## Capacity of Multiple Antenna Gaussian Broadcast Channel at High SNR

Vinod Prabhakaran

(Professors Kannan Ramchandran and David N. C. Tse)

(DARPA) F30602-00-2-053, MICRO with matching grant from Qualcomm, (NSF) ANI-981456, (NSF) CCR-01-1878, and (NSF) CCR-009607

The downlink problem in a wireless system with multiple transmit antennas and multiple users can be modeled by a multiple input multiple output Gaussian broadcast channel. The capacity region of this channel is still an open problem. Caire and Shamai [1] applied a technique known as "dirty-paper coding," due to Costa [2], to find an achievable region. It was later shown [3] that the maximum sum rate of this region is also the maximum possible sum rate. It is widely believed that this achievable region is in fact optimal. We attempt to show that this conjecture is true at high SNRs. We hope that solving this problem would give insights into the general problem.

- [1]
- G. Caire and S. Shamai, "On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel,"
*IEEE Trans. Information Theory* (submitted).
- [2]
- M. Costa, "Writing on Dirty Paper,"
*IEEE. Trans. Information Theory,* Vol. 29, May 1983.
- [3]
- P. Viswanath and D. Tse, "Sum Capacity of the Multiple Antenna Gaussian Broadcast Channel and Uplink-Downlink Duality,"
*IEEE Trans. Information Theory* (submitted).

Send mail to the author : (vinodmp@eecs.berkeley.edu)

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