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The MISO Interference Channel as a Model for Non-Orthogonal Spectrum Sharing
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The demand for wireless communications services has increased during the last decades. To meet this demand, there is a need for allocating larger frequency bands. However, most of the frequency bands (or spectrum) suitable for wireless communication are occupied and allocated to licensed systems. Long-term (order of years) contracts enforce the operators to use separate bands. Also, within an operator, neighboring cells have used separate frequency bands to avoid causing interference to each others' mobile users. The drawback of such operation is low spectral efficiency due to unused spectrum and low flexibility in the allocation of resources for the mobile users. To overcome these problems, so-called spectrum sharing has been proposed. The idea is that different operators (inter-operator spectrum sharing) or neighboring cells (intra-operator spectrum sharing) can borrow spectral resources from each other for short time frames (order of milliseconds). For each of these spectrum sharing scenarios, we can use either orthogonal or non-orthogonal spectrum sharing.

In orthogonal spectrum sharing, the operator that borrows the spectrum can use it exclusively. Hence, the operators will not cause interference to each others users. The drawback with orthogonal sharing is that it might not exploit all degrees of freedom or diversity in the wireless channels. In non-orthogonal spectrum sharing, two or more operators or neighboring cells of one operator, simultaneously use the same piece of spectrum at a given physical location. One drawback of such sharing is that the operators or base stations cause interference to each others' users. This can substantially degrade the performance of the mobile users. On the other hand, the flexibility increases and we can potentially increase the number of served users or the data rate of the users with non-orthogonal sharing.

In this thesis, we focus on the downlink of the non-orthogonal spectrum sharing scenario. We use the interference channel (IC) as a model to understand the impact of the interference and how the operations can be coordinated. An IC consists of $K$ transmitter (TX)-receiver (RX) pairs, e.g., base station-mobile user pairs, where each TX serves one RX. Since the TX-RX pairs operate simultaneously in the same frequency band, they causeinterference to each other. To suppress the interference, we can employ multiple antennas at the TXs. Then, the TXs are able to steer, or beamform, the radiated power such that they provide the intended RXs with strong signals and cause weak interference to the unintended RXs. The IC with multiple-antennas TXs and single-antenna RXs constitutes a multiple-input single-output (MISO) IC.

In the first part of this thesis, we gain understanding of the fundamental performance limits of the two-user MISO IC, i.e., there are two TX-RX pairs. We study various achievable rate regions and methods for computing them. The first contribution is on efficient computation of the outer boundary of the rate region when the TXs have instantaneous channel state information (CSI) and the receivers are capable to perform successive interference cancellation. We split the problem in to the four subproblems corresponding to the different combinations of decoding strategies (decode interference or treat it as noise). The optimization problems we solve are scalar and quasi-concave and can be solved either on closed form or by a numerical gradient ascend method. The second contribution is on the ergodic rate region with statistical CSI. We characterize the transmit covariance matrices which potentially yield points on the outer boundary of the rate region. Using these characterizations, we can reduce the search space in the design of the optimal transmit covariance matrices. The third contribution considers a slow-fading channel and provides four different definitions of outage rate regions. These definitions depend on whether there is instantaneous or statistical CSI and whether outage is declared individually or in common. In the two latter contributions, the RXs treat interference as noise.

The second part of this thesis addresses the resource allocation problem in a small cellular network. The first contribution considers the inter-operator spectrum sharing problem in a single cell. The results illustrate that if user selection is not possible and there are always users to serve for both operators, there is no gain of non-orthogonal spectrum sharing over orthogonal sharing. For the same setup, the second contribution considers the user selection problem. The base stations select one user each to serve. The computational complexity of optimal user selection is high. Therefore, we propose to use simple beamforming schemes in order to select a user pair. Once a pair is chosen, we use optimal beamforming. The performance loss of this algorithm, compared to using optimal beamforming vectors for the scheduling is negligible.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. , 50 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1555
National Category
Communication Systems
Identifiers
URN: urn:nbn:se:liu:diva-100820DOI: 10.3384/diss.diva-100820ISBN: 978-91-7519-478-3 (print)OAI: oai:DiVA.org:liu-100820DiVA: diva2:663764
Public defence
2014-01-27, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Opponent
Supervisors
Available from: 2013-11-27 Created: 2013-11-12 Last updated: 2016-12-22Bibliographically approved
List of papers
1. Efficient Computation of Pareto Optimal Beamforming Vectors for the MISO Interference Channel with Successive Interference Cancellation
Open this publication in new window or tab >>Efficient Computation of Pareto Optimal Beamforming Vectors for the MISO Interference Channel with Successive Interference Cancellation
2013 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 19, 4782-4795 p.Article in journal (Refereed) Published
Abstract [en]

We study the two-user multiple-input single-output (MISO) Gaussian interference channel where the transmitters have perfect channel state information and employ single-stream beamforming. The receivers are capable of performing successive interference cancellation, so when the interfering signal is strong enough, it can be decoded, treating the desired signal as noise, and subtracted from the received signal, before the desired signal is decoded. We propose efficient methods to compute the Pareto-optimal rate points and corresponding beamforming vector pairs, by maximizing the rate of one link given the rate of the other link. We do so by splitting the original problem into four subproblems corresponding to the combinations of the receivers' decoding strategies-either decode the interference or treat it as additive noise. We utilize recently proposed parameterizations of the optimal beamforming vectors to equivalently reformulate each subproblem as a quasi-concave problem, which we solve very efficiently either analytically or via scalar numerical optimization. The computational complexity of the proposed methods is several orders-of-magnitude less than the complexity of the state-of-the-art methods. We use the proposed methods to illustrate the effect of the strength and spatial correlation of the channels on the shape of the rate region.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2013
Keyword
Beamforming, interference channel, interference cancellation, multiple-input single-output (MISO), Pareto boundary, Pareto optimality, rate region.
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-93845 (URN)10.1109/TSP.2013.2271748 (DOI)000324342900012 ()
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research eLLIIT - The Linköping‐Lund Initiative on IT and Mobile CommunicationsEU, FP7, Seventh Framework Programme, 248001
Available from: 2013-06-11 Created: 2013-06-11 Last updated: 2017-12-06
2. Parameterization of the MISO IFC Rate Region: The Case of Partial Channel State Information
Open this publication in new window or tab >>Parameterization of the MISO IFC Rate Region: The Case of Partial Channel State Information
2010 (English)In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 9, no 2, 500-504 p.Article in journal (Refereed) Published
Abstract [en]

We study the achievable rate region of the multiple-input  single-output (MISO) interference channel (IFC), under the  assumption that all receivers treat the interference as additive  Gaussian noise. We assume the case of two users, and that the  channel state information (CSI) is only partially known at the  transmitters. Our main result is a characterization of  Pareto-optimal transmit strategies, for channel matrices that  satisfy a certain technical condition. Numerical examples are  provided to illustrate the theoretical results.

Keyword
Ergodic rate region, interference channel, multiple-input single-output channel, multistream transmission, Pareto optimality
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-52178 (URN)10.1109/TWC.2010.02.081371 (DOI)000274383100004 ()
Note
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible ©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Johannes Lindblom, Erik G. Larsson and Eduard A. Jorswieck, Parameterization of the MISO IFC Rate Region: The Case of Partial Channel State Information, 2010, IEEE Transactions on Wireless Communications. http://dx.doi.org/10.1109/TWC.2010.02.081371 Available from: 2009-12-08 Created: 2009-12-08 Last updated: 2017-12-12
3. Selfishness and Altruism on the MISO Interference Channel: The Case of Partial Transmitter CSI
Open this publication in new window or tab >>Selfishness and Altruism on the MISO Interference Channel: The Case of Partial Transmitter CSI
2009 (English)In: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 13, no 9, 667-669 p.Article in journal (Refereed) Published
Abstract [en]

We study the achievable ergodic rate region of the two-user multiple-input single-output interference channel, under the assumptions that the receivers treat interference as additive Gaussian noise and the transmitters only have statistical channel knowledge. Initially, we provide a closed-form expression for the ergodic rates and derive the Nash-equilibrium and zero-forcing transmit beamforming strategies. Then, we show that combinations of the aforementioned selfish and altruistic, respectively, strategies achieve Pareto-optimal rate pairs.

Keyword
Beamforming, ergodic rate region, game theory, interference channel, Pareto optimality
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-21518 (URN)10.1109/LCOMM.2009.090970 (DOI)
Note
©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Johannes Lindblom, Eleftherios Karipidis and Erik G. Larsson, Selfishness and Altruism on the MISO Interference Channel: The Case of Partial Transmitter CSI, 2009, IEEE Communications Letters, (13), 9, 667-669. http://dx.doi.org/10.1109/LCOMM.2009.090970 Available from: 2009-10-02 Created: 2009-10-02 Last updated: 2017-12-13
4. Achievable Outage Rate Regions for the MISO Interference Channel
Open this publication in new window or tab >>Achievable Outage Rate Regions for the MISO Interference Channel
2013 (English)In: IEEE Wireless Communications Letters, ISSN 2162-2337, E-ISSN 2162-2345, Vol. 2, no 4, 439-442 p.Article in journal (Refereed) Published
Abstract [en]

We consider the slow-fading two-user multiple-input single-output (MISO) interference channel. We want to understand which rate points can be achieved, allowing a non-zero outage probability. We do so by defining four different outage rate regions. The definitions differ on whether the rates are declared in outage jointly or individually and whether the transmitters have instantaneous or statistical channel state information (CSI). The focus is on the instantaneous CSI case with individual outage, where we propose a stochastic mapping from the rate point and the channel realization to the beamforming vectors. A major contribution is that we prove that the stochastic component of this mapping is independent of the actual channel realization.

Place, publisher, year, edition, pages
IEEE Communications Society, 2013
Keyword
Achievable rate region, beamforming, interference channel, MISO, outage probability
National Category
Communication Systems
Identifiers
urn:nbn:se:liu:diva-91840 (URN)10.1109/WCL.2013.051513.130186 (DOI)000209696800019 ()
Funder
EU, FP7, Seventh Framework Programme, 248001ELLIIT - The Linköping‐Lund Initiative on IT and Mobile CommunicationsSwedish Foundation for Strategic Research Swedish Research Council
Note

At the time for thesis presentation publication was in status: Manuscript

Available from: 2013-05-02 Created: 2013-05-02 Last updated: 2017-12-06Bibliographically approved
5. Does non-orthogonal spectrum sharing in the same cell improve the sum-rate of wireless operators?
Open this publication in new window or tab >>Does non-orthogonal spectrum sharing in the same cell improve the sum-rate of wireless operators?
2012 (English)In: Proceedings of the 13th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2012, 6-10 p.Conference paper, Published paper (Refereed)
Abstract [en]

We study non-orthogonal spectrum sharing to determine under what circumstances operators can gain by such sharing. To model the spectrum sharing, we use the multiple-input single-output (MISO) interference channel (IC) assuming that the operators transmit in the same band. For the baseline scenario of no sharing, we use the MISO broadcast channel (BC) assuming that the operators transmit in disjunct bands. For both the IC and BC, we give achievable (lower) and upper bounds on the maximum sum-rate. While these bounds are well-known we also propose a new fast algorithm for finding a lower bound on the sum-rate of the BC using linear beamforming.

We use the bounds to numerically evaluate the potential gain of non-orthogonal spectrum sharing. In this study we assume that the operators efficiently utilize all their spatial degrees of freedom. We will see that the gains from spectrum sharing under these circumstances are limited.

National Category
Communication Systems Telecommunications
Identifiers
urn:nbn:se:liu:diva-76729 (URN)10.1109/SPAWC.2012.6292981 (DOI)000320276200002 ()978-1-4673-0970-7 (ISBN)978-1-4673-0969-1 (ISBN)978-1-4673-0971-4 (ISBN)
Conference
The 13th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 17 Jun - 20 Jun 2012, Cesme, Turkey
Funder
eLLIIT - The Linköping‐Lund Initiative on IT and Mobile CommunicationsKnut and Alice Wallenberg FoundationSwedish Research CouncilEU, FP7, Seventh Framework Programme, 248001
Available from: 2012-04-18 Created: 2012-04-18 Last updated: 2016-08-31
6. Joint User Selection and Beamforming Schemes for Inter-Operator Spectrum Sharing
Open this publication in new window or tab >>Joint User Selection and Beamforming Schemes for Inter-Operator Spectrum Sharing
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We consider the downlink of an inter-operator spectrum sharing scenario where two operators share the same piece of spectrum and use it simultaneously. A base station of one operator cooperates with a base station of the other operator in order perform joint user selection and beamforming using a central unit. Optimal scheduling, in the sense of maximizing sum-rate or proportional fairness, is in many cases impractical due to high computational complexity. Therefore, we propose a heuristic algorithm that schedules users based on simple beamforming techniques. Once the users are scheduled, we compute the optimal beamforming vectors for them. This method still performs an exhaustive user search. Therefore, we also propose a greedy user selection scheme. From numerical evaluations, we notice that these schemes perform close to the optimal selection. Also, we use our proposed methods to identify when spectrum sharing provides extra gains over the non-sharing scenario.

Keyword
Beamforming, spectrum sharing, user selection
National Category
Engineering and Technology Communication Systems
Identifiers
urn:nbn:se:liu:diva-100813 (URN)
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research ELLIIT - The Linköping‐Lund Initiative on IT and Mobile Communications
Note

This manuscript will not be published.

Available from: 2013-11-12 Created: 2013-11-12 Last updated: 2017-01-13Bibliographically approved

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