Decentralized practical design and centralized benchmark for analog network coding

This article proposes both centralized and decentralized design schemes for an analog network coding multipleinput multiple-output system with a relay node between two end nodes. The proposed centralized scheme is called the generalized iterative approach (GIA). It jointly designs the precoders and decoders at the two end nodes, and the processor at the relay to maximize the sum mutual information. Numerical results for the per-node power constraint show the convergence behavior of the GIA and give a performance benchmark for the analog network coding scheme. The proposed decentralized scheme is a practical joint transceiver and signaling design scheme. The keys to its low signaling load are time-division duplex and a symmetric relay processing matrix. The proposed signaling protocol enables the needed information, including channel state information (CSI), to be available at each node. With the needed CSI, a novel symmetric processor design at the relay is developed to maximize an approximate sum mutual information formula (to reduce the signaling loading, the precoders at both end nodes and the noise propagated from the relay are not considered). Employing singular value decomposition transceivers at the two end nodes, it is remarkable that the proposed decentralized approach performs almost as well as the centralized GIA design. It is concluded that the proposed decentralized scheme is a feasible way to implement analog network coding systems.