Duality, Dirty Paper Coding, and Capacity for Multiuser Wireless Channels

We determine a duality between broadcast and multiple access channels that can be used to obtain the capacity region and optimal transmission strategy for one channel based on the capacity-achieving transmission strategy and region for the dual channel. This duality result in applicable to additive Gaussian noise and fading channels for several different notions of fading channel capacity, including ergodic capacity, outage capacity, and minimum rate capacity. We show that duality can be used to obtain any of these capacities for the fading broadcast channel from the same capacity on the dual MAC channel, and vice versa. We then apply this general result to obtain the minimum rate capacity of the fading multiple access channel, which also yields the ergodic and outage capacity as special cases. Next we turn our attention to broadcast channels with multiple antennas at the transmitter and receiver (the MIMO channel). Since this channel is in general non-degraded, its capacity region remains an unsolved problem. We establish a duality between the achievable region of the MIMO broadcast channel using Costa’s “dirty-paper” coding and the capacity region of the MIMO multiple-access channel, which is easy to compute. We also show that the dirty paper achievable region yields the sum-rate capacity of the MIMO broadcast channel.