Distributed Beamforming Phase Synchronization Algorithms with multiple spatial constraints

In some applications, closed-loop feedback from the destination to the sources is undesirable due to the relatively high cost of communication over this link and required complexity incurred at the destination.
Open-loop phase synchronization systems minimize interaction between the source nodes and the destination by increasing the level of inter-source interactions.
[...] In open-loop master-slave synchronization, one source node is designated as the master and the remaining source nodes are slaves so the feedback is from the master source node to the slave nodes and it does not involve the destination.
This algorithm consists in five steps, as follows:
1. For frequency synchronization, the master source node broadcasts a sinusoidal signal to the slave nodes, and each slave node estimates and corrects its frequency offset.
2. Phase synchronization among the source nodes is then achieved through a closed-loop method using a TDD protocol between the master source node and the slave source nodes.
3. Each source must estimate its channel response to the destination. This is achieved by having the destination broadcast a beacon, a sinusoidal signal at the carrier frequency, to the source nodes.
4. Since the sources have already been synchronized, each source node can independently estimate its own complex channel gain to the destination using its frequency and phase-synchronized LO.
5. The source nodes can then transmit as a distributed beamformer to the destination by applying the complex conjugate of these gains, typically at baseband, to their transmitted signals. [...]