Distributed beamforming for information transfer in sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
Convergence of a Class of Decentralized Beamforming Algorithms
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Distributed transmit beamforming: challenges and recent progress
IEEE Communications Magazine
Collaborative beamforming for distributed wireless ad hoc sensor networks
IEEE Transactions on Signal Processing
Feedback assisted stochastic gradient adaptation of multiantenna transmission
IEEE Transactions on Wireless Communications
On the Feasibility of Distributed Beamforming in Wireless Networks
IEEE Transactions on Wireless Communications
On the capacity of large Gaussian relay networks
IEEE Transactions on Information Theory
On the power efficiency of sensory and ad hoc wireless networks
IEEE Transactions on Information Theory
What is the value of limited feedback for MIMO channels?
IEEE Communications Magazine
Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly
Distributed transmit beamforming: challenges and recent progress
IEEE Communications Magazine
Pilot-assisted distributed co-phasing for wireless sensor networks
SECON'09 Proceedings of the 6th Annual IEEE communications society conference on Sensor, Mesh and Ad Hoc Communications and Networks
On the diversity order of non-orthogonal amplify-and-forward over block-fading channels
IEEE Transactions on Wireless Communications
Cooperative transmission for wireless relay networks using limited feedback
IEEE Transactions on Signal Processing
A random search framework for convergence analysis of distributed beamforming with feedback
IEEE Transactions on Information Theory
Fully wireless implementation of distributed beamforming on a software-defined radio platform
Proceedings of the 11th international conference on Information Processing in Sensor Networks
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The concept of distributed transmit beamforming is implicit in many key results of network information theory. However, its implementation in a wireless network involves the fundamental challenge of ensuring phase coherence of the radio frequency signals from the different transmitters in the presence of unknown phase offsets between the transmitters and unknown channel gains from the transmitters to the receiver. In this paper, it is shown that such phase alignment can be achieved using distributed adaptation by the transmitters with minimal feedback from the receiver. Specifically, each transmitter independently makes a small random adjustment to its phase at each iteration, while the receiver broadcasts a single bit of feedback, indicating whether the signal-to-noise ratio (SNR) improved or worsened after the current iteration. The transmitters keep the "good" phase adjustments and discard the "bad" ones, thus implementing a distributed ascent algorithm. It is shown that, for a broad class of distributions for the random phase adjustments, this procedure leads to asymptotic phase coherence with probability one. A simple analytical model, borrowing ideas from statistical mechanics, is used to characterize the progress of the algorithm, and to provide guidance on parameter choices. This analytical model is based on a conjecture on the distribution of the received phases when the number of transmitters becomes large. Finally, the proposed system is shown to be scalable: the random phase perturbations can be chosen such that the convergence time is linear in the number of collaborating nodes.