  The focus of this work is on the analysis of transmit beamforming schemes
with a low-rate feedback link in wireless sensor/relay networks, where nodes in
the network need to implement beamforming in a distributed manner.
Specifically, the problem of distributed phase alignment is considered, where
neither the transmitters nor the receiver has perfect channel state
information, but there is a low-rate feedback link from the receiver to the
transmitters. In this setting, a framework is proposed for systematically
analyzing the performance of distributed beamforming schemes. To illustrate the
advantage of this framework, a simple adaptive distributed beamforming scheme
that was recently proposed by Mudambai et al. is studied. Two important
properties for the received signal magnitude function are derived. Using these
properties and the systematic framework, it is shown that the adaptive
distributed beamforming scheme converges both in probability and in mean.
Furthermore, it is established that the time required for the adaptive scheme
to converge in mean scales linearly with respect to the number of sensor/relay
nodes.
