Downlink Resource Allocation in Multi-Carrier Systems: Frequency-Selective vs. Equal Power Allocation Hyang-Won Lee and Song Chong School of EECS, KAIST, Daejeon, Korea mslhw@netsys.kaist.ac.kr, songgee.kaist.ac.kr Abstract-In this paper, dynamic subcarrier and power al- allocation in OFDM systems [2]-[6]1. Their objectives are location problem is considered in the context of asymptotic to maximize total throughput or utility, or to minimize total utility maximization in multi-carrier systems. Using gradient- transmit power subject to rate and power constraints. Such a based resource allocation, we formulate an optimization problem involving subcarrier and transmit power allocation for each time snap-shot approach is quite suitable for short-term guarantee, slot, and propose an optimal algorithm solving the problem. but it has some limitations in long-term sense. First, it can Since the optimal algorithm is impractical due to its complexity, seriously degrade the efficiency of the system due to its limited a simple suboptimal algorithm is also proposed based on gen- flexibility in resource allocation. In the framework, a resource eralized Benders decomposition. Furthermore, we identify the allocation is enforced to satisfy all the requirements and to performance of equal power allocation policy by showing that achieve optimality at each time slot. Consequently, all the users equal power allocation is not always near optimal in general reqe shulmelere ateach slot evers utility maximization problem and characterizing the optimality requiring some guarantee should be served at each slot even if condition of equal power allocation. This result not only justifies some of them are under bad channel condition. This restriction the use of our dynamic power allocation, but also generalizes leads to the decrease of system capacity. Second, in line with the performance of equal power allocation, which is well-known the first one, the computational complexity of the resource to be approximately optimal to the sum capacity maximization allocation algorithm developed from the framework could be problem in high SNR (signal-to-noise ratio) regime. Our algo- inevitably high b eveloped soluthe m e obtaine rithms and analysis are verified through extensive simulations. inevitably high because the optimal solution must be obtained at each time slot. In contrast, long-term approach focuses on optimizing the I. INTRODUCTION asymptotic system performance. The resource allocation in this framework may not be optimal at each time slot, but it As the demand for high data rates over wireless networks in- t creases, most of wireless standards such as IEEE 802.11/16/20 eventually achieves the asymptotic optimality. Obviously, this have adopted OFDM (orthogonal frequency division multi- approach permits higher degree of flexibility in allocating the plexing) technology due to its high degree of flexibility and resource, so it opens up the possibility for improving the long- predominant performance over other air interface technologies, term system performance and reducing the complexity of the multi-carrier algorithm performed at each time slot. The PF (proportional Accodingy, te reoure alocaton poble infair) scheduling [7], proposed for Qualcomm's HDR (high systems has become a very important issue and attracted many far ceuig[] rpsdfrQacm' D hg systarhems. Thasb e aiffvery impotalint wishsuecdatratedmay i data rate) system, typically reflects this philosophy. In fact, the resarchers. Thae difficultyaindeauslicongtw suciprblemeso es, PF scheduling is a special case of gradient-based scheduling, that we have to simltaneously controlmultiple resources which selects the achievable data rate vector whose projection e.g., subcarrier, power and bit, considering wireless channel . . . conditions. onto the gradient of the aggregate network utility becomes maximal. The gradient-based scheduling can be regarded as One way to address the problem is snap-shot approach findi. The gratevtor maximizing the su oeghted in which the resource allocation is developed through an rates wherete weitsr margina ties. It hasgbee optimization problem defined for fixed channel gain and is applied to time-varying channels. In [1], Wong et al. solve the proved in several researches [8]-[10] that such a gradient- total transmit power minimization problem with rate and BER based scheduling maximizes the aggregate utility over the long-term throughput region. (bit error rate) requirement constraints and propose an adap- Bynusingtheogradient tivesubaffer,bitandpowr alocaionschme n mltiser By using the gradient-based scheduling, Huang et al. define ive subcarrier, bit and power allocaion scheme in muliuser . . i OFDM systems. Since their pioneering work, there have been aloniksbare adpwralcto poleinOD several related works that take snap-shot approach for resource sses[1.Te dp h N-aemdlfo 1]t impose concavity in the problem. Their model iS roughly inter- This work was supported by the center for Broadband OFDM Mobile Access (BrOMA) at POSTECH through the ITRC program of the Korean 1I should be noted that [6] also addresses the long-term optimal resource MIC, supervised by JITA (IITA-2006-C1090-0603-0037). allocation by means of time diversity. 1-4244-0992-6/07/$25.00 © 2007 IEEE