Abstract

The capacity of a Gaussian vector channel remains the same if the input and the output are interchanged. This duality relation, when generalized to multiuser channels, has been instrumental in a recent characterization of the Gaussian vector broadcast channel sum capacity. This paper examines the uplink-downlink duality from a convex optimization viewpoint. The main result is a new and simple derivation of uplinkdownlink duality as a special case of a duality between two minimax optimization problems. The new derivation generalizes the previous solution for Gaussian vector broadcast channels under a power constraint to channels with linear covariance input constraints. It also illustrates that the minimax representation of the broadcast channel sum capacity is more general than the duality representation.

Citations

501	Writing on dirty paper - Costa - 1983
218	On the achievable throughput of a multiantenna Gaussian broadcast channel - Caire, Shamai - 2003
137	achievable rates, and sum-rate capacity of gaussian MIMO broadcast channels - Vishwanath, Jindal, et al. - 2003
134	Sum capacity of gaussian vector broadcast channels - Yu, Cioffi - 2004
46	On the duality of Gaussian multiple-access and broadcast channels - Jindal, Vishwanath, et al. - 2004
43	An outer bound on the capacity region of broadcast channel - Sato - 1978
20	Sum Capacity of the Multiple Antenna Gaussian Broadcast Channel and Uplink-Downlink Duality - Viswanath, Tse - 2003