An extremal inequality and the capacity region of the degraded MIMO compound Gaussian broadcast channel with multiple users

Weingarten et al. characterized the capacity region of a two-user compound MIMO broadcast channel when the two users exhibit a certain degradedness order. To show that Gaussian inputs attain the capacity region, they proved a new extremal inequality and made use of the channel enhancement technique. In this paper, we prove a generalization of the extremal inequality considered by Weingarten et al. We then apply the generalized extremal inequality to characterize the capacity region of the N-user compound MIMO Gaussian broadcast channel when the N users exhibit a degradedness order similar to the two-user case.