfer link; and (2) relatively large distance with no direct reachability. Analytical expressions for individual and joint optimal PA, RP, and PS are obtained by exploiting convexity of outage minimization problem for the no direct link case. In case of direct source-to-destination link, multipseudoconvexity of joint-optimal PA, RP, and PS problem is proved, and alternating optimization is used to find the global optimal solution. Numerical results show that the joint optimal solutions, although strongly influenced by the harvested power requirement at the destination, can provide respectively 64% and 100% outage improvement over the fixed allocation scheme for without and with direct link.

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    Joint Optimization Schemes for Cooperative Wireless Information and Power Transfer Over Rician Channels
  • 44.
    Mishra, Deepak
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Johansson, Håkan
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Optimal Channel Estimation for Hybrid Energy Beamforming Under Phase Shifter Impairments2019In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 67, no 6, p. 4309-4325Article in journal (Refereed)
    Abstract [en]

    Smart multiantenna wireless power transmission can enable perpetual operation of energy harvesting (EH) nodes in the Internet-of-Things. Moreover, to overcome the increased hardware cost and space constraints associated with having large antenna arrays at the radio frequency (RF) energy source, the hybrid energy beamforming (EBF) architecture with single RF chain can be adopted. Using the recently proposed hybrid EBF architecture modeling the practical analog phase shifter impairments (API), we derive the optimal least-squares estimator for the energy source to an EH user channel. Next, the average harvested power at the user is derived while considering the nonlinear RF EH model and a tight analytical approximation for it is also presented by exploring the practical limits on the API. Using these developments, the jointly global optimal transmit power and time allocation for channel estimation (CE) and EBF phases, that maximizes the average energy stored at the EH user is derived in closed form. Numerical results validate the proposed analysis and present nontrivial design insights on the impact of API and CE errors on the achievable EBF performance. It is shown that the optimized hybrid EBF protocol with joint resource allocation yields an average performance improvement of 37% over benchmark fixed allocation scheme.

  • 45.
    Mishra, Deepak
    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.
    Sum Throughput Maximization in Multi-Tag Backscattering to Multiantenna Reader2019In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 67, no 8, p. 5689-5705Article in journal (Refereed)
    Abstract [en]

    Backscatter communication (BSC) is being realized as the core technology for pervasive sustainable Internet-of-Things applications. However, owing to the resource limitations of passive tags, the efficient usage of multiple antennas at the reader is essential for both downlink excitation and uplink detection. This paper targets at maximizing the achievable sum-backscattered throughput by jointly optimizing the transceiver (TRX) design at the reader and backscattering coefficients (BCs) at the tags. Since this joint problem is nonconvex, we first present individually optimal designs for the TRX and BC. We show that with precoder and combiner designs at the reader, respectively, targeting downlink energy beamforming and uplink Wiener filtering operations, the BC optimization at tags can be reduced to a binary power control problem. Next, the asymptotically optimal joint-TRX-BC designs are proposed for both low- and high-signal-to-noise ratio regimes. Based on these developments, an iterative low-complexity algorithm is proposed to yield an efficient jointly suboptimal design. Thereafter, we discuss the practical utility of the proposed designs to other application settings, such as wireless powered communication networks and BSC with imperfect channel state information. Finally, selected numerical results, validating the analysis and shedding novel insights, demonstrate that the proposed designs can yield significant enhancement in the sum-backscattered throughput over existing benchmarks.

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  • 46.
    Mollén, Christopher
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Ericsson, Sweden; Ericsson, Peoples R China; Eidgenoss TH Zurich, Switzerland; Univ Texas Austin, TX 78712 USA; Apple, CA 92307 USA.
    Gustavsson, Ulf
    Ericsson Res, Sweden.
    Eriksson, Thomas
    Chalmers Univ Technol, Sweden.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Impact of Spatial Filtering on Distortion From Low-Noise Amplifiers in Massive MIMO Base Stations2018In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 66, no 12, p. 6050-6067Article in journal (Refereed)
    Abstract [en]

    In massive multiple-input-multiple-output base stations, power consumption and cost of the low-noise amplifiers (LNAs) can be substantial because of the many antennas. We investigate the feasibility of inexpensive, power efficient LNAs, which inherently are less linear. A polynomial model is used to characterize the nonlinear LNAs and to derive the second-order statistics and spatial correlation of the distortion. We show that, with spatial matched filtering (maximum-ratio combining) at the receiver, some distortion terms combine coherently, and that the signal-to-interference-and-noise ratio of the symbol estimates therefore is limited by the linearity of the LNAs. Furthermore, it is studied how the power from a blocker in the adjacent frequency band leaks into the main band and creates distortion. The distortion term that scales cubically with the power received from the blocker has a spatial correlation that can be filtered out by spatial processing and only the coherent term that scales quadratically with the power remains. When the blocker is in free-space line-of-sight and the LNAs are identical, this quadratic term has the same spatial direction as the desired signal, and hence cannot be removed by linear receiver processing.

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    Impact of Spatial Filtering on Distortion From Low-Noise Amplifiers in Massive MIMO Base Stations
  • 47.
    Mollén, Christopher
    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.
    Eriksson, Thomas
    Chalmers tekniska högskola, Sweden.
    Waveforms for the Massive MIMO Downlink: Amplifier Efficiency, Distortion and Performance2016In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 46, no 12, p. 5050-5063Article in journal (Refereed)
    Abstract [en]

    In massive multiple-input multiple-output (MIMO), most precoders result in downlink signals that suffer from high peak-to-average ratio (PAR), independently of modulation order and whether single-carrier or orthogonal frequency-division multiplexing (OFDM) transmission is used. The high PAR lowers the power efficiency of the base-station amplifiers. To increase the power efficiency, low-PAR precoders have been proposed. In this paper, we compare different transmission methods for massive MIMO in terms of the power consumed by the amplifiers. It is found that: 1) OFDM and single-carrier transmission have the same performance over a hardened massive MIMO channel and 2) when the higher amplifier power efficiency of low-PAR precoding is taken into account, conventional and low-PAR precoders lead to approximately the same power consumption. Since downlink signals with low PAR allow for simpler and cheaper hardware, than signals with high PAR, therefore, the results suggest that low-PAR precoding with either single-carrier or OFDM transmission should be used in a massive MIMO base station.

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  • 48.
    Moltafet, Mohammad
    et al.
    Univ Oulu, Finland.
    Leinonen, Markus
    Univ Oulu, Finland.
    Codreanu, Marian
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Average AoI in Multi-Source Systems With Source-Aware Packet Management2021In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 69, no 2, p. 1121-1133Article in journal (Refereed)
    Abstract [en]

    We study the information freshness under three different source aware packet management policies in a status update system consisting of two independent sources and one server. The packets of each source are generated according to the Poisson process and the packets are served according to an exponentially distributed service time. We derive the average age of information (AoI) of each source using the stochastic hybrid systems (SHS) technique for each packet management policy. In Policy 1, the queue can contain at most two waiting packets at the same time (in addition to the packet under service), one packet of source 1 and one packet of source 2. When the server is busy at an arrival of a packet, the possible packet of the same source waiting in the queue (hence, source-aware) is replaced by the arrived fresh packet. In Policy 2, the system (i.e., the waiting queue and the server) can contain at most two packets, one from each source. When the server is busy at an arrival of a packet, the possible packet of the same source in the system is replaced by the fresh packet. Policy 3 is similar to Policy 2 but it does not permit preemption in service, i.e., while a packet is under service all new arrivals from the same source are blocked and cleared. Numerical results are provided to assess the fairness between sources and the sum average AoI of the proposed policies.

  • 49.
    Moltafet, Mohammad
    et al.
    Univ Oulu, Finland.
    Leinonen, Markus
    Univ Oulu, Finland.
    Codreanu, Marian
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Moment Generating Function of Age of Information in Multisource M/G/1/1 Queueing Systems2022In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 70, no 10, p. 6503-6516Article in journal (Refereed)
    Abstract [en]

    We consider a multi-source status update system, where each source generates status update packets according to a Poisson process which are then served according to a generally distributed service time. For this multi-source M/G/1/1 queueing model, we consider a self-preemptive packet management policy and derive the moment generating functions (MGFs) of the age of information (AoI) and peak AoI of each source. According to the policy, an arriving fresh packet preempts the possible packet of the same source in the system. Furthermore, we derive the MGFs of the AoI and peak AoI for the globally preemptive and non-preemptive policies, for which only the average AoI and peak AoI have been derived earlier. Finally, we use the MGFs to derive the average AoI and peak AoI in a two-source M/G/1/1 queueing model under each policy. Numerical results show the effect of the service time distribution parameters on the average AoI. The results also highlight the importance of higher moments of the AoI.

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  • 50.
    Moltafet, Mohammad
    et al.
    Univ Oulu, Finland.
    Leinonen, Markus
    Univ Oulu, Finland.
    Codreanu, Marian
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    On the Age of Information in Multi-Source Queueing Models2020In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 68, no 8, p. 5003-5017Article in journal (Refereed)
    Abstract [en]

    Freshness of status update packets is essential for enabling services where a destination needs the most recent measurements of various sensors. In this paper, we study the information freshness of single-server multi-source queueing models under a first-come first-served (FCFS) serving policy. In the considered model, each source independently generates status update packets according to a Poisson process. The information freshness of the status updates of each source is evaluated by the average age of information (AoI). We derive an exact expression for the average AoI for the case with exponentially distributed service time, i.e., for a multi-source M/M/1 queueing model. Moreover, we derive three approximate expressions for the average AoI for a multi-source M/G/1 queueing model having a general service time distribution. Simulation results are provided to validate the derived exact average AoI expression, to assess the tightness of the proposed approximations, and to demonstrate the AoI behavior for different system parameters.

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