IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 54, NO. 5, SEPTEMBER 2005 1773 OFDM Power Loading Using Limited Feedback David J. Love, Member, IEEE, and Robert W. Heath, Jr., Member, IEEE Abstract—Orthogonal frequency division multiplexing (OFDM) is a practical broadband signaling technique for use in multipath fading channels. Over the past ten years, research has shown that power loading, where the power allocations on the OFDM fre- quency tones are jointly optimized, can improve error rate or ca- pacity performance. The implementation of power loading, how- ever, is dependent on the presence of complete forward link channel knowledge at the transmitter. In systems using frequency division duplexing (FDD), this assumption is unrealistic. In this paper, we propose power loading for OFDM symbols using a limited num- ber of feedback bits sent from the receiver to the transmitter. The power loading vector is designed at the receiver, which is assumed to have perfect knowledge of the forward link channel, and con- veyed back to the transmitter over a limited rate feedback chan- nel. To allow for the vector to be represented by a small number of bits, the power loading vector is restricted to lie in a finite set, or codebook, of power loading vectors. This codebook is designed offline and known a priori to both the transmitter and receiver. We present two power allocation selection algorithms that opti- mize the probability of symbol error and capacity, respectively. Simulation results show that the proposed limited feedback tech- niques provide performance close to full channel knowledge power loading. Index Terms—Limited feedback, orthogonal frequency division multiplexing, power loading. I. INTRODUCTION R ESEARCH has consistently shown that multicarrier mod- ulation (MCM) is a practical and powerful technique for combatting intersymbol interference in multipath communica- tion channels. A popular implementation of MCM, called or- thogonal frequency division multiplexing (OFDM), has been or is expected to be included in current and next generation wireless standards such as IEEE 802.16 [1], IEEE 802.11a [2], and IEEE 802.20. In OFDM, a broadband signal is constructed from narrowband signals or tones. The broadband signal is con- structed in the frequency domain, converted to a time domain signal using an orthogonal transformation, and then appended with a cyclic prefix before transmission. One simple method for improving system performance is by optimally allocating the transmit power among the different fre- Manuscript received December 30, 2004. This material is based in part upon work supported by the Texas Advanced Technology Program under Grant No. 003658-0614-2001, the National Instruments Foundation, the Samsung Ad- vanced Institute of Technology, the National Science Foundation under Grants CCF0513916 and CCF05141945, and SBC Foundation. This work appeared in part at the IEEE Military Communication Conference, Monterey, CA, Oct. 31-Nov. 3, 2004. The review of this paper was coordinated by Dr. Z. Xu. D. J. Love is with the Center for Wireless Systems and Applications, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA (email: djlove@ecn.purdue.edu). R. W. Heath Jr., is with the Wireless Networking and Communications Group, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712 USA (email: rheath@ece.utexas.edu). Digital Object Identifier 10.1109/TVT.2005.853473 quency tones, commonly called power loading. Power loading can be used to optimize error rate performance [3]–[7], capac- ity [8]–[12], and transmit power [13] when knowledge of the for- ward link channel is available at the transmitter. Power loading particularly enhances performance when it is combined with rate adaptation to optimize some performance criterion [4], [6]–[13]. While it is sometimes possible to use the reverse link channel estimate to design power loading for the forward link in time division duplexing (TDD) systems (see, for example, the imper- fect channel estimate work in [14]–[17]), problems arise when power loading is implemented with frequency division duplex- ing (FDD). FDD systems lack forward and reverse link channel reciprocity because the forward and reverse links fade indepen- dently. There are three methods for implementing power loading that overcome this channel reciprocity problem. Linear precod- ing techniques (see [18]–[20]) provide excellent performance without any form of channel knowledge at the transmitter. The second option is to use statistical or partial channel information to design the power loading allocation [21]–[24]. Alternatively, FDD systems can perform power loading using channel infor- mation conveyed from the receiver to the transmitter over a low rate feedback channel. Signaling techniques that use a low rate feedback channel, often called limited feedback signaling, have been previously studied in the multiple antenna literature for use with channel quantization feedback [25], [26], limited feedback beamforming [27]–[30], limited feedback precoding [31]–[34] and limited feedback covariance optimization [35]–[37]. In this paper, we propose power loading in OFDM wireless systems using limited feedback sent from the receiver to the transmitter. We consider limited feedback schemes that optimize an error rate or capacity criterion. Our limited feedback power loading framework works by using a codebook of power load- ing vectors designed offline and known to both the transmitter and receiver. The receiver, which has full forward link channel knowledge, chooses one of the codebook power loading vectors and conveys the vector to the transmitter over a lowrate feed- back channel. We present codebook designs for both error rate criterion and capacity criterion loading. For each criterion, we characterize the optimal full channel knowledge loading algo- rithm and then use the vector quantization Lloyd algorithm (see, for example, [38]) to generate a codebook. Other recent work in limited feedback for multicarrier systems includes [39]–[41]. We also present a capacity optimizing limited feedback strat- egy called multimode power loading which operates similarly to the algorithm proposed by Leke and Cioffi in [12]. In mul- timode power loading, the codebook is designed by choosing all possible on-off tone configurations. For an M tone OFDM system, the multi-mode power loading codebook would con- sist of 2 M − 1 unit vectors constructed by normalizing all pos- sible nonzero vector combinations of 1’s and 0’s. This tech- nique was perviously considered for limited feedback linear 0018-9545/$20.00 © 2005 IEEE