Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Microwave Mobile Communications
Microwave Mobile Communications
Convex Optimization
XORs in the air: practical wireless network coding
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
MIMO Wireless Communications
Space-Time Wireless Systems: From Array Processing to MIMO Communications
Space-Time Wireless Systems: From Array Processing to MIMO Communications
Foundations and Trends® in Networking
Duplex schemes in multiple antenna two-hop relaying
EURASIP Journal on Advances in Signal Processing
Piggyback a Common Message on Half-Duplex Bidirectional Relaying
IEEE Transactions on Wireless Communications
IEEE Transactions on Information Theory
Broadcast Capacity Region of Two-Phase Bidirectional Relaying
IEEE Transactions on Information Theory
Capacity limits of MIMO channels
IEEE Journal on Selected Areas in Communications
Spectral efficient protocols for half-duplex fading relay channels
IEEE Journal on Selected Areas in Communications
On the optimal transmission for the MIMO bidirectional broadcast channel
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Optimal coding strategies for bidirectional broadcast channels under channel uncertainty
IEEE Transactions on Communications
Beamforming-based physical layer network coding for non-regenerative multi-way relaying
EURASIP Journal on Wireless Communications and Networking - Special issue on physical-layer network coding for wireless cooperative networks
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We consider a three-node network where a relay node establishes a bidirectional communication between the two other nodes using a spectrally efficient decode-and-forward protocol. In the first phase we have the classical multiple-access channel where both nodes transmit a message to the relay node, which then decodes the messages. In the second phase the relay broadcasts a re-encoded composition of them based on the network coding idea. This means that each receiving node uses the same data stream to infer on its intended message. We characterize the optimal transmit strategy for the broadcast phase where either the relay node or the two other nodes are equipped with multiple antennas. Our main result shows that beamforming into the subspace spanned by the channels is always an optimal transmit strategy for the multiple-input single-output bidirectional broadcast channel. Thereby, it shows that correlation between the channels is advantageous. Moreover, this leads to a parametrization of the optimal transmit strategy which specifies the whole capacity region. In retrospect the results are intuitively clear since the single-beam transmit strategy reflects the single stream processing due to the network coding approach.