6 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 1, JANUARY 2005 Combined Power and Rate Adaptation for Wireless Cellular Systems Chin Choy Chai, Tjeng Thiang Tjhung, and Leng Chye Leck Abstract—We extend the throughput optimization technique of Qiu and Chawla for adaptive modulation, to combine power and rate adaptation in wireless cellular systems. We develop new com- bined power and rate control algorithms for wireless multimedia systems, in which the transmitted powers and rates of different media users are adapted based on the signal-to-interference power ratio. Using simulations, we show that with appropriately chosen power and rate limits, our proposed combined power and rate con- trol algorithms can achieve a higher throughput when compared to previously proposed algorithms with power control only. Index Terms—Cellular systems, fading, power and rate adapta- tion, shadowing. I. INTRODUCTION V ARIOUS data traffics with different quality-of-service (QoS) requirements are expected to be supported by future wireless communication systems. Typically, the real- and nonreal-time traffics have very different signal-to-interfer- ence power ratio (SIR) and delay requirements. To efficiently utilize the limited radio and power resources, future systems should be equipped with the capability of dynamically adapting both transmission power and rate, matching different service requirements, as well as variations in the quality of wireless radio channels. A combined power and rate adaptation scheme has been proposed for direct-sequence code-division multiple-access (DS/CDMA) systems over the Rayleigh-fading channels in [1] and over the Nakagami-fading channels in [2]. Under a deep fade, when the transmitted power has been increased to a preassigned maximum level, a further gain in performance can be obtained by reducing the data rate. It was shown in [1] that a substantial increase in the aggregate users data transmission rate can be achieved while in [2], a substantial increase in power gain can be realized, over the power only adaptation scheme. In [3], algorithms for adapting the modulation scheme and power according to varying channel conditions have been developed, and a significantly higher throughput achieved over the SIR-balancing power control scheme. However, one major shortcoming of adaptive modulation system is that the allowed dynamic range of signal power or signal-to-noise-ratio (SNR) level, can be easily exceeded by power level variations due to fading and interference. To overcome this shortcoming, Manuscript received July 20, 2002; revised June 23, 2003, December 11, 2003; accepted December 16, 2003. The editor coordinating the review of this paper and approving it for publication is M. Zorzi. C. C. Chai and T. T. Tjhung are with the Institute for Infocomm Research, Sin- gapore 119613 (e-mail: chaicc@i2r.a-star.edu.sg; tjhungtt@i2r.a-star.edu.sg). L. C. Leck is with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260. Digital Object Identifier 10.1109/TWC.2004.840233 Ue et al. [4] proposed a symbol rate controlled adaptive mod- ulation system using 16-quadrature amplitude modulation (16QAM). The symbol rate is controlled according to channel conditions, where a lower symbol rate is achieved by repeating identical 16QAM symbols consecutively at the maximum symbol rate . The main aim of our work is to develop algorithms for adapting the symbol rate, as well as the power level for system users in a multiple access system. We derive new power and rate adaptation algorithms to optimize the system performance based on the received SIR. Unlike previous works, the proposed algorithms aim to search for optimal powers, as well as optimal transmission rates for all system users, given their channel gains, maximum as well as minimum power and rate limits. The tolerable system interference level determines the power limits, whereas the rate limits are dictated by the tolerable delay of the respective traffics. We also show that the proposed power and rate adaptation algorithms can achieve higher throughput when compared to the power only adaptation scheme in [3]. II. SYSTEM AND CHANNEL MODELS We consider a cellular wireless communication system sup- porting several types of medium, each with different QoS re- quirements. Both the transmission power and rate of system users can be adapted to maximize overall system performance. All signals are transmitted in packets, at their adaptively and optimally allocated rate within each synchronized fixed-length time-slot, as shown in Fig. 1. By adapting the transmission rate of users within each time-slot, their transmission delays are af- fected. The minimum rate limit of user is dependent on the specified tolerable delay. Let and , denote, respectively, a set of co-channel users and their serving base stations. These transmitter/receiver pairs or communication links concurrently use a specific frequency channel. Let denote the path gain matrix, where is the path gain from mobile user to base station (or from base station to user ). We consider slow fading condition where every can be assumed to be constant over at least a packet duration. Let denote the transmission power vector, where denotes the transmission power of terminal ; and denotes the set of feasible transmis- sion power vectors. The and represent, respectively, the minimum and maximum transmission power limits. Let denote the transmission rate vector, where denotes the transmission rate of terminal ; and denotes the continuous range of feasible trans- mission rate vectors. The and 1536-1276/$20.00 © 2005 IEEE