On the capacity of the multiple antenna broadcast channel

The capacity region of the multiple antenna (transmit and receive) broadcast channel is considered. We propose an outer bound to the capacity region by converting this nondegraded broadcast channel into a degraded one with users privy to the signals of users ordered below them. We extend our proof techniques in the characterization of the sum capacity of the multiple antenna broadcast channel to evaluate this outer bound with Gaussian inputs. Our main result is the observation that if Gaussian inputs are optimal to the constructed degraded channel, then the capacity region of the multiple antenna broadcast channel is characterized.