1. Introduction

2. Methods for Estimating the Location of Radio Transmission Sources

3. Numerical Analysis and Results

3.1. Comparison of LoS rate between HAPS and UAV

In Section 2, we discussed various location estimation methods. However, the accuracy of such methods varies greatly depending on whether the environment between the receiving antenna and the radio source is a LoS environment or an NLoS environment. In this section, we perform a ray tracing simulation using the SBR (Shooting and Bouncing Rays method) in MATLAB to compare the LoS rate between the case using HAPS and the case using a UAV. In this analysis, the case in which a direct wave (a radio wave that is not reflected by any obstacle) reaches the receiving antenna was considered as the LoS environment and vice versa is considered an NLoS environment.

3.1.1. Simulation Model

Simulations were performed using a 3D model environment that mimics the town of Chicago that pre-exists in MATLAB, shown in Figure 7.

An overall view of the simulation is shown in Figure 8. The simulation was conducted assuming that the HAPS was 2,000 m above the ground and the UAV was 200 m above the ground.

For simplicity, we will use the simulation of the LoS rate over the town to illustrate the simulation. First, random radio sources are generated in the town as shown in Fig. 9. Here, the height of each antenna was set to 10 meters.

Figure 9. Randomly generated radio wave sources.

Figure 9. Randomly generated radio wave sources.

Next, as shown in Figure 10, a receiving antenna (in this case, a UAV) is generated over the town, the number of direct waves is calculated using a ray tracing simulation, and the LoS rate is calculated by calculating the ratio of the number of direct waves to the number of radio wave sources. In this simulation, the number of radio wave sources is set to 1000. The same simulation is performed for HAPS.

When the simulation is performed away from the center, receivers are generated in several directions as shown in Figure 11, and the average value of the LoS ratio obtained from each receiver is used as the LoS ratio.

3.1.2. Results

The results of the simulation conducted above are shown in Figure 12. The LoS ratio of the HAPS was about 100% when the center of the urban area where the radio source was generated was directly below the HAPS, and about 60% at a distance of 20 km (elevation angle 45°). On the other hand, when a UAV was used, the LoS ratio was about 30% even when the center of the urban area was directly below the UAV, indicating that the majority of the radio sources were out of sight. Therefore, an altitude of about HAPS is considered necessary for position estimation by angle estimation.

3.2. Location Estimation Simulation

In order to realize a simulation of radio source location estimation using HAPS, we used MATLAB to estimate the location of radio sources. Several location estimation methods were discussed in Section 2 but considering the wide search area and required estimation accuracy, the Beamformer method and the MUSIC method were used in our simulation. As a comparison, a case in which location estimation was performed at the altitude of the UAV was also simulated. In our analysis, the location estimation simulation was performed for a non-mobile illegal radio source located outdoors in an urban area, as shown in Figure 7.

The simulation process is shown in Figure 13. (1) A radio source is randomly generated, (2) A ray traccing simulation is performed to obtain information about arriving radio waves (direction of arrival, number of reflections, propagation distance, etc.), and (3) Received signal is generated from the aforementioned information. The direction of arrival is estimated by using each estimation method applied on the received data generated in (3). Then, location estimation is performed using triangularization method. By comparing the randomly generated coordinates of the radio source with the estimated coordinates, the location estimation of the radio source using HAPS and other methods is evaluated. Figure 13 shows an overview of the simulation.

3.2.1. Receiving and Transmitting Antenna Configuration

Table 1 shows the antenna specifications for estimating the location of a radio wave source using ray tracing simulation. Hereafter, the transmitting antenna is denoted as Tx and the receiving antenna as Rx.

The receiving antenna was modeled after the cylinder antenna used in HAPS as a base station for the simulation. The actual prototype cylinder antenna can be found in [12].

In this paper, the cylinder antenna consists of $N=$ 36 elements as depicted in Figure 14, where each element was assumed to be omni-directional and the maximum gain was set to 0dBi in the simulation.

3.2.2. Radio propagation model

This section describes the radio propagation model used in the simulation of radio source location estimation using HAPS. In this simulation, statistical data were not used in the propagation model because a ray tracing simulation was conducted to determine specific radio waves. The free propagation loss was modeled using Friis formula as follows,

$${PL}_{fsp}=10lo{g}_{10}{\left({\displaystyle \frac{4\pi d}{\lambda }}\right)}^2\left[dB\right]$$

(37)

where $d$ and $\lambda$ are the distance between the transceiver pairs and the wavelength of the considering radio wave, respectively.

The overall path loss can be expressed by Equation (38), where the additional attenuation $L_{ref}$ due to earth and building reflections was calculated using the Fresnel equation. The permittivity and conductivity of the surface materials used in these calculations were taken from the ITU-R study [13]. Assuming that both the ground surface and the building are concrete, the relative permittivity and conductivity were calculated as 5.31 and 0.0548 [S/m], respectively.

$$PL=P{L}_{fspl}+P{L}_{ref} \left[dB\right]$$

(38)

3.2.3. Signal processing system

This section describes the signal processing performed in the location estimation simulation. First, the analytical signal input to the cylinder antenna is obtained by generating a single radio source in a 3D model and considering the case where L radio waves are incident from the source. The propagation loss $P{L}_l\left[dB\right] (l=\mathrm{1,2},\dots ,L)$ is obtained from Equation (39) using the propagation distance and other data obtained from the ray tracing simulation, and the input power is calculated by following formula.

$$P_l=10\times {10}^{-\left({\displaystyle \frac{P{L}_l}{10}}\right)} \left[W\right] (l=\mathrm{1,2},\dots ,L)$$

(39)

Using this value, the propagation time delay against the direct wave ${\tau }_l(l=\mathrm{1,2},\dots ,L)$, $({\tau }_1=0)$and the times of reflection $m_l(l=\mathrm{1,2},\dots ,L)$, the complex waveform of the l-th wave can be written by the following formula.

$$F_l\left(t\right)=\sqrt{P_l}\mathit{exp}\left\{j2\pi f\left(t-{\tau }_l\right)\right\}·{\left(-1\right)}^{m_l} \left(l=\mathrm{1,2},\dots L\right)$$

(40)

The array matrix for the cylinder antennas is then expressed by the following equation [9].

$$\mathit{A}=\left[\mathit{a}\left({\theta }_1,{\varphi }_1,f\right),\dots ,\mathit{a}\left({\theta }_L,{\varphi }_L,f\right)\right]$$

(41)

$$\mathit{a}\left({\theta }_l,{\varphi }_l,f\right)={\left[\exp \left\{j2\pi {\displaystyle \frac{f}{c}}{\mathit{r}}_1^T\mathit{L}\left({\theta }_l,{\varphi }_l\right)\right\} ,\dots ,\exp \left\{j2\pi {\displaystyle \frac{f}{c}}{\mathit{r}}_N^T\mathit{L}\left({\theta }_l,{\varphi }_l\right)\right\} \right]}^T(l=\mathrm{1,2},\dots ,L)$$

(42)

$$\mathit{L}\left(\theta ,\varphi \right)\triangleq \left[\mathrm{s}\mathrm{i}\mathrm{n}\theta \mathrm{c}\mathrm{o}\mathrm{s}\varphi ,\mathrm{s}\mathrm{i}\mathrm{n}\theta \mathrm{s}\mathrm{i}\mathrm{n}\varphi ,\mathrm{c}\mathrm{o}\mathrm{s}\theta \right]$$

(43)

where ${\mathit{r}}_k(k=\mathrm{1,2},\dots ,N)$ is the position vector of each element, and $\theta$ and $\varphi$ are the elevation and azimuth angles to the reference point, respectively.

The thermal noise power $P_N$ generated at the receiving antenna is given by,

$$P_N=10{\mathit{log}}_{10}\left(kTB\right)+NF \left[dBW\right]$$

(44)

where $k, T, B, NF$ are Boltzmann's constant, absolute temperature of the noise source, bandwidth, and noise figure, respectively. The absolute temperature in the HAPS environment was assumed to be 216.5 [K] and the bandwidth was 10 [MHz]. The noise figure was calculated as 3 dB [14]. As a result, the thermal noise power $P_N$was about $-102$ [dBm] in HAPSs environment while in the UAV environment, the thermal noise power was slightly higher since the absolute temperature at the UAV altitude is about 288 [K]. Using Equations (40), (41), and (44), the input vector $\mathit{X}\left(t\right)$ to each antenna is expressed by the following equation.

$$\mathit{X}\left(t\right)=\mathit{A}\mathit{F}\left(t\right)+\mathit{N}\left(t\right)$$

(45)

$$\mathit{F}\left(t\right)={\left[F_1\left(t\right),F_2\left(t\right),\dots ,F_L\left(t\right)\right]}^T$$

(46)

In the above equation,$\mathit{N}\left(t\right)$is the thermal noise vector, whose components are independent complex Gaussian processes with mean zero and variance (power) of $P_N$. The input vector obtained by substituting appropriate values for t in Equation (45) for different time samples, was used as the input complex signal for the cylinder array. The number of samples was set to 100 in this paper. By applying the aforementioned Beamformer and MUSIC methods to the obtained input vector $\mathit{X}\left(t\right)$, the direction of arrival from the radio source was estimated and used for the location estimation method described in the next section. The direction of arrival with the highest power obtained by the Beamformer and MUSIC methods was used as the estimated direction of arrival.

3.2.4. Location Estimation Method

This section describes a method for obtaining the estimated coordinates of a radio source from the direction of arrival obtained by the MUSIC and Beamformer methods. In this simulation, the direction of arrival of radio waves is estimated from three points as shown in Figure 15.

The latitude and longitude of each HAPS observation point are converted to the Cartesian coordinate system, and a direction line is created in the x-y coordinate system from the direction of arrival. Figure 16 shows two localization methods from the estimated angular information. In the left-hand side case that all angular information is available from the three sensors, the center of gravity of the intersections of each directional line is considered as the estimated coordinates of the emitter. In the right-hand side case that the angular information from one of three sensors is missing, the estimated coordinates are the intersection points of the direction lines of the remaining sensors where angular information is available. For all other cases, the location of the emitter is considered to be unidentified (undetected).

3.2.5. Results

The 3D city model shown in Figure 7 was used to randomly generate 1,000 radio wave sources, and the location of each source was estimated using the method described in the previous section. The horizontal distance between the center of the urban area where there exist illegal radio sources and the hovering sensors was varied as different scenarios in our below evaluation results. Three scenarios of sensor altitudes i.e. HAPS, UAV and DEURAS are also separately evaluated in this section.

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HAPS altitude

Table 3 shows the results of the localization using HAPS at three points 5 km away from the urban area. The Beamformer and MUSIC methods were used to estimate the direction of arrival. The estimation probability denotes the percentage that the emitter can be identified (with localization errors) via our proposed system as mentioned in Figure 16. The stochastics of the estimation errors were derived only from emitters which were identified by our proposed method. From Table 3, it is observed that there was no significant difference in the results between the Beamformer and MUSIC methods, and 90% of the estimated locations were within 30 meters of the true coordinates.

Table 4 shows the results of the estimation using HAPS at three locations 10 km away from the urban area. Since the sensors are more distanced from the sources compared to the 5-km case, we can observe a slight degradation in terms of localization accuracies as compared to these in Table 3.

Furthermore, Table 5 shows the results of the estimation using HAPS at three locations 20 km away from the urban area. Similar to the two aforementioned scenarios, neither the Beamformer nor the MUSIC method showed a significant difference in results. Also, the accuracy of the estimation was poorer at greater distances compared to the cases at 5km and 10 km. Furthermore, only about 83.6% of the radio transmitting sources in urban areas could be obtained.

The CDF of localization errors for these scenarios is summarized in Figure 17.

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UAV altitude

Similarly, a simulation was conducted assuming a UAV with the height of the receiving antenna changed to 200 meters. In addition, because the effect of reflections is likely to increase at the altitude of the UAV, the simulation was performed considering radio waves that can be reflected up to four times. Table 6, Table 7 and Table 8 show the results of the estimation using UAVs at three locations 5 km, 10km and 20km away from the urban area, respectively.

In Table 6, only 20% of the total number of radio sources could be identified due to the low LoS ratio as described in Section 3-1. The localization estimation error of the radio sources that could be identified was also larger than that of the HAPS case.

Table 7 shows the results of the estimation using UAVs at three locations 10 km away from the urban area. As in the 5-km case, the number of radio sources that could be identified was small. However, the estimation error and the CDF90% value was slightly improved against the 5 km case. This is thought to be due to the fact that the 10 km environment has smaller multipath components compared to the 5km case, such that angular estimation has higher accuracy.

Table 8 shows the results of the estimation using UAVs at three locations 20 km away from the urban area. Both the estimated probability and localization accuracy are degraded in this case. It is thought to be due to the fact that the sensors are located too far away such that the arrival waves after multiple reflections are too weak compared to the noise level.

The CDF of localization errors for these different scenarios is summarized in Fig. 18.

Figure 18. CDF of errors using UAV at each distance.

Figure 18. CDF of errors using UAV at each distance.

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DEURAS

Finally, a model simulating the DEURAS system was created by installing the receiving antennas on the rooftop of buildings with good visibility in an urban area, as shown in Figure 19. Other system parameters were the same as those for UAVs.

Table 9 shows the evaluation results of position estimation simulations using the Beamformer and MUSIC methods where DEURAS sensors are located as shown in Figure 19. Compared to location estimation using UAVs, the estimation accuracy is still poorer, except for the fact that DEURAS can provide a higher estimated probability since the sensors are close to the sources.

For a fair comparison, we conducted new simulations that HAPS and UAVs were deployed at three points at a distance of 500 m from the center of the urban area (just right above the area similar to the case of DEURAS system).

Table 10 shows the evaluation results of the estimation using HAPS at three locations 500 m away from the urban area. Similarly, Table 11 shows the results of the evaluation when estimating using UAVs at three locations 500 m away from the urban area.

Figure 20 shows summarized the CDF of localization errors of all scenarios. These results show that HAPS shows the best performance in terms of both estimated probability and localization accuracy. It is owing to the fact that HAPS has higher LoS ratio to guarantee higher estimated probability, and also direct waves are more likely to arrive at HAPS rather than multiple reflection paths that increase the angular estimation accuracy.

4. Conclusions

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