NDLI: Hard Fairness Versus Proportional Fairness in Wireless Communications: The Single-Cell Case

Content Provider	IEEE Xplore Digital Library
Author	Caire, G. Muller, R.R. Knopp, R.
Copyright Year	1963
Abstract	We consider a wireless communication system formed by a single cell with one base station and K user terminals. User channels are characterized by frequency-selective fading due to small-scale effects, modeled as a set of M parallel block-fading channels, and a frequency-flat distance-dependent path loss. We compare delay-limited systems with variable-rate systems under fairness constraints, in terms of the achieved system spectral efficiency C (bit/s/Hz) versus E_b/N₀. The considered delay-limited systems impose "hard-fairness": every user transmits at its desired rate on all blocks, independently of its fading conditions. The variable-rate system imposes "proportional fairness" via the popular Proportional Fair Scheduling (PFS) algorithm, currently implemented in 3G wireless for data (delay-tolerant) applications. We find simple iterative resource allocation algorithms that converge to the optimal delay-limited throughput for orthogonal (frequency-division multiple access (FDMA)/time-division multiple access (TDMA)) and optimal (superposition/interference cancellation) signaling. In the limit of large K and finite M we find closed-form expressions for C as a function of E_b/N₀. We show that in this limit, the optimal allocation policy consists of letting each user transmit on its best subchannel only. Also, we find a simple closed-form expression for the throughput of PFS in a cellular environment, that holds for any K and M. Finally, we obtain closed-form expressions for C versus E_b/N ₀ in the low and high spectral efficiency regimes. The conclusions of our analysis in terms of system design guidelines are as follows: a) if hard fairness is a requirement, orthogonal access incurs a large throughput penalty with respect to the optimal (superposition coding) strategy, especially in the regime of high spectral efficiency; b) for high spectral efficiency, PFS does not provide any significant gain and may even perform worse than the optimal delay-limited system, despite the fact that the imposed fairness constraint is laxer; c) for low to moderate spectral efficiency, the stricter hard-fairness constraint incurs in a large throughput penalty with respect to PFS
Sponsorship	IEEE Information Theory Society
Starting Page	1366
Ending Page	1385
Page Count	20
File Size	722050
File Format	PDF
ISSN	00189448
Volume Number	53
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-04-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Wireless communication Throughput Delay systems Closed-form solution Frequency Fading Iterative algorithms Base stations Scheduling algorithm Resource management uplink–downlink duality Code-division multiple access (CDMA) delay- limited capacity proportional fair scheduling
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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