IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 60, NO. 1, JANUARY 2012 415 On the Rate Gap Between Multi- and Single-Cell Processing Under Opportunistic Scheduling Hans Jørgen Bang, David Gesbert, Fellow, IEEE, and Pål Orten Abstract—Base station (BS) coordination is a key technique to handle intercell interference (ICI) in cellular networks. Nev- ertheless, recent work on scheduling indicates that the value of coordination is less prominent when the number of users grows large. More specifically, the loss in sum rate due to ICI in unco- ordinated networks can be made arbitrarily small as the number of users goes to infinity. However, the gap in performance for a finite number of users has remained unknown so far. From this perspective we study the gains of multicell zero-forcing beam- forming (ZFBF) on the downlink of a Wyner-type network. We first identify the beamforming weights and the optimal scheduling policy under a per-base power constraint. To compare ZFBF with single-cell processing (SCP) we focus on the extra number of users that is needed per cell to compensate for ICI. Specifically, we find the number of users with ZFBF and with SCP that gives the same mean postscheduling signal-to-interference-plus-noise ratio (SINR) as an interference free network with users. The results show that the ratio grows logarithmically with . Finally, we demonstrate that the difference in sum-rate between SCP and multicell ZFBF goes to zero as . As a consequence of the slow convergence there is a significant gain with multicell ZFBF for all practical numbers of users. Index Terms—Base station (BS) coordination, multiuser sched- uling, zero-forcing beamforming (ZFBF). I. INTRODUCTION I N conventional cellular systems signal transmission and re- ception are done independently on a per-cell basis. This may result in considerable intercell interference (ICI) which will ultimately limit the capacity. However, by interconnecting the base station (BSs) and coordinating their actions the ICI can be greatly reduced [1], [2]. A key driver for practical deployment of BS coordination is that the main complexity burden is on the network side and not the mobile users. Recently there has been much work on the information theoretic nature of coordinated networks [3], [4]. In the ideal case, the downlink can be viewed as vector broadcast channel Manuscript received September 02, 2010; revised June 01, 2011; accepted September 09, 2011. Date of publication October 06, 2011; date of current ver- sion December 16, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Ye (Geoffrey) Li. The work of D. Gesbert was supported by the FP7 ARTIST4G project. This work was presented in part at SPAWC’2009PerugiaJune2009. H. J. Bang is with Elliptic Labs, Oslo 0473, Norway (e-mail: hans@ellipti- clabs.com). D. Gesbert is with the Eurécom Institute, Sophia Antipolis 06560, France (e-mail: david.gesbert@eurecome.fr). P. Orten is with UniK-University Graduate Center, University of Oslo, Oslo N-0317, Norway. He is also with ABB Corporate Research, Oslo, Norway (e-mail: porten@unik.no). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2011.2170681 in which dirty paper coding (DPC) is the capacity achieving strategy. Unfortunately, for many practical applications DPC is prohibitively complex. Suboptimal techniques with lower complexities such as linear precoding are therefore of great interest. In this paper, we consider BS coordination in the form of multicell zero-forcing beamforming (ZFBF). ZFBF is a well- known linear precoding technique that attempts to cancel all interference at the expense of a reduction in useful signal power. Even though ZFBF is suboptimal in the class of linear precoders it is known to incur little loss in the high signal-to-noise (SNR) regime or when the number of users is sufficiently high [5]. In the paper, we are particularly keen to compare the rate gap between ZFBF and single-cell processing (SCP) under muli- tuser scheduling. The reason for this is twofold. First of all, there is an inevitable increase in complexity with any BS coordination scheme relative to conventional SCP. To justify the use of BS co- ordination there must therefore be an accompanied gain in per- formance. Second, recent work on scheduling shows that there can be substantial gains in SCP networks with multiple fading users. Specifically, in [6] and [7] it was shown that the loss in sum-rate incurred by ICI can be made arbitrarily small as the number of users go infinity. In [8] the focus was on interbeam interference in single-cell beamforming. However, a reinterpre- tation of some quantities gives a similar conclusion. A corollary to these results is that the value of BS coordination will eventu- ally diminish as the number of users increases. Nevertheless, the implications of this asymptotic behavior for a moderate to large number of users depend crucially on the rate of convergence. The analytical study of BS coordination is notoriously dif- ficult. Previous works have therefore mainly resorted to net- work and interference model simplifications in order to obtain insights arising from closed-form expressions [3], [4], [9]–[11]. This will also be our approach here. Specifically, we assume a linear cell-array, where each user only receives a signal from the two closest BSs. This is a slight variation of Wyner’s clas- sical model introduced in [9]. Similar network and interference models were recently used in [3] and [4], with the exception that the cells were arranged on a circular array. However, this differ- ence is insignificant as the number of cells goes to infinity. In [3], the focus was on upper and lower bounds for the per- cell sum-rate under multicell DPC. In particular, the per-cell sum-rate was shown to scale as with the number of users per cell. In [4], the performances of several suboptimal network coordination strategies were characterized. However, no explicit expressions for ZFBF together with Rayleigh fading were given. In [10] ZFBF and multiuser scheduling were studied using a model where each user could see the three closest BSs. A suboptimal scheduling strategy was proposed and shown to 1053-587X/$26.00 © 2011 IEEE