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On the Complexity of Maximizing the Minimum Shannon Capacity by Joint Cell, Channel and Power Allocation in Wireless Communication Networks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We consider wireless telecommunications systems with orthogonal frequency bands, where each band is referred to as a channel, e.g., Orthogonal Frequency-Division Multiple Access (OFDMA). For a given snap-shot in time, the joint cell, channel and power allocation optimization problem is presented, both in downlink and in uplink. The objective is to maximize the minimum total Shannon capacity of any mobile user in the system, subject to system constraints. The corresponding decision problems are proved to be NP-hard. We also show that for any constant ρ > 0, a sufficiently large number of channels ensure that the optimization problems are not ρ-approximable, unless P is equal to NP. Furthermore, we show that the inapproximability property remains when solely considering the power allocation problem, i.e., given a feasible cell and channel allocation. This power allocation optimization problem is not convex in general, but in the simplified setting where each transmitter is allowed to use only one single channel, there exists known approaches to attain the global optimum. In this setting, we prove that any solution that fulfills the KKT conditions is a global optimum.

National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-40400OAI: oai:DiVA.org:kth-40400DiVA: diva2:441086
Note
Condensed version published in IEEE International Workshop on Quality of Service QC 20110914Available from: 2011-09-14 Created: 2011-09-14 Last updated: 2011-09-15Bibliographically approved
In thesis
1. Optimization of Joint Cell, Channel and Power Allocation in Wireless Communication Networks
Open this publication in new window or tab >>Optimization of Joint Cell, Channel and Power Allocation in Wireless Communication Networks
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we formulate joint cell, channel and power allocation problems within wireless communication networks. The objectives are to maximize the user with mini- mum data throughput (Shannon capacity) or to maximize the total system throughput, referred to as the max-min and max-sum problem respectively. The complexity is stud- ied together with proposed optimization- and heuristic-based approaches.

In the first paper an overall joint cell, channel and power allocation max-min prob- lem is formulated. We show that the decision problem is NP-hard and that the op- timization problem is not approximable unless P is equal to NP, for instances with a sufficiently large number of channels. Further, it follows that for a feasible binary cell and channel allocation, the remaining continuous power allocation optimization problem is still not approximable unless P is equal to NP. In addition, it is shown that first-order optimality conditions give global optimum of the single channel power al- location optimization problem, although the problem is in general not convex.

In the following two papers heuristics for solving the overall problem are proposed. In the second paper we consider the single channel problem with convex combinations of the max-min and the max-sum objective functions. This variable utility provides the ability of tuning the amount of fairness and total throughput. The third paper investi- gates the multiple channel setting. On a system with three cells, eight mobile users and three channels, we perform an exhaustive search over feasible cell and channel alloca- tions. The exhaustive search is then compared to the less computationally expensive heuristic approaches, presenting potential earnings to strive for. A conclusion is that several of the proposed heuristics perform very well.

The final paper incorporates fixed relay stations into the overall joint cell, channel and power allocation max-min problem. The complexity is inherited from the formula- tion without relay stations. Further, we propose a heuristic channel allocation approach that shows good performance, compared to an optimization based approach, in numer- ical simulations on the relay setting.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. xxiv, 20 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 11:05
Keyword
Wireless multicell networks, Optimization, OFDMA, Shannon capacity, Complexity, NP-hard, Relays, Allocation problems, Heuristic algorithms
National Category
Computational Mathematics Communication Systems Telecommunications
Identifiers
urn:nbn:se:kth:diva-40274 (URN)978-91-7501-084-7 (ISBN)
Public defence
2011-10-07, D3, Lindstedtsvägen 5, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
Financial support by the Swedish Foundation for Strategic Research (SSF) QC 20110915Available from: 2011-09-15 Created: 2011-09-14 Last updated: 2011-09-15Bibliographically approved

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Citation style
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