| 1. |
- Angel Vazquez, Miguel, et al.
(författare)
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Deploying Artificial Intelligence in the Wireless Infrastructure : the Challenges Ahead
- 2019
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Ingår i: 2019 IEEE 2nd 5G World Forum (5GWF). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781728136271 ; , s. 458-459
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Konferensbidrag (refereegranskat)abstract
- The adoption of artificial intelligence (AI) techniques entails a substantial change in the wireless ecosystem where data as well as their owners become crucial. As a result, the roll out of AI techniques in wireless systems raises a plethora of questions. In this context, we describe the challenges observed by the wireless stakeholders when deploying AI. Furthermore, we introduce the recent discussion in field of ethics that appear when managing wireless communications data.
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| 2. |
- Azari, Amin, 1988-
(författare)
-
Serving IoT Communications over Cellular Networks : Challenges and Solutions in Radio Resource Management for Massive and Critical IoT Communications
- 2018
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Internet of Things (IoT) communications refer to the interconnections of smart devices, with reduced human intervention, which enable them to participate more actively in everyday life. It is expected that introduction of a scalable, energy efficient, and reliable IoT connectivity solution can bring enormous benefits to the society, especially in healthcare, wellbeing, and smart homes and industries. In the last two decades, there have been efforts in academia and industry to enable IoT connectivity over the legacy communications infrastructure. In recent years, it is becoming more and more clear that the characteristics and requirements of the IoT traffic are way different from the legacy traffic originating from existing communications services like voice and web surfing, and hence, IoT-specific communications systems and protocols have received profound attention. Until now, several revolutionary solutions, including cellular narrowband-IoT, SigFox, and LoRaWAN, have been proposed/implemented. As each of these solutions focuses on a subset of performance indicators at the cost of sacrificing the others, there is still lack of a dominant player in the market capable of delivering scalable, energy efficient, and reliable IoT connectivity. The present work is devoted to characterizing state-of-the-art technologies for enabling large-scale IoT connectivity, their limitations, and our contributions in performance assessment and enhancement for them. Especially, we focus on grant-free radio access and investigate its applications in supporting massive and critical IoT communications. The main contributions presented in this work include (a) developing an analytical framework for energy/latency/reliability assessment of IoT communications over grant-based and grant-free systems; (b) developing advanced RRM techniques for energy and spectrum efficient serving of massive and critical IoT communications, respectively; and (c) developing advanced data transmission/reception protocols for grant-free IoT networks. The performance evaluation results indicate that supporting IoT devices with stringent energy/delay constraints over limited radio resources calls for aggressive technologies breaking the barrier of the legacy interference-free orthogonal communications.
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| 3. |
- Björnson, Emil, et al.
(författare)
-
Circuit-aware design of energy-efficient massive MIMO systems
- 2014
-
Ingår i: ISCCSP 2014 - 2014 6th International Symposium on Communications, Control and Signal Processing, Proceedings. - 9781479928903 ; , s. 101-104
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Konferensbidrag (refereegranskat)abstract
- Densification is a key to greater throughput in cellular networks. The full potential of coordinated multipoint (CoMP) can be realized by massive multiple-input multiple-output (MIMO) systems, where each base station (BS) has very many antennas. However, the improved throughput comes at the price of more infrastructure; hardware cost and circuit power consumption scale linearly/affinely with the number of antennas. In this paper, we show that one can make the circuit power increase with only the square root of the number of antennas by circuit-aware system design. To this end, we derive achievable user rates for a system model with hardware imperfections and show how the level of imperfections can be gradually increased while maintaining high throughput. The connection between this scaling law and the circuit power consumption is established for different circuits at the BS.
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| 4. |
- Björnson, Emil, Professor, 1983-, et al.
(författare)
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Massive MIMO for Maximal Spectral Efficiency : How Many Users and Pilots Should Be Allocated?
- 2016
-
Ingår i: IEEE Transactions on Wireless Communications. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 1536-1276 .- 1558-2248. ; 15:2, s. 1293-1308
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Tidskriftsartikel (refereegranskat)abstract
- Massive MIMO is a promising technique for increasing the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas M than scheduled users K because the users' channels are likely to be near-orthogonal when M/K > 10. However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users K-star depends on M and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of K-star in the large-M regime is derived in closed form, while simulations are used to show what happens at finite M, in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal M/K is less than 10 in many cases of practical relevance. Interestingly, K-star depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same K.
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| 5. |
- Björnson, Emil, et al.
(författare)
-
Massive MIMO Systems With Non-Ideal Hardware : Energy Efficiency, Estimation, and Capacity Limits
- 2014
-
Ingår i: IEEE Transactions on Information Theory. - : IEEE Press. - 0018-9448 .- 1557-9654. ; 60:11, s. 7112-7139
-
Tidskriftsartikel (refereegranskat)abstract
- The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.
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| 6. |
- Björnson, Emil, Professor, 1983-, et al.
(författare)
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Massive MIMO with Imperfect Channel Covariance Information
- 2016
-
Ingår i: 2016 50TH ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS AND COMPUTERS. - : IEEE COMPUTER SOC. - 9781538639542 ; , s. 974-978
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Konferensbidrag (refereegranskat)abstract
- This work investigates the impact of imperfect statistical information in the uplink of massive MIMO systems. In particular, we first show why covariance information is needed and then propose two schemes for covariance matrix estimation. A lower bound on the spectral efficiency (SE) of any combining scheme is derived, under imperfect covariance knowledge, and a closed-form expression is computed for maximum-ratio combining. We show that having covariance information is not critical, but that it is relatively easy to acquire it and to achieve SE close to the ideal case of having perfect statistical information.
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| 7. |
- Björnson, Emil, et al.
(författare)
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Massive MIMO with Non-Ideal Arbitrary Arrays : Hardware Scaling Laws and Circuit-Aware Design
- 2015
-
Ingår i: IEEE Transactions on Wireless Communications. - 1536-1276 .- 1558-2248. ; 14:8, s. 4353-4368
-
Tidskriftsartikel (refereegranskat)abstract
- Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas N. Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today's conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phase-drifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with N while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as root N, instead of linearly, by careful circuit-aware system design.
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| 8. |
- Björnson, Emil, et al.
(författare)
-
Multiobjective Signal Processing Optimization : The way to balance conflicting metrics in 5G systems
- 2014
-
Ingår i: IEEE signal processing magazine (Print). - : IEEE. - 1053-5888 .- 1558-0792. ; 31:6, s. 14-23
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Tidskriftsartikel (refereegranskat)abstract
- The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: any data service is instantly accessible everywhere. With each generation of cellular networks, we have moved closer to this wireless dream; first by delivering wireless access to voice communications, then by providing wireless data services, and recently by delivering a Wi-Fi-like experience with wide-area coverage and user mobility management. The support for high data rates has been the main objective in recent years [1], as seen from the academic focus on sum-rate optimization and the efforts from standardization bodies to meet the peak rate requirements specified in IMT-Advanced. In contrast, a variety of metrics/objectives are put forward in the technological preparations for fifth-generation (5G) networks: higher peak rates, improved coverage with uniform user experience, higher reliability and lower latency, better energy efficiency (EE), lower-cost user devices and services, better scalability with number of devices, etc. These multiple objectives are coupled, often in a conflicting manner such that improvements in one objective lead to degradation in the other objectives. Hence, the design of future networks calls for new optimization tools that properly handle the existence of multiple objectives and tradeoffs between them.
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| 9. |
- Björnson, Emil, Professor, 1983-, et al.
(författare)
-
On the impact of transceiver impairments on af relaying
- 2013
-
Ingår i: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 4948-4952, s. 4948-4952
-
Konferensbidrag (refereegranskat)abstract
- Recently, it was shown that transceiver hardware impairments have a detrimental impact on the performance of communication systems, especially for high-rate systems. The vast majority of technical contributions in the area of relaying assume ideal transceiver hardware. This paper quantifies the impact of transceiver hardware impairments in dual-hop Amplify-and-Forward (AF) relaying, both for fixed and variable gain relays. The outage probability (OP) in this practical scenario is a function of the instantaneous end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives closed-form expressions for the exact and asymptotic OPs under Rayleigh fading, accounting for hardware impairments at both the transmitter and the relay. The performance loss is small at low spectral efficiency, but can otherwise be very substantial. In particular, it turns out that for high signal-to-noise ratio (SNR), the instantaneous end-to-end SNDR converges to a deterministic constant, called the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in stark contrast to the ideal hardware case for which the end-to-end SNDR grows without bound in the high SNR regime.
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| 10. |
- Björnson, Emil, et al.
(författare)
-
Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?
- 2015
-
Ingår i: IEEE Transactions on Wireless Communications. - : Institute of Electrical and Electronics Engineers (IEEE). - 1536-1276 .- 1558-2248. ; 14:6, s. 3059-3075
-
Tidskriftsartikel (refereegranskat)abstract
- Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.
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| 11. |
- Björnson, Emil, et al.
(författare)
-
Optimizing multi-cell massive MIMO for spectral efficiency : How Many users should be scheduled?
- 2014
-
Ingår i: 2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014. - : IEEE conference proceedings. - 9781479970889 ; , s. 612-616
-
Konferensbidrag (refereegranskat)abstract
- Massive MIMO is a promising technique to increase the spectral efficiency of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent beamforming. A common rule-of-thumb is that these systems should have an order of magnitude more antennas, N, than scheduled users, K, because the users' channels are then likely to be quasi-orthogonal. However, it has not been proved that this rule-of-thumb actually maximizes the spectral efficiency. In this paper, we analyze how the optimal number of scheduled users, K, depends on N and other system parameters. The value of K in the large-N regime is derived in closed form, while simulations are used to show what happens at finite N, in different interference scenarios, and for different beamforming.
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| 12. |
- Debbah, Merouane, et al.
(författare)
-
Intermediate report about wireless secrecy metrics and preliminary algorithms : NEWCOM++ DR.A.1
- 2008
-
Rapport (refereegranskat)abstract
- This deliverable provides a first overview of the state of the art on wireless security metrics and algorithms,which are particularly very important with respect to the intrinsic vulnerability of the wirelessmedium. The first part deals with building practical physical layer information-theoretic secure schemes.Indeed, Shannon formalized the concepts of capacity (as a transmission efficiency measure) and equivocation(as a measure of secrecy). While the concept of capacity has been extended to fading channelswith the introduction of concepts like the outage capacity or the ergodic capacity, similar paths are yet tobe developed concerning equivocation. In the second part, we present a taxonomy of threats for wirelessnetworks, and particularly for wireless sensor networks, in terms of the affected protocol layers. Besides,an overview to attack tree and attack graph techniques as formal means for describing and measuringvulnerabilities and thus also for assessing also the security level of wireless sensor networks is provided.Finally, an overview to suitable security concepts for wireless networks is given
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| 13. |
- Gabry, Frederic
(författare)
-
Secrecy in Cognitive Radio Networks
- 2014
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- With the considerable growth of wireless networks in recent years, the issue of network security has taken an important role in the design of communication devices and protocols. Indeed, due to the broadcast nature of these networks, communications can potentially be attacked by malicious parties, and therefore, the protection of transmitted data has become a main concern in today's communications. On the other hand the cooperation of nodes overhearing the transmission may potentially lead to a better performance. In this thesis we combine both fundamental concepts of cooperation and secrecy in wireless networks. In particular we investigate the cooperation between transmitters in a cognitive radio network where the secondary receiver is treated as a potential eavesdropper to the primary transmission. We study this novel model focusing on several fundamental aspects.First we derive achievable rate regions for different transmission schemes, such as cooperative jamming and relaying, with and without primary message knowledge at the secondary transmitter. For these schemes, we formulate and solve three relevant power allocation problems: the maximization of the achievable primary and secondary rates, and the minimization of the secondary transmitting power. We model the interaction between the transmitting users as a Stackelberg game corresponding to a more realistic power allocation problem. We solve the game and illustrate its impact on the achievable rates.Secondly we generalize our system model by introducing the multi-phase clean relaying (CR) scheme, which takes into account the message-learning constraint at the secondary transmitter, and we derive the achievable rate region for this scheme. We compare our CR scheme to other transmission strategies such as dirty paper coding, interference neutralization, and pure cooperative jamming. Thirdly we extend our model to the generalized scenario where multiple secondary transmitter-receiver pairs wish to access the spectrum. For this scenario, we define and study several types of games between the primary network and the secondary pairs, such as Stackelberg games, power control games, and auction games. We derive the equilibrium of each game considered, which allows us to predict the behavior of the users in the cognitive radio network with multiple secondary pairs.Moreover we consider the important concept of energy efficiency (EE) for the performance of the cognitive radio network and we derive the power allocation and power splitting maximizing the secondary transmitter's energy efficiency. An important EE Stackelberg game between the two transmitters is formulated, and the impact of the game theoretic interaction is analyzed. Finally we motivate and investigate information theoretic secrecy using key agreement techniques in wireless networks. In particular we derive achievable secret key rate regions for two different key agreement schemes in Gaussian channels using several transmission strategies such as power control and cooperative jamming. The interaction between transmitting users is analyzed from a game theoretic perspective using non-cooperative game theory.For every fundamental perspective considered for the analysis of the model studied in the thesis, our results are illustrated through numerical examples based on a geometrical setup, highlighting the impact of the node geometry on the achievable rates, the optimal strategies, the games' equilibria and the impact of the game theoretic interaction between transmitters on the system performance.
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| 14. |
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| 15. |
- Kammoun, Abla, et al.
(författare)
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Linear Precoding Based on Polynomial Expansion : Large-Scale Multi-Cell MIMO Systems
- 2014
-
Ingår i: IEEE Journal on Selected Topics in Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1932-4553 .- 1941-0484. ; 8:5, s. 861-875
-
Tidskriftsartikel (refereegranskat)abstract
- Large-scale MIMO systems can yield a substantial improvements in spectral efficiency for future communication systems. Due to the finer spatial resolution and array gain achieved by a massive number of antennas at the base station, these systems have shown to be robust to inter-user interference and the use of linear precoding appears to be asymptotically optimal. However, from a practical point of view, most precoding schemes exhibit prohibitively high computational complexity as the system dimensions increase. For example, the near-optimal regularized zero forcing (RZF) precoding requires the inversion of a large matrix. To solve this issue, we propose in this paper to approximate the matrix inverse by a truncated polynomial expansion (TPE), where the polynomial coefficients are optimized to maximize the system performance. This technique has been recently applied in single cell scenarios and it was shown that a small number of coefficients is sufficient to reach performance similar to that of RZF, while it was not possible to surpass RZF. In a realistic multi-cell scenario involving large-scale multi-user MIMO systems, the optimization of RZF precoding has, thus far, not been feasible. This is mainly attributed to the high complexity of the scenario and the non-linear impact of the necessary regularizing parameters. On the other hand, the scalar coefficients in TPE precoding give hope for possible throughput optimization. To this end, we exploit random matrix theory to derive a deterministic expression of the asymptotic signal-to-interference-and-noise ratio for each user based on channel statistics. We also provide an optimization algorithm to approximate the coefficients that maximize the network-wide weighted max-min fairness. The optimization weights can be used to mimic the user throughput distribution of RZF precoding. Using simulations, we compare the network throughput of the proposed TPE precoding with that of the suboptimal RZF scheme and show that our scheme can achieve higher throughput using a TPE order of only 5.
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| 16. |
- Li, Jingya, et al.
(författare)
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Joint Precoding and Load Balancing Optimization for Energy-Efficient Heterogeneous Networks
- 2015
-
Ingår i: IEEE Transactions on Wireless Communications. - : IEEE Press. - 1536-1276 .- 1558-2248. ; 14:10, s. 5810-5822
-
Tidskriftsartikel (refereegranskat)abstract
- This paper considers a downlink heterogeneous network, where different types of multiantenna base stations (BSs) communicate with a number of single-antenna users. Multiple BSs can serve the users by spatial multiflow transmission techniques. Assuming imperfect channel state information at both BSs and users, the precoding, load balancing, and BS operation mode are jointly optimized for improving the network energy efficiency. We minimize the weighted total power consumption while satisfying quality-of-service constraints at the users. This problem is nonconvex, but we prove that for each BS mode combination, the considered problem has a hidden convexity structure. Thus, the optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the nonconvex objective function, a heuristic algorithm is proposed to obtain a suboptimal solution of low complexity. We show that although multicell joint transmission is allowed, in most cases, it is optimal for each user to be served by a single BS. The optimal BS association condition is parameterized, which reveals how it is impacted by different system parameters. Simulation results indicate that putting a BS into sleep mode by proper load balancing is an important solution for energy savings.
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| 17. |
- Li, Jingya, 1986, et al.
(författare)
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Optimal Design of Energy-Efficient HetNets: Joint Precoding and Load Balancing
- 2015
-
Ingår i: IEEE International Conference on Communications. - : IEEE. - 1550-3607. - 9781467364324 ; , s. 4664-4669
-
Konferensbidrag (refereegranskat)abstract
- This paper considers the downlink of a heterogeneous network, where multiple base stations (BSs) can serve the users by non-coherent multiflow beamforming. We assume imperfect channel state information at both BSs and users. The objective is to jointly optimize the precoding, load balancing, and BS operation mode (active or sleep) for improving the energy efficiency of the network. The considered problem is to minimize the weighted total power consumption (both circuit power and dynamic transmit power), while satisfying per-user quality of service constraints and per-BS transmit power constraints. This problem is non-convex, but we prove that for each combination of BS modes, the considered problem has a hidden convexity structure. Thus, the global optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the non-convex power consumption functions, a heuristic algorithm is proposed to obtain a local optimal solution with low complexity. Simulation results illustrate that our proposed algorithms significantly reduce the total power consumption, compared to the scheme where all BSs are continuously active. This implies that putting a BS into sleep mode by proper load balancing is an important solution for energy savings in heterogeneous networks.
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| 18. |
- Lindskog, Stefan, et al.
(författare)
-
NEWCOM++ DRA.2: Advanced algorithms and metrics for wireless secrecy and security
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The report deals with Advanced Algorithms and Metrics for Wireless Secrecy and Security developed within the framework of Newcom++ (contrarily to the first report which was an overview of existing results). As far as wireless secrecy is concerned, the notion of information theoretic secrecy capacity is extended to different types of channels such as the interference channel, the relay channel as well as the wiretap frequency selective channel. Practical algorithms are derived in the case of multi-carrier channels such as the OFDM case through the notion of Vandermonde precoding. In the second part of the report, Wireless security focuses on Wireless Sensor Networks. After an overview of different wireless technologies, a risk analysis approach is proposed together with a taxonomy of wireless security attacks and descriptions of threats and known vulnerabilities in wireless networks in general. Finally, a framework that enables a formal reasoning and description of a WSN system is provided
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| 19. |
- Lindskog, Stefan, et al.
(författare)
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NEWCOM++ DRA.3: Final report about security in wireless networks
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The report deals with advanced schemes for Wireless Secrecy and Security evaluation tools developed within the framework of Newcom++. As far as wireless secrecy is concerned, different cases are treated, namely the multi-antenna fading case, the frequency selective channel case (with OFDM modulation) and the the relay channel case. Besides the major information theoretic consideration related to capacity issues, physical layer coding, Secure Lossy Source Coding as well as classical precoding (through beamforming) schemes are analyzed. The second part of the report is dedicated to security evaluation tools and provides a framework for a formal reasoning and description of wireless sensor networks (WSN). Some input models for the design and evaluation of WSN security are provided, especially for 6LoWPAN Networks. The report finishes with an important contribution related to a Penetration Testing tool developed for 6LoWPAN
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| 20. |
- Marzetta, Thomas L., et al.
(författare)
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Special issue on Massive MIMO
- 2013
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Ingår i: Journal of Communications and Networks. - : IEEE. - 1229-2370 .- 1976-5541. ; 15:4, s. 333-337
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Demand for wireless communications is projected to grow by more than a factor of forty or more over the next five years. A potential technology for meeting this demand is Massive MIMO (also called Large-Scale Antenna Systems, Large-Scale MIMO, ARGOS, Full-Dimension MIMO, or Hyper-MIMO), a form of multiuser multipleantenna wireless which promises orders-of-magnitude improvements in spectral-efficiency over 4G technology, and accompanying improvements in radiated energy-efficiency. The distinguishing feature of Massive MIMO is that a large number of service-antennas ?? possibly hundreds or even thousands ?? work for a significantly smaller number of active autonomous terminals. Upsetting the traditional parity between service antennas and terminals in this manner is a game-changer: The simplest multiplexing precoding and decoding algorithms can be nearly optimal, expensive ultra-linear forty-Watt power amplifiers are replaced by many low-power units, and the favorable action of the law of large numbers can greatly facilitate power-control and resource-allocation.
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| 21. |
- Matthaiou, Michail, et al.
(författare)
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Two-Way Relaying Under the Presence of Relay Transceiver Hardware Impairments
- 2013
-
Ingår i: IEEE Communications Letters. - 1089-7798 .- 1558-2558. ; 17:6, s. 1136-1139
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Tidskriftsartikel (refereegranskat)abstract
- Hardware impairments in physical transceivers are known to have a deleterious effect on communication systems; however, very few contributions have investigated their impact on relaying. This paper quantifies the impact of transceiver impairments in a two-way amplify-and-forward configuration. More specifically, the effective signal-to-noise-and-distortion ratios at both transmitter nodes are obtained. These are used to deduce exact and asymptotic closed-form expressions for the outage probabilities (OPs), as well as tractable formulations for the symbol error rates (SERs). It is explicitly shown that non-zero lower bounds on the OP and SER exist in the high-power regime-this stands in contrast to the special case of ideal hardware, where the OP and SER go asymptotically to zero.
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| 22. |
- Mohamad, Medhat, 1987-
(författare)
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Spectrally Precoded OFDM-Design and Analysis
- 2019
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Despite shifting towards mm-wave bands, the sub-6 GHz band will continue to be a fundamental spectral band in 5G. However, the severe congestion in this band makes a well-constrained spectrum a critical requirementof 5G. A well-constrained spectrum means that the communications regimes should dwell within their dedicated spectral bands and do not interfere with other systems working on neighboring bands. Consequently, the communi-cations community seeks convenient modulation schemes.The 5G standards have already defined cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) as the modulation scheme for most of the sub-6 GHz band. However, the high out-of-band (OOB) emission phe-nomenon in OFDM is unfavorable for some regimes operating in 5G. Therefore, to legitimize OFDM in all 5G regimes, we need to suppress the OFDM OOB emission.Since the discontinuous nature of the OFDM signal is the main reason forthe high OOB emission, one solution is to render the discontinuous OFDM signal continuous. Two factors control this discontinuity: the physical shape of the modulated signal and the correlation of the data symbols that modulate the OFDM signal.While most traditional approaches focus on reshaping the OFDM signal to render it continuous, in this work, we give our attention to the spectral precoding approaches. These approaches manipulate the correlation of the data symbols to control the high OOB emission in OFDM.After almost ten years of analytical and theoretical study of the spectralprecoding approaches in the literature, we believe it is time to investigate the practicality and ability of spectral precoding methods to compete with traditional approaches. Consequently, we check whether spectral precoding satisfies the spectral requirements of LTE measures. We analyze the precoders' implementation complexity and provide methodologies to reduce it. We design practical spectral precoders that match with the practical OFDM transmitters, and we study spectral precoding extensibility toward MIMO (and massive MIMO) systems.Moreover, in this work, we introduce the first proof-of-concept prototype of spectrally precoded OFDM. In the prototype, we use software-defined radios (SDRs) to perform a real-time examination of how spectral precoding improves the spectral containment of OFDM systems.
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| 23. |
- Mueller, Axel, et al.
(författare)
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Interference-Aware RZF Precoding for Multicell Downlink Systems
- 2015
-
Ingår i: IEEE Transactions on Signal Processing. - 1053-587X .- 1941-0476. ; 63:15, s. 3959-3973
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Tidskriftsartikel (refereegranskat)abstract
- Recently, a structure of an optimal linear precoder for multi cell downlink systems has been described, and many other references have used simplified versions of this precoder to obtain promising performance gains. These gains have been hypothesized to stem from the additional degrees of freedom that allow for interference mitigation through interference relegation to orthogonal subspaces. However, no conclusive or rigorous understanding has yet been developed. In this paper, we build on an intuitive interference induction trade-off and the aforementioned preceding structure to propose an interference aware RZF (iaRZF) preceding scheme for multi cell downlink systems, and we analyze its rate performance. Special emphasis is placed on the induced interference mitigation mechanism of iaRZF. For example, we will verify the intuitive expectation that the precoder structure can either completely remove induced inter-cell or intra-cell interference. We state new results from large-scale random matrix theory that make it possible to give more intuitive and insightful explanations of the precoder behavior, also for cases involving imperfect channel state information (CSI). We remark especially that the interference-aware precoder makes use of all available information about interfering channels to improve performance. Even very poor CSI allows for significant sum-rate gains. Our obtained insights are then used to propose heuristic precoder parameters for arbitrary systems, whose effectiveness are shown in more involved system scenarios. Furthermore, calculation and implementation of these parameters does not require explicit inter base station cooperation.
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| 24. |
- Mueller, Axel, et al.
(författare)
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Linear precoding based on polynomial expansion : reducing complexity in massive MIMO
- 2016
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Ingår i: EURASIP Journal on Wireless Communications and Networking. - : SPRINGEROPEN. - 1687-1472 .- 1687-1499.
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Tidskriftsartikel (refereegranskat)abstract
- Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively "antenna-efficient" regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
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| 25. |
- Noguet, Dominique, et al.
(författare)
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Sensing techniques for Cognitive Radio - State of the art and trends
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This document was initiated in the framework of the IEEE Standards Coordinating Committee 411(Dynamic Spectrum Access Networks) within the 1900.6 Working group (Spectrum SensingInterfaces and Data Structures for Dynamic Spectrum Access and other Advanced RadioCommunication Systems).This documents aims at identifying the spectrum sensing techniques being used of researched and thatmay be considered for the 1900.6 standardization activities. Although it gathers State of the Artmaterial, this document does not aim at being a scientific paper in that regard that the equations arenot always justified or demonstrated. However, it provides sufficient information to have a goodperspective on the problems to solve, the techniques that have been proposed and the one that mayemerge in the next few years. Links to a wide bibliography section is systematically provided toenable the reader to get more technical details.Since 1900.6 deals with Spectrum Sensing, the focus is put on this issue in this paper.Section 3 deals with single sensor spectrum sensing. In this section, the level of a priori knowledgeabout the signal to detect is discussed and different techniques are presented according to thisparameter.Section 4 is somehow an extension of section 3 in which the problem is extended to the identificationof systems in presence through the estimation of key specific parameters. The example of OFDMsignal is highlighted for which sub-carrier spacing one of the parameters considered to differentiatethe standards.Section 5 extends the scope of section 3 by considering several sensors. Cooperative sensing andcollaborative sensing are discussed in this section.Section 6 briefly discussed the estimation of the load of a system. This information may be adetermining parameter to decide on the network to get connected to.Section 7 provides application examples of the spectrum sensing techniques described previously inscenarios involving standardized wireless systems. Performance of the techniques is discussed.Section 8 reminds that a cognitive radio often has to sense information that is not captured byspectrum sensing. For instance, battery lifetime may be relevant for decision making in batteryoperated devices.
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| 26. |
- Prasad, Ganesh, et al.
(författare)
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QoS-aware Power Allocation and Relay Placement in Green Cooperative FSO Communications
- 2019
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Ingår i: 2019 IEEE WIRELESS COMMUNICATIONS AND NETWORKING CONFERENCE (WCNC). - : IEEE. - 9781538676462
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Konferensbidrag (refereegranskat)abstract
- Due to increasing quality-of-service (QoS) demand in already congested radio spectrum, there is a need for designing energy-efficient free space optical (FSO) communication networks. Considering a realistic fading model incorporating the fluctuations in angle-of-arrival, we minimize the outage probability for error free transmission of high data volumes through optimizing the power allocation (PA) and relay placement (RP) in a dual-hop decode-and-forward (DF) relay-assisted cooperative FSO communication with coherent detection and direct link unavailability. As this problem is nonconvex, first the optimal PA between source and relay is obtained using a global optimization algorithm. Also, a closed form for the solution is obtained using a tight analytical approximation with the assumption that atmospheric turbulence over both the links is nearly same. Next, we optimize the RP followed by the outage probability is jointly minimized using alternating optimization algorithm. Numerical results validate the outage analysis and provide key insights on optimal PA and RP yielding an outage enhancement of around 37% over the benchmark scheme.
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| 27. |
- Rihan, Mohamed, et al.
(författare)
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Passive Versus Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication : Challenges and Opportunities
- 2024
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Ingår i: IEEE Network. - : Institute of Electrical and Electronics Engineers (IEEE). - 0890-8044 .- 1558-156X. ; 38:3, s. 218-226
-
Tidskriftsartikel (refereegranskat)abstract
- Reconfigurable intelligent surfaces (RISs) have emerged as a revolutionary technology for controlling wireless channels to improve the performance of wireless communication and radar systems. However, the performance improvement of these wireless systems is shown to be limited due to the multiplicative fading effect. Active RISs have been introduced to circumvent this effect while simultaneously increasing the degrees-of-freedom in the design of RIS-assisted networks. On a parallel theme, integrated sensing and communications (ISAC) has been identified as one of the promising 6G paradigms for enabling sensing and communication functionalities within an integrated platform, which allows more efficient use of energy and spectral resources at a reasonable cost, and paves the way to the birth of new use-cases and applications. This article investigates the roles of active and passive RISs in different ISAC scenarios. Indeed, while there is abundant literature covering the use of both passive and active RISs for wireless communications, there is still a shortage in studying their benefits for radar and ISAC scenarios. This paper presents an overview of the currently available studies on the use of active and passive RISs for ISAC purposes and provides numerical examples to show the superiority and greater flexibility of active RISs in the context of ISAC. Finally, possible use cases for active RISs in modern ISAC systems are explored, and research challenges are highlighted along with the relevant opportunities that RISs offer.
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| 28. |
- Sanguinetti, Luca, et al.
(författare)
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Energy Consumption in Multi-User MIMO Systems : Impact of User Mobility
- 2014
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Ingår i: 2014 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP). - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 4743-4747
-
Konferensbidrag (refereegranskat)abstract
- In this work, we consider the downlink of a single-cell multi-user multiple-input multiple-output system in which zero-forcing precoding is used at the base station (BS) to serve a certain number of user equipments (UEs). A fixed data rate is guaranteed at each UE. The UEs move around in the cell according to a Brownian motion, thus the path losses change over time and the energy consumption fluctuates accordingly. We aim at determining the distribution of the energy consumption. To this end, we analyze the asymptotic regime where the number of antennas at the BS and the number of UEs grow large with a given ratio. It turns out that the energy consumption is asymptotically a Gaussian random variable whose mean and variance are derived analytically. These results can, for example, be used to approximate the probability that a battery-powered BS runs out of energy within a certain time period.
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| 29. |
- Sanguinetti, Luca, et al.
(författare)
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Large System Analysis of the Energy Consumption Distribution in Multi-User MIMO Systems With Mobility
- 2015
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Ingår i: IEEE Transactions on Wireless Communications. - : Institute of Electrical and Electronics Engineers (IEEE). - 1536-1276 .- 1558-2248. ; 14:3, s. 1730-1745
-
Tidskriftsartikel (refereegranskat)abstract
- In this work, we consider the downlink of a single-cell multi-user MIMO system in which the base station (BS) makes use of N antennas to communicate with K single-antenna user equipments (UEs). The UEs move around in the cell according to a random walk mobility model. We aim at determining the energy consumption distribution when different linear precoding techniques are used at the BS to guarantee target rates within a finite time interval T. The analysis is conducted in the asymptotic regime where N and K grow large with fixed ratio under the assumption of perfect channel state information (CSI). Both recent and standard results from large system analysis are used to provide concise formulae for the asymptotic transmit powers and beamforming vectors for all considered schemes. These results are eventually used to provide a deterministic approximation of the energy consumption and to study its fluctuations around this value in the form of a central limit theorem. Closed-form expressions for the asymptotic means and variances are given. Numerical results are used to validate the accuracy of the theoretical analysis and to make comparisons. We show how the results can be used to approximate the probability that a battery-powered BS runs out of energy and also to design the cell radius for minimizing the energy consumption per unit area. The imperfect CSI case is also briefly considered.
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| 30. |
- Shalmashi, Serveh, et al.
(författare)
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Closed-Form Optimality Characterization of Network-Assisted Device-to-Device Communications
- 2014
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Ingår i: Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC).
-
Konferensbidrag (refereegranskat)abstract
- This paper considers the mode selection problem for network-assisted device-to-device (D2D) communications with multiple antennas at base station. We study transmission in both dedicated and shared frequency bands. Given the type of resources (i.e., dedicated or shared), the user equipment (UE) decides to transmit in the conventional cellular mode or directly to its corresponding receiver in D2D mode. We formulate this problem under two different objectives. The first problem is to maximize the quality-of-service (QoS) given a transmit power, and the second problem is to minimize the transmit power given a QoS requirement. We derive closed-form results for the optimal decision and show that the two problem formulations behave differently. Taking a geometrical approach, we study the area around the transmitter UE where the receiving UE should be to have D2D mode optimality, and how it is affected by the transmit power, QoS, and the number of base station antennas.
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| 31. |
- Shalmashi, Serveh, et al.
(författare)
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Energy Efficiency and Sum Rate Tradeoffs for Massive MIMO Systems with Underlaid Device-to-Device Communications
- 2016
-
Ingår i: EURASIP Journal on Wireless Communications and Networking. - : Springer. - 1687-1472 .- 1687-1499.
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we investigate the coexistence of two technologies that have been put forward for the fifth generation (5G) of cellular networks, namely, network-assisted device-to-device (D2D) communications and massive MIMO (multiple-input multiple-output). Potential benefits of both technologies are known individually, but the tradeoffs resulting from their coexistence have not been adequately addressed. To this end, we assume that D2D users reuse the downlink resources of cellular networks in an underlay fashion. In addition, multiple antennas at the BS are used in order to obtain precoding gains and simultaneously support multiple cellular users using multiuser or massive MIMO technique. Two metrics are considered, namely the average sum rate (ASR) and energy efficiency (EE). We derive tractable and directly computable expressions and study the tradeoffs between the ASR and EE as functions of the number of BS antennas, the number of cellular users and the density of D2D users within a given coverage area. Our results show that both the ASR and EE behave differently in scenarios with low and high density of D2D users, and that coexistence of underlay D2D communications and massive MIMO is mainly beneficial in low densities of D2D users.
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| 32. |
- Shalmashi, Serveh, et al.
(författare)
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Energy Efficiency and Sum Rate when Massive MIMO meets Device-to-Device Communication
- 2015
-
Ingår i: Proc. of the IEEE International Conference on Communications (ICC). - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 627-632
-
Konferensbidrag (refereegranskat)abstract
- This paper considers a scenario of short-range communication, known as device-to-device (D2D) communication, where D2D users reuse the downlink resources of a cellular network to transmit directly to their corresponding receivers. In addition, multiple antennas at the base station (BS) are used in order to simultaneously support multiple cellular users using multiuser or massive MIMO. The network model considers a fixed number of cellular users and that D2D users are distributed according to a homogeneous Poisson point process (PPP). Two metrics are studied, namely, average sum rate (ASR) and energy efficiency (EE). We derive tractable expressions and study the tradeoffs between the ASR and EE as functions of the number of BS antennas and density of D2D users for a given coverage area.
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| 33. |
- Shariati, Nafiseh, et al.
(författare)
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Low-Complexity Channel Estimation in Large-Scale MIMO using Polynomial Expansion
- 2013
-
Ingår i: 2013 IEEE 24th International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC). - : IEEE conference proceedings. - 9781467362351 ; , s. 1157-1162
-
Konferensbidrag (refereegranskat)abstract
- This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as "massive MIMO". Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.
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| 34. |
- Shariati, Nafiseh, et al.
(författare)
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Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO with Arbitrary Statistics
- 2014
-
Ingår i: IEEE Journal on Selected Topics in Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1932-4553 .- 1941-0484. ; 8:5, s. 815-830
-
Tidskriftsartikel (refereegranskat)abstract
- This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as “massive MIMO”, where there are hundreds of antennas at one side of the link. Motivated by the fact that computational complexity is one of the main challenges in such systems, a set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced for arbitrary channel and interference statistics. While the conventional minimum mean square error (MMSE) estimator has cubic complexity in the dimension of the covariance matrices, due to an inversion operation, our proposed estimators significantly reduce this to square complexity by approximating the inverse by a L-degree matrix polynomial. The coefficients of the polynomial are optimized to minimize the mean square error (MSE) of the estimate. We show numerically that near-optimal MSEs are achieved with low polynomial degrees. We also derive the exact computational complexity of the proposed estimators, in terms of the floating-point operations (FLOPs), by which we prove that the proposed estimators outperform the conventional estimators in large-scale MIMO systems of practical dimensions while providing a reasonable MSEs. Moreover, we show that L needs not scale with the system dimensions to maintain a certain normalized MSE. By analyzing different interference scenarios, we observe that the relative MSE loss of using the low-complexity PEACH estimators is smaller in realistic scenarios with pilot contamination. On the other hand, PEACH estimators are not well suited for noise-limited scenarios with high pilot power; therefore, we also introduce the low-complexity diagonalized estimator that performs well in this regime. Finally, we also investigate numerically how the estimation performance is affected by having imperfect statistical knowledge. High robustness is achieved for large-dimensional matrices by us- ng a new covariance estimate which is an affine function of the sample covariance matrix and a regularization term.
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| 35. |
- Tran, Thi-Thuy-Quynh, et al.
(författare)
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Network Coding with Multimedia Transmission and Cognitive Networking: An Implementation based on Software-Defined Radio
- 2020
-
Ingår i: REV Journal on Electronics and Communications. ; 10:3-4, s. 72-84
-
Tidskriftsartikel (refereegranskat)abstract
- Network coding (NC) is considered a breakthrough to improve throughput, robustness, and security of wireless networks. Although the theoretical aspects of NC have been extensively investigated, there have been only few experiments with pure NC schematics. This paper presents an implementation of NC under a two-way relay model and extends it to two non-straightforward scenarios: (i) multimedia transmission with layered coding and multiple-description coding, and (ii) cognitive radio with Vandermonde frequency division multiplexing (VFDM). The implementation is in real time and based on software-defined radio (SDR). The experimental results show that, by combining NC and source coding, we can control the quality of the received multimedia content in an on-demand manner. Whereas in the VFDM-based cognitive radio, the quality of the received content in the primary receiver is low (due to imperfect channel estimation) yet retrievable. Our implementation results serve as a proof for the practicability of network coding in relevant applications.
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| 36. |
- Van Chien, Trinh, et al.
(författare)
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Uplink Power Control in Massive MIMO with Double Scattering Channels
- 2022
-
Ingår i: IEEE Transactions on Wireless Communications. - : Institute of Electrical and Electronics Engineers (IEEE). - 1536-1276 .- 1558-2248. ; 21:3, s. 1989-2005
-
Tidskriftsartikel (refereegranskat)abstract
- Massive multiple-input multiple-output (MIMO) is a key technology for improving the spectral and energy efficiency in 5G-and-beyond wireless networks. For a tractable analysis, most of the previous works on Massive MIMO have been focused on the system performance with complex Gaussian channel impulse responses under rich-scattering environments. In contrast, this paper investigates the uplink ergodic spectral efficiency (SE) of each user under the double scattering channel model. We derive a closed-form expression of the uplink ergodic SE by exploiting the maximum ratio (MR) combining technique based on imperfect channel state information. We further study the asymptotic SE behaviors as a function of the number of antennas at each base station (BS) and the number of scatterers available at each radio channel. We then formulate and solve a total energy optimization problem for the uplink data transmission that aims at simultaneously satisfying the required SEs from all the users with limited data power resource. Notably, our proposed algorithms can cope with the congestion issue appearing when at least one user is served by lower SE than requested. Numerical results illustrate the effectiveness of the closed-form ergodic SE over Monte-Carlo simulations. Besides, the system can still provide the required SEs to many users even under congestion.
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| 37. |
- Vehkapera, Mikko, et al.
(författare)
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Asymptotic Analysis of SU-MIMO Channels With Transmitter Noise and Mismatched Joint Decoding
- 2015
-
Ingår i: IEEE Transactions on Communications. - : Institute of Electrical and Electronics Engineers (IEEE). - 0090-6778 .- 1558-0857. ; 63:3, s. 749-765
-
Tidskriftsartikel (refereegranskat)abstract
- Hardware impairments in radio-frequency components of a wireless system cause unavoidable distortions to transmission that are not captured by the conventional linear channel model. In this paper, a "binoisy" single-user multiple-input multiple-output (SU-MIMO) relation is considered where the additional distortions are modeled via an additive noise term at the transmit side. Through this extended SU-MIMO channel model, the effects of transceiver hardware impairments on the achievable rate of multi-antenna point-to-point systems are studied. Channel input distributions encompassing practical discrete modulation schemes, such as, QAM and PSK, as well as Gaussian signaling are covered. In addition, the impact of mismatched detection and decoding when the receiver has insufficient information about the non-idealities is investigated. The numerical results show that for realistic system parameters, the effects of transmit-side noise and mismatched decoding become significant only at high modulation orders.
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