Code design for multiple-input multiple-output broadcast channels

Recent information theoretical results indicate that dirty-paper coding (DPC) achieves the entire capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). This thesis presents practical code designs for Gaussian BCs based on DPC. To simplify our designs, we assume constraints on the individual rates for each user instead of the customary constraint on transmitter power. The objective therefore is to minimize the transmitter power such that the practical decoders of all users are able to operate at the given rate constraints. The enabling element of our code designs is a practical DPC scheme based on nested turbo codes. We start with Cover's simplest two-user Gaussian BC as a toy example and present a code design that operates 1.44 dB away from the capacity region boundary at the transmission rate of 1 bit per sample per dimension for each user. Then we consider the case of the multiple-input multiple-output BC and develop a practical limit-approaching code design under the assumption that the channel state information is available perfectly at the receivers as well as at the transmitter. The optimal precoding strategy in this case can be derived by invoking duality between the MIMO BC and MIMO multiple access channel (MAC). However, this approach requires transformation of the optimal MAC covariances to their corresponding counterparts in the BC domain. To avoid these computationally complex transformations, we derive a closed-form expression for the optimal precoding matrix for the two-user case and use it to determine the optimal precoding strategy. For more than two users we propose a low-complexity suboptimal strategy, which, for three transmit antennas at the base station and three users (each with a single receive antenna), performs only 0.2 dB worse than the optimal scheme. Our obtained results are only 1.5 dB away from the capacity limit. Moreover simulations indicate that our practical DPC based scheme significantly outperforms the prevalent suboptimal strategies such as time division multiplexing and zero forcing beamforming. The drawback of DPC based designs is the requirement of channel state information at the transmitter. However, if the channel state information can be communicated back to the transmitter effectively, DPC does indeed have a promising future in code designs for MIMO BCs.