Adaptively Induced Fluctuations for Multiuser Diversity: Two-dimensional Parameters and Cellular Interference Rahul Dangui Corporate R&D Qualcomm, Inc. 5775, Morehouse Drive San Diego, California Email: dangui@comm.csl.uiuc.edu Bruce Hajek Dept. of Electrical and Computer Engineering and the Coordinated Science Laboratory University of Illinois at Urbana-Champaign Urbana, Illinois Email: b-hajek@comm.csl.uiuc.edu Abstract— This study extends recent work on using adaptive phase fluctuations to enhance multiuser diversity in the downlink of a cellular network. Feedback at the base station is limited and Rayleigh fading is assumed. Our main findings are presented along three main axes. First, we study a single-cell environment with adaptive fluc- tuations induced between multiple transmit antennae at the base station. Phase fluctuations of three transmit antennae are induced based on a two-dimensional mapping of their relative phases. A one to two dB improvement of the performance is obtained over the two-antennae case. For two transmit antennae, we also investigate another two-dimensional problem by jointly varying the phase difference and power allocation between two antennae. Our simulations show somewhat surprisingly that an equal power-splitting with adaptive phase fluctuations provides better performance than the joint strategy. Second, we take into account the effects of intercell inter- ference. The impact of neighboring cells using the same trans- mission frequency and executing the same adaptive algorithm is accounted for. A simple model is studied by considering a single interfering cell with parameters chosen to account for the power of the six nearest interfering cells. Our simulations and analysis probe the consequences of the fact that intercell interference noise is burstier than thermal noise. We find that multiuser diversity is more effective against interference than against Gaussian thermal noise with equal power. However, the interfering noise tends to become Gaussian when the number of interferers increases. The performance is also observed to be insensitive to the phase variation strategy of the interfering station. We further consider a more detailed model involving the simultaneous simulation of the six nearest interfering cells, with users randomly distributed in the cells. Third, fairness issues are taken into account. We observe that fairness decreases throughput but we still observe a multiuser diversity gain. 1 Keywords - Wireless communications; Rayleigh fading chan- nels; multiuser diversity; multiple antennae; propagation; intercell interference; power control; Monte Carlo simulations; fairness mechanisms; scheduling algorithms; 1 This work was supported in part by the National Science Foundation under grants NSF CCR 99-79381 and NSF ITR 00-85929. A shorter version of this paper was presented at the IEEE Vehicular Technology Conference, Dallas, Fall 2005. This work is based on the M.S. thesis of the first author, completed at UIUC. I. I NTRODUCTION The concept of multiuser diversity is central to this paper and may be described as follows. It is reasonable to assume that the channels between distinct users and a base station fade independently. If the base station has information about the channel quality, it can take advantage of this independence to transmit in a given time slot only to the user with the best channel. This is the multiuser diversity effect. This concept has its roots in information theoretic results as follows. First, Knopp and Humblet [1] showed that in the case of a single-cell uplink with multiple users communicating over time-varying channels, an optimal strategy from a capacity point of view is to receive data at any given time only from the user with the best channel. Assuming that the channels can be perfectly tracked at the mobile users and the base station, Tse [2] showed that the total downlink information capacity can be achieved by transmitting only to the user with the best channel at any time. Viswanath et al. [3] proposed to further improve the performances of [2] by inducing fluctuations through the phase variation of an additional transmit antenna at the base station. They studied this phenomenon in the case of complete feedback: this is called opportunistic beamforming. The same signal is transmitted though both antennae with the phase difference being varied randomly. The use of multiple antennae enables large and fast channel fluctuations, even in slow fading or little scattering environments. Moreover, this requires no more signal processing than the one-antenna case. It is therefore easier to implement than techniques based on space-time processing or smart antennae. In this paper, we extend the work of [4] by considering a two-dimensional search which can be applied to phase fluctuations of three transmit antennae or joint power-phase fluctuations of two transmit antennae. We also address the issues of intercell interference and fairness.