DMT of Multi-hop Cooperative Networks - Part I: Basic Results
  In this two-part paper, the DMT of cooperative multi-hop networks is examined. The focus is on single-source single-sink (ss-ss) multi-hop relay networks having slow-fading links and relays that potentially possess multiple antennas. The present paper examines the two end-points of the DMT of full-duplex networks. In particular, the maximum achievable diversity of arbitrary multi-terminal wireless networks is shown to be equal to the min-cut. The maximum multiplexing gain of arbitrary full-duplex ss-ss networks is shown to be equal to the min-cut rank, using a new connection to a deterministic network. We also prove some basic results including a proof that the colored noise encountered in AF protocols for cooperative networks can be treated as white noise for DMT computations. The DMT of a parallel channel with independent MIMO links is also computed here. As an application of these basic results, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable for full-duplex networks with single antenna nodes. All protocols in this paper are explicit and rely only upon amplify-and-forward (AF) relaying. Half duplex networks are studied, and explicit codes for all protocols proposed in both parts, are provided in the companion paper. 
K. Sreeram, S. Birenjith, P. Vijay Kumar