D. Tse and S. Hanly, "Multi-Access Fading Channels: Part I: Polymatroid Structure, Optimal Resource Allocation and Throughput Capacities", IEEE Transactions on Information Theory, v. 44, No. 7, Nov., 1998, pp. 2796-2815.
S. Hanly and D. Tse, "Multi-Access Fading Channels: Part II: Delay-Limited Capacities", IEEE Transactions on Information Theory, v. 44, No. 7, Nov., 1998, pp. 2816-2831.
laid the theoretical foundation for this line of work. These papers present a theory of information theoretically optimal power and rate allocation for multiple access (uplink) fading channels. The optimal solution is the multiuser analog of Shannon's water-filling power allocation for point-to-point channels.Analogous results are also obtained for the broadcast channel (downlink):
D. Tse, "Optimal Power Allocation over Parallel Gaussian Broadcast Channels", unpublished manuscript.
An important consequence of the solution, first observed by Knopp and Humblet, is the notion of multiuser diversity: the performance of such an information theoretic optimal system improves with the number of users in the systems. A system with large number of independently fading users ensures that at any time there is a strong user to whom resources can be allocated.
The theory has been translated into practice. A scheduling algorithm, which exploits the inherent multiuser diversity while maintaining fairness among users, has been implemented as the standard algorithm in Qualcomm's HDR (High Data Rate) system (1xEV-DO).The diversity benefit is exploited by trackingthe channel fluctuations of the users and scheduling transmissions to users when their instantaneous channel quality is near the peak.
The performance of such a system depends on the peak rather than the average channel conditions. In practice, the multiuser diversity gain is limited in environments with little scattering and/or slow fading, where the dynamic range of the channel fluctuations is small and the peaks are close to the average. In such environments, we propose the use of multiple transmit antennas to induce large and fast channel fluctuations so that multiuser diversity can still be exploited. We term such a technique opportunistic beamforming using dumb antennas . Traditionally, multiple antennas have been used to provide diversity by reducing channel fluctuations, so this is really a completely opposite way of using antennas. This technique also has interesting ramifications at the network level.
P. Viswanath, D. Tse and R. Laroia, "Opportunistic Beamforming using Dumb Antennas", IEEE Transactions on Information Theory, vol. 48(6), June, 2002.
For a quick overview of the basic ideas, see the following presentation:
" Opportunistic Communications: Smart Scheduling and Dumb Antennas", Intel, January 28, 2002.
This work is supported by the National Science Foundation under grants #NCR-9734090 and #CCR-01-18784