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Efficient Computation of Pareto Optimal Beamforming Vectors for the MISO Interference Channel with Successive Interference Cancellation
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7599-4367
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. Vol. 61, no 19, 4782-4795 p.
Keyword [en]
Beamforming, interference channel, interference cancellation, multiple-input single-output (MISO), Pareto boundary, Pareto optimality, rate region.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-93845DOI: 10.1109/TSP.2013.2271748ISI: 000324342900012OAI: diva2:627150
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: 2016-08-31
In thesis
1. The MISO Interference Channel as a Model for Non-Orthogonal Spectrum Sharing
Open this publication in new window or tab >>The MISO Interference Channel as a Model for Non-Orthogonal Spectrum Sharing
2014 (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, 2014. 50 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1555
National Category
Communication Systems
urn:nbn:se:liu:diva-100820 (URN)10.3384/diss.diva-100820 (DOI)978-91-7519-478-3 (print) (ISBN)
Public defence
2014-01-27, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Available from: 2013-11-27 Created: 2013-11-12 Last updated: 2016-08-31Bibliographically approved

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