342 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 1, JANUARY 2014 Joint Subchannel Assignment and Power Allocation for OFDMA Femtocell Networks Duy Trong Ngo, Suman Khakurel, Student Member, IEEE, Tho Le-Ngoc, Fellow, IEEE Abstract—In this paper, we propose a joint subchannel and power allocation algorithm for the downlink of an or- thogonal frequency-division multiple access (OFDMA) mixed femtocell/macrocell network deployment. Specifically, the total throughput of all femtocell user equipments (FUEs) is maximized while the network capacity of an existing macrocell is always protected. Towards this end, we employ an iterative approach in which OFDM subchannels and transmit powers of base stations (BS) are alternatively assigned and optimized at every step. For a fixed power allocation, we prove that the optimal policy in each cell is to give each subchannel to the user with the highest signal-to-interference-plus-noise ratio (SINR) on that subchannel. For a given subchannel assignment, we adopt the successive convex approximation (SCA) approach and transform the highly nonconvex power allocation problem into a sequence of convex subproblems. In the arithmetic-geometric mean (AGM) approximation, we apply geometric programming to find optimal solutions after condensing a posynomial into a monomial. On the other hand, logarithmic and d ifference-of-two-c oncave-functions (D.C.) approximations lead us to solving a series of convex relaxation programs. With the three proposed SCA-based power optimization solutions, we show that the overall joint subchannel and power allocation algorithm converges to some local maxi- mum of the original design problem. While a central processing unit is required to implement the AGM approximation-based solution, each BS locally computes the optimal subchannel and power allocation for its own servicing cell in the logarithmic and D.C. approximation-based solutions. Numerical examples confirm the merits of the proposed algorithm. Index Terms—Convex optimization, femtocell, heterogeneous networks, iterative algorithm, power allocation, macrocell QoS protection, subchannel assignment, successive convex approxima- tion. I. I NTRODUCTION D ENSE small-cell heterogeneous networks, i.e., femto- cells, have recently been promoted as an enabling so- lution to meet the ever increasing demand for ubiquitous wireless coverage and higher throughput [1]–[3]. With a large number of small cells, more active user equipments (UEs) can be packed into a given area in the same radio spectrum, Manuscript received April 13, 2013; revised August 9 and October 18, 2013; accepted October 19, 2013. The associate editor coordinating the review of this paper and approving it for publication was M. Elkashlan. This work is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) grants and the Alexander Graham Bell Canada Graduate Scholarship. Part of this paper was presented at the 2013 IEEE Vehicular Technology Conference (VTC-Spring’13), Dresden, Germany. D. T. Ngo is with the School of Electrical Engineering and Computer Science, the University of Newcastle, Callaghan, NSW 2308, Australia (e- mail: duy.ngo@newcastle.edu.au). D. T. Ngo is the corresponding author. S. Khakurel and T. Le-Ngoc are with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada H3A 0E9 (e-mail: suman.khakurel@mail.mcgill.ca; tho.le-ngoc@mcgill.ca). Digital Object Identifier 10.1109/TWC.2013.111313.130645 allowing for a greater area spectral efficiency. Installed by end- users in a plug-and-play fashion, femtocells are highly cost- effective since the traditional site survey and network planning process is no longer needed. Thanks to the close transmitter- receiver proximity, femtocells can lower their transmit power while achieving a high signal-to-interference-plus-noise ratio (SINR) for substantially improved indoor coverage. Moreover, significant data traffic originating from indoor environments can be offloaded from the existing macrocell to the newly deployed femtocells. Compared to the orthogonal deployment, cochannel de- ployment is more attractive in these heterogeneous network settings as it can offer a much higher spectral efficiency [4]– [6]. Here, the critical issue of signal interference arises as femtocell user equipments (FUEs) utilize the spectrum already allocated to the macrocell user equipments (MUEs) [7], [8]. It is therefore imperative to limit the cross-tier interference induced by FUEs to MUEs, who have a strictly higher priority in accessing the underlying frequency bands. If successful, the ongoing operation of existing MUEs can be protected, whilst the lower-tier FUEs exploit the residual network capacity beyond what is needed to support the quality-of-service (QoS) requirements of all MUEs [9], [10]. However, it remains very challenging to effectively manage the random and severe inter- ference resulting from the deployment of numerous unplanned small cells. Because of its flexibility in allocating the radio spectrum, orthogonal frequency-division multiple access (OFDMA) has been used as the air-interface technology by Long Term Evolution (LTE) femtocells, i.e., home evolved Node Bs (HeNBs) [11], [12]. With OFDMA, the intracell interference is eliminated thanks to the exclusive channel assignment, in which a subchannel is allotted to at most one UE in each cell at any given time. Nonetheless, cochannel deployment implies that an OFDM subchannel can be shared by UEs from different cells, giving rise to the intercell interference. Further- more, there is another source of technical difficulty here—the subchannel assignment problem which involves the allocation of the limited radio frequencies to different UEs in multiple cells. To directly solve this combinatorial problem, approaches with an exponential complexity are required. Therefore, the successful development of any resource allocation scheme for OFDMA-based femtocell networks certainly relies upon how one can effectively overcome such a difficult problem. In [13], the joint allocation of resource blocks and trans- mit powers is investigated for the downlink transmission of OFDMA-based femtocells. It is shown that the formulated exact-potential game always converges to a Nash equilibrium when a best-response adaptive strategy is applied. Also taking 1536-1276/14$31.00 c  2014 IEEE