  Communication networks are often designed and analyzed assuming tight
synchronization among nodes. However, in applications that require
communication in the energy-efficient regime of low signal-to-noise ratios,
establishing tight synchronization among nodes in the network can result in a
significant energy overhead. Motivated by a recent result showing that
near-optimal energy efficiency can be achieved over the AWGN channel without
requiring tight synchronization, we consider the question of whether the
potential gains of cooperative communication can be achieved in the absence of
synchronization. We focus on the symmetric Gaussian diamond network and
establish that cooperative-communication gains are indeed feasible even with
unsynchronized nodes. More precisely, we show that the capacity per unit energy
of the unsynchronized symmetric Gaussian diamond network is within a constant
factor of the capacity per unit energy of the corresponding synchronized
network. To this end, we propose a distributed relaying scheme that does not
require tight synchronization but nevertheless achieves most of the energy
gains of coherent combining.
