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The focus of this work is on the analysis of transmit beamforming schemeswith a low-rate feedback link in wireless sensor/relay networks, where nodes inthe network need to implement beamforming in a distributed manner.Specifically, the problem of distributed phase alignment is considered, whereneither the transmitters nor the receiver has perfect channel stateinformation, but there is a low-rate feedback link from the receiver to thetransmitters. In this setting, a framework is proposed for systematicallyanalyzing the performance of distributed beamforming schemes. To illustrate theadvantage of this framework, a simple adaptive distributed beamforming schemethat was recently proposed by Mudambai et al. is studied. Two importantproperties for the received signal magnitude function are derived. Using theseproperties and the systematic framework, it is shown that the adaptivedistributed beamforming scheme converges both in probability and in mean.Furthermore, it is established that the time required for the adaptive schemeto converge in mean scales linearly with respect to the number of sensor/relaynodes.

A Random Search Framework for Convergence Analysis of Distributed Beamforming with Feedback