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. 2017 Aug 20;17(8):1918.
doi: 10.3390/s17081918.

Evolutionary Beamforming Optimization for Radio Frequency Charging in Wireless Rechargeable Sensor Networks

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Free PMC article

Evolutionary Beamforming Optimization for Radio Frequency Charging in Wireless Rechargeable Sensor Networks

Ke-Han Yao et al. Sensors (Basel). .
Free PMC article

Abstract

This paper investigates how to efficiently charge sensor nodes in a wireless rechargeable sensor network (WRSN) with radio frequency (RF) chargers to make the network sustainable. An RF charger is assumed to be equipped with a uniform circular array (UCA) of 12 antennas with the radius λ, where λ is the RF wavelength. The UCA can steer most RF energy in a target direction to charge a specific WRSN node by the beamforming technology. Two evolutionary algorithms (EAs) using the evolution strategy (ES), namely the Evolutionary Beamforming Optimization (EBO) algorithm and the Evolutionary Beamforming Optimization Reseeding (EBO-R) algorithm, are proposed to nearly optimize the power ratio of the UCA beamforming peak side lobe (PSL) and the main lobe (ML) aimed at the given target direction. The proposed algorithms are simulated for performance evaluation and are compared with a related algorithm, called Particle Swarm Optimization Gravitational Search Algorithm-Explore (PSOGSA-Explore), to show their superiority.

Keywords: RF charging; antenna array; beamforming; evolution strategy; evolutionary algorithm.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
An antenna array can steer the strongest energy beams to aim at different directions, e.g., directions to the (a) upper right sensor; (b) rightmost sensor; and (c) lower right sensor.
Figure 2
Figure 2
The beamforming radiation pattern or beam pattern showing the main lobe and side lobes.
Figure 3
Figure 3
The phase of a waveform measured in degrees between 0° and 360°.
Figure 4
Figure 4
Constructive and destructive interference of waves.
Figure 5
Figure 5
The beams caused by interference.
Figure 6
Figure 6
(a) The beam pattern of an antenna array beamforming, and (b) its associated Cartesian coordinate representation.
Figure 7
Figure 7
The geometric illustration of an N-element uniform circular array (UCA).
Figure 8
Figure 8
A UCA with the radius λ consisting of 12 elements separated by λ/3.
Figure 9
Figure 9
Beam patterns of different algorithms (20 generations).
Figure 10
Figure 10
Beam patterns of different algorithms (50 generations).
Figure 11
Figure 11
Beam patterns of different algorithms (100 generations).
Figure 12
Figure 12
Cumulative distribution function (CDF) comparisons of different algorithms.
Figure 13
Figure 13
Run time comparisons of different algorithms.

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