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In this two-part paper, the DMT of cooperative multi-hop networks isexamined. The focus is on single-source single-sink (ss-ss) multi-hop relaynetworks having slow-fading links and relays that potentially possess multipleantennas. The present paper examines the two end-points of the DMT offull-duplex networks. In particular, the maximum achievable diversity ofarbitrary 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 shownto be equal to the min-cut rank, using a new connection to a deterministicnetwork. We also prove some basic results including a proof that the colorednoise encountered in AF protocols for cooperative networks can be treated aswhite noise for DMT computations. The DMT of a parallel channel withindependent MIMO links is also computed here. As an application of these basicresults, we prove that a linear tradeoff between maximum diversity and maximummultiplexing gain is achievable for full-duplex networks with single antennanodes. All protocols in this paper are explicit and rely only uponamplify-and-forward (AF) relaying. Half duplex networks are studied, andexplicit codes for all protocols proposed in both parts, are provided in thecompanion paper.

DMT of Multi-hop Cooperative Networks - Part I: Basic Results