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  • 201.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jaldén, Niklas
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimality Properties, Distributed Strategies, and Measurement-Based Evaluation of Coordinated Multicell OFDMA Transmission2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 12, p. 6086-6101Article in journal (Refereed)
    Abstract [en]

    The throughput of multicell systems is inherently limited by interference andthe available communication resources. Coordinated resource allocation is the key to efficient performance, but the demand on backhaul signaling andcomputational resources grows rapidly with number of cells, terminals, andsubcarriers. To handle this, we propose a novel multicell framework with dynamic cooperation clusters where each terminal is jointly served by a small set of base stations. Each base station coordinates interference to neighboring terminals only, thus limiting backhaul signalling and making the framework scalable. This framework can describe anything from interference channels to ideal joint multicell transmission. The resource allocation (i.e., precoding and scheduling) is formulated as an optimization problem (P1) with performance described by arbitrary monotonic functions of the signal-to-interference-and-noise ratios (SINRs) and arbitrary linear power constraints. Although (P1) is nonconvex and difficult to solve optimally, we are able to prove: 1) optimalityof single-stream beamforming; 2) conditions for full power usage; and 3) a precoding parametrization based on a few parameters between zero and one. These optimality properties are used to propose low-complexity strategies: both a centralized scheme and a distributed version that only requires local channel knowledge and processing. We evaluate the performance on measuredmulticell channels and observe that the proposed strategies achieve close-to-optimal performance among centralized and distributed solutions, respectively. In addition, we show that multicell interference coordination can give substantial improvements in sum performance, but that joint transmission is very sensitive to synchronization errors and that some terminals can experience performance degradations.

  • 202.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    Dresden University of Technology, Communications Theory, Communications Laboratory, Dresden, Germany.
    Optimal Resource Allocation in Coordinated Multi-Cell Systems2013Book (Refereed)
    Abstract [en]

    The use of multiple antennas at base stations is a key component in the design of cellular communication systems that can meet high-capacity demands in the downlink. Under ideal conditions, the gain of employing multiple antennas is well-recognized: the data throughput increases linearly with the number of transmit antennas if the spatial dimension is utilized to serve many users in parallel. The practical performance of multi-cell systems is, however, limited by a variety of nonidealities, such as insufficient channel knowledge, high computational complexity, heterogeneous user conditions, limited backhaul capacity, transceiver impairments, and the constrained level of coordination between base stations.

    This tutorial presents a general framework for modeling different multi-cell scenarios, including clustered joint transmission, coordinated beamforming, interference channels, cognitive radio, and spectrum sharing between operators. The framework enables joint analysis and insights that are both scenario independent and dependent.

    The performance of multi-cell systems depends on the resource allocation; that is, how the time, power, frequency, and spatial resources are divided among users. A comprehensive characterization of resource allocation problem categories is provided, along with the signal processing algorithms that solve them. The inherent difficulties are revealed: (a) the overwhelming spatial degrees-of-freedom created by the multitude of transmit antennas; and (b) the fundamental tradeoff between maximizing aggregate system throughput and maintaining user fairness. The tutorial provides a pragmatic foundation for resource allocation where the system utility metric can be selected to achieve practical feasibility. The structure of optimal resource allocation is also derived, in terms of beamforming parameterizations and optimal operating points.

    This tutorial provides a solid ground and understanding for optimization of practical multi-cell systems, including the impact of the nonidealities mentioned above. The Matlab code is available online for some of the examples and algorithms in this tutorial.

    Note: The supplementary Matlab Code is available at http://dx.doi.org/10.1561/0100000069_supp

  • 203.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Alcatel-Lucent Chair on Flexible Radio, Supélec, France.
    Jorswieck, Eduard
    Dresden University of Technology, Communications Theory, Communications Laboratory, Dresden, Germany.
    Optimal Resource Allocation in Coordinated Multi-Cell Systems: Matlab Code2013Report (Other academic)
    Abstract [en]

    This is the documentation of the Matlab code supplement to the monograph "Optimal Resource Allocation in Coordinated Multi-Cell Systems" by Emil Björnson and Eduard Jorswieck; see [1] for the full publication details.

    This documentation is distributed along with the code package mentioned above. The package contains Matlab implementations of many of the algorithms described in [1]. The use of these algorithms is exemplified by Matlab scripts (m-files) that generate some of the figures shown in the monograph. The algorithms are briefly described in Section 5 and the selected example figures are described and shown in Section 6. Please note that the all channel vectors are generated randomly as Rayleigh fading in these examples, thus this code package is not able to reproduce exactly the same curves as was shown in the monograph.

  • 204.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard A.
    Dresden University of Technology (TUD), Germany.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Impact of Spatial Correlation and Precoding Design in OSTBC MIMO Systems2010In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 9, no 11, p. 3578-3589Article in journal (Refereed)
    Abstract [en]

    The impact of transmission design and spatial correlation on the symbol error rate (SER) is analyzed for multi-antenna communication links. The receiver has perfect channel state information (CSI), while the transmitter has either statistical or no CSI. The transmission is based on orthogonal space-time block codes (OSTBCs) and linear precoding. The precoding strategy that minimizes the worst-case SER is derived for the case when the transmitter has no CSI. Based on this strategy, the intuitive result that spatial correlation degrades the SER performance is proved mathematically. In the case when the transmitter knows the channel statistics, the correlation matrix is assumed to be jointly-correlated (a generalization of the Kronecker model). The eigenvectors of the SER-optimal precoding matrix are shown to originate from the correlation matrix and the remaining power allocation is a convex problem. Equal power allocation is SER-optimal at high SNR. Beamforming is SER-optimal at low SNR, or for increasing constellation sizes, and its optimality range is characterized. A heuristic low-complexity power allocation is proposed and evaluated numerically. Finally, it is proved analytically that receive-side correlation always degrades the SER. Transmit-side correlation will however improve the SER at low to medium SNR, while its impact is negligible at high SNR.

  • 205.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    Dresden University of Technology, Germany.
    Debbah, Merouane
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Multiobjective Signal Processing Optimization: The way to balance conflicting metrics in 5G systems2014In: IEEE signal processing magazine (Print), ISSN 1053-5888, E-ISSN 1558-0792, Vol. 31, no 6, p. 14-23Article in journal (Refereed)
    Abstract [en]

    The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: any data service is instantly accessible everywhere. With each generation of cellular networks, we have moved closer to this wireless dream; first by delivering wireless access to voice communications, then by providing wireless data services, and recently by delivering a Wi-Fi-like experience with wide-area coverage and user mobility management. The support for high data rates has been the main objective in recent years [1], as seen from the academic focus on sum-rate optimization and the efforts from standardization bodies to meet the peak rate requirements specified in IMT-Advanced. In contrast, a variety of metrics/objectives are put forward in the technological preparations for fifth-generation (5G) networks: higher peak rates, improved coverage with uniform user experience, higher reliability and lower latency, better energy efficiency (EE), lower-cost user devices and services, better scalability with number of devices, etc. These multiple objectives are coupled, often in a conflicting manner such that improvements in one objective lead to degradation in the other objectives. Hence, the design of future networks calls for new optimization tools that properly handle the existence of multiple objectives and tradeoffs between them.

  • 206.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Alcatel-Lucent Department on Flexible Radio, SUPELEC, Gif-sur-Yvette, France .
    Kountouris, M.
    Debbah, M.
    Massive MIMO and small cells: Improving energy efficiency by optimal soft-cell coordination2013In: 2013 20th International Conference on Telecommunications, ICT 2013, IEEE Computer Society, 2013, p. 6632074-Conference paper (Refereed)
    Abstract [en]

    To improve the cellular energy efficiency, without sacrificing quality-of-service (QoS) at the users, the network topology must be densified to enable higher spatial reuse. We analyze a combination of two densification approaches, namely "massive" multiple-input multiple-output (MIMO) base stations and small-cell access points. If the latter are operator-deployed, a spatial soft-cell approach can be taken where the multiple transmitters serve the users by joint non-coherent multiflow beamforming. We minimize the total power consumption (both dynamic emitted power and static hardware power) while satisfying QoS constraints. This problem is proved to have a hidden convexity that enables efficient solution algorithms. Interestingly, the optimal solution promotes exclusive assignment of users to transmitters. Furthermore, we provide promising simulation results showing how the total power consumption can be greatly improved by combining massive MIMO and small cells; this is possible with both optimal and low-complexity beamforming.

  • 207.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kountouris, Marios
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems With Multi-Antenna Users2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 13, p. 3431-3446Article in journal (Refereed)
    Abstract [en]

    In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are near-orthogonal, for multi-stream multiplexing to users with well-conditioned channels, and/or to enable interference-aware receive combining. In this paper, we try to answer the question if the data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user-the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multi-user diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization.

  • 208.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Matthaiou, M.
    Debbah, M.
    A New Look at Dual-Hop Relaying: Performance Limits with Hardware Impairments2013In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 61, no 11, p. 4512-4525Article in journal (Refereed)
    Abstract [en]

    Physical transceivers have hardware impairments that create distortions which degrade the performance of communication systems. The vast majority of technical contributions in the area of relaying neglect hardware impairments and, thus, assume ideal hardware. Such approximations make sense in low-rate systems, but can lead to very misleading results when analyzing future high-rate systems. This paper quantifies the impact of hardware impairments on dual-hop relaying, for both amplify-and-forward and decode-and-forward protocols. The outage probability (OP) in these practical scenarios is a function of the effective end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives new closed-form expressions for the exact and asymptotic OPs, accounting for hardware impairments at the source, relay, and destination. A similar analysis for the ergodic capacity is also pursued, resulting in new upper bounds. We assume that both hops are subject to independent but non-identically distributed Nakagami-m fading. This paper validates that the performance loss is small at low rates, but otherwise can be very substantial. In particular, it is proved that for high signal-to-noise ratio (SNR), the end-to-end SNDR converges to a deterministic constant, coined the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in contrast to the ideal hardware case in which the end-to-end SNDR grows without bound in the high-SNR regime. Finally, we provide fundamental design guidelines for selecting hardware that satisfies the requirements of a practical relaying system.

  • 209.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. SUPELEC, France .
    Matthaiou, M.
    Debbah, M.
    Massive MIMO systems with hardware-constrained base stations2014Conference paper (Refereed)
    Abstract [en]

    Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas. Such large antenna arrays offer huge spatial degrees-of-freedom for transmission optimization; in particular, great signal gains, resilience to imperfect channel knowledge, and small inter-user interference are all achievable without extensive inter-cell coordination. The key to cost-efficient deployment of large arrays is the use of hardware-constrained base stations with low-cost antenna elements, as compared to today's expensive and power-hungry BSs. Low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the excessive degrees-of-freedom of massive MIMO would bring robustness to such imperfections. We herein prove this claim for an uplink channel with multiplicative phase-drift, additive distortion noise, and noise amplification. Specifically, we derive a closed-form scaling law that shows how fast the imperfections increase with the number of antennas.

  • 210.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. SUPELEC, France.
    Matthaiou, Michail
    Debbah, Mérouane
    Circuit-aware design of energy-efficient massive MIMO systems2014In: ISCCSP 2014 - 2014 6th International Symposium on Communications, Control and Signal Processing, Proceedings, 2014, p. 101-104Conference paper (Refereed)
    Abstract [en]

    Densification is a key to greater throughput in cellular networks. The full potential of coordinated multipoint (CoMP) can be realized by massive multiple-input multiple-output (MIMO) systems, where each base station (BS) has very many antennas. However, the improved throughput comes at the price of more infrastructure; hardware cost and circuit power consumption scale linearly/affinely with the number of antennas. In this paper, we show that one can make the circuit power increase with only the square root of the number of antennas by circuit-aware system design. To this end, we derive achievable user rates for a system model with hardware imperfections and show how the level of imperfections can be gradually increased while maintaining high throughput. The connection between this scaling law and the circuit power consumption is established for different circuits at the BS.

  • 211.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ntontin, Konstantinos
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Channel quantization design in multiuser MIMO systems: Asymptotic versus practical conclusions2011In: Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, IEEE Signal Processing Society, 2011, p. 3072-3075Conference paper (Refereed)
    Abstract [en]

    Feedback of channel state information (CSI) is necessary to achieve high throughput and low outage probability in multiuser multi antenna systems. There are two types of CSI: directional and quality information. Many papers have analyzed the importance of these in asymptotic regimes. However, we show that such results should be handled with care, as very different conclusions can be drawn depending on the spatial correlation and number of users. There fore, we propose a quantization framework and evaluate the tradeoff between directional and quality feedback under practical conditions.

  • 212.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels With Rician Disturbance2010In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 58, no 3, p. 1807-1820Article in journal (Refereed)
    Abstract [en]

    In this paper, we create a framework for training-based channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation in Rician fading multi-antenna systems is analyzed, and especially the design of mean square error (MSE) minimizing training sequences. By considering Kronecker-structured systems with a combination of noise and interference and arbitrary training sequence length, we collect and generalize several previous results in the framework. We clarify the conditions for achieving the optimal training sequence structure and show when the spatial training power allocation can be solved explicitly. We also prove that spatial correlation improves the estimation performance and establish how it determines the optimal training sequence length. The analytic results for Kronecker-structured systems are used to derive a heuristic training sequence under general unstructured statistics. The MMSE estimator of the squared Frobenius norm of the channel matrix is also derived and shown to provide far better gain estimates than other approaches. It is shown under which conditions training sequences that minimize the non-convex MSE can be derived explicitly or with low complexity. Numerical examples are used to evaluate the performance of the two estimators for different training sequences and system statistics. We also illustrate how the optimal length of the training sequence often can be shorter than the number of transmit antennas.

  • 213.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Exploiting long-term statistics in spatially correlated multi-user MIMO systems with quantized channel norm feedback2008In: 2008 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, IEEE , 2008, p. 3117-3120Conference paper (Refereed)
    Abstract [en]

    In wireless multiple antenna and multi-user systems, the spatial dimensions may be exploited to increase the performance by means of antenna gain, spatial diversity, and multi-user diversity. A limiting factor in such systems is the channel information required by the transmitter to control the intra-cell interference. Herein, the properties of spatially correlated channels with long-term statistical information at the transmitter and fixed-rate feedback of the quantized Euclidean channel norm are analyzed using a spectral subspace decomposition framework. A spatial division multiple access scheme is proposed with interference suppression at the receiver and joint scheduling and zero-forcing beamforming at the transmitter. Closed-form expressions for first and second order moments of the feedback conditional channel statistics are derived. It is shown that only a few bits of feedback are required to achieve reliable rate estimation and weighted sum-rate maximization.

  • 214.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the Principles of Multicell Precoding with Centralized and Distributed Cooperation2009In: 2009 INTERNATIONAL CONFERENCE ON WIRELESS COMMUNICATIONS AND SIGNAL PROCESSING (WCSP 2009), NEW YORK: IEEE , 2009, p. 1644-1648Conference paper (Refereed)
    Abstract [en]

    Cooperative precoding is an attractive way of improving the performance in multicell downlink scenarios. By serving each terminal through multiple surrounding base stations, inter-cell interference can be coordinated and higher spectral efficiency achieved, especially for terminals at cell edges. The optimal performance of multicell precoding is well-known as it can be treated as a single cell with distributed antennas. However, the requirements on backhaul signaling and computational power scales rapidly in large and dense networks, which often makes such fully centralized approaches impractical. In this paper, we review and generalize some recent work on multicell precoding with both centralized and distributed cooperation. We propose practical precoding strategies under Rician channel conditions, and illustrate how the major gain of multicell precoding originates from having good base station synchronization and not from making centralized precoding decisions.

  • 215.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pilot-based Bayesian Channel Norm Estimation in Rayleigh Fading Multi-antenna Systems2008In: Proceedings of the twentieth Nordic Conference on Radio Science and Communications, Växjö, Sweden, 2008Conference paper (Other academic)
    Abstract [en]

    Pilot-based estimation of the squared Euclidean norm of the channel vector of a Rayleigh fading system is considered. Unlike most previous work in the area of estimation of multiple antenna channels, we consider Bayesian estimation where the long-term channel statistics are known a priori. Closed-form expressions of the minimum mean square error (MMSE) estimator and its mean squared error (MSE) are derived for the cases of either an unweighted or a weighted unitary pilot matrix. The problem of finding the optimal pilot weighting, in the sense of minimizing the average MSE, is solved and a simple algorithm is proposed to achieve this power allocation numerically. The numerical evaluation shows that an optimal weighting can significantly improve the estimation quality in spatially correlated environments.

  • 216.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Post-User-Selection Quantization and Estimation of Correlated Frobenius and Spectral Channel Norms2008In: 2008 IEEE 19TH INTERNATIONAL SYMPOSIUM ON PERSONAL, INDOOR AND MOBILE RADIO COMMUNICATIONS, NEW YORK: IEEE , 2008, p. 2751-2756Conference paper (Refereed)
    Abstract [en]

    This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented.

  • 217.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Training-based Bayesian MIMO channel and channel norm estimation2009In: 2009 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1- 8, PROCEEDINGS, IEEE , 2009, p. 2701-2704Conference paper (Refereed)
    Abstract [en]

    Training-based estimation of channel state information in multi-antenna systems is analyzed herein. Closed-form expressions for the general Bayesian minimum mean square error (MMSE) estimators of the channel matrix and the squared channel norm are derived in a Rayleigh fading environment with known statistics at the receiver side. When the second-order channel statistics are available also at the transmitter, this information can be exploited in the training sequence design to improve the performance. Herein, mean square error (MSE) minimizing training sequences are considered. The structure of the general solution is developed, with explicit expressions at high and low SNRs and in the special case of uncorrelated receive antennas. The optimal length of the training sequence is equal or smaller than the number of transmit antennas.

  • 218.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    Communication Theory, Communications Laboratory, Dresden University of Technology, D-01062 Dresden, Germany.
    On the impact of spatial correlation and precoder design on the performance of MIMO systems with space-time coding2009In: 2009 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1- 8, PROCEEDINGS, IEEE , 2009, p. 2741-2744Conference paper (Refereed)
    Abstract [en]

    The symbol error performance of spatially correlated multi-antenna systems is analyzed herein. When the transmitter only has statistical channel information, the use of space-time block codes still permits spatial multiplexing and mitigation of fading. The statistical information can be used for precoding to optimize some quality measure. Herein, we analyze the performance in terms of the symbol error rate (SER). It is shown analytically that spatial correlation at the receiver decreases the performance both without precoding and with an SER minimizing precoder. Without precoding, correlation should also be avoided at the transmitter side, but with an SER minimizing precoder the performance is actually improved by increasing spatial correlation at the transmitter. The structure of the optimized precoder is analyzed and the asymptotic properties at high and low SNRs are characterized and illustrated numerically.

  • 219.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Papadogiannis, A.
    Matthaiou, M.
    Debbah, M.
    On the impact of transceiver impairments on af relaying2013In: ICASSP IEEE Int Conf Acoust Speech Signal Process Proc, 2013, p. 4948-4952Conference paper (Refereed)
    Abstract [en]

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

  • 220.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sanguinetti, L.
    Hoydis, J.
    Debbah, M.
    Designing multi-user MIMO for energy efficiency: When is massive MIMO the answer?2014In: IEEE Wireless Communications and Networking Conference, WCNC, 2014, p. 242-247Conference paper (Refereed)
    Abstract [en]

    Assume that a multi-user multiple-input multiple-output (MIMO) communication system must be designed to cover a given area with maximal energy efficiency (bits/Joule). What are the optimal values for the number of antennas, active users, and transmit power? By using a new model that describes how these three parameters affect the total energy efficiency of the system, this work provides closed-form expressions for their optimal values and interactions. In sharp contrast to common belief, the transmit power is found to increase (not decrease) with the number of antennas. This implies that energy efficient systems can operate at high signal-to-noise ratio (SNR) regimes in which the use of interference-suppressing precoding schemes is essential. Numerical results show that the maximal energy efficiency is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve relatively many users using interference-suppressing regularized zero-forcing precoding.

  • 221.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sanguinetti, Luca
    SUPELEC, Alcatel Lucent Chair Flexible Radio, Gif Sur Yvette, France.;Univ Pisa, Dip Ingn Informaz, Pisa, Italy..
    Hoydis, Jakob
    Bell Labs, Alcatel Lucent, Stuttgart, Germany..
    Debbah, Merouane
    SUPELEC, Alcatel Lucent Chair Flexible Radio, Gif Sur Yvette, France..
    Designing Multi-User MIMO for Energy Efficiency: When is Massive MIMO the Answer?2014In: 2014 IEEE WIRELESS COMMUNICATIONS AND NETWORKING CONFERENCE (WCNC), IEEE , 2014, p. 242-247Conference paper (Refereed)
    Abstract [en]

    Assume that a multi-user multiple-input multiple output (MIMO) communication system must be designed to cover a given area with maximal energy efficiency (bits/Joule). What are the optimal values for the number of antennas, active users, and transmit power? By using a new model that describes how these three parameters affect the total energy efficiency of the system, this work provides closed-form expressions for their optimal values and interactions. In sharp contrast to common belief, the transmit power is found to increase (not decrease) with the number of antennas. This implies that energy efficient systems can operate at high signal-to-noise ratio (SNR) regimes in which the use of interference-suppressing precoding schemes is essential. Numerical results show that the maximal energy efficiency is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve relatively many users using interference-suppressing regularized zero-forcing precoding.

  • 222.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zakhour, Randa
    Mobile Communications Department, EURECOM.
    Gesbert, David
    Mobile Communications Department, EURECOM.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cooperative Multicell Precoding: Rate Region Characterization and Distributed Strategies With Instantaneous and Statistical CSI2010In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 58, no 8, p. 4298-4310Article in journal (Refereed)
    Abstract [en]

    Base station cooperation is an attractive way of increasing the spectral efficiency in multiantenna communication. By serving each terminal through several base stations in a given area, intercell interference can be coordinated and higher performance achieved, especially for terminals at cell edges. Most previous work in the area has assumed that base stations have common knowledge of both data dedicated to all terminals and full or partial channel state information (CSI) of all links. Herein, we analyze the case of distributed cooperation where each base station has only local CSI, either instantaneous or statistical. In the case of instantaneous CSI, the beamforming vectors that can attain the outer boundary of the achievable rate region are characterized for an arbitrary number of multiantenna transmitters and single-antenna receivers. This characterization only requires local CSI and justifies distributed precoding design based on a novel virtual signal-to-interference noise ratio (SINR) framework, which can handle an arbitrary SNR and achieves the optimal multiplexing gain. The local power allocation between terminals is solved heuristically. Conceptually, analogous results for the achievable rate region characterization and precoding design are derived in the case of local statistical CSI. The benefits of distributed cooperative transmission are illustrated numerically, and it is shown that most of the performance with centralized cooperation can be obtained using only local CSI.

  • 223.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zakhour, Randa
    Mobile Communications Department EURECOM 06560 Sophia Antipolis, France.
    Gesbert, David
    Mobile Communications Department EURECOM 06560 Sophia Antipolis, France.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Distributed Multicell and Multiantenna Precoding: Characterization and Performance Evaluation2009In: GLOBECOM 2009: 2009 IEEE GLOBAL TELECOMMUNICATIONS CONFERENCE, VOLS 1-8 / [ed] Ulema M, IEEE , 2009, p. 1-6Conference paper (Refereed)
    Abstract [en]

    This paper considers downlink multiantenna communication with base stations that perform cooperative precoding in a distributed fashion. Most previous work in the area has assumed that transmitters have common knowledge of both data symbols of all users and full or partial channel state information (CSI). Herein, we assume that each base station only has local CSI, either instantaneous or statistical. For the case of instantaneous CSI, a parametrization of the beamforming vectors used to achieve the outer boundary of the achievable rate region is obtained for two multi-antenna transmitters and two single-antenna receivers. Distributed generalizations of classical beamforming approaches that satisfy this parametrization are provided, and it is shown how the distributed precoding design can be improved using the so-called virtual SINR framework [1]. Conceptually analog results for both the parametrization and the beamforming design are derived in the case of local statistical CSI. Heuristics on the distributed power allocation are provided in both cases, and the performance is illustrated numerically.

  • 224.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zetterberg, Per
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimal Coordinated Beamforming in the Multicell Downlink with Transceiver Impairments2012In: 2012 IEEE Global Telecommunications Conference (GLOBECOM), New York: IEEE conference proceedings, 2012, p. 4775-4780Conference paper (Refereed)
    Abstract [en]

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

  • 225.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Zetterberg, Per
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Capacity Limits and Multiplexing Gains of MIMO Channels with Transceiver Impairments2013In: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 17, no 1, p. 91-94Article in journal (Refereed)
    Abstract [en]

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

  • 226.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zheng, Gan
    Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Robust Monotonic Optimization Framework for Multicell MISO Systems2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 5, p. 2508-2523Article in journal (Refereed)
    Abstract [en]

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

  • 227. Björsell, Niclas
    et al.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Statistical Evaluation of ADC Histogram Tests with Arbitrary Stimuli Signal2005In: ADDA 2005, 2005, p. 259-264Conference paper (Refereed)
  • 228.
    Björsell, Niclas
    et al.
    Gävle Universitet.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Achievable ADC Performance by Post-Correction Utilizing Dynamic Modeling of the Integral Nonlinearity2008In: EURASIP Journal on Advances in Signal Processing, ISSN 1110-8657, p. 497187-1-497187-10Article in journal (Refereed)
    Abstract [en]

    There is a need for a universal dynamic model of analog-to-digital converters (ADC’s) aimed for postcorrection. However, it is complicated to fully describe the properties of an ADC by a single model. An alternative is to split up the ADC model in different components, where each component has unique properties. In this paper, a model based on three components is used, and a performance analysis for each component is presented. Each component can be postcorrected individually and by the method that best suits the application. The purpose of postcorrection of an ADC is to improve the performance. Hence, for each component, expressions for the potential improvement have been developed. The measures of performance are total harmonic distortion (THD) and signal to noise and distortion (SINAD), and to some extent spurious-free dynamic range (SFDR).

  • 229. Björsell, Niclas
    et al.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Analog-to-Digital Converters for High-Speed Applications2005In: GigaHz 2005, 2005, p. 151-154Conference paper (Refereed)
  • 230. Björsell, Niclas
    et al.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dynamic behavior models of analog to digital converters aimed for post-correction in wideband applications2006In: 18th IMEKO World Congress 2006: Metrology for a Sustainable Development, 2006, p. 1344-1348Conference paper (Refereed)
    Abstract [en]

    In this paper a dynamic behavior model of analog to digital converters is proposed. The model is aimed for post correction in wideband applications. The suggested post correction method is a combination of look up tables and model based correction.The model consists of three components. The first is a component represented by a Hammerstein model; that is a static nonlinearity followed by a time invariant linear filter. The second component is a nonparametric model caused by significant deviation from the characterized integral nonlinearity and the output from the Hammerstein model. The third component contains of the remaining deviation and is considered as a random model error.Results from simulations verify that the examined ADC can be described by an ordinary Hammerstein model and a static look-up table.

  • 231.
    Björsell, Niclas
    et al.
    Gävle Universitet.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Histogram Tests for Wideband Applications2008In: IEEE Transactions on Instrumentation and Measurement, ISSN 0018-9456, E-ISSN 1557-9662, Vol. 57, no 1, p. 70-75Article in journal (Refereed)
    Abstract [en]

    Characterization and testing of analog-to-digital converters (ADCs) are important for many reasons. A histogram test is a common method to characterize the linearity features of an ADC. Two commonly used stimulus signals are sine waves and Gaussian noise. This paper presents a metrological comparison between Gaussian and sine-wave histogram tests for wide-band applications, that is, we evaluate the performance of the characterization of the ADC and the usability of postcorrection. A postcorrection procedure involves the characterization of the ADC nonlinearity and then the use of this information by processing the ADC output samples to remove the distortion. The results show that the Gaussian histogram test gives reasonable accuracy in measuring nonlinearities. However, it does not result in a suitable model for postcorrection in wideband applications. A single-tone sine-wave histogram will be a better basis for postcorrection. The best result can be obtained if the lookup table is trained with several single-tone sine waves in the frequency band.

  • 232. Björsell, Niclas
    et al.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Gaussian and Sine Wave Histogram Tests for Wideband Applications2005In: Proceedings of the IEEE Instrumentation and Measurement Technology Conference, IEEE , 2005, p. 677-682Conference paper (Refereed)
    Abstract [en]

    Characterization and testing of analog-to-digital converters (ADCs) are interesting in many different aspects. Histogram test is a common method to characterize the linearity features of an ADC. Two commonly used stimuli signals are sine waves and Gaussian noise. This paper will present a metrological comparison between Gaussian and sine wave histogram tests for wideband applications; that is evaluate the performance in characterization of the ADC and the usability of post-correction. A post-correction procedure involves characterization of the ADC non-linearity and then utilization of this information by processing the ADC output samples to remove the distortion. The results indicates that even though the Gaussian histogram test seems to give reasonable accuracy to measure non-linearities it is not thereby a suitable model for post-correction. A single-tone sine wave histogram will most likely be a better solution. Best result is to train the look-up table with several single-tone sine waves in the frequency band.

  • 233.
    Björsell, Niclas
    et al.
    Gävle Universitet.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Truncated Gaussian Noise in ADC Histogram Tests2007In: Measurement, ISSN 0263-2241, E-ISSN 1873-412X, Vol. 40, no 1, p. 36-42Article in journal (Refereed)
    Abstract [en]

    One method to characterize analogue to digital converters (ADCs) is to use a histogram, where Gaussian noise may be used as stimulus signal. However, a Gaussian noise signal that excites all transition levels also generates input values outside working range of the ADC. Modern signal generators can generate arbitrary signals. Hence, excluding undesired values outside the ADC full scale can minimize test sequences. Truncating the signal to the working range gives further advantages, which are explored in this paper. The Cramer-Rao lower bound and a minimum variance estimator for histogram tests with an arbitrary stimulus are derived. These are applied for truncated Gaussian noise and the result is theoretically evaluated and compared to untruncated noise. It is shown that accuracy increases for a fixed sample length and that variation over transition levels decrease.

  • 234.
    Björsell, Niclas
    et al.
    University of Gävle.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Medawar, Samer
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Improved estimate of parametric models for analogue to digital converters by using weighted integral nonlinearity data2010In: 17th Symposium IMEKO TC4 - Measurement of Electrical Quantities, 15th International Workshop on ADC Modelling and Testing, and 3rd Symposium IMEKO TC19 - Environmental Measurements, 2010, p. 597-600Conference paper (Refereed)
    Abstract [en]

    Error modelling has played a major role in generating post-corrections of analogue to digital converters (ADC). Benefits by using parametric models for post-correction are that they requires less memory and that they are easier to identify for arbitrary signals. However, the parameters are estimated in two steps; firstly, the integral nonlinearity (INL) is estimated and secondly, the model parameters. In this paper we propose a method to improve the performance in the second step, by utilizing information about the statistical properties of the first step.

  • 235.
    Björsell, Niclas
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Isaksson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rönnow, Daniel
    Kautz-Volterra modelling of an analogue-to-digital converter using a stepped three-tone excitation2007In: 12th IMEKO TC-4 International Workshop on ADC MODELLING AND TESTING, 2007, p. 107-112Conference paper (Refereed)
    Abstract [en]

    In many test and measurement applications, the analogue-to-digital converter (ADC) is the limiting component. Using post-correction methods can improve the performance of the component as well as the over all measurement system. In this paper an ADC is characterised by a Kautz-Volterra (KV) model, which utilises a model-based post-correction of the ADC with general properties and a reasonable number of parameters. Results that are based on measurements on a high-speed 12-bit ADC, shows good results for a third order model.

  • 236.
    Björsell, Niclas
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Isaksson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rönnow, Daniel
    Gävle Universitet.
    Kautz-Volterra modelling of analogue-to-digital converters2010In: Computer Standards & Interfaces, ISSN 0920-5489, E-ISSN 1872-7018, Vol. 32, no 3, p. 126-129Article in journal (Refereed)
    Abstract [en]

    In many test and measurement applications, the analogue-to-digital converter (ADC) is the limiting component. Using post-correction methods can improve the performance of the component as well as the overall measurement system. In this paper an ADC is characterised by a Kautz–Volterra (KV) model, which utilises a model-based post-correction of the ADC with general properties and a reasonable number of parameters. It is also shown that the inverse model has the same dynamic properties as the direct KV model. Results that are based on measurements on a high-speed 12-bit ADC show good results for a third-order model.

  • 237.
    Björsell, Niclas
    et al.
    University of Gävle, Radio center for measurement technology.
    Nader, Charles
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Multi-tone design for out-of-band characterization of nonlinear RF modules using harmonic sampling2010In: 2010 IEEE International Instrumentation and Measurement Technology Conference, I2MTC 2010 - Proceedings, IEEE , 2010, p. 620-623Conference paper (Refereed)
    Abstract [en]

    In this paper we evaluate the generation of a multi-tone set for characterizing the behavior of nonlinear radio frequency (RF) modules in its out-of-band when harmonic sampling is used as digitizer. The purpose is to provide the reader with a tool to select proper frequencies and record length for a given application and test-bed. The method is based on simulations and the use of Sidon sequences. The proposed method is applicable to sparse discrete frequency multi-tones.

  • 238. Björsell, Niklas
    et al.
    Suchánek, Petr
    Czech Tech Univ Prague.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rönnow, Daniel
    Gävle Universitet.
    Measuring Volterra Kernels of Analog To Digital Converters Using a Stepped Three-Tone Scan2008In: IEEE Transactions on Instrumentation and Measurement, ISSN 0018-9456, E-ISSN 1557-9662, Vol. 57, no 4, p. 666-671Article in journal (Refereed)
    Abstract [en]

    The Volterra theory can be used to mathematically model nonlinear dynamic components such as analog-to-digital converters (ADCs). This paper describes how frequency-domain Volterra kernels of an ADC are determined from measurements. The elements of the Volterra theory are given, and practical issues are considered, such as methods for signal conditioning and finding the appropriate test signals scenario and suitable sampling frequency. The results show that, for the used pipeline ADC, the frequency dependence is significantly stronger for second-order difference products than for sum products and the linear frequency dependence was not as pronounced as that of the second-order Volterra kernel. It is suggested that the Volterra kernels have the symmetry properties of a specific box model, namely, the parallel Hammerstein system.

  • 239.
    Blasco-Serrano, Ricardo
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Coding Strategies for Compress-and-Forward Relaying2010Licentiate thesis, monograph (Other academic)
    Abstract [en]

    The deployment of large communication networks with many autonomous devices has opened new possibilities for transmission. In particular cooperation among the different nodes has been identified as an enabling technology to satisfy the increasing demand of resources. This thesis studies different coding strategies for cooperation in relay channels in the form of compress-and-forward.

    In the first part of this thesis we consider the application of the newly introduced polar codes for compress-and-forward relaying in relay channels with orthogonal receivers. First we construct polar codes for compress-and-forward relaying based on Slepian-Wolf coding for the scenario where the capacity of the relay-destination channel is large enough. We then consider the more general picture where the capacity of the relay-destination channel is arbitrary. As for Wyner-Ziv coding, we employ nested polar codes for source and channel coding that allow for compression at any desired distortion and exploit the correlation between the observations of the source transmission to minimize the transmission rate over the relay-destination channel. This construction allows for transmission at the prominent compress-and-forward rate under some additional constraints.

    In the second part of this thesis we propose a new coding strategy for compress-and-forward relaying for half-duplex Gaussian channels. Our code construction is based on simple code concatenation for joint source-channel coding at the relay and iterative decoding at the destination. Finally, we propose several realizations of the structure at the relay and different iterative decoding algorithms in order to adapt the construction to different scenarios. Our simulation results show remarkable performance gains over other cooperation strategies such as decode-and-forward and amplify-and-forward in the scenarios where both source-relay and relay-destination links have low signal-to-noise ratios.

  • 240.
    Blasco-Serrano, Ricardo
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Compression and Coordination in Networks2013Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The current trends in communications suggest that the transfer of information between machines will soon predominate over the traditional human-oriented exchange. The new applications in machine-to-machine communications demand for a new type of networks that are much larger and, especially, much denser. However, there are currently many challenges that hinder an efficient deployment of such networks. In this thesis, we study some fundamental and practical aspects of two of these challenges: coordination and compression.

    The problem of coordination in a network is that of organizing the nodes to make them work together. The information-theoretic abstraction of this corresponds to generating actions with a desired empirical distribution. In this thesis, we construct polar codes for coordination for a variety of topologies. These codes combine elements of source coding, used to produce the actions, with elements of channel coding, used to obtain efficient descriptions. We show that our constructions achieve several fundamental coordination limits in a structured manner and with affordable complexity.

    Then, we consider the problem of coordinating communications to control the interference created to an external observer, measured in terms of its empirical distribution.

    To study the relationship between communication and interference, we introduce the notion of communication-interference capacity region. We obtain a complete characterization of this region for the single user scenario and a partial solution for a multiple user case. Our results reveal a fundamental tradeoff between communication, coordination, and interference in this type of networks.

    The second problem considered in this thesis, compression, involves capturing the essence of data and discarding the irrelevant aspects to obtain compact representations. This takes on a new dimension in networks, where the importance of data is no longer a local matter. In this thesis, we show that polar codes are also suitable for achieving information-theoretic bounds that involve compression in networks. More precisely, we extend our coordination constructions to realize compress-and-forward relaying with affordable complexity.

    In the last part of the thesis, we take a network approach to the problem of compressive sensing and develop methods for partial support set recovery. We use these methods to characterize the tradeoff between the measurement rate and the mean square error. Finally, we show that partial support recovery is instrumental in minimizing measurement outages when estimating random sparse signals. 

  • 241.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Lv, Jing
    Dresden University of Technology.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    Dresden University of Technology.
    Kliks, Adrian
    Poznan University of Technology.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Comparison of Underlay and Overlay Spectrum Sharing Strategies in MISO Cognitive Channels2012In: 2012 7th International ICST Conference on Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM), IEEE Computer Society, 2012, p. 224-229Conference paper (Refereed)
    Abstract [en]

    We consider an extension of the cognitive radio channel model in which the secondary transmitter has to obtain (“learn”) the primary message in a first phase rather than having non-causal knowledge of it. We propose an achievable rate region that combines elements of decode-and-forward relaying with coding for the pure cognitive radio channel model. Moreover, we find the choice of parameters that maximize the secondary rate under a primary rate constraint. Finally, we compare numerically the performance of our system to that of an underlay scheme that combines beamforming, rate splitting, and successive decoding. We observe that although the overlay design provides higher rates, the losses due to the first phase are quite severe. In fact, for the considered scenarios, cleverly designed underlay schemes can provide comparable performance.

  • 242.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Lv, Jing
    Dresden University of Technology.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jorswieck, Eduard
    Dresden University of Technology.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Multi-antenna transmission for underlay and overlay cognitive radio with explicit message-learning phase2013In: EURASIP Journal on Wireless Communications and Networking, ISSN 1687-1472, E-ISSN 1687-1499Article in journal (Refereed)
  • 243.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rathi, Vishwambhar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Polar Codes for Cooperative Relaying2012In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 60, no 11, p. 3263-3273Article in journal (Refereed)
    Abstract [en]

    We consider the symmetric discrete memoryless relay channel with orthogonal receiver components and show that polar codes are suitable for decode-and-forward and compress-and-forward relaying. In the first case we prove that polar codes are capacity achieving for the physically degraded relay channel; for stochastically degraded relay channels our construction provides an achievable rate. In the second case we construct sequences of polar codes that achieve the compress-and-forward rate by nesting polar codes for source compression into polar codes for channel coding. In both cases our constructions inherit most of the properties of polar codes. In particular, the encoding and decoding algorithms and the bound on the block error probability O(2 (N beta)) which holds for any 0 < beta < 1/2.

  • 244.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
    Rathi, Vishwambhar
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Polar codes for compress-and-forward in binary relay channels2010In: 44th Asilomar Conference on Signals, Systems and Computers, Asilomar 2010, IEEE conference proceedings, 2010, p. 1743-1747Conference paper (Refereed)
    Abstract [en]

    We construct polar codes for binary relay channels with orthogonal receiver components. We show that polar codes achieve the cut-set bound when the channels are symmetric and the relay-destination link supports compress-and-forward relaying based on Slepian-Wolf coding. More generally, we show that a particular version of the compress-and-forward rate is achievable using polar codes for Wyner-Ziv coding. In both cases the block error probability can be bounded as O(2-Nβ) for 0 < β < 1/2 and sufficiently large block length N.

  • 245.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
    Bandwidth efficient compress-and-forward relaying based on joint source-channel coding2011In: 2011 IEEE Wireless Communications and Networking Conference, WCNC 2011, IEEE conference proceedings, 2011, p. 1800-1804Conference paper (Refereed)
    Abstract [en]

    We propose a new code design for compress-and-forward relaying over bandlimited relay-to-destination channels. The main contribution of this paper is a code design based on joint (source-channel) coding and modulation that uses the correlation between the observations at the relay and the destination as protection against channel errors. This allows for relay nodes with reduced complexity, shifting most of the processing requirements to the destination node. Moreover, by using scalar quantizers with an entropy constraint our system provides remarkable performance in channel conditions where neither amplify-and-forward nor compress-and-forward efficiently exploit the presence of a relay node. Simulation results confirm the benefits of our proposed system.

  • 246.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Communication and interference coordination2014In: 2014 Information Theory and Applications Workshop, ITA 2014 - Conference Proceedings, IEEE conference proceedings, 2014, p. 6804218-Conference paper (Refereed)
    Abstract [en]

    We study the problem of controlling the interference created to an external observer by a communication processes. We model the interference in terms of its type (empirical distribution), and we analyze the consequences of placing constraints on the admissible type. Considering a single interfering link, we characterize the communication-interference capacity region. Then, we look at a scenario where the interference is jointly created by two users allowed to coordinate their actions prior to transmission. In this case, the tradeoff involves communication and interference as well as coordination. We establish an achievable communication-interference region and show that efficiency is significantly improved by coordination.

  • 247.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Compress-and-forward relaying based on symbol-wise joint source-channel coding2010In: IEEE International Conference on Communications, IEEE conference proceedings, 2010, p. 1-5Conference paper (Refereed)
    Abstract [en]

    We propose a new compress-and-forward implementation for the relay channel based on joint source-channel coding techniques. The relay performs scalar quantization of its observation in combination with a redundant index mapping. Our system utilizes the correlation between the quantized signal and the direct-link observation of the transmitted symbols as redundancy for error protection on the relay-to-destination link. In order to fully exploit this correlation the destination requires iterative decoding to recover the quantized observation sent by the relay. Once regenerated, this quantized signal is optimally combined with the direct-link observation to decode the message conveyed by the source. By quantizing the observed signal itself rather than a measure on the reliability of the information bits (e.g. a posteriori probabilities from a decoder), and by using digital communication methods on the relay-to-destination link our system yields superior performance to that of amplify-and-forward, decode-and-forward and previous implementations of compress-and-forward based on soft decoding.

  • 248.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Polar Codes for Coordination in Cascade Networks2012In: International Zurich Seminar on Communications: February 29-March 2, 2012, Sorell Hotel Zürichberg, Zurich, Switzerland proceedings, Zürich: Eidgenössische Technische Hochschule Zürich , 2012, p. 55-58Conference paper (Refereed)
    Abstract [en]

    We consider coordination in cascade networks and construct sequences of polar codes that achieve any point in a special region of the empirical coordination capacity region. Our design combines elements of source coding to generate actions with the desired type with elements of channel coding to minimize the communication rate. Moreover, we bound the probability of malfunction of a polar code for empirical coordination. Possible generalizations and open problems are discussed.

  • 249.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Ericsson Research.
    Zachariah, Dave
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Division of Systems and Control. Division of Systems and Control. Uppsala University.
    Sundman, Dennis
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Measurement Rate-MSE Tradeoff for Compressive Sensing Through Partial Support Recovery2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 18, p. 4643-4658Article in journal (Refereed)
    Abstract [en]

    We study the fundamental relationship between two relevant quantities in compressive sensing: the measurement rate, which characterizes the asymptotic behavior of the dimensions of the measurement matrix in terms of the ratio m/ log n (m being the number of measurements and n the dimension of the sparse signal), and the mean square estimation error. First, we use an information-theoretic approach to derive sufficient conditions on the measurement rate to reliably recover a part of the support set that represents a certain fraction of the total signal power when the sparsity level is fixed. Second, we characterize the mean square error of an estimator that uses partial support set information. Using these two parts, we derive a tradeoff between the measurement rate and the mean square error. This tradeoff is achievable using a two-step approach: first support set recovery, then estimation of the active components. Finally, for both deterministic and random signals, we perform a numerical evaluation to verify the advantages of the methods based on partial support set recovery.

  • 250.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zachariah, Dave
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sundman, Dennis
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    An Achievable Measurement Rate-MSE Tradeoff in Compressive Sensing Through Partial Support Recovery2013In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New York: IEEE , 2013, p. 6426-6430Conference paper (Refereed)
    Abstract [en]

    For compressive sensing, we derive achievable performance guarantees for recovering partial support sets of sparse vectors. The guarantees are determined in terms of the fraction of signal power to be detected and the measurement rate, defined as a relation between the dimensions of the measurement matrix. Based on this result we derive a tradeoff between the measurement rate and the mean square error, and illustrate it by a numerical example.

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