On the Optimal Transmit Strategy for the MIMO Bidirectional Broadcast Channel

In this work the transmit covariance matrix optimization problem for the MIMO Gaussian bidirectional broadcast channel is studied. A half-duplex relay node establishes bidirectional communication between two nodes using a decode-and-forward protocol. In the initial multiple access phase both nodes transmit their messages to the relay node. In the succeeding phase the relay broadcasts an optimal re-encoded message so that both nodes can decode the other’s message using their own message as side information. The capacity region of the bidirectional broadcast channel is completely characterized by a weighted rate sum maximization problem, which can be solved by the presented iterative fixed point algorithm. The study of the structure of the problem shows that if the channels have orthogonal subspaces and an invariant property is fulfilled, then there exist equivalent transmit strategies with different ranks. Furthermore, closed-form results are obtained for two special cases. In particular, a procedure to obtain the optimal transmit covariance matrix is derived for the case where we have invertible channels and a full-rank transmission is optimal. Moreover, for parallel channels the optimal solution is completely characterized and discussed, which also solves the optimal power allocation problem for a single-antenna OFDM system.

• Multi-antenna Systems
• Signal Processing

@article{OJWB09otot,
   author          = "T. J. Oechtering and E. A. Jorswieck and R. F. Wyrembelski and H. Boche", 
   title           = "{On the Optimal Transmit Strategy for the MIMO Bidirectional Broadcast Channel}", 
   journal         = "IEEE Transactions on Communications", 
   volume          = "57", 
   number          = "12", 
   pages           = "3817--3826", 
   month           = dec, 
   year            = "2009", 
}