A Simple Method for Solving the Power Fluctuation Issue of a Base Station’s Surrounding Areas Based on Half Tyler Distribution

Abstract

This paper proposes array antennas based on half Tyler (HT) distribution that can realize omnidirectional null-free (ONF) beams. Array 1 employs the usual edge feeding approach, working at 3.5 GHz with a bandwidth of 0.25 GHz, whereas array 2 operates at 26 GHz with a bandwidth of 3 GHz. We evaluated the far-field performance of linear arrays consisting of 6, 8, 12, and 16 elements. The simulation and measurement results show that the proposed HT approach can achieve a near-ONF pattern and cover a broad area of ±42° on an eight-element linear array. The ONF beam reduces community power fluctuations and increases power by 20 dBm in surrounding areas of the base station (BS). The fluctuation treatment effect can be influenced by adjusting the weighting of sidelobe depression (dp): compared to the uniformly excited one, for example, the maximum ONF gain of an eight-element linear operating at 3.5 GHz is only reduced by 0.5 dB when dp = −30 and by 1–2 dB when dp = −60.

1. Introduction

Uniformly excited array antennas inevitably generate radio power nulls, whose signal level is much lower than that of the surrounding area, due to the propagation and coupling characteristics of electromagnetic waves, as seen in Figure 1. This leads to increases in power fluctuations (PFs), poor communication quality, and limitations on the base station (BS) site selection process, which needs to be sure that these regions do not point to user groups [1]. Furthermore, 5G/6G communication technology proposes the large-scale distributed base station (BS) approach to provide faster data rates, reduced latency, and higher reliability communication, but this also results in more nulls at the same coverage [2]. Solving the PF problem in the configuration of directional antenna arrays is important because omnidirectional antennas cannot give better gains and data rates.

In the early stages of research in this field, by processing pattern roots, Lawson–Woodward theorem, and Newton iteration, scientists filled the antenna’s first null of the lower sidelobe to enhance the power quality near the BS and help reduce signal fluctuations [3,4,5,6,7,8,9,10]. The first null must now be filled in along with the other nulls in the sector to satisfy the demands for higher communication quality due to the advancements in communication technology. Researchers have employed a variety of algorithms, including genetic, particle swarm, and others, to fill the first null as computational science has advanced. These algorithms need lots of raw data for extensive training and learning [11,12,13,14,15]. Many experts have proposed or loaded some special structures to fill nulls of the pattern [16,17,18,19,20,21,22], which is suitable to fill a single antenna well but has little effect on the array. In addition, it is possible to solve the coupling problem and fill the null well by constructing particular decoupling structures within the array [23,24,25].

Although the cosecant square beam can provide more uniform coverage, it often requires an antenna or a leaky wave reflection surface, neither of which is appropriate for the BS [26,27,28]. To compensate for the communication quality of single-beam antennas in nonmain lobe beam directions, multi-input and multi-output (MIMO) technology is proposed in a 5G communication system, causing the emergence of multi-beam array antennas. Generally speaking, there are three methods for creating a high-gain multibeam array: first, by designing antenna units that can produce multiple beams and arranging them into an array [29]; second, by combining linear arrays with beams originating from different directions [30]; and others, by controlling the directions of multiple beams within the array using electrically adjustable components. On the other hand, an increasing number of beams results in complex feeding networks and higher energy consumption. To improve coverage and address communication blind spots well, a reflective intelligent surface (RIS) is considered as a key technology for 6G communication [31]. An RIS can further enhance directionality while achieving beam-switching capabilities depending on numerous electrically adjustable components, instead of using radio frequency channels. A large number of RIS-distributed plans have emerged to obtain better signal coverage [32]; in other words, resolving the vertical beam coverage issue in a way that minimizes the number of beams required vertically or only requires numerous beams horizontally can solve the feeding network energy problems in MIMO and reduce the RIS costs.

Therefore, we need to find better base station antenna (BSA) techniques. After repeated numerous simulations and verification, we discovered that the array can generate almost-omnidirectional null-free (ONF) beams, which means its radiation pattern almost contains zero nulls, if its excitations follow the half Tyler (HT) distribution. The Tyler technique, which has so far been frequently employed to suppress the sidelobe, is now used for the first time to produce an ONF beam. This simply uses the first N terms of 2N weighted random numbers obeying Tyler distribution as the excitations of the N array antenna, where N is arbitrary, negating the requirement for an objective function and intricate iteration processes. Taking the N = 12 array as an example, it is possible to observe almost all of the uniform (all-“1”) array’s nulls. Figure 2 shows the flow chart of the ONF beam and HT excitation method. Even the ONF effect improves when the excitation amplitudes are squared (HT²), indicating a higher amplitude variation between elements. The ONF beam oriented vertically can effectively resolve the power distribution and blind area of the BS antenna.

This manuscript will be divided into four parts to introduce our work: the first section presents an introduction; the second section presents the HT beam simulations; the third part presents the measurements; and the fourth part presents the conclusion.

2. HT Distribution and Simulation Results

2.1. Elements and Linear Array

Figure 3 displays two randomly generated elements using F4BM with ${ϵ}_r=2.2$ and $\tan \delta =0.0007$. The element employing the edge feed is a vertical (we can also call it 0°) polarization structure composed of a copper ground at the bottom of the F4BM and an etched copper patch on top of the F4BM, with a height of 1.57 mm. The specific dimensions of element A are listed in Figure 3a as follows: a = 16.4 mm, b = 9.7 mm, c = 26.1 mm, and L = 50 mm. Element B, which uses the aperture-coupled feed, is a 45° polarization antenna that consists of a square copper patch with edge length d = 2.9 mm on the top of the upper F4BM1 (i.e., the upper F4BM) with a height of 1.016 mm, a copper ground with an etched slot between the upper and the lower dielectric (F4BM1 and 2; F4BM2’s height is 0.203 mm), and a feed stripe at the bottom of F4BM2 (i.e., the lower F4BM). Figure 3b lists the material parameters of element B: i.e., e = 2.2 mm, f = 3.4 mm, L₂ = 13 mm.

$$\mathsf{\Gamma }=\frac{Z_{in}-Z_0}{Z_{in}+Z_0}$$

(1)

$$\left|S_{11}\right|=20\mathrm{l}\mathrm{g}\left|\mathsf{\Gamma }\right|$$

(2)

|S₁₁| can be obtained using Equations (1) and (2), where $\mathsf{\Gamma }$ is the return loss of the antenna, Z_in is the impedance of the antenna, and Z₀ is the impedance of the feed (50 Ω in the work). Generally, people think antennas can operate well when its |S₁₁| is less than −10 dB. These elements are analyzed using commercial computer simulation technology 2019 (CST2019) software. We can enhance their electromagnetic characteristics by modifying the structure factors. Figure 4 shows the final S-parameter results. Figure 4a,b show that element A is a narrow-band antenna whose center resonator frequency is 3.5 GHz and frequency band is about 0.25 GHz, and element B is a broad-band antenna that can work at 22–27 GHz. Figure 5 shows their radiation patterns, based on which we can determine that their maximum gains are 7.2 dBi and 6.1 dBi, respectively, when they are operating independently at 3.5 GHz and 26 GHz. First, we determine the unit number N of the linear array. Following that, we must generate 2N Taylor random numbers, choose the first N items, and apply sidelobe depression (dp) weighting to them, as shown in Equation (7), where nl is the sampling times, N is twice the number of elements, and qh is the desired weighted Tyler excitations.

$$at={10}^{-\frac{dp}{20}}$$

(3)

$$a=\log (at+\sqrt{a{t}^2-1})$$

(4)

$$\mathrm{s}\mathrm{g}\mathrm{m}=\mathrm{n}\mathrm{l}/\sqrt{a^2+{\left(nl-5\right)}^2}$$

(5)

$$\mathrm{S}=\prod _{m=1}^{nl-1}(1-n^2/(\mathrm{n}\mathrm{l}/\sqrt{a^2+{\left(nl-5\right)}^2}\times \sqrt{a^2+{\left(m-5\right)}^2}))$$

(6)

$$qh=1+2\times \frac{\sum _{n=1}^{nl-1}\frac{\frac{\mathsf{\Gamma }{\left(n1\right)}^2}{\mathsf{\Gamma }\left(nl-n\right)}}{\mathsf{\Gamma }\left(nl+n\right)}\times s\times \cos (\frac{4}{N}-1)}{N-1}\times n\times \pi$$

(7)

At this stage, we can adjust the suppression degree as needed. To satisfy the demand of higher gain and specific anti-power fluctuations, it can use a higher dp, such as −30 dB. For higher anti-power fluctuations, it can use a lower dp, such as −60 dB. We will describe carefully the differences observed with different dp values in this paper. We can obtain the ONF beam by using the N-weighted data as the excitations of an N-unit array. We validate these using two such antennas with different frequencies, polarizations, feed techniques, and bandwidths. Additionally, we can obtain the steering ONF beam by modifying the phase difference of each unit. As seen in Figure 6, we construct an N-unit linear array using the elements A and B described above, respectively, where N is an arbitrary number. Additionally, there are half wavelengths, approximately, between elements d1 and d2. We will introduce the results of these linear arrays with different N values, such as N = 8, 12, 16, and so on, when using the proposed method and analyze the difference.

Assuming the linear array is placed on the BS with a height H of 30 m, as shown in Figure 1, and an angle of α between the antenna and vertical direction, we can use Equation (9) to determine the power distribution in the cell before and after ONF formation at 15 mW of input power:

$${Power}_{dis\left(i\right)}=10\times \lg \left(15\right)+\mathrm{g}\mathrm{a}\mathrm{i}\mathrm{n}\left(\mathrm{i}\right)-\mathrm{l}\mathrm{p}$$

(8)

$$lp=32.45+20\times \mathrm{l}\mathrm{g}\left(\mathrm{M}\mathrm{H}\mathrm{z}\right)+20\times \mathrm{l}\mathrm{g}\left(\mathrm{d}\mathrm{i}\mathrm{s}\right(\mathrm{i})/1000)$$

(9)

where Power_dis(i) is the power of the ith point in the horizontal direction, gain(i) is the antenna gain pointing to the ith point, lp is the air loss (which can be determine using Equation (8)), and dis(i) is the distance between the antenna and the point i on the ground, which can be obtained via the trigonometric function. We simulated N unit linear arrays’ far-field patterns and used these results to fit the power distribution of them. Figure 7a displays the patterns of 12 units of linear antennas with various processing techniques when the dp is set at −60. From this, we can learn that the maximum gain of the 3.5 GHz uniformly excited antenna is 17.9 dBi and that of the HT-excited antenna is 15.9 dB. The maximum gain of the HT² (the square root of HT excitation)-excited antenna, operating at 3.5 GHz, is 14.55 dBi. The maximum gain of the 26 GHz uniformly stimulated antenna is 16.2 dBi, and this is 14.83 dBi for the HT antenna, and 13.64 dBi for the HT² antenna. The HT antenna can fill all of the nulls of the all-“1” antenna and achieve the ONF beam when the dp is −60, but its gain will be 1.4 dB lower at 26 GHz and 2 dB lower at 3.5 GHz than that of the uniform antenna. The maximum gain becomes lower than that of the HT antenna but the level of null filling is higher when we further increase the proportion of excitation power distribution across units, i.e., by adopting HT² excitation distribution. Figure 7b illustrates that the 3.5 GHz antenna, following HT processing, has an obvious advantage in terms of power near the base station range, with a gain of approximately 10–35 dB at the null point, and a range of 400 m. The 26 GHz HT antenna can also further increase the power by 26 dB at the null point. In order to maintain higher communication quality, our ONF beam can simultaneously sustain high radiation power within 200 m: for instance, exceeding −75 dbm at 3.5 GHz and −90 dbm at 26 GHz. Accordingly, the ONF beam can solve the power fluctuation issue in the BS. We additionally investigate the impact of the HT approach on different linear arrays.

Table 1. Linear array excitation amplitude (W).

N	1	2	3	4	5	6	7	8
6	0.02	0.081	0.25	0.517	0.808	1
8	0.02	0.053	0.144	0.293	0.492	0.707	0.892	1
12	0.02	0.034	0.074	0.138	0.226	0.338	0.469	0.609
16	0.02	0.028	0.05	0.086	0.135	0.198	0.273	0.362
N	9	10	11	12	13	14	15	16
12	0.746	0.856	0.953	1
16	0.459	0.562	0.666	0.764	0.852	0.923	0.974	1

lists the corresponding excitations, and Figure 8a–c show the far-field patterns. As is shown in Figure 8b, the maximum HT gain of 3.5 GHz is 14.03 dBi, which is 2 dB lower than that of the uniformly excited (all-“1”) array, and the maximum HT gain of the 26 GHz array is 13.76 dBi, which is 1 dB lower than that of all-“1” array when N = 8. Furthermore, the far-field gain curve is smoother, and the null-filling effect is improved when the excitation amplitude is squared. The same difference in situation also appears on the 6-, 12-, and 16-element arrays, as shown in Figure 7 and Figure 8. Therefore, we can deduce that the wavelength and the distance between the elements are related to the difference. The maximum gain of the 8-element uniform array is 16.17 dBi in Figure 8b, while the maximum gain of the 12-element HT null-free array is 15.9 dBi in Figure 7a, which is quite near to 16.17 dBi. Even though the gain currently declines by roughly 2–3 dB, we can enhance it by adding more elements. According to our simulations, the proposed HT method fits well for arbitrary structures, frequency, or feeding ways in N element arrays, and the gain reduction caused by HT can easily be improved by increasing N.

Adjusting the sidelobe suppression (dp) degree can also improve the gain performance, as shown in Figure 8d: the maximum ONF gain of the 8-element linear array operating at 3.5 GHz is only reduced by 0.5 dB compared with the uniformly excited array when dp = −30 dB; the maximum gain is reduced by 2 dB when dp = −60 dB; and the maximum gain is reduced by 3 dB when dp = −100 dB and −120 dB. Thus, we can deduce that the gain difference no longer changes when dp is lower than −100 dB. Furthermore, Figure 8d indicates that when the absolute value of dp increases, the gain at the null point increases. This implies that the filling effect improves and the beam widens, but the maximum gain decreases, necessitating a balance between the filling effect and the gain when required.

In this paper, we choose dp = −60 dB because, incidentally, the feed network is more complex at that value than it is at −30 dB. We can find that the gain pattern is not symmetrical since the HT excitations are asymmetric, and this causes the upper sidelobe (−90~0 deg arrange) to converge faster, which plays a significant role in upper-sidelobe suppression. The beam’s scanning ability is one of the important indexes of a BSA. Since the HT does not change the excitations’ phase, Figure 9 illustrates that we can change the beam direction by varying the phase difference, which can be as much as ±200°, ±150°, ±100°, or 0, and it also can realize a beam navigation ability of ±42° since the HT approach does not change the phase of the excitations.

2.2. HT Feed Network Design of a Linear Array

We designed a step-by-step power division network for the 3.5 GHz array, as shown in Figure 10, wherein the powerdivider1 contributes seven signals with powers of 0.02, 0.053, 0.144, 0.293, 0.492, 0.707, and 0.892 W into a sum power of 2.6 W. The division ratio is 2.6:1, and the power ratios of the rest of the stages are 1.42:1, 1.04:1, 0.74:1, 0.5:1, and 0.37:1. These power dividers are cascaded to form an HT power division network, and the phase can be adjusted by modifying the branch lengths. The phase of the leftmost unit, for example, 100°, is used as the reference. To produce a 100° phase unit with the phase of 50°, its branch length needs to be changed by about (100–50) * wavelength/360. We used this network to perform a full-wave simulation of the eight-element linear array. These results are displayed in Figure 11, where the pattern is an ONF beam with a maximum gain of 14 dBm and |S₁₁| is approximately −24 dB at 3.5 GHz. Therefore, the HT method can be used in an array stimulated by a microstrip network.

2.3. M × N Planar Array

Regarding the N HT excitations whose dp is −60 dB as a horizontal $\overrightarrow{a}$ and the M HT excitations whose dp is −60 dB as a vertical $\overrightarrow{b}$, their vector sum is $\overrightarrow{c}$, as shown in Figure 12; subsequently, we can obtain HT excitations of the planar array. Feeding the planar array seen in Figure 13a requires using the modulus of $\overrightarrow{c}$ as the amplitude and the $\theta$ of it as the phase of the source. Figure 13b illustrates that the far-field gain pattern is ONF following HT formation when M × N is 4 × 12. Figure 13c shows that the null filling is successful even when M × N is 8 × 8. The HT method can still improve gain at most null positions by 10–20 dB when applied on a 12 × 12 planar array, as shown in Figure 13d; the filled curve can be processed more smoothly by varying the amount of dp, and the maximum gain is almost identical to the uniform one.

3. Measurement

We fabricated and tested eight-element linear arrays operating at 3.5 GHz and 26 GHz. Figure 14a illustrates that the 3.5 GHz HT array is fed via an HT network. The amplitude and phase alterations of radio frequency channels provide distinct control over each excitation of the 26 GHz HT array, as demonstrated in Figure 14b. The S and VSWR parameters of the two antennas are analyzed using a vector network analyzer (VNA), as depicted in Figure 15. Despite frequency variations caused by manufacturing accuracy and measurement errors, the |S₁₁| of both antennas can fall below −20 dB at the operating frequency, as shown in Figure 15a,b. The VSWR results displayed in Figure 15c,d agree to the S parameter well, and the VSWR values are all lower than 1.5 at the operating frequency. However, a very thick tin was used during welding because the thickness of the 3.5 GHz HT array is half of the distance between the SMA connector’s core and the ground. Nevertheless, this means that under stress, the SMA and the antenna are virtually connected, which could cause the antenna to have multiple frequency points in the test but not influence its good performance at 3.5 GHz. For the 26 GHz antenna, we employed a GPPO-JHD1 connector but the VNA with an SMA connector; thus, we chose a transfer radio line with length of 10 cm to connect them in this measurement, and this line was not applied in simulations, so the loss of the line makes the measured |S₁₁| and VSWR perform better than the simulations.

Figure 16a displays the normalized far-field pattern of the HT antenna operating at 3.5 GHz. It is clear that the simulated and experimental results agree well. The simulation and actual beam scanning test results are compared for the HT antenna operating at 26 GHz, as Figure 16b illustrates. The dashed line is the simulation result; the test line is the actual line. The simulation and the measurement results are in good agreement. The measured results of the two antennas further prove advantages regarding the simplicity, null-filling effect, and beam scanning range of the ONF beam depending on the HT approach.

The comparison with works of recent years is shown in

Table 2. Comparison with recent achievements.

Paper/Year	Method	Complexity	Far-Field Pattern	Beam Scanning
[7]/2013	Schelkunoff roots	high	Null-filled	\
[12]/2014	TI-IWOA	high	Filling 1 null	\
[13]/2021	DRA and AFSA	high	Arbitrary	yes
[14]/2014	GA	high	Null-filled	no
[23]/2020	Decoupling structure	high	Null-filled	no
[24]/2016	Complex control	high	Filling 1 null	\
[25]/2022	Coupling cancellation	high	Existing nulls	±60°
This work	HT method	low	Null-free	±42°

. We judge the complexity of these methods from aspects of whether requiring special sampling, iterations or structures. It can be seen that HT method proposed here has advantages in simplicity, null filling effect and beam scanning range.

4. Conclusions

This work proposes an HT-forming technique for multiband array antennas. We evaluated the far-field performance of linear arrays consisting of 6, 8, 12, 16, and M × N elements. The findings of our simulations and measurements demonstrate that the proposed method can achieve an ONF pattern in these array antennas, and using the HT linear array and comparing it with the uniform array increases the power under the base station tower by over 20 dB. Overall, the whole cell’s power distribution is improved. Additionally, the proposed HT linear array antenna can scan at an angle of ±42°, and the sidelobe suppression (dp) weighting parameter allows for flexible adjustment of the anti-power fluctuation effect and gain: compared to the uniformly excited one, for example, the maximum ONF gain of an eight-element linear array operating at 3.5 GHz is only reduced by 0.5 dB when dp = −30 dB and by 2 dB when dp = −60. This can be used to improve communication quality near a BS and can also be applied in MIMO systems to optimize the number of beams in order to reduce cost and increase efficiency.