I. Introduction
Microwave power transfer (MPT) is attracting attention for use in Internet of Things (IoT) and medical devices [
1,
2] because it has the potential to transmit power over long distances, irrespective of the receiver’s (Rx) location. However, it also has the disadvantage of low efficiency due to path loss. To overcome this drawback, the transmitter (Tx) configures a massive array antenna and increases the magnitude of the radiated signal per channel. Unfortunately, this approach intensifies the sidelobe, which can adversely affect the surrounding electronics, as well as human beings; therefore, it is necessary to lower the sidelobe level (SLL) while maintaining the magnitude of the main lobe.
Several studies have been conducted on high-efficiency MPT, such as retro-reflective beamforming [
3,
4]. This technique, which has been investigated for radar applications, transfers power efficiently by tracking the location of the Rx through a pilot signal and transmitting power in the same direction. Other studies on MPT have used look-up tables (LUTs) [
5]. In this method, phase values for an array antenna that can transmit power optimally in the direction of the designated Rx antenna are stored in an LUT, with the beamforming directed toward the located Rx antenna. Although [
3–
5] achieved high efficiency under ideal conditions, they did not consider lowering the SLL; hence, MPT studies aiming to reduce SLL are underway [
6–
9].
A few researchers have applied various techniques for the non-uniform distribution of the magnitude of signals from array antennas; for example, [
6] studied this for the application of MPT to drones. In their simulation, the researchers suppressed the SLL to −17.7 dB by applying a Gaussian function to the amplitude distribution of a 1 × 14 Tx array antenna at 5.8 GHz. In [
7], the results for uniform amplitude distribution were compared to those for applying the Kaiser function to the amplitude distribution of an array antenna. The researchers verified through simulation that their technique reduced the SLL to −12.8 dB at 9.5 GHz. In [
8], the Taylor function was applied to the feeding network of an array antenna. The researchers fabricated a 1 × 8 array antenna at 28 GHz and confirmed the reduction of SLL to −15.2 dB. Study [
9] matched the weighting coefficient of the Chebyshev function to the feeding line impedance of an antenna.
The researchers designed a 1 × 5 array antenna at 9.3 GHz and verified the suppression of the SLL to −17.4 dB. However, the elements fabricated in these studies could only form one beam pattern for a fixed SLL. Different elements may be needed to achieve a minimum SLL for different beam directions. To overcome this drawback, we propose an adaptive beamforming system with sidelobe suppression that can actively form the desired beam. This paper presents a method for lowering SLL by adjusting the amplitude distribution of a two-dimensional planar array antenna (PAA). The phase distribution of a signal applied to an array antenna determines the direction of the main beam, and the amplitude distribution determines the SLL, main beamwidth, and nulls [
10]; therefore, to reduce SLL, the amplitude of the array antenna must be distributed non-uniformly. This study proposes a method for obtaining an amplitude distribution matrix with the weight of each antenna as an element in an
M ×
N PAA. This
M ×
N matrix is derived as the product of the amplitude distribution vectors of two linear array antennas (LAAs) constituting the PAA. To lower the SLL while maintaining the total transmission power, we increased the amplitude of the signal applied to the central element of the array antenna and lowered the amplitude of the signal applied to the side element using the tapered amplitude distribution method [
10]. Although this method reduces the sidelobe of the beam pattern, it weakens directivity owing to the widening of the beamwidth; therefore, we used the Chebyshev tapered amplitude distribution method, which is efficient and possesses the strongest directivity among distribution methods with the same maximum SLL [
11]. Moreover, by limiting all sidelobes to the same level, we minimized the RF radiation power in all directions, except for the main lobe.
To verify the validity of the proposed method, we designed a digital beamforming system with a 4 × 4 Tx array and an Rx operating at 5.8 GHz. The Tx of the digital beamforming system was an adaptive device capable of generating signals with the desired phase and amplitude. Furthermore, for MPT, the Tx consisted of a digital Tx stage for RF signal generation and a power amplification (PA) stage. The magnitude of the signal from each channel of the Tx had a least significant bit (LSB) of 0.2 dB, and the phase had an LSB of 0.36°. The maximum output power per channel was 1 W. We conducted the measurements in the far field and verified the performance using the received power.
The remainder of this paper is organized as follows. Section II describes the sidelobe suppression method for the PAA. Section III explains the design, implementation, and simulation of the digital beamforming system for verification. Section IV conducts the experiments and discusses system performance. Finally, Section V presents the study’s conclusions.
II. Sidelobe Suppression Beamforming
Fig. 1 shows a schematic diagram illustrating the relationship between sidelobe and directivity during beamforming. It depicts steering of the main beam in the direction for received power and sidelobe suppression in the direction of the person to reduce power. As mentioned in the previous section, the sidelobe can be altered by manipulating the amplitude distribution of the array antenna, but a nonuniform amplitude distribution can widen the main lobe’s beamwidth [
10], weakening the directivity of the array antenna. Directivity is the yardstick for power transmission in the intended direction; therefore, the SLL must be reduced as much as possible, and an amplitude distribution applied with high directivity. To this end, studies frequently use a tapered amplitude distribution to increase the amplitude of the central element antenna and decrease that of the side element antenna. The Chebyshev taper has the narrowest main lobe beamwidth, given a limited SLL [
11]; therefore, we applied the Chebyshev taper to the amplitude distribution through an array factor (AF) of far-field approximation.
Fig. 2 depicts the structure of the PAA. As shown in
Fig. 2, the PAA consists of two intersecting LAAs, and AF is equal to the product of the AFs of the two LAAs. The AFs of the two LAAs are as follows [
10]:
where am and bn are the amplitude distributions of the x- and y-axis LAAs, M and N are the numbers of x-axis and y-axis array elements, dx and dy are the spacings between the elements of the x-axis and y-axis LAAs, and ψx and ψy are the phases of the x-axis and y-axis LAAs, respectively. k is the wave number, θ is the elevation angle, and φ is the azimuth angle. The amplitude distributions of the two axes, am and bn, can be expressed as 1 × M and 1 × N vectors, respectively,
Furthermore, the AF of the PAA can be expressed by the product of
Eqs. (1) and
(2), as follows:
where wm,n is the product of am and bn. An M × N matrix with wm,n, which is the amplitude distribution of the PAA, can then be expressed as follows:
To obtain
Eq. (6), we analyzed the AFs of the LAA for the two axes. Since the phase and amplitude distributions are independent of each other in this process of obtaining the amplitude distribution, the phase (
ψx and
ψy) that determines the beam direction can be considered a constant; therefore, in
Eq. (1), the AF of the
x-axis LAA is a series of exponential functions that can be expressed as follows:
where
z = e j(kdx sinθ cosφ +ψ x).
Eq. (7) is the same as the (
M – 1)
th order equation, and can therefore be rewritten as
Because
Eq. (8) is a polynomial of the degree (
M – 1) equation, it can be expressed as a product of (
M – 1) linear terms, as follows:
where
zi are the roots in the AF,
βi are the null directions, and
i ranges from 1 to
M – 1; hence, if the null directions are known, the roots of the AF can be found, and the AF expressed as the product of linear terms can be completed. The AF equation, which is the product of a linear term, is developed in polynomial form, and the coefficients of each term are mapped to the amplitude coefficients of the array antenna; hence, it describes the process for finding the null directions by mapping the Chebyshev polynomial [
11] using the array factor. To this end, the difference in magnitude between the main lobe and the sidelobe is defined as follows:
where (θML, φML) is the main lobe direction and (θSL, φSL) is the sidelobe direction. We then derived the null directions (βi) using the following equations:
and
This process is explained in detail in [
12].
To determine the roots of the AF, null directions obtained through
Eq. (12) were assigned to
Eq. (10), and
Eq. (9) was expanded as follows:
where wxp is the weight of the pth order term, and p ranges from 1 to M – 1. If aM is a coefficient that determines the overall magnitude of the amplitude distribution, then the coefficient of each order (wxp) can be expressed as a ratio; therefore, the amplitude distribution vector (1 × M) can be expressed as follows:
Applying
Eqs. (7)–
(14) to the
y-axis LAA yields the following vector:
where wyq is the weight of qth order term, and q ranges from 1 to N – 1.
The coefficients of the linear vector in
Eqs. (15) and
(16) are the same as those of the Chebyshev taper, gradually increasing from the side element of the vector to the central element; hence, if
Eqs. (15) and
(16) are applied as weights of the array antenna, the radiated power from the side element antenna is low, and the radiated power from the central element antenna is high. This technique is often used to determine the weights in array antennas to form low sidelobes [
9]. In this study, we need to know the amplitude distribution to be applied to the PAA; therefore,
W, which is the Chebyshev tapered amplitude distribution for the
M ×
N PAA, could be obtained through
Eq. (6). This process ends by mapping the elements of
W to the amplitude weights of each element of the PAA, allowing the realization of beamforming with an expected SLL.
Fig. 3 illustrates the process flowchart for obtaining the Chebyshev tapered amplitude distribution for sidelobe suppression beamforming.
IV. Experimental Verification
Fig. 11 shows a photograph of the experimental setup for sidelobe suppression beamforming. The Tx was connected to the PC to control the beamforming system. The Rx was connected to a spectrum analyzer (Anritsu MS2713E) to measure the RF power and an electronic load (Keithley 2380-120-60) to measure the DC power. The gain of the transmitted RF signal was adjusted based on the three amplitude distributions obtained in Section III-2. The total RF power from the array antenna was fixed at 7.5 W (38.8 dBm) in all cases.
Two experiments were conducted to verify the performance of the beamforming system. In the first, the radiation patterns of the
zx and
zy planes were measured. As shown in
Fig. 11, this was based on the relative power by rotating the Tx array antenna in place while fixing the position of the Rx at the center.
Fig. 12 illustrates the normalized radiation pattern plotted by measuring the received RF power from −90° to resemble that shown in
Fig. 8, which resulted from the simulation. Compared with the SLL with
W1, which was a uniform distribution, the SLL while applying
W3 decreased by 7.5 dB from −11.6 dB to −19.1 dB on the
zx plane and 4.4 dB from −11.5 dB to −15.9 dB on the
zy plane. However, we confirmed that the received RF power at the central position (0°) decreased by only 0.6 dB, from 21.0 dBm to 20.4 dBm. Furthermore, we verified that the rectified DC power also decreased by only 9.3 mW, from 67.8 mW to 58.5 mW.
In the second experiment, we verified the performance of beamforming in specific directions. As depicted in
Fig. 11, the received RF power of 15 × 15 points was measured on the plane (700 × 700 mm
2) where the Rx could exist. The phase values for each channel of the main beam direction were adjusted by (5), giving the AF of the far field approximation. The main beam direction was set as (
θ,
φ), with the center of the Tx array antenna as the origin in spherical coordinate systems. The experiment was conducted for three main beam directions, when (
θ,
φ) was (0°, 0°), (20°, 135°), and (20°, 220°), respectively. Therefore, nine experiments in total were conducted for the three cases of amplitude distribution and three cases of phase distribution.
Table 2 shows the distributions except for
W1 and (0°, 0°) where all the amplitudes and phases of the channels were identical.
Fig. 13 shows a color map obtained by measuring the 15 × 15 points of normalized received RF power for the nine experiments. We confirmed that the region with the sidelobe had smaller power in
W2 and
W3 than in
W1. Additionally, we verified the widening of the main lobe with an increase in the area occupied by power in the direction of the main lobe.
Table 3 summarizes the results of the second experiment, including the received RF power and SLL for the nine measurements. Furthermore, we calculated Δpower and ΔSLL (the differences between the received power and the SLL) from the uniform amplitude distribution (i.e.,
W1). In (0°, 0°)—the case with central beamforming—received power was the same as in the first experiment, but the SLL decreased further. This occurred because the origin of the measured 15 × 15 points was 1 m away from the Tx, but the remaining points were at greater distances than 1 m, meaning that the received power was lower. Therefore, in the case of beamforming toward the center, we confirmed ΔSLL to be 9.3 dB at the maximum. In (20°, 135°)—the case with the second direction—ΔSLL and Δpower were 5.9 dB and 0.8 dB in
W3, respectively. Additionally, in (20°, 220°)—the case with the third direction—ΔSLL and Δpower were 6.8 dB and 0.5 dB in
W3, respectively. These results proved that the received power barely decreased and that the SLL decreased significantly.
The experimental results compared with other studies on MPT are listed in
Table 4. As mentioned earlier, the comparison was based on the beam pattern of the
zx plane in
Fig. 12, which resulted from the first experiment. Studies [
3–
5] focused on the beamforming technique without considering lowering the sidelobe, and, in most cases, demonstrated high SLL. Additionally, [
6–
9] designed and manufactured a Tx device using a technique to lower the SLL, but different elements may be required to achieve a minimum SLL for other beam directions. The proposed sidelobe suppression beamforming system is suitable for safe wireless power transmission with high received power and low SLL.
V. Conclusion
This paper proposes a sidelobe suppression beamforming scheme for an MPT system with PAA. The technique applied to the proposed system involves controlling the magnitude of the signal transmitted from the array antenna. To apply this to a two-dimensional PAA, we described the procedure for obtaining the amplitude distribution matrix (M × N). Furthermore, to minimize decreased directivity due to the non-uniform amplitude distribution and to lower the SLL, we used the Chebyshev taper for the amplitude distribution.
To verify the proposed scheme, we implemented a digital beamforming system with a 4 × 4 Tx array and an Rx at 5.8 GHz. The radiation pattern results while adjusting the amplitude distribution confirmed that the SLL decreased by 7.5 dB to −19.1 dB on the zx plane, and by 4.4 dB to −15.9 dB on the zy plane, compared with uniform distribution. Furthermore, we verified that the received RF power was 20.4 dBm, even with sidelobe suppression. This amounted to a reduction of only 0.6 dB compared with the uniform distribution case. Through a color map, we demonstrated that the area occupied by the sidelobe decreased in the three-directional beamforming experiment. Moreover, compared with other studies, the proposed system has independent and flexible amplitude and phase control. Consequently, the adaptive beamforming system presented in this paper should be capable of delivering efficient and safe MPT by accurately forming a designed beam pattern.