Multi - User Multiple Antenna Systems : Theoretical Limits and Practical Strategies

Hailed as a very important breakthrough in recent times, multiple antenna systems, also called as multiple input multiple output (MIMO) systems have been shown to have enormous gains over conventional systems in point-to-point scenarios for both wireless and wire-line environments. A very important litmus test for the real promise of MIMO systems is in their performance in multi-user scenarios. The two most common multi-user configurations are: many transmitters communicating with one receiver (MAC or uplink) system and one transmitter sending information to many receivers (BC or downlink) system. The MIMO MAC system has many similarities to the MIMO point-to-point system, and hence many results about the fundamental capacity limits and the potential gains of the MIMO MAC are known. The capacity limits for the MIMO BC, however, is still an open problem due to a lack of a general theory to solve such problems. This thesis presents our progress in analyzing the fundamental capacity limits of MIMO BC. We derive a fundamental connection between the MIMO MAC and BC systems we term duality. Then, we derive a new outer bound on the capacity region (defined as the simultaneous set of rates that can be transmitted with negligible error) of the MIMO BC called the discrete same marginals (DSM) outer bound. Using duality, we show that this outer bound matches the best achievable region known (called Marton’s region) when the input to the channel is constrained to have a Gaussian distribution. For the sum-capacity (subset of the capacity region where the sum of the rates is maximum) of the MIMO BC, it is easy to show that Gaussian inputs are optimal, and hence we obtain a complete characterization of the sum-capacity of these channels. Lastly, we derive asymptotic results for both the MAC and BC as the number of antennas in the system grows to infinity, where we show that identical capacity gains can be obtained for the multi-user MIMO systems as promised for point-to-point systems.