Deterministic Differential Search Algorithm for Distributed Sensor/Relay Networks

For distributed sensor/relay networks, high reliability and power efficiency are often required. However, several implementation issues arise in practice. One such problem is that all the distributed transmitters have limited power supply since the power source of the transmitters cannot be recharged continually. To resolve this, distributed beamforming has been proposed as a viable solution where all distributed transmitters seek to align in phase at the receiver end. However, it is difficult to implement such transmit beamforming in a distributed fashion in practice since perfect channel state information (CSI) need to be made available at all distributed transmitters, requiring tremendous overhead to feed back CSI from the receiver to all distributed transmitters. In literature, the efforts of designing efficient distributed phase alignment algorithms can be categorized into two class: deterministic phase adjustment or random phase perturbation algorithms. In [1], [2], Mudumbai et al proposed and provided initial analysis for an adaptive distributed beamforming which requires only a single bit feedback. In [3], [4], a general set of adaptive distributed beamforming algorithms was reformulated as a local random search algorithm and analyzed. A bio-inspired robust adaptive random search algorithm was proposed and analyzed in [5]. On the other hand, several deterministic distributed beamforming algorithms were also proposed. For example, Thibault et al introduced a deterministic algorithm with individual power constraint [6]. For amplify-and-forward wireless relay networks, an algorithm using additive deterministic perturbations was presented in [7]. Fertl et al further investigated a multiplicative deterministic perturbations for distributed beamforming under a total power constraint [8]. In this paper, we propose a novel algorithm that belongs to the category of deterministic phase adjustment algorithm: the Deterministic Differential Search Algorithm (DDSA), where the differences between the measured received signal strength (RSS) are utilized judiciously to help us predict the deterministic phase adjustment done at distributed transmitters. Numerical simulations demonstrate rapid convergence to a predetermined threshold.