Bio-inspired optimization algorithms applied to rectenna design
© The Author(s) 2018
Received: 7 September 2017
Accepted: 30 November 2017
Published: 3 January 2018
A comparative study of the use of bio-inspired optimization technologies including the Cuckoo Search (CS) algorithm, the Differential Evolution (DE) algorithm, and Quantum-behaved Particle Swarm Optimization (QPSO) in the design of microstrip patch antennas for use in RF energy harvesting systems is presented. Radio frequency (RF) energy harvesting is considered as an eco-friendly energy source and has become a focus of intense research especially for use in distributed sensor networks. In a RF energy harvesting system, the antenna is responsible for capturing RF signals over a certain frequency band, and it is a vital element in determining the performance of the RF energy harvester. In this paper, a new mathematical weighted evaluation model involving antenna efficiency, center frequency, and bandwidth is proposed to evaluate the performance of a rectangular microstrip patch antenna (RMPA) for a RF harvesting system based on both the transmission-line model and the cavity model. With the evaluation model as the objective function, bio-inspired optimization approaches are utilized to determine the geometrical parameters of the optimal antenna based on given constraints. Moreover, the optimised designs of an antenna for harvesting energy from the Global System for Mobile Communications (GSM) frequency band are proposed via the mathematical model and bio-inspired optimization approaches using simulations. Furthermore, a comparative study of the DE, CS, and QPSO techniques is conducted via the evaluation of the properties of the antenna designs.
With the advance of technologies including the Internet of Things (IoT) and wearable electronics, the demand for mobile electrical devices has surged. Battery depletion has become a fundamental bottleneck which limits the performance of these devices . Considering the conventional fact that batteries have to be replaced or replenished manually after depletion, deeper implications exist for devices such as implantable heart pumps for which the replacement or recharging of the battery by cable is inconvenient and high-cost . RF energy harvesting technology provides an alternative to this and has recently received significant attention in the research community demonstrating its potential as a sustainable energy source for low power electronics [3–7].
Average RF power density in London 
Average power density
1805 MHz ∼ 1880 MHz
84 nW/ cm2
1710 MHz ∼ 1785 MHz
925 MHz ∼ 960MHz
880 MHz ∼ 915MHz
0.45 nW/ cm2
2110 MHz ∼ 2170 MHz
12 nW/ cm2
1920 MHz ∼ 1980 MHz
0.46 nW/ cm2
2400 MHz ∼ 2500 MHz
6 nW/ cm2
Summary of performance of variety of up-to-date antenna design
M. Arrawatia, et al. 
0.87 GHz ∼ 1.05 GHz
S. Ghosh, et al. 
0.935 GHz ∼ 0.96 GHz
H. Saghlatoon, et al. 
0.6 GHz ∼ 1.5 GHz
A. Dadgarpour, et al. 
2.5 GHz ∼ 3.9 GHz
≥ 10.9 dBi
M. W. Zeng, et al. 
1.73 GHz ∼ 1.84 GHz
M. Arrawatia, et al.
0.85 GHz ∼ 1.94 GHz
≥ 2 dBi
J. Wen, et al.
1.7 GHz ∼ 3.6 GHz
D. Yang, et al.
3.15 GHz ∼ 10.65 GHz
R. Maher, et al. 
2.1 GHz ∼ 7GHz
J. Y. Li, et al. 
2.48 GHz ∼ 9.51GHz
K. P. Esselle, et al. 
4 GHz ∼ 9.5GHz
≥ 7.4 dBi
W. Han, et al. 
6.12 GHz ∼ 6.84 GHz
In a RF energy harvesting system, the antenna, which is responsible for receiving RF signals over a certain frequency band, is an important element in the design of the RF energy harvester. The design of the antenna involves several parameters, some of which induce contradictory modifications of antenna performances. In this paper, a new mathematical weighted evaluation model involving antenna efficiency, center frequency, and bandwidth is proposed to evaluate the performance of a rectangular microstrip patch antenna (RMPA) based on both the transmission-line model and the cavity model. With the mathematic modeling of a RMPA, three bio-inspired optimization technologies including the Cuckoo Search (CS) algorithm, the Differential Evolution (DE) algorithm, and Quantum-behaved Particle Swarm Optimization (QPSO)are used to optimize the design of RMPA with certain constraints. The simulation processes and designed antennas’ performances are also presented and compared. With the evaluation model as the objective function, bio-inspired optimization approaches are utilized to determine the geometrical parameters of the optimal antenna based on given constraints.
The paper is organized as follows:“Mathematic modeling of RMPA”section introduces the basic architecture and properties of a RMPA, and a mathematical model is proposed based on the cavity and transmission line models. Additionally, the objective function and constraints for optimization are derived. The“Bio-inspired algorithms for antenna design” section describes the current implementation of the optimal antenna design algorithms including QPSO, CS, and DE. Finally, based on the performance of designed antennas, the properties of three bio-inspired algorithms are discussed and compared.
Mathematic modeling of RMPA
where the η a ,η m and η r respectively represent the efficiency of receiving antenna, impedance matching network, and rectifying circuit. The magnitude of P T is correlated with the design frequency band of antenna. Accordingly, the optimum antenna design for a RF harvesting system requires two features: high antenna efficiency and appropriate frequency band. In more detail, the performance of the antenna used for a RF energy harvester mainly depends on the antenna gain, bandwidth, return loss, and center frequency. However, there is a trade-off between antenna size and performance.
Architecture of a RMPA
Nomenclature of important parameters
Center frequency of antenna
Antenna efficiency of antenna
Band width of antenna
Return loss of antenna
Input power of rectenna
Output power of rectenna
Efficiency of antenna
Efficiency of matching circuit
Efficiency of rectifier circuit
Transmitted power from source
Width of RMPA
Length of RMPA
Feed width of RMPA
Inset feed length
Vacuum dielectric constant
Minimum constraint of antenna size
Maximum constraint of antenna size
Antenna input impedance
Voltage reflection coefficient
Voltage standing wave ratio
Quality factor due to radiation losses
Quality factor due to conduction losses
Quality factor due to dielectric losses
Quality factor due to surface waves
Total quality factor
Loss tangent of the substrate material
The speed of EM wave
Spatial angular frequency of wave
Radiation power of antenna
Maximum radiation intensity
Directivity of antenna with single slot
Directivity of array factor AF
Efficient bandwidth ratio
Aimed lower conner frequency
Aimed upper conner frequency
Designed lower conner frequency
Designed upper conner frequency
Conductivity of patch
Directivity of antenna
ntenna Radiation efficiency
Nomenclature of important parameters
Potential energy distribution
Best position of particle in the direction d
Local attractor of particle j in direction d
Gaussian distributed number within [0,1]
Random value within [0,1]
Input impedance of a RMPA
where G1 = G2, B1 = B2 and owing to that the two slots of the antenna are identical.
Resonant frequency of A RMPA
Antenna gain of a RMPA
Hence, antenna gain depends on radiation efficiency as well as directivity. The two parameters are calculated separately as follows.
Antenna efficiency of a RMPA
Bandwidth of a RMPA
Bio-inspired algorithms for antenna design
CS algorithm for antenna design
Therefore, the overall procedure of optimizing the antenna design for a RF harvesting system is shown as Algorithm 1, which has been implemented by MATLAB and Python.
Differential evolution for RMPA design
Finally, the locally optimal solutions will be selected and the global optimum value can be found. Based on the four steps mentioned, the overall pseudo code also implemented in MATLAB and Python is shown as Algorithm 2.
QPSO algorithm for RMPA design
The evolutionary particle swarm optimization (PSO) is a global search technique with incomparable advantages in searching speed and precision. It was originally introduced by Kennedy and Eberhar [34–36]. The basic idea of PSO is inspired by the social behavior of interactions between members including birds and fish. There are three main attractive features of PSO: robust search ability, fast computation and easy implementation [34, 35, 37]. In addition to its advantages, it has a slow solution fine-tuning ability of the solution, which sucks the solution towards the locally optimum value.
Accordingly, QPSO, as the modified PSO technology, was proposed to enhance the global search ability. The essential difference between the QPSO and PSO is that the movement of particles follows the principles of quantum mechanics instead of Newtonian mechanics.
During the whole procedure, the local optimal value would be updated. The overall process is described in Algorithm 3
Some assumed properties of designed antenna
Height of substrate
Optimal antenna for GSM1800
Parameters setting of algorithms QPSO, CS, and DE
Number of nest
Numbers of population
Test case 1: antenna size should be less than 100 mm
Summary of the properties of designed antenna based on QPSO, CS, and DE for antenna size less than 100 mm
Antenna gain (dBi)
Efficient bandwidth ratio
Patch width (mm)
Patch length (mm)
Inset feed length (mm)
Notch width (mm)
Run time (s)
Test case 2: antenna size should be less than 150mm
Comparison between the properties of designed antenna based on QPSO, CS, and DE for antenna size less than 150 mm
Antenna gain (dBi)
Efficient bandwidth ratio
Patch width (mm)
Patch length (mm)
Inset feed length (mm)
3.23 · 10−5
Notch width (mm)
Run time (s)
The general anatomy of an RF energy harvester has been explained and examined. Some state of the art designs for receiving antenna including both narrow-band and broad band antennas have been introduced. In the second part, a mathematical weighted evaluation model involving antenna efficiency, center frequency, bandwidth, and gain was proposed to evaluate the performance of a RMPA for a RF harvesting system.The heuristic optimization approaches CS, DE, and QPSO were introduced and then utilized to give optimal designs for a GSM1800 receiving antenna. The proposed optimization algorithms successfully achieved optimal solutions under two different antenna size constraints. The overall comparison between QPSO, DE, and CS showed that the DE based optimization design approach provides the best solution and hence has the best globally optimum value search ability. This can significantly enhance antenna performance. Moreover, among the three optimization approaches, the CS algorithm has the best robustness. Furthermore, the simulations using QPSO based algorithm indicate its superiority displaying a faster convergence speed than DE and CS in the application of solving a complex electromagnetic problem.
Availability of data and materials
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