IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 3, APRIL 2012 561 Throughput Optimization, Spectrum Allocation, and Access Control in Two-Tier Femtocell Networks Wang Chi Cheung, Student Member, IEEE, Tony Q. S. Quek, Member, IEEE, and Marios Kountouris, Member, IEEE Abstract—The deployment of femtocells in a macrocell net- work is an economical and effective way to increase network capacity and coverage. Nevertheless, such deployment is challeng- ing due to the presence of inter-tier and intra-tier interference, and the ad hoc operation of femtocells. Motivated by the flexible subchannel allocation capability of OFDMA, we investigate the effect of spectrum allocation in two-tier networks, where the macrocells employ closed access policy and the femtocells can operate in either open or closed access. By introducing a tractable model, we derive the success probability for each tier under different spectrum allocation and femtocell access policies. In particular, we consider joint subchannel allocation, in which the whole spectrum is shared by both tiers, as well as disjoint subchannel allocation, whereby disjoint sets of subchannels are assigned to both tiers. We formulate the throughput maximiza- tion problem subject to quality of service constraints in terms of success probabilities and per-tier minimum rates, and provide insights into the optimal spectrum allocation. Our results indicate that with closed access femtocells, the optimized joint and disjoint subchannel allocations provide the highest throughput among all schemes in sparse and dense femtocell networks, respectively. With open access femtocells, the optimized joint subchannel allocation provides the highest possible throughput for all femtocell densities. Index Terms—Femtocell network, OFDMA, downlink, spec- trum allocation, throughput optimization, access control, stochas- tic geometry I. I NTRODUCTION T WO-tier femtocell networks, which consist of a macro- cell network overlaid with femtocell access points (FAPs), are under intense study due to their improved coverage and enhanced data rates. In conventional single-tier networks, the macrocell base stations (MBSs) have to cater for the needs of both outdoor and indoor users, which leads to poor indoor coverage and the appearance of dead spots [1]–[3]. In contrast, by deploying FAPs, indoor users can enjoy high- quality wireless services from their designated FAPs in close proximity, and outdoor users can experience higher capacity Manuscript received 1 March 2011; revised 25 August 2011. The material in this paper has been presented in part at the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Prague, Czech, May 2011, and at the IEEE Wireless Communications and Networking Conference (WCNC), Paris, France, April 2012. W. C. Cheung was with the Institute for Infocomm Research. He is now with the Operations Research Center, Massachusetts Institute of Tech- nology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA (e-mail: wangchi@mit.edu). T. Q. S. Quek is with the Institute for Infocomm Research, A ∗ STAR, 1 Fusionopolis Way, #21-01 Connexis South Tower, Singapore 138632 (e-mail: qsquek@ieee.org). M. Kountouris is with SUPELEC (Ecole Sup´ erieure d’Electricit´ e), Gif-sur- Yvette, France (e-mail: marios.kountouris@supelec.fr). Digital Object Identifier 10.1109/JSAC.2012.120406. gains due to traffic offload by FAPs through the backhaul. Moreover, FAPs have the economical advantage of being less costly to be manufactured and maintained than MBSs. Thus, femtocells are a promising and cost effective pathway to cater for the ever increasing appetite for high data-rate wireless applications in the near future. Nevertheless, one of the major challenges in deploying femtocells is the incursion of inter-tier interference due to aggressive frequency reuse, which can deteriorate the effec- tiveness of femtocell architecture. When both tiers share the whole spectrum, indoor user communication is hindered by interference from undesignated FAPs as well as MBSs, and the same holds for outdoor users. This problem is further exacerbated by the random deployment of FAPs, being often installed and controlled by their subscribed users, thus making centralized interference management not viable. These diffi- culties sparked off a significant amount of research on a variety of interference management schemes for two-tier femtocell networks, such as power control [4]–[6], multiple antennas [7]–[9], adaptive FAP access scheme [10]–[12], cognitive radio [13], [14], and spectrum allocation [15]–[18]. In this work, we study a femtocell-aided macrocell network using stochastic geometric tools, and quantify the effect of both spectrum allocation and closed/open access policies on the link reliability of each tier and on the total network throughput. The whole spectrum is partitioned into equal and consecutive orthogonal suchannels via orthogonal frequency- division multiple access (OFDMA), and we study the effect of subchannel allocation on each tier. We focus on two common types of allocations, namely disjoint subchannel allocation, where the two tiers are assigned disjoint sets of subchannels, and joint subchannel allocation, where the two tiers share the whole spectrum. For each subchannel allocation scheme, we also investigate the effect of closed and open access FAPs. When femtocells are configured as closed access, each FAP is only accessible by its femtocell users. When they are configured as open access, a FAP could be accessed by both its users and all cochannel macrocell users. Here, we quantify the enhancement in macrocell user’s link reliability when it can hand over its communication from its closest MBS to its closest FAP under the condition that the FAP is sufficiently near, and we also analyze its benefits to the network throughput under optimal joint allocation scheme. A. Related Work Interference modeling in two-tier networks using stochas- tic geometry has gathered considerable attention due to its 0733-8716/12/$25.00 c  2012 IEEE