  In this two-part paper, we consider the multiantenna multihop relay channels
in which the source signal arrives at the destination through N independent
relaying hops in series. The main concern of this work is to design relaying
strategies that utilize efficiently the relays in such a way that the diversity
is maximized. In part I, we focus on the amplify-and-forward (AF) strategy with
which the relays simply scale the received signal and retransmit it. More
specifically, we characterize the diversity-multiplexing tradeoff (DMT) of the
AF scheme in a general multihop channel with arbitrary number of antennas and
arbitrary number of hops. The DMT is in closed-form expression as a function of
the number of antennas at each node. First, we provide some basic results on
the DMT of the general Rayleigh product channels. It turns out that these
results have very simple and intuitive interpretation. Then, the results are
applied to the AF multihop channels which is shown to be equivalent to the
Rayleigh product channel, in the DMT sense. Finally, the project-and-forward
(PF) scheme, a variant of the AF scheme, is proposed. We show that the PF
scheme has the same DMT as the AF scheme, while the PF can have significant
power gain over the AF scheme in some cases. In part II, we will derive the
upper bound on the diversity of the multihop channels and show that it can be
achieved by partitioning the multihop channel into AF subchannels.
