Duality, dirty paper coding, and capacity for multiuser wireless channels

We introduce techniques that shed new light on the capacity analysis of multiuser channels, and apply these techniques to broadcast and multiple access channels. We rst 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 is applicable to additive Gaussian noise and fading channels for several di erent notions of fading channel capacity, including ergodic capacity, outage capacity, and minimum rate capacity. Duality provides a powerful connection between the broadcast channel and multiple access channel capacity regions that solves many open capacity problems, and also greatly simpli es the calculation of known regions. We next consider the dirty paper coding strategy of Costa for broadcast channels. Dirty paper coding exploits the known interference between users in a broadcast channel to presubtract out this interference. We apply this coding strategy to broadcast channels with multiple antennas at the transmitter and receiver (the MIMO channel). We show that dirty paper coding provides signi cant rate gains over the high-data-rate (HDR) strategy used in current cellular systems. We next turn our attention to the MIMO broadcast channel capacity region. Since this channel is in general non-degraded, its capacity region remains an unsolved problem. We rst establish a duality between the achievable region of the MIMO broadcast channel using dirty paper coding and the capacity region of the dual MIMO multiple-access channel, which is easy to compute. We then show that dirty paper coding achieves sumrate capacity of the MIMO broadcast channel. The proof exploits duality, dirty paper coding, and clever upper bounding techniques.