On the Achievable Diversity-Multiplexing Tradeoffs in Half-Duplex   Cooperative Channels
  In this paper, we propose novel cooperative transmission protocols for delay limited coherent fading channels consisting of N (half-duplex and single-antenna) partners and one cell site. In our work, we differentiate between the relay, cooperative broadcast (down-link), and cooperative multiple-access (up-link) channels. For the relay channel, we investigate two classes of cooperation schemes; namely, Amplify and Forward (AF) protocols and Decode and Forward (DF) protocols. For the first class, we establish an upper bound on the achievable diversity-multiplexing tradeoff with a single relay. We then construct a new AF protocol that achieves this upper bound. The proposed algorithm is then extended to the general case with N-1 relays where it is shown to outperform the space-time coded protocol of Laneman and Worenell without requiring decoding/encoding at the relays. For the class of DF protocols, we develop a dynamic decode and forward (DDF) protocol that achieves the optimal tradeoff for multiplexing gains 0 < r < 1/N. Furthermore, with a single relay, the DDF protocol is shown to dominate the class of AF protocols for all multiplexing gains. The superiority of the DDF protocol is shown to be more significant in the cooperative broadcast channel. The situation is reversed in the cooperative multiple-access channel where we propose a new AF protocol that achieves the optimal tradeoff for all multiplexing gains. A distinguishing feature of the proposed protocols in the three scenarios is that they do not rely on orthogonal subspaces, allowing for a more efficient use of resources. In fact, using our results one can argue that the sub-optimality of previously proposed protocols stems from their use of orthogonal subspaces rather than the half-duplex constraint. 
Kambiz Azarian, Hesham El Gamal and Philip Schniter