Improving the Reverberation Chamber Performance Using a Reconfigurable Source Stirring Antenna Array

Abstract

An antenna array composed of 16 asymmetric distributed monopoles on a circular dielectric substrate is proposed to use as a reconfigurable source stirrer in a reverberation chamber (RC). The distance between antennas is above $\raisebox{1ex}{$\lambda $}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ to ensure the isolation between antennas below −15 dB. In order to ensure the mutual independence of the stirring modes of the antenna array, the 16 monopoles are asymmetrically distributed on both sides with X and Y as axes. The stirring efficiency of a stirrer is related to its size, and usually a higher stirring efficiency means a larger stirrer. The source stirring technique can achieve high efficiency, but the rotation of a source stirring antenna is limited to the radius of the turntable in an RC. To solve this problem, we propose to use an antenna array as a reconfigurable source stirrer, which can achieve a high efficiency of source stirring. As the antenna array can achieve source stirring and mechanical stirring at the same time, the source stirring section is not limited to the radius of the turntable; the switch between the selected antennas of the antenna array can increase the actual stirring samples of the stirring. Thus, the efficiency can be improved significantly and has been verified by the measurement results. The volume occupied by the conventional mechanical stirrer is reduced, which improves the working volume. The figures of merit, such as the field uniformity (FU), the independent sample numbers, the average K-factor, and the total scattering cross-section (TSCS), are measured and compared to the conventional mechanical stirring, mechanical stirring, and source stirring of the antenna array. Measurement results of the reconfigurable stir are illustrated below. FU has the best convergence and the lowest value, below 0.5 dB. The independent sample number is the largest. K-factor is the lowest, and most ranges are below −15 dB. Additionally, the proposed method has the largest TSCS, above 2 ${\mathrm{m}}^2$. These confirm that the proposed reconfigurable source stirring technique outperforms other three stirring techniques significantly. The antenna array can be easy to disassemble and install in different RC. With a wide range of working band, the proposed method can be applied to 5G OTA testing.

1. Introduction

A reverberation chamber (RC) is an electrically large metallic cavity that can generate random electromagnetic (EM) fields by applying different stirring methods, such as frequency stirring, mechanical stirring, and source stirring. RCs have been widely used in the electromagnetic field (EMC) [1,2]. The electromagnetic field in an RC can be considered as statistically uniform and isotropic, when it is well stirred. With the rapid development of the wireless industry, finding an efficient and repeatable over-the-air (OTA) testing method is very important. Because of its particular advantages, RCs have been widely used in various OTA [3,4] testing nowadays. There are mainly two methods to stir the EM field in an RC: changing the boundary conditions or changing the source distribution inside the cavity. The most widely used method of stirring is to rotate metal plates in an RC, which is the conventional mechanical stirring, and it is easy to setup and operate. However, it takes a long time to rotate to gather large independent samples and always occupies a large volume to rotate. The source stirring method usually has a high stirring efficiency [5] and does not require large stirrers that decrease the volume occupied. This method needs to move the source in the cavity [6], and the stir efficiency is limited to the radius of the rotation. Another source stirring technique is antenna stirring, which is realized by switching in different antennas. Thus, the antenna stirring uses less time than the mechanical stirring. As the stirring positions need to be independent of each other, the correlations between antennas need to be as small as possible. This requirement limits the distance between antennas and the number of antennas that can be used in [7].

In this work, we propose to use an antenna array as a stirrer in an RC with inner dimensions of 0.938 m × 1.166 m × 1.439 m. The monopoles of the antenna array are distributed on a circular dielectric substrate with a radius of 170 mm. The monopoles and antenna array are designed according to $\lambda$ and meet the isolation requirements [8,9,10]. The antenna array is used to combine the mechanical stirring and source stirring techniques. Thus, the stirring efficiency can be effectively improved. Compared to the conventional mechanical stirrers, the antenna array occupies a much smaller volume, so we can increase the available test volume significantly. In order to identify the contribution of the source stirring and mechanical stirring of the antenna array, the measured results are compared with the source and mechanical stirring of the antenna array and the conventional mechanical stirring.

The configuration of the system is shown in Section 2. The measurement results are presented in Section 3. The conclusions are given in Section 4.

2. Measurement Setup

The system setup of the RC is shown in Figure 1a. The RC contains two conventional mechanical stirrers and one turntable platform. A wideband dipole antenna was adopted as the receiving antenna (Rx), which was used in [11]. An antenna in the antenna array was used as the transmitting antenna (Tx). The Rx was fixed on a plastic tube. The conventional mechanical stirrers were composed of two metal stirrers: a vertical stirrer (V) and a horizontal stirrer (H). The setup for different stirring methods is shown in Figure 1b. The H and the V stirrers were fixed inside the RC, and controlled by motor to rotate together. The antenna array was fixed on the turntable platform that is controlled by computer. According to the standard of IEC61000 [1], the resonance frequencies can be calculated by:

$$F_{l,m,n}=150\sqrt{\frac{l^2}{L}+\frac{m^2}{W}+\frac{n^2}{H}}$$

(1)

where $l$, $m$, and $n$ are the mode indices (at least two of which are nonzero), and $L$, $W$, and $H$ are the chamber dimensions (in $m$). Thus, the resonance frequency $F_0$ of the fundamental mode can be calculated as 280.714 MHz.

The setup of the antenna array in the RC is shown in Figure 1. To ensure the independence of the stirring positions, there were 16 monopole antennas asymmetrically distributed on the dielectric substrate. The distance between the antennas was set to be more than $\lambda ∕2$ in the operating frequency band to ensure the coupling between the antenna elements was below −15 dB. The antennas were placed staggered from each other on the horizontal and vertical axes in position, and parallel to the X or Y axis in the orientation. The working bandwidth of the antennas ranged from 2.25 to 2.59 GHz and from 5.03 to 7.08 GHz, as the antenna array was originally designed for 5G OTA testing. In this experiment, we set the test frequency band from 100 MHz to 20 GHz. The seven antennas were fed on the outer circle of the 16 antennas in sequence for source stirring. The antenna array was rotated for mechanical stirring. Reconfigurable source stirring can be achieved by combing these two operations. The antenna array was placed on a turntable that can rotate $360°$ by any step needed and controlled by a computer. A dipole antenna was used as receiver antenna (Rx) and located on a transparent plastic rod. The S-parameters were measured by a vector network analyzer (VNA) and recorded by a computer. The measurement workflow is shown in Figure 2. A description of the four stirring techniques is presented in

Table 1. Description of the stirring scenario.

Title 1	Stirring Scenario	Hybrid Stirring
Reconfigurable source stirring	Feed seven antennas in sequence and repeat rotating for each antenna	☑Feed antenna array ☑Rotate antenna array ☒Rotate metal stirrers
Conventional mechanical stirring	Rotate the metal stirrers, and V and H stirrers	☒Feed antenna array ☒Rotate antenna array ☑Rotate metal stirrers
Mechanical stirring of antenna array	Rotate the antenna array without feeding	☒Feed antenna array ☑Rotate antenna array ☒Rotate metal stirrers
Source stirring of antenna array	Feeding the seven antennas in sequence without rotating	☑Feed antenna array ☒Rotate antenna array ☒Rotate metal stirrers

.

In the measurement, considering the calculation formula of the different parameters, the rotation angle was set as $1°$, $2°$ and $10°$, respectively. Each rotation angle corresponded to a number of positions and a number of S-parameter samples. The measured S-parameters were recorded from 100 MHz to 20 GHz.

As a comparison, we rotated the conventional mechanical stirrer and the antenna array as mechanical stirring. The seven antennas were fed separately without rotation as source stirring.

3. Measurement Results

The measurement results were recorded and calculated to characterize the performance of the antenna array. The typical figures of merit were compared, such as the FU, the correlation coefficient, the independent sample numbers, the average K-factor, and the TSCS [12,13].

For the stirring process of the proposed reconfigurable antenna array, we fed seven antennas in sequence and repeated the rotating of the turntable for each antenna. The turntable rotates $10°$/step in 1 revolution, which obtains 36 samples. To measure the FU, five Rx antenna positions in the working volume were used, which can be regarded as five cases. Hence, we obtained 252 (7 × 36) samples of measured $S_{21}$ for each Rx antenna position. The measured standard deviation (STD) $\sigma$ can be calculated from the standard of IEC61000 [1].

$$\sigma =\sqrt{\frac{{{\displaystyle \sum }}_{n=1}^5{\left(P_n-P_{av}\right)}^2}{n-1}}$$

(2)

where $n$ is 5. $P_{av}$ is the mean value of the 5 average power transfer functions $P_n$ (each averaged over 252 samples), which can be calculated from $S_{21}$. Additionally, the results were converted into dB in the FU below.

The calculated results are shown and compared with other scenarios in Figure 3a. It can be observed that the FU of the reconfigurable source stirring is much better than that of the other three; the value is the smallest and converged better.

The correlation coefficients r of the seven antennas can be obtained using the following formula [1].

$$r=\frac{\frac{1}{n-1}{{\displaystyle \sum }}_i^n\left(x_i-u_x\right)\left(y_i-u_y\right)}{\sqrt{\left(\frac{{{\displaystyle \sum }}_i^n{\left(x_i-u_x\right)}^2}{n-1}\right)\left(\frac{{{\displaystyle \sum }}_i^n{\left(y_i-u_y\right)}^2}{n-1}\right)}}$$

(3)

The results were measured and presented in Figure 3b. As can be seen, the correlation coefficient between any 2 of the 7 antennas, with a number of 21 combinations, are below 0.37, essentially from 1 GHz to 20 GHz. The measured results confirm that the seven antennas are independent from each other. We also obtained the correlated angle $\Delta \theta$ from the correlation coefficient, and the independent sample numbers can be calculated by:

$$N=\frac{360}{\Delta \theta }$$

(4)

where $\Delta \theta$ is the minimum rotation angle of the stirrer when the correlation coefficient drops below 0.37. The results of the reconfigurable source stirring were measured and shown in Figure 4a [5]. The rotation was set as $1°$/step in one revolution and the number of the Rx antenna position was 1. As the test sample numbers of the source stirring were limited to 7, its independent sample numbers were not measured and compared in this paper. We compared the results with the mechanical stirring of the antenna array and the conventional mechanical stirring. As can be seen, the reconfigurable source stirring has the highest value among the three stirring techniques.

The K-factor can be obtained from [14]:

$$k=\frac{{\left|\langle S_{21}\rangle {}_m\right|}^2}{{\langle \left|S_{21,s}\right|}^2\rangle {}_m}=\frac{{\left|\langle S_{21}\rangle {}_m\right|}^2}{{\left({\left|S_{21}-\langle S_{21}\rangle {}_m\right|}^2\right)}_m}$$

(5)

The measured average K-factors over frequency and antenna positions (${\langle K\rangle }_{f,a}$) are shown in Figure 4b. The test setup is the same as the FU. It is interesting to note that the value of the conventional mechanical stirring and the source stirring are close to each other. Not surprisingly, the reconfigurable source stirring outperforms the other three stirring techniques and has the smallest average K-factor.

To quantify the stirring efficiency, $TSCS$ is better than the FU and average K-factor, because $TSCS$ is not affected by losses in the $RC$. We can obtain the $TSCS$ from [14]:

$$TSCS=\frac{V}{c_0{\tau }_s}$$

(6)

and

$${\tau }_s=\frac{{\langle K\rangle }_f{\tau }_{RC}}{1-{\langle K\rangle }_f}$$

(7)

where ${\tau }_{RC}$ is the chamber decay time and can be extracted from the measured S-parameters [5]. The turntable here rotates 10°/step in one revolution. The Rx antenna position is 1. ${\tau }_s$ is the extracted value of the scattering damping time, which can be obtained from Equation (7). The measured results are illustrated in Figure 5. We can confirm that ${\tau }_s$ of the reconfigurable source stirring is significantly better than that of the other three stirring techniques [15,16,17]. The value of the conventional mechanical stirring and the source stirring are close to each other. As the reconfigurable source stirring is the combination of the mechanical stirring and source stirring, the results demonstrate that the combination leads to a better performance of the reconfigurable source stirring.

By applying (2), the TSCS can be obtained and is shown in Figure 6. There is a limit for the TSCS of mechanical stirring [5], but not for the source stirring as the source can be moved in RC. The source stirring usually has a higher equivalent TSCS, and a higher stirring efficiency [18,19,20]. In this work, source stirring has only seven positions for stirring, so the TSCS is close to the conventional mechanical stirring. The results confirm that the reconfigurable source stirring combining the source stirring with the mechanical stirring obtain a significantly high efficiency. Because the working bandwidth is limited by the antennas, some fluctuations exist at high frequencies of the TSCS.

We found that the mechanical stirring of the antenna array has the worst performance in an RC that does not match its size. The performance of the source stirring and conventional mechanical stirring were close to each other, and the reconfigurable source stirring outperformed the other three stirring techniques significantly.

4. Conclusions

An antenna array was used as a reconfigurable source stirrer in RC measurements. We compared its performance to the mechanical stirring and source stirring of the antenna array and the conventional mechanical stirring of the metal stirrers. The stirring efficiency were characterized by the FU, the independent sample numbers, the average K-factor, and the TSCS. The numerical results of these parameters are illustrated below in

Table 2. Comparison of mean value between the proposed work with other stirring methods in an RC.

	Reconfigurable Source Stirring	Conventional Mechanical Stirring	Mechanical Stirring of Antenna Array	Source Stirring of Antenna Array
FU (dB)	0.3	0.8	2.5	1.5
K-factor (dB)	−17	−8	−2	−8
${\tau }_s$ (ns)	2	12	150	12
$\mathrm{TSCS} ({\mathrm{m}}^2$)	2.5	0.4	0.4	0.05

. The comparison results confirm that the reconfigurable source stirring outperforms the other three stirring techniques and has the highest stirring efficiency. It is worth noting that the stirring volume (the volume occupied by the rotating mechanical stirrer) occupied by the antenna array is 0.0035 ${\mathrm{m}}^3,$ while that of the metal stirrers (V-stirrer and H-stirrer) are 0.1405 ${\mathrm{m}}^3$. The stirring volume of the antenna array is much smaller than that of the metal stirrers. A smaller stirring volume leads to a bigger testing volume for the antenna array.

Due to the limitations of the test conditions, we could only feed the seven antennas on the outer circle of the antenna array, and feed one antenna at a time while rotating. In the future, when we have better experimental conditions, multi-antenna excitation can be achieved. We can then increase the combination numbers: if we feed two antennas, there can be $C_7^2=21$ combinations, and if we feed three antennas, there can be $C_7^3=35$ combinations. The number of antennas that can be excited of this antenna array can rise from 7 to 16, and the combination number will increase again. Thus, the performance of this antenna array can be further improved.