Sum Capacity of a Gaussian Vector Broadcast Channel

This paper characterizes the sum capacity of a class of non-degraded Gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers. Coordination is allowed among the transmit terminals, but not among the different receivers. The sum capacity is shown to be a saddlepoint of a Gaussian mutual information game, where a signal player chooses a transmit covariance matrix to maximize the mutual information, and a noise player chooses a fictitious noise correlation to minimize the mutual information. This result holds for the class of Gaussian channels whose saddle-point satisfies a full rank condition. Further, the sum capacity is achieved using a precoding method for Gaussian channels with additive side information non-causally known at the transmitter. The optimal precoding structure is shown to correspond to a decision-feedback equalizer that decomposes the broadcast channel into a series of single-user channels with interference pre-subtracted at the transmitter. ∗Manuscript submitted to the IEEE transactions on Information Theory on November 6, 2001. This work will be presented in the IEEE Information Theory Symposium (ISIT) 2002. This work was supported by a Stanford Graduate Fellowship, and in part by Alcatel, Fujitsu, Samsung, France Telecom, IBM, Voyan, Sony, and Telcordia.