Compact Amplitude-Only Direction Finding Based on a Deep Neural Network with a Single-Patch Multi-Beam Antenna

Abstract

In this paper, a compact direction-finding system based on a deep neural network (DNN) with a single-patch multi-beam antenna is proposed. To achieve multiple beams, the patch is divided into four sectors by metal vias, and the pattern is tilted in the theta direction due to the coupled mode of the divided patch structure. This design allows a single-patch multi-beam antenna to generate eight beams using a combination of four excitation ports assigned to the four-divided sectors. This approach increases the amount of training data required for DNN-based direction finding without requiring multiple antennas, thus improving the accuracy of estimation probability. Furthermore, compared to our previous work, the parasitic elements are applied to improve the estimation probability by reducing the beamwidth of the antenna. The size of the antenna for the proposed direction-finding system is 0.44λ × 0.44λ × 0.008λ with a 97.7% estimation probability. The direction-finding performance has been validated and compared through the experiment to show higher accuracy with compactness than previously studied works.

1. Introduction

Direction finding is used in various military and civilian fields such as wireless communications, electronic warfare, IoT, and vehicles [1,2,3,4,5]. Direction finding estimates the angle of the received signal through various processes using the amplitude, phase, or both of the received signals [6,7]. Amplitude comparison is a straightforward method of angle estimation that uses the magnitude of the received signal. Compared to phase-based methods, this approach offers a simpler system configuration and set-up [8,9,10,11]. On the other hand, MUSIC (multiple signal classification) and ESPRIT (estimation of signal parameters via rotation invariance) are typical methods of the angle of arrival estimation using phase, with high estimation accuracy [12,13,14,15]. However, these direction-finding methodologies often require repeated sampling, which is suboptimal for resolving fast-moving targets, supporting large sensor arrays, and minimizing computational time and cost.

Recently, direction-finding methods with deep neural networks (DNNs) have been researched. Compared to MUSIC or ESPRIT, the DNN has the advantage of not requiring complex computation and being able to implement real-time application [16,17]. The direction finding of complex processes such as conventional MUSIC is replaced with DNN, and various studies are being conducted with the aim of simplifying the computational complexity and system [18,19,20,21]. These studies are useful in areas that require complex multi-signal discrimination with improved computational complexity, but in areas such as sensors and the IoT with low complexity, simple amplitude comparison methods are suitable instead.

The accuracy of DNN-based direction finding using amplitude comparison depends on the amount of training data. In order to increase the amount of training data, the antenna is mechanically rotated, or multiple antennas are used to accumulate the received power value [22,23], as shown in Figure 1. However, these methods increase the physical size of the system. Not only the amount of training data but also the quality is important, and when comparing amplitudes, the distinction between the received power values must be clear to reduce the ambiguity of direction finding.

In this paper, a direction-finding method based on a DNN with only one antenna structure with multi beams without additional multi antennas to increase the training data is proposed. In order to generate a multi-beam with a single antenna structure, the patch antenna is divided into four sectors by metal vias. Due to this structure, the patch operates in a coupled mode in the superposed form of even and odd mode, and the field distributions at the divided edge of the patch are asymmetrical, unlike conventional patches. In addition, the divided patch has a directional pattern in different directions. A single-patch multi-beam antenna generates eight beams with a combination of four excitation ports assigned to four-divided sectors of the patch. In addition, the beamwidth of the pattern is reduced to improve the quality of the training data by clarifying the amplitude difference between patterns. The shape of the electric field distribution at the edge of the patch is modified through the shape deformation of the patch, thereby reducing the beamwidth. In addition, based on an antenna with eight beams, the corresponding sectors where the transmission antenna is located are estimated. The number of sectors is 8 which is divided by 45 degrees in the horizontal plane, and after placing the transmission antenna only once in each sector, training data are generated based on the received power value.

This paper is organized as follows. First, an antenna with multi-beam capability is proposed for the purpose of increasing the amount of training data for a DNN-based direction-finding system. Second, the antenna is fabricated and measured. Finally, the direction-finding performance based on the increased training data due to a single-patch multi-beam antenna is verified through experiments.

2. Single-Patch Multi-Beam Antenna

To increase the amount of training data available for DNN-based direction finding, a multi-beam antenna was designed starting with a basic microstrip patch antenna operating at 2.4 GHz, as shown in Figure 2a. The size of the patch is 29.5 mm $\times$ 29.5 mm. The height and dielectric constant of the substrate are 1 mm and 4.3, respectively. The electric field is strongly distributed on the upper and lower edges of the basic patch as shown in Figure 2b. In addition, the radiation pattern has directivity in the +z direction, as shown in Figure 2c. The realized gain of the antenna is 6 dB.

To generate the coupled mode, the basic patch is divided into two sectors using the metallic vias, as shown in Figure 3a. The radius of the metal via is 0.5 mm, and the spacing between the vias is 1.75 mm. As studied in [24], the two-divided antenna structure operates in a coupled mode in the superposed form of the even and odd modes, and the field distributions at the edge of the upper and lower sectors are asymmetrical, as shown in Figure 3b. Due to the asymmetry of the field distribution at the patch edge, the radiation pattern is inclined in the -y direction. The realized gain of the antenna is 5.96 dB.

In order to utilize the additional coupled mode, metal vias are inserted in the y-axis direction. Due to the four-divided patch structure, the feeding point is shifted by 5 mm in the $-$x-axis direction, considering actual coaxial probe feeding.

The adjustment of the feeding point caused the coupled mode to occur at 3.5 GHz in the higher-order mode. Therefore, the patch size is slightly increased to 42 mm $\times$ 42 mm to resonate at 2.4 GHz while maintaining an additional coupled mode, as shown in Figure 4. Then, the feeding point is adjusted from $-$6 mm to $-$17 mm in the y-axis direction for matching the four-divided antenna. Figure 5a illustrates the structure of the patch that has increased in size. The electric field distribution and radiation pattern are shown in Figure 5b,c, respectively. The realized gain of the antenna is 2.56 dB in single feeding and 2.73 dB in dual feeding. The gain the of antenna is reduced due to the split field distribution of patch edges due to coupled mode and higher-order mode operation. This type of antenna has multiple beams depending on the divided field distribution and combination of excitation and has been studied with a similar structure in [25,26].

The electric field distribution and radiation pattern by the excitation port are shown in

Table 1. Electric field distribution with different port excitation.

Port 1	Port 2	Port 3	Port 4
Ports 1 and 2	Ports 2 and 3	Ports 3 and 4	Ports 4 and 1

and Figure 6, respectively.

However, when a single port is used for excitation, the wide beamwidth of the radiation pattern can cause ambiguity in signal level resolution between patterns, as previously studied in [27]. In the amplitude comparison method, the distinction between the received power values for each pattern should be clear because ambiguity occurs in areas where patterns overlap due to the wide beamwidth. These issues are directly related to the quality of the training data. To address this issue, slight modifications were made to the patch structure. In order to reduce the beamwidth, the field distribution of the aperture of the antenna must be increased. However, increasing the antenna size to increase the size of the aperture increases the resonance length, so the effect of increasing the size of the aperture is replaced by using parasitic elements that do not significantly affect the resonance length, as shown in Figure 7. The length of the parasitic element is set to 19 mm, which is slightly shorter than the resonance length (21 mm) of the divided patch so that the parasitic element acts like a director to spread the field at the edge of the patch outward.

The electric field distribution and the radiation pattern of the final single-patch multi-beam antenna structure by the excitation port are presented in

Table 2. The electric field distribution of the final antenna with different port excitation.

Port 1	Port 2	Port 3	Port 4
Ports 1 and 2	Ports 2 and 3	Ports 3 and 4	Ports 4 and 1

and Figure 8, respectively.

The electric field distribution of the final antenna structure exhibits a slight increase in the field distribution at the divided patch edges for both single and dual excitations. The radiation patterns show that the beamwidth of the antenna slightly decreases from 230° to 190° for single-port excitation, which reduces ambiguity between patterns. For dual excitation, the beamwidth is reduced from 180° to 140°. The realized gains of the final antenna are 2.68 dB and 2.93 dB for single and dual feeding, respectively. These improved patterns contribute to the increased accuracy in direction-finding estimation by clarifying the resolution of the power values received for each pattern. The beam characteristics according to excitation by the port are summarized in

Table 3. Radiation characteristics of the final antenna with different port excitation.

Excitation Port	Beam Peak Direction	Beamwidth	Gain
1	$135°$	$190°$	2.68 dB
2	$225°$	$190°$	2.68 dB
3	$315°$	$190°$	2.68 dB
4	$45°$	$190°$	2.68 dB
1 and 2	$180°$	$140°$	2.93 dB
2 and 3	$270°$	$140°$	2.93 dB
3 and 4	0$°$	$140°$	2.93 dB
4 and 1	$90°$	$140°$	2.93 dB

.

3. Fabrication and Measurement of the Single-Patch Multi-Beam Antenna

The designed and fabricated structure of the antenna is shown in Figure 9. The substrate of the antenna is FR-4(${\epsilon }_r$ = 4.3, height = 1 mm). The operating frequency of the antenna is 2.4 GHz. The total size of the antenna is 55 mm $\times$ 55 mm $\times$ 1 mm. Coaxial probe feeding is used to excite the four ports. The measurement of return loss is conducted by using Agilent (Santa Clara, CA, USA)’s MS4644B Vector Network Analyzer. In addition, the radiation pattern is measured in the anechoic chamber. The return loss and radiation pattern of the single-patch multi-beam antenna are shown in Figure 10 and Figure 11, respectively.

Since the antenna structure is symmetrical, the measured results of port 1 are shown for single feeding, while the results of ports 1 and 2 are shown for dual feeding. The return loss of a single-patch multi-beam antenna is well matched with simulation and measurement for both single and dual feeding at 2.4 GHz. The measured gains of the final antenna at 2.4 GHz were 2.64 dB and 2.9 dB in single and dual feeding, respectively.

4. Experiment of Direction Finding

The entire schematic of the direction-finding system with the single-patch multi-beam antenna is shown in Figure 12. The eight radiation patterns from the single antenna receive the powers (p1, …, pN) from the target in the azimuth plane, and the received powers are input into the training data of the DNN algorithm.

In the DNN architecture, let p = [P₁, ⋯, P_N] ^⊺ denote the measured power according to various patterns as training input data and a = [a₁, ⋯, a_L] ^⊺ denote the classified direction sector as training output data in the training phase, where N is the number of patterns and L is the number of direction sectors. p and a are datasets for supervised training according to each angle in the direction sector. For direction finding through supervised training, the neural network architecture comprises a sparse auto-encoder (SAE) and softmax classifier layer [28] for output classification. The SAE helps to reduce the influence of noise and perturbations in the input [29]. Therefore, in many propagation environments, the training input data can reduce the effect of distortion.

In the training phase, the values of the hidden layer units are expressed as

h = f(Wp + b)

(1)

where f(⋅) is a non-linear activation function, W ∈ ℝ ^M×N denotes the weight matrix, and b = [b₁, ⋯, b_M]^⊺ denotes the bias vectors where M is the number of nodes in the hidden layer greater than or equal to the number of inputs. The weight and bias values are updated and determined by the repetitive backpropagation using the measured power values in the multiple hidden layers. After the training phase, the test data are used as the input to verify that the proposed system can find the correct direction.

The direction-finding experiment is conducted in the following order. First, the azimuth plane to be detected is divided into eight sectors with an equal angle of 45°. For training the DNN algorithm, signal sources are placed in order for all sectors. In addition, signals generated from signal sources for each sector are received with eight patterns of the single-patch multi-beam antenna, as shown in Figure 13a. Finally, the eight signal values for all sectors are used as training data for the DNN algorithm. After training is completed, the direction-finding performance is presented by suggesting the actual number of sectors where arbitrarily placed signal sources are located, as shown in Figure 13b.

The direction-finding experiment is performed in a sufficiently large space where the LOS (line-of-sight) environment is almost satisfied. The test antenna of the Tx (transmission) used a microstrip patch antenna operating at 2.4 GHz. The test antenna is connected to the signal generator and transmits continuous wave signals at 2.4 GHz. The test antenna and single-patch multi-beam antenna are 1.5 m away from the ground to reduce reflection on the ground. The SP4T (single pole four-throw) switch is controlled by an FPGA (field programmable gate array) to perform the generation of eight beams. The received power values are accumulated in the laptop through the SDR (software-defined radio) equipment USRP-2922. Training data required for DNN inputs are constructed based on the received power values according to the location of each sector of the test antenna. The test antenna is located only once per sector, and training data are generated based on the received power value. Initial training data are set as from the power value received in eight patterns when the test antenna is located in sector 1 to the power value received in eight patterns when the test antenna is located in sector 8. Then, after placing the test antenna in an arbitrary position, the received power values are entered into the DNN to present the probability of the number of times the antenna’s position is estimated to be actually located in the sector. The experimental set-up of direction finding with a single-patch multi-beam antenna is shown in Figure 14.

The estimated probabilities by sector from the DNN are shown in Figure 15.

Figure 15 shows the estimated probabilities by sector. Figure 15a is the result before improving sector estimation ambiguity, and Figure 15b is the result of improving sector estimation ambiguity by reducing beamwidth by applying parasitic elements to the single-patch multi-beam antennas. Based on the power value measured for each sector, a set of 5000 power value data per sector is trained. In addition, when an arbitrary power value is input, it shows the number of times the sector is correctly estimated and its probability. Red indicates incorrect estimation and green indicates correct estimation. For example, in Figure 15a, when the test antenna is in any position within sector 1, the number of times that it correctly estimated sectors by using the DNN algorithm is 4791, and the number of times that it incorrectly estimated as sector 7 is sector 18. In addition, at this time, the probability correctly estimated as sector 1 is 95.8%. However, as a result of estimation using a single-patch multi-beam antenna that improves estimation ambiguity by applying a parasitic element, the number of times that it correctly estimated sectors by using the DNN algorithm is 4983, and the number of times that it incorrectly estimated as sector 7 is sector 15. In addition, at this time, the probability correctly estimated as sector 1 is 99.7%. As shown in Figure 15b, the average estimated probability increased from 94.2 % to 97.7 % after improved sector estimation ambiguity.

5. Conclusions

In this paper, a direction-finding method based on a DNN with only one antenna structure with multi beams without additional multi antennas to increase the amount of training data is proposed. To reduce the size and complexity of the system, the antenna for direction finding used a single-patch multi-beam antenna. Metal vias were employed to divide the field distribution of the patch to generate multiple beams of a single patch by using coupled mode. A single-patch multi-beam antenna generates eight beams with a combination of four excitation ports assigned to four-divided sectors of the patch. In addition, the direction-finding performance is verified based on the DNN algorithm using the power values received with eight patterns generated from this antenna. The proposed direction-finding system has lower complexity and higher estimation probability, even in a small size, compared to similar references, as summarized in

Table 4. Comparison of performance with other studies.

Ref.	Number of Estimation Sectors	Antenna Size	Complexity	Number of Antennas	Estimation Probability
[22]	8	3.46 $\mathsf{\lambda }$  $\times$ 3.4 6$\mathsf{\lambda }$  $\times$ 0.48  $\mathsf{\lambda }$	Medium	4	96.3 %
[23]	8	1.4  $\mathsf{\lambda }$  $\times$ 1.46  $\mathsf{\lambda }$  $\times$  $\mathsf{\pi }$  $\times$ 0.48  $\mathsf{\lambda }$	High	8	96.8 %
[27]	8	0.44 $\mathsf{\lambda }$  $\times$ 0.44 $\mathsf{\lambda }$  $\times$ 0.008 $\mathsf{\lambda }$	Low	1	94.2 %
This work	8	0.44 $\mathsf{\lambda }$  $\times$ 0.44 $\mathsf{\lambda }$  $\times$ 0.008 $\mathsf{\lambda }$	Low	1	97.7 %

. The estimation probability of the proposed antenna is at least 0.9% to 3.5% higher than that of the references [22,23] and our previous work [27] without adding antennas or increasing the size, using only a single antenna. The proposed system is expected to be used for the IoT or sensors that require low complexity and simple structure direction finding. Future works aim to increase the number of sectors to be estimated and to make the number of excitation combinations of antennas more diverse for higher resolution or additional direction finding in the elevation plane.