Optimal Transmission for the MIMO Bidirectional Broadcast Channel in the Wideband Regime

This paper considers a transmit strategy for an AWGN MIMO bidirectional broadcast channel in the wideband regime. In order to characterize the boundaries of the wideband capacity and energy per bit regions, the transmit strategy at the relay is designed to maximize the weighted wideband rate sum. A closed form of the optimal transmit covariance matrix is derived, which shows that a single beam transmit strategy is optimal. The transmit strategies for some special cases are also analyzed. The fairness versus energy efficiency tradeoff is then discussed. In addition, an extension to multipair MIMO bidirectional broadcast channel is studied in which we show that serving a certain pair with full power is optimal in the sense of maximizing the achievable weighted wideband rate sum. Finally, a discussion on the conjecture of the minimum energy per bit for multi-pair systems is provided.