Triple-Band Single-Layer Rectenna for Outdoor RF Energy Harvesting Applications

A triple-band single-layer rectenna for outdoor RF energy applications is introduced in this paper. The proposed rectenna operates in the frequency bands of LoRa, GSM-1800, and UMTS-2100 networks. To obtain a triple-band operation, a modified E-shaped patch antenna is used. The receiving module (antenna) of the rectenna system is optimized in terms of its reflection coefficient to match the RF-to-DC rectifier. The final geometry of the proposed antenna is derived by the application of the Moth Search Algorithm and a commercial electromagnetic solver. The impedance matching network of the proposed system is obtained based on a three-step process, including the minimization of the reflection coefficient versus frequency, as well as the minimization of the reflection coefficient variations and the maximization of the DC output voltage versus RF input power. The proposed RF-to-DC rectifier is designed based on the Greinacher topology. The designed rectenna is fabricated on a single layer of FR-4 substrate. Measured results show that our proposed rectenna can harvest RF energy from outdoor (ambient and dedicated) sources with an efficiency of greater than 52%.


Introduction
At present, wireless sensor network devices that use modern technology, such as the Internet of Things (IoT) [1], require less and less power for their operation [2,3]. To extend the use of these devices, i.e., to reduce their battery replacement during wireless network operation, several techniques have been developed. Radio Frequency (RF) Energy Harvesting (EH) is one of these techniques, which is mostly based on ambient radio wave sources in wireless network systems [4,5]. Although RF EH technology was introduced to the research community in recent years, noteworthy work is already reported in the literature.
The microstrip patch antenna has been widely used as an RF energy harvester in various applications and for different frequency bands of operation [6][7][8][9]. It exhibits several comparative advantages, such as ease of fabrication, relatively low cost, small physical size compared to the wavelength of the operating frequency, and medium complexity [10][11][12]. Therefore, it has been established as an attractive technique for RF EH applications [13].
The key performance numbers of an antenna to harvest satisfactory values of energy from the environment include the reflection coefficient (S 11 parameter) of the system, the gain, Stochastic algorithms are classified into heuristics and meta-heuristics. The latter ones, due to their trade-off mechanisms of randomization and local search which they are equipped, usually achieve a better performance score [27]. Moth Search (MS) is a newly introduced metaheuristic algorithm for global optimization problems [28]. It is a bioinspired algorithm that is based on two distinctive movement features of moths in nature; the phototaxis, i.e., a movement of a living organism (mostly referred to flying insects) towards to or away from a source of light, and the Lévy flight, i.e., a random path in which the step-lengths have a probability distribution whose tails are not exponentially bounded.
In this work, we design and fabricate a novel triple-band single-layer rectenna for outdoor RF energy harvesting applications. The proposed rectenna can harvest RF energy both from ambient and dedicated sources, due to its tuning operation in the frequency bands of LoRa and mobile communication (GSM-1800 and UMTS-2100) networks. It comprises a modified E-shaped patch antenna that is designed on a single layer of FR-4 substrate, providing low-cost fabrication prototyping. The triple-band operation of the antenna -module has been achieved by the combination of the MS optimization algorithm and a commercial high-frequency electromagnetic simulation software.
The main contributions of this paper are summarized as follows: • Use of the MS algorithm (MSA) to obtain an optimal solution for the antenna module of an electromagnetic radiation harvesting system. • Performance improvement of the IMN based on a three-step process that includes the minimization of the reflection coefficient (stopping criterion of −20 dB), the minimization of the S 11 magnitude variations at the frequencies of operation over an RF input power range of 20 dB (−10 dBm to 10 dBm), and the maximization of the provided DC output voltage at the same range of RF input power.
The RF-to-DC rectifier of the proposed rectenna is based on the Greinacher topology. To the best of the authors' knowledge, this is the first time that (a) a triple-band rectenna is designed to operate in the frequency bands of LoRa, GSM-1800, and UMTS-2100 networks, (b) the MSA is applied to obtain an optimal solution in a real problem of application in electromagnetics, and (c) a three-step process is applied to obtain a feasible solution for the IMN of the proposed rectenna.
This work is an extended version of the preliminary study published in [29]. The rest of the paper is structured as follows. Section 2 describes the mathematical model of the MSA, the optimization process of the proposed antenna, the computation process of the proposed RF-to-DC rectifier, and the rectenna prototype fabrication. Section 3 depicts the experimental setup that has been used to perform the measurements, as well as the main results of the fabricated rectenna (reflection coefficient, radiation pattern, gain, and PCE). Finally, our concluding remarks are outlined in Section 4.

Moth Search Algorithm Description
Moths are a group of insects that include all the species in the order of Lepidoptera, but butterflies. Many species of moths, especially their caterpillars, are significant agricultural pests in many areas around the world. The two most important features of moths that characterize their motion in the natural environment are phototaxis and Lévy flight. Phototaxis is the tendency of a living organism to fly towards or away from a source of light. Although the cause of the phototaxis is still unknown, one of the strong hypotheses assumes that moths fly to a source light through a spiral trajectory to maintain a fixed angle to the celestial light. Lévy flight is one of the most important flight trajectories in natural environments that is adopted by many species. It is a random path in which the step size is subject to Lévy distribution, i.e., a probability distribution whose tails are not exponentially bounded. The MSA adopts these two features to model a nature-inspired swarm intelligence (SI) meta-heuristic technique that can be applied in various global optimization problems [28].
To describe the optimization process of MSA, let us consider as NPop, the population of moths, which is divided into two equal sub-populations, NPop A and NPop B . Each i moth (i is the population index of the moths, i.e., i = 1, 2, . . . NPop) is ranked based on the score of its objective function. This ranking score is used to classify each moth into one of the two sub-populations. Because the i moth with the best position, e.g., m g best (g is the generation index of the moths, i.e., g = 1, 2, . . . MaxGen), will be the one that is closest to the source light, we can easily derive that the moths that are classified to NPop A sub-population are closer to the light source, and the moths that are classified to NPop B sub-population are faraway from the light source.
Based on the previous classification, the position of the i-th moth at the g-th generation in NPop A sub-population (Lévy flight) is expressed by where m g i and m g+1 i are the current and the next position at generation g, f sc is a scale factor associated with the optimization problem, and L(x) is the Lévy distribution defined by where index ∈ (1, 3] is an index number, Γ is the gamma function, x is a positive number, and f sc is a scale factor given by where step max is the maximum step size of the random path that is subject to Lévy distribution. Accordingly, the the position of the i-th moth at g-th generation in NPop B subpopulation (straight flight) is expressed by where m g best,j is the best solution (the moth member of the population with the best position) at g-th generation, j is the decision variables index of the optimization problem, i.e., j = 1, 2, . . . MaxVar, and f ac is an acceleration factor associated with the optimization problem, which is given by In (4), the position vector of the g + 1 generation is controlled by a random number rand ∈ [0, 1], thus with a probability of 50% to be updated by one of the two equation parts. Algorithm 1 summarizes the pseudo-code of the optimization process described by the MSA.
The time complexity of the MS algorithm at each iteration can be expressed as where NPop is the population size, D is the number of decision variables, and F is the time complexity of the given optimization function. Set iA = 1 and index = 1.5 8: for (iA = 1; iA + +; iA ≤ NPop A ) do 9: Compute the scale factor f sc using (3) 10: Compute the Lévy distribution parameter value using (2) 11: Compute the position of each moth using (1) Set iB = 1 15: for (iB = 1; iB + +; iB ≤ NPop B ) do 16: Set j = 1 17: for (j = 1; j + +; j ≤ MaxVar) do 18: if (rand ≥ 0.5) then 19: Compute the position of each moth using (4a) 20: else 21: Compute the acceleration factor using (5) 22: Compute the position of each moth using (4b) 23: end if 24: end for 25: end for 26: Compute the updated fitness value OF(m g i,j ) for each moth 27: Update the moth with the best position m g best,j based on the fitness value 28: end for

MSA Performance Evaluation
The performance evaluation of the MSA is carried out by using seven popular metaheuristic algorithms, namely the Particle Swarm Optimization (PSO) [30], the Differential Evolution (DE) [31], the Biogeography Based Optimization (BBO) [32], the Grey Wolf Optimizer (GWO) [33], the Artificial Bee Colony (ABC) [34], the Teaching Learning Based Optimization (TLBO) [35], and the Ant Colony Optimization (ACO) [36]. To evaluate the performance of MSA against the previously mentioned algorithms, 10 common test functions are used (  Table 1 summarizes the performance results (mean values of the computed fitness function for the 100 independent trials) of the MSA against 7 popular meta-heuristic algorithms. From the presented results we can conclude that the MS algorithm achieves the best score in 7 out of 10 test functions, with the second-best score by the TLBO algorithm. To better evaluate the performance results, the non-parametric Friedman test is applied, with its results summarized in Table 2. Once again, from the presented results, we can conclude that the MS algorithm achieves the best mean ranking, with the second and the third-best score by TLBO and PSO, accordingly.

Triple-Band Single-Layer Rectenna
The word "rectenna" originates from the combination of the terms rectifier and antenna. Thus, in the research field of electromagnetics, a rectenna refers to the system that incorporates RF EH capabilities from ambient and dedicated RF sources, as well as power conversion capabilities from the RF input to a DC output. The first feature is acquired by the use of an RF receiving module, such as an antenna operating at specific operating frequency bands of interest. The latter one is obtained by the application of a power conversion module, such as an RF-to-DC rectifier. To achieve the maximum PCE, i.e., the maximum RF power conversion to DC output voltage, the two aforementioned modules should be matched in terms of their impedance. Therefore, an IMN is often required between the antenna and the RF-to-DC rectifier to adjust the impedance of these two modules, which in most cases differs. Figure 1 illustrates a typical multiband rectenna block diagram.

Antenna Design Procedure
To design a multiband antenna as an RF receiving module in a rectenna, suitable for RF EH applications, is, in most cases, a complex and demanding task. The analytical approach of this task is not a convenient solution, and, in many cases, will lead to poor results. Thus, in most cases, an optimization method is required. In this work, we combine the MSA as a global optimizer in real engineering problems along with a high-frequency electromagnetic solver (HFSS, © 2020 ANSYS, Inc., Canonsburg, PA 15317, USA) to obtain a feasible solution of the antenna receiving -module. Figure 2 displays the geometry of the proposed modified E-shaped patch antenna as a receiving module in a rectenna system. It comprises a patch antenna with a modified E-shape as an RF energy harvester. The length of the microstrip line is properly selected to adjust the input impedance of the patch antenna to the characteristic impedance of 50 Ω. The antenna is placed on an FR-4 substrate (thickness = 1.6 mm, relative permittivity r = 4.4, tanδ = 0.02 (Values are retrieved from the commercial solver's database.). Beneath the substrate, a ground plane is adjusted. We should point out that boundary conditions of finite conductivity, i.e., conductivity = 5.80 × 10 7 Siemens/m and relative permeability = 1, are adopted for the radiator, the microstrip line, and the ground plane of the proposed antenna. If we observe the shape of the radiator that is illustrated in Figure 2a, we can conclude that the proposed modified E-shaped antenna requires 13 parameters (i.e., decision variables of the optimization problem) to describe its full geometry. Therefore, in our case, and to define these parameters, the choice of an optimization algorithm, such as the MSA, is a straightforward process. The objective of the previously described optimization problem is to minimize the reflected power of the proposed antenna, i.e., to minimize the reflection coefficient or the S 11 magnitude of the proposed antenna. The minimization of the reflected power should occur at three different frequencies that are included in the frequency bands of (a) LoRa (863-870 MHz), (b) GSM-1800 (1710-1880 MHz), and (c) UMTS-2100 (1905.1-2155.3 MHz). At each iteration, an obtained solution by the highfrequency electromagnetic simulation software is accepted and stored, if the reflection coefficient value (S 11 magnitude) is equal to or less than a predefined limit. Considering all the above, the objective function of the given optimization problem can be formulated as The optimization process is applied as follows. Firstly, the parameters of the MSA are defined for each member of the moth population NPop. A set of decision variables MaxVar is selected, which defines the geometry of the proposed antenna model, for each member of the moth population. Secondly, the antenna model is parsed from the high-frequency electromagnetic solver and the reflection coefficient at the desired frequencies is computed. Thirdly, based on the output of the solver, the position of each moth at sub-populations NPop A and NPop B is also computed. Finally, the fitness function for each member of the population is evaluated and the above process is repeated until stopping criteria are met. Table 3 lists the optimal solution (decision variables of the optimization problem) of the modified E-shaped patch antenna obtained by the optimization process using the MS algorithm. This feasible solution corresponds to the parameters of the proposed antenna that describe its geometry.

Proposed RF-to-DC Rectifier Design
The rectifier is the key element of the rectenna system and the cornerstone of the overall design. It detects and converts RF energy to DC voltage, to power up low consumption electronic devices or charge a battery cell [37]. The indispensable rectifying elements of the circuit can be either a set of diodes or transistors. In the proposed design, we used a Schottky diode because of its low threshold voltage [38]. Specifically, the Avago's HSMS285C (SOT-323) zero bias Schottky diode, with a low forward voltage value of V F = 150 mV, is used [39]. Figure 3 portrays the configuration of the Greinacher voltage-doubler that has been applied in our design. The voltage-doubler uses two zero bias Schottky surface mount diodes (Avago HSMS285C series), and two AVX surface mount ceramic capacitors (MLCCs) C 1 = C 2 = 100 pF. Two different impedance matching branches consisting of several conductor lines, and with appropriate width (W) and length (L), comprise the proposed IMN. This design ensures impedance matching between the rectifier and the antenna for the given frequencies, as Figure 3b depicts. For the configuration of the proposed design, we consider a standard antenna port of Z A = 50 Ω. Table 4 lists the optimal physical parameters of the transmission lines obtained by the S-parameter simulation controller toolbox (ADS-© Keysight Technologies 2000-2021, Santa Rosa, CA 95403-1738, USA) using the Gradient optimizer. We should also point out that, due to the variations of the input impedance of the rectifying circuit versus the RF input power, the Large-Signal S-Parameter simulation tool of the previously mentioned software is applied.  The computation process is as follows. After the selection of the circuit's topology, as long as its peripheral elements, such as diodes, resistors, and capacitors, the Harmonic Balance method (Advanced Design System (ADS-© Keysight Technologies 2000-2021, Santa Rosa, CA 95403-1738, USA)) is applied to compute the reflection coefficient versus the frequency of the provided circuit. Also, the power conversion versus the output load is evaluated. Depending on the results, the next step includes the tuning of the physical parameters that contribute to the IMN. Finally, the efficiency versus the incident RF input signal of the overall system is computed.

Experimental Setup
An experimental evaluation of the prototype rectenna was performed to assess its main key performance numbers. For the antenna module assessment, we have included the reflected power or the reflection coefficient versus the frequency, and the performance numbers of radiation pattern, the HPBW, and the maximum gain, at the frequencies of operation. Moreover, for the rectifier module, the DC output voltage and the PCE have been also comprised. The experimental validation of the prototype rectenna was performed in a controlled environment (see Figure 5) by using the following equipment: The measurement process is described as follows. The vector network analyzer is used to obtain the measured reflection coefficient (S 11 ) for both the antenna and the RF-to-DC rectifier. For the radiation patterns and the gain of the fabricated antenna, the signal generator is used to feed the transmitter antenna (double-ridged waveguide horn antenna) at the frequencies of interest (Figure 5a). The distance between the transmitter antenna and the antenna under test (AUT) is in the far-field region. The EMC analyzer is attached to the AUT to record the measurement results. Moreover, the Friis transmission equation is used to compute the gain values of the AUT. Finally, for the PCE measurements, a signal generator is used to feed the RF-to-DC rectifier under test (RUT), with the measured DC voltage values indicated in the digital multimeter (Figure 5b).
One may notice that the fabricated antenna is experimentally evaluated in a controlled environment. Performing a set of measurements for the experimental validation of a rectifying antenna in an anechoic chamber exhibits the advantage of accuracy in the recorded values of the key performance numbers, such as the gain and the radiation pattern. The configuration of an anechoic chamber allows only the presence of the incident field in the AUT, eliminating any reflected signal and multi-path propagation. The experimental validation of a rectifying antenna in a controlled environment generally increases the measurement uncertainty, due to the presence of the reflected signals and multipath propagation. However, this feature can significantly deteriorate when the AUT, as well as the transmitting antenna, is in the far-field from any obstacle in the surrounding space.    Figure 8 portrays the computed results in a 3D polar plot of the realized gain for the modified E-shaped patch antenna. From the presented graphs, we can derive that the maximum computed values of the realized gain are 4.56 dBi, 2.95 dBi, and 1.38 dBi, for the frequency band of LoRa, GSM-1800, and UMTS-2100 networks, respectively. Following the measurement process described in Section 3.1, the maximum measured gain values of the antenna are 4.3 dBi, 2.62 dBi, and 1.14 dBi, for the previously mentioned frequency bands, accordingly. At this point, we should point out that the fabricated antenna does not exhibit high gain values. However, this is insignificant for a receiving module in a rectenna system, when it harvests the ambient energy of the surrounding environment [13,40].

Proposed RF-to-DC Rectifier Results
The voltage-doubler input impedance for the triple-band design has been computed using the S-parameters simulator of the Advanced Design System (ADS). We consider a standard antenna port of 50 Ω. The size of the impedance matching circuit has been optimized and adjusted to the input impedance of the overall system. The derived values of the computed impedance are 52.43 − j0.84, 53.16 − j3.46, and 49.34 + j1.31, at the frequencies of 865 MHz, 1840 MHz, and 1954 MHz, accordingly. Figure 9 compares the computed against the measured results versus frequency of the reflection coefficient (S 11 magnitude) for the proposed triple-band RF-to-DC rectifier at a reference level of RF input power equal to 0 dBm. From the presented graph we can derive that the tripleband rectifying circuit operates satisfactorily in the following frequency bands:   Figure 10a displays the computed RF-to-DC PCE as a function of the output load resistance for various levels of the input power P in . From the presented plots we can easily derive that the optimum (i.e., the load value that achieves the maximum PCE) output load is equal to 14 kΩ. The overall system RF-to-DC efficiency n is computed as where P DC is the DC output power, P in is the RF input power, V out is the output DC voltage, and R L is the output load resistance. Figure 10b portrays both the PCE and the DC output voltage versus the input power level for the proposed triple-band rectifier. The maximum efficiency is 39.5% for an input power level of 6 dBm, whereas the efficiency is greater than 20% for an RF input signal greater than −11 dBm. Also, it is worth noting that the DC output is above 0.2 V for an input power level equal to −16 dBm, whereas for RF power greater than −11 dBm, the DC output value surpasses 0.5 V.
(a) (b) Figure 10. (a) Computed RF-to-DC power conversion efficiency versus the output load resistance for various levels of the P in and (b) Total computed RF-to-DC power conversion efficiency (triple-tone) and DC output versus P in . Figure 11a demonstrates the comparative results of the computed against the measured efficiency versus the input power level at the frequency of 865 MHz (LoRa). The measured peak efficiency is 52.6% for an input power of 2.8 dBm. Also, the input power dynamic range for efficiency greater than 20% is 20 dB (−10 dBm to 10 dBm). Figure 11b illustrates the comparative results of the efficiency at the frequency of 1840 MHz (GSM-1800). The maximum measured efficiency is 27.1%. The dynamic range of the input power for efficiency greater than 20% is 16.2 dB (−6.2 dBm to 10 dBm). Finally, Figure 11c presents the comparative results of the efficiency at the frequency of 1954 MHz (UMTS-2100). From the given graph we can derive that the peak efficiency is 30% and the input power dynamic range for efficiency greater than 20% is 15 dB (−6.2 to 8.8 dBm). It is worth noting that computed and measured results of the PCE are in acceptable agreement.  Table 5 lists the comparative measured results of the proposed work against selected related publications from the literature. The key parameter numbers that are selected for comparison are the substrate of the rectenna, the frequency bands of operation, the maximum achieved gain of the antenna, the implemented technique for the IMN, the RF input power level, and the PCE, as well as the DC output voltage of the RF-to-DC rectifier. From the presented results we can conclude that our proposed rectifier exhibits competitive results against other related work. It is fabricated on a cheap substrate (FR-4) and it presents a fine-tuning operation (by evaluating both the reflection coefficient of the antenna and the RF-to-DC rectifier) at the frequency bands of interest. Moreover, it has acceptable gain values at the tuning frequencies and it adopts an IMN technique with a relatively medium complexity. Finally, the proposed rectenna achieves satisfactory PCE and high DC output voltage values, which make it a strong candidate for RF energy harvesting applications.

Conclusions
In this work, we have presented a triple-band single-layer rectenna for outdoor RF energy harvesting applications. The proposed rectenna operates satisfactorily in the frequency bands of LoRa, GSM-1800, and UMTS-2100 networks. The proposed rectenna is equipped with a modified E-shaped patch antenna. The optimal solution of the antenna is obtained by combining the MS optimization algorithm and a commercial high-frequency electromagnetic solver. The IMN of the proposed rectenna is designed based on a series of shunted and shorted stubs. The final geometry of the IMN is obtained by applying a threestep process, including the minimization of the refection coefficient values at the desired frequencies of operation, the minimization of the variations of the reflection coefficient values over an RF input power range, and the maximization of the DC output voltage over the same RF input power range. The Greinacher voltage-doubler topology is selected to harvest RF signals into DC voltage. The proposed rectenna is fabricated and evaluated in a controlled environment. Measured results of the proposed rectenna exhibit tripleband tuning operation in the previously mentioned frequency bands, broadside operation (maximum HPBW of 120 deg), acceptable gain values (maximum gain of 4.3 dBi), and maximum PCE of 52.6%. These results make it a promising candidate for various RF harvesting applications, such as IoT or wireless sensor networks. Future work includes the investigation of alternative techniques for the feeding of the antenna, the inclusion of both the antenna and the IMN in the optimization process, and the experimental assessment of the fabricated system in a real environment by harvesting RF energy from both dedicated and ambient sources.