Duality, achievable rates, and sum-rate capacity of gaussian mimo broadcast channels

TLDR

A multiuser MIMO Gaussian broadcast channel, with multiple antennas at transmitter and receivers, has an unsolved capacity region because it is generally nondegraded. The paper establishes a duality between the dirty‑paper achievable region for the MIMO BC and the easily computable capacity region of the MIMO MAC. By exploiting this duality, the authors reduce the computational complexity of computing the dirty‑paper achievable region for the MIMO BC. The dirty‑paper achievable region attains the sum‑rate capacity of the MIMO BC, as its maximum sum rate matches an upper bound. Citation: IEEE International Symposium on Information Theory, Washington, DC, June 2001, p.322.

Abstract

We consider a multiuser multiple-input multiple- output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. We establish a duality between what is termed the "dirty paper" achievable region (the Caire-Shamai (see Proc. IEEE Int. Symp. Information Theory, Washington, DC, June 2001, p.322) achievable region) for the MIMO BC and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the MIMO BC.