Near‐ground propagation in automotive radar and communication obstructed deployments: Measurements and modelling
2022; Institution of Engineering and Technology; Volume: 16; Issue: 6 Linguagem: Inglês
10.1049/mia2.12241
ISSN1751-8733
AutoresDmitrii Solomitckii, Vasilii Semkin, Matias Turunen, Markus Allén, Mikko Valkama,
Tópico(s)Ultra-Wideband Communications Technology
ResumoIET Microwaves, Antennas & PropagationVolume 16, Issue 6 p. 316-326 ORIGINAL RESEARCHOpen Access Near-ground propagation in automotive radar and communication obstructed deployments: Measurements and modelling Dmitrii Solomitckii, Corresponding Author Dmitrii Solomitckii dmitrii.solomitckii@tuni.fi orcid.org/0000-0002-6143-393X Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, Tampere, Finland Correspondence Dmitrii Solomitckii, Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, FI-33101, Tampere, Finland. Email: dmitrii.solomitckii@tuni.fiSearch for more papers by this authorVasilii Semkin, Vasilii Semkin VTT Technical Research Centre of Finland Ltd., Espoo, FinlandSearch for more papers by this authorMatias Turunen, Matias Turunen Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, Tampere, FinlandSearch for more papers by this authorMarkus Allén, Markus Allén Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, Tampere, FinlandSearch for more papers by this authorMikko Valkama, Mikko Valkama Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, Tampere, FinlandSearch for more papers by this author Dmitrii Solomitckii, Corresponding Author Dmitrii Solomitckii dmitrii.solomitckii@tuni.fi orcid.org/0000-0002-6143-393X Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, Tampere, Finland Correspondence Dmitrii Solomitckii, Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, FI-33101, Tampere, Finland. Email: dmitrii.solomitckii@tuni.fiSearch for more papers by this authorVasilii Semkin, Vasilii Semkin VTT Technical Research Centre of Finland Ltd., Espoo, FinlandSearch for more papers by this authorMatias Turunen, Matias Turunen Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, Tampere, FinlandSearch for more papers by this authorMarkus Allén, Markus Allén Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, Tampere, FinlandSearch for more papers by this authorMikko Valkama, Mikko Valkama Faculty of Information Technology and Communication Sciences, Electrical Engineering Unit, Tampere University, Tampere, FinlandSearch for more papers by this author First published: 18 March 2022 https://doi.org/10.1049/mia2.12241AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Wireless communication and radars will play a crucial role for autonomous vehicles in the nearest future. However, the blockage caused by surrounding cars can degrade communication performance, while automotive radars are never aimed to operate in such conditions. Therefore, in this paper, the authors propose the concept of near-ground propagation, reducing the blockage effect in the road traffic conditions. Specifically, the radio waves may freely propagate under the blocking car's bottom if the antennas are placed as low as possible to the road. Based on the measured and modelled results presented in the paper, it may be claimed that near-ground communication and radar sensing are feasible and may combat even heavily obstructed cases. Nevertheless, some challenges associated with antenna locations were encountered. For example, it was discovered that antenna height at 0.5 m acts less effectively against blockage than at 0.3 m. Next, the 27 dB excess loss at the 0.5 m antenna height in the radar deployment is larger than 17 dB at 0.3 m. In its turn, the higher ground clearance of the blocking vehicle positively affects the near-ground performance. Additionally, the signal propagation at the grazing angle crucially reduces the relevant losses. 1 INTRODUCTION The emergence of autonomous vehicles and road infrastructure opens a new chapter in the wireless communication and sensing topic for the automotive industry. According to Ref. [1], the autonomous (driverless) car market was valued at 20.97 billion USD in 2020, with an expectation to rise to 61.93 billion USD in the next 5 years. Following such great perspectives, nowadays, many companies are actively involved in research and development to find a niche in this segment. As a result, we may regularly observe new prototypes with a full or partial level of autonomy. For example, some car brands already offer commercial models with an advanced autopilot capability, including driving along the curved road, guided by marking lines and signs and slowing down in case of potential danger. However, in such partially autonomous vehicles, the driver is still irreplaceable here since extra-human visual control is required [2]. Hence, wireless technologies do not play a vital role here but are bordered by driving assistance, safety and comfort enhancements. On the contrary, fully autonomous vehicles (e.g. Waymo, Zoox, Apple etc.) may raise the importance of wireless technologies as they determine the possibility to exploit such fully autonomous vehicles safely and reliably on public roads to a large extent. In other words, the operation of such vehicles is impossible without deploying wireless technologies and related infrastructure around them. In addition to the R&D, the standardising and documenting work on the automotive wireless technologies is underway. For example, the Third Generation Partnership Project (3GPP) proposed combining LTE and 5G New Radio (NR) to achieve the best performance [3] in vehicular scenarios. In this standard, communication partially occurs at millimetre-wave (mmWave and at microwave) frequencies with antennas installed in the bumper/radiator area. On the other hand, a distinct wireless technology, radar sensing, is well described and classified in recommendations from the International Telecommunication Union (ITU) [4]. Additionally, because of similar nature as well as cost and spectrum benefits, converging the radar and communication parts in a single hardware unit [5] might be a logical step forward. Nevertheless, radar and communication follow their own life journey and do not intersect in any standardisation documents so far; there are many open issues. Apparently, line-of-sight (LOS) is a working condition typically required for vehicular communication and radar sensing. However, the appearance of a car without or broken communication equipment in dense traffic may turn the LOS into the obstructed LOS (OLOS) scenario, where special methods should be applied to connect blocked vehicles. For example, the link might be rebuilt by the car relaying [6] method or employing the infrastructure roadside units (RSU) as intermediate nodes [7]. However, underdeveloped road infrastructure or traffic jams may drop the performance of the suggested schemes. Hence, the following logically correct issue is raised: Is there a way to keep the vehicles connected in the OLOS conditions without infrastructure assistance or relaying? In this paper, a solution to install the communicating antenna as close as possible to the road, enabling signal propagation between the obstructing vehicle and pavement (waveguide-like propagation), is suggested. This effect may keep the vehicles connected and expand the existing radar capabilities even in an OLOS scenario. Such phenomenon is called near-ground propagation in vehicular deployment. This topic was partly presented earlier in Ref. [8]. This paper extends the original work by introducing a detailed analysis and deterministic site-specific modelling. In general, near-ground propagation has already been covered in the literature earlier mainly for agricultural or forest scenarios [9-13]. Specifically, in Ref. [10], the authors presented a methodology to model the near-ground short-range propagation loss in the forest areas. The attenuation of the received power was measured for both transmitter (Tx) and receiver (Rx) antennas at 0.2 and 0.4 m heights, respectively. Later, in Ref. [9, 11], the same group of authors developed the near-ground narrowband radio channel model for agricultural wireless sensor networks. A pretty similar problem is explored in Ref. [12], where the continuous-wave measurements at 917.5 MHz in a forest terrain with a focus on path-loss in a device-to-device communication scenario were carried out in a few kilometre ranges extending at 1.5, 2.5, and 3.5 m height. Finally, in Ref. [13], 300 and 1900 MHz narrowband and wideband channel measurement results are presented for near-ground propagation. As a part of it, the antenna height, radiation patterns and foliage effects were investigated. Besides agriculture and forest use cases, near-ground propagation can be found in some other applications. For example, in Ref. [14], the functionality of a military man-portable near-ground radio transceiver is introduced. The results of this study show a significant deviation of signal strength when the position of a soldier is changed. Further, in Ref. [15], based on analysis of the propagation environment and received ultrawideband signal in outdoor near-ground environments, the main path-loss models are considered. Also, in Ref. [16], near-ground localisation is explored. In the research study, the antenna height-dependent time of arrival error model is developed. Another quite exciting outcome was obtained in Ref. [17], where an efficient two-segment ultrawideband radio channel model is introduced in very near-ground environments at height 0–20 cm. Later, the model was validated by measurement at 4.3 GHz with a bandwidth of 1 GHz. Finally, the results in Ref. [18-20] demonstrate the measurement and modelling results of the near-ground propagation without focussing on any application. Nonetheless, all these earlier studies on near-ground propagation did not consider any vehicular deployments. Therefore, we aim to fill this gap by introducing the near-ground propagation in the OLOS vehicular deployment. Specifically, the goals and contributions of this paper can be stated as follows: To introduce the measured results of radar and communication parts obtained by the authors in the OLOS scenario with a near-ground propagation effect. To propose and validate the method for practical modelling of the OLOS scenario with a near-ground propagation effect. To perform the sensitivity analysis of the OLOS scenario with a near-ground propagation. The paper is organised as follows. First, the antenna height requirement is determined for the realisation of near-ground vehicular applications in Section 2. Next, the deployment of interest and the measurement equipment are introduced in Section 3. Similar, but virtual deployment and modelling methods are described in Section 4. The measurement, modelling and sensitivity analysis results are provided in Section 5. Finally, the conclusions and discussions are presented in Section 6. 2 THE NEAR-GROUND DEFINITION IN VEHICULAR DEPLOYMENTS As it was mentioned in Section 1, the antenna should be attached as low as possible to the road surface in order to create the near-ground propagation effect. Moreover, the number of near-ground applications with distinguishing heights have been considered. Hence, only a use case defines how close the antennas should be to the ground. This section will define the near-ground height for vehicular application based on geometrical measurements, observations, and in-depth literature review. Based on the empirical studies (listed in Table 1), typical ground clearance11 The distance between the road pavement and the lowest point of the central part of the car. a of road vehicles varies within a relatively small range of up to 20 ± 10 cm with respect to, for instance, length or height [21]. Exotic off-road or sport cars are rear and are not considered in this work. Based on the under-car geometry (subfigure in Figure 1a), the immediate intuitive intention to place the antenna at some constructive elements (protruding parts of axles, gearbox, driveshaft etc.) looks unrealistic for the following reasons. First, the location of the elements varies from model to model. Therefore, every vehicle should be considered individually, which may complicate the development of a common standard. Second, the constructive elements may be a subject to stress, vibrations or dust affecting the near-ground propagation performance. Following this and the data in Table 1, the suitable area for the near-ground antenna placement was defined in the lowest point of the car bumper at height 0.3 m for cars and 0.5 m for trucks. These two reference values will be used further thoroughly in our study. Also, front and rear bumper lower heights b and c listed in Table 1 and shown in Figure 1a will be considered in Section 5 as additional parameters, affecting the signal propagation. TABLE 1. Measured dimensions of some road vehicles N Model a, m b, m c, m 1 Kia Ceed (2015) 0.14 0.18 0.27 2 Saab 9-3 Aero (2002) 0.13 0.16 0.23 3 Audi A4 (2018) 0.13 0.17 0.26 4 Mini Cooper (2010) 0.15 0.19 0.24 5 Skoda Octavia (2018) 0.16 0.20 0.27 6 Mercedes-Benz ML (2011) 0.20 0.28 0.35 7 Toyota Land Cruiser (2012) 0.23 0.3 0.38 8 MAN (not identified) 0.25 0.50 0.45 9 SISU (not identified) 0.27 0.45 0.40 FIGURE 1Open in figure viewerPowerPoint (a) Deployment for the measurement of the total received power in communication part. (b) The virtual modelling deployment for communication part built in Wireless Insite 3 MEASUREMENT METHODOLOGY First, the measurements were performed to prove the concept of near-ground propagation in the OLOS deployment. The measurement scenario and the utilised mmWave setup are described below. 3.1 Measurement scenario The measurements were carried out on the territory of Tampere University with the mmWave setup developed at the Faculty of Information Technology and Communication Sciences. In this measurement campaign, two deployments were considered: (i) communication (shown in Figure 1a) and (ii) radar (presented in Figure 2a). In the first scenario, two abstract vehicles communicate through antennas (red and black triangles in Figure 1a) installed on the lowest points of their bumpers. The signal blocking vehicle Kia Ceed (the white car in Figure 1a) is located between the antennas to form the required OLOS scenario. The antennas height H as well as distances D1 and D2 are taken as variables to mimic different vehicle types and road conditions. Specifically, two heights (H) of 0.3 and 0.5 m refer to the lowest bumper point of a passenger car and a truck (as defined in Section 2), while the D1 = D2 = 1–10 m characterise the varying vehicular density on the road: short D1 and D2 relate to traffic jam, while large ones describe sparse road density. FIGURE 2Open in figure viewerPowerPoint (a) Deployment for the measurement of the backscattering power in the radar part. (b) The virtual modelling deployment for the radar part built in Wireless Insite The second measurement scenario focusses on the automotive radar operation in the OLOS condition. In such a scenario, the presence of the near-ground propagation potentially may give extra awareness about the front and rear dynamics in the traffic flow, using the backscattering from the vehicles in the traffic queue. Therefore, to imitate this use-case, the radar transceiver, represented by collocated Tx and Rx antennas, is engaged in the scenario. Furthermore, in addition to the blocking Kia Ceed, Saab 9-3 Aero (black car in Figure 2b) was appended to imitate the mobility in the traffic queue. The distance D3 had a discrete range from 1 to 5 m with 1 m step, while D4 dynamically varied from 1 to 15 m when the vehicle drove. Values of H are similar to the communication scenario. First, the mmWave setup (transceiver) is installed at a certain distance D3 to the blocking vehicle. Then, by the command of the equipment operator, Saab 9-3 Aero starts moving, and D4 begins increasing. The measurements are performed while the car is driving. The requirement for smooth linear acceleration was determined to avoid significant deviation of the captured data. The maximal speed 2 m/s was chosen for safety reasons. 3.2 Measurement equipment Radar and communication setups were assembled and utilised for the measurement of the radar and communication deployments explained in Section 3.1. The transmitting part was common while receiving parts are individual for each setup. The total received power P tot com ${P}_{\text{tot}}^{\text{com}}$ and the backscattering P bsc rad ${P}_{\text{bsc}}^{\text{rad}}$ power were selected as measuring values of interest. It is noteworthy that the antenna radiation patterns were measured in the anechoic chamber at Aalto University. The measurement results are shown in Figure 3. FIGURE 3Open in figure viewerPowerPoint Co-polar measurement and modelling of the radiation pattern of the horn antenna PE9851A-20 Radar/Communication Tx: The NI PXIe-5840 vector signal transceiver (VST) generated the modulated OFDM signal with 200 MHz bandwidth and 60 kHz subcarrier at an intermediate frequency (IF) of 3.5 GHz. The Tx Pasternack PE9851A-20 horn antenna was installed on the tripods at the height of H. The transmitted power was 10 dBm. Finally, the Keysight N5183B signal generator is operated as the local oscillator with external mixers to up-convert the IF signal to 27.7 GHz. Communication Rx: The 27.7 GHz spectrum analyser (SA) Anritsu MS2760A was employed to measure P tot com ${P}_{\text{tot}}^{\text{com}}$ at the resolution bandwidth of 100 kHz and measurement bandwidth of 200 MHz. In these conditions, it had the noise level of −55.5 dBm. The PE9851A-20 horn antenna with 20 dBi gain and the 17° half-power beamwidth were attached to the SA by a cable with the 8 dB insertion loss. Radar Rx: The NI PXIe-5840 VST received P bsc rad ${P}_{\text{bsc}}^{\text{rad}}$ at an IF of 3.5 GHz through similar Pasternack antennas installed on the tripods at the height of H. The radar collocated antennas were spatially separated by 0.1 m. The Keysight N5183B signal generator used as down-converter. For all the measurements, the duration was constant: 10 ms. Finally, sub-carrier-domain processing algorithms were developed [22] to post process the measurement results. 4 MODELLING The ray tracing (RT) techniques in Wireless Insite [23] (WI) software was selected for simulation of near-ground propagation in the OLOS conditions. There are couple of reasons for choosing this. First, the multipath representation exposes a fairly intuitive picture of the propagation mechanisms happening between the car bottom and ground. For example, this approach enables the classification of the dominant and weak effects under the vehicle. Second, the sizes of the vehicle and the ground are large compared to that of the wavelength (λ ≈ 1 cm), suggesting ideal conditions for utilisation of geometrical optics (GO) and uniform theory of diffraction (UTD) [24] of the RT. Alternatively, full-wave methods are inefficient for such cases since, for instance, triangulation would require much memory and an unreasonably long computational time. Third, the employment of the radar theory for the radar deployment explained in Section 1 looks quite controversial due to the large dimensions of the ground and vehicle. This fact contradicts to the basics, where the object–radar distance should be infinitely large to turn the detecting object into a point scatterer [25]. Moreover, the selection of WI is validated in Section 5.3 by the LOS calibrating measurements, where the backscattering from the car is well approximated by the Friis equation (FE; see Figure 5a,b). A simplified 3D model of Kia Ceed was created to simulate the OLOS near-ground scenario in the Wireless Insite environment for the communication part (shown in Figure 1b). First, an image of the original Kia Ceed was uploaded, and then, using the built-in shape editor, a 2D contour was outlined and extruded to a 3D model. Apparently, due to the near-ground propagation, the contour of the blocking vehicle (Kia Ceed) should be as accurate as possible (i.e. geometry and overhangs of bumpers, ground clearance etc.), while some other details might be neglected or simplified. For example, it was speculated that the car model is completely PEC, which is a fairly rough approximation since the bumper, for instance, is hollow, made of plastic, and has a lot of metallic elements and wires behind it. However, it is pretty challenging to reproduce all the internals for any car, and hence it was suggested to nullify their contribution. Also, the bottom of the virtual vehicle is shortened to entirely flat for the same reasons. Nevertheless, the obtained accuracy of the modelling results in Section 4 was reasonable even with these simplifications. The simulated radar deployment is shown in Figure 2b, where another simplified 3D model of Saab 9-3 was added. The Rx-route is collocated with the Tx-route, representing the Tx-/Rx-route in the rear side of the blocking vehicle. Special batch functions were realised to perform the multi-frame dynamics of the Saab model; its position may change by 1 m forward in each frame. For each position, the signals on the transceivers were calculated in WI and were stored. This total number of discrete positions is 10, that is, the maximal distance is 10 m. The PE9851A-20 antenna was utilised at the Tx and Rx sides. The measured and the calculated patterns (with Wireless Insite) are presented in Figure 3. The discrepancy between the measured and simulated antenna patterns do not significantly affect the final result because of coaxiality between the antennas and the absence of any side objects. The maximum realised gain of 19.2 dBi was obtained in the modelling, while the gain of 20 dBi was measured. Despite the relatively low antenna location, the ground impact on the main lobe, thoroughly utilised in the manuscript, is not significant. Specifically, at H = 0.3 m and HPBW = 17°, the main beam starts interacting with the ground at 0.98 m, whereas the far-field zone begins from 0.47 m. The utilised simulation parameters are listed in Table 2. The RT built-in models are well described in Ref. [27] and will not be highlighted in this paper. However, an in-depth analysis of the reflected signal in the context of near-ground propagation will be performed in Section 5. Specifically, the equation describing the single-reflecting signal might be written as follows: E r = E i ‖ E i ⊥ ⋅ R ‖ 0 0 R ⊥ ⋅ ρ s ⋅ e − j k s ′ s ′ , (1)where s′ the Tx–Rx distance, E i ‖ and E i ⊥ ${E}_{\mathrm{i}}^{\perp }$ are incident electrical fields. Further, R‖ and R⊥ are Fresnel reflection coefficients for horizontal and vertical polarisations, which are defined as follows: R ‖ = − ϵ c cos ( θ ) + ϵ c − sin ( θ ) 2 ϵ c cos ( θ ) + ϵ c − sin ( θ ) 2 ${R}_{{\Vert}}=\frac{-{{\epsilon}}_{c}\mathrm{cos}(\theta )+\sqrt{{{\epsilon}}_{c}-\mathrm{sin}{(\theta )}^{2}}}{{{\epsilon}}_{c}\mathrm{cos}(\theta )+\sqrt{{{\epsilon}}_{c}-\mathrm{sin}{(\theta )}^{2}}}$ (2) R ⊥ = cos ( θ ) − ϵ c − sin ( θ ) 2 cos ( θ ) + ϵ c − sin ( θ ) 2 ${R}_{\perp }=\frac{\mathrm{cos}(\theta )-\sqrt{{{\epsilon}}_{c}-\mathrm{sin}{(\theta )}^{2}}}{\mathrm{cos}(\theta )+\sqrt{{{\epsilon}}_{c}-\mathrm{sin}{(\theta )}^{2}}}$ (3) TABLE 2. Modelling parameters N Model Value Notes 1 ϵc of road 4.4 - j0.2 [26] 2 σh of road, m 0, 0.001 3 Material of car(-s) PEC From WI database 4 # Of refl., pcs 1–3 5 # Of trans., pcs 0 6 # Of diffr., pcs 1 7 # Of multipaths, pcs 50 per each Tx-Rx pair At the same time, the signal reflecting from a rough plane undergoes additional attenuation, specified by the roughness coefficient ρs. The attenuation rate depends on the angle of incidence θ (see explanation in Figure 1a), the wavelength λ, and the size of the irregularities σs as follows: ρ s = exp − 1 2 4 π σ h cos ( θ ) λ 2 . ${\rho }_{s}=\mathrm{exp}\left(-\,\frac{1}{2}{\left(\frac{4\pi {\sigma }_{h}\mathrm{cos}(\theta )}{\lambda }\right)}^{2}\right).$ (4) From the mathematical point of view, a distinctive feature of Equations 2-4 is approaching to unity at θ → 90°. It means that roughness and dielectric parameters of the road become negligible at grazing angles, enabling the lossless reflecting field, in theory. This positive feature will be discussed in the next sections. 5 RESULTS 5.1 Total received power in the OLOS near-ground vehicular deployment First, about hundreds measurements of the P tot com ${P}_{\text{tot}}^{\text{com}}$ at the distance ranges D1 = 1–10 m and D2 = 1–10 m at H = 0.3 and 0.5 m were carried out in the communication scenario, described in Section 3.1. In these measurements, the discrete values of D1 and D2 were varied with step Δmeas. = 1 m. For each discrete distance of D1, 10 power samples were captured along the range D2 from 0 to 10 m. Later, the measured data was stored and tabulated. The results of these hundreds measurements at H = 0.3 m were collected in a single plot and shown in Figure 4. In this paper, the data at H = 0.5 m is not depicted similar to Figure 4, since it highly correlates with H = 0.3 m and does not discover any new finding. Therefore, on the basis of Figure 4, the following conclusions can be obtained. At shortest D1 or D2 the P tot com ${P}_{\text{tot}}^{\text{com}}$ approaches to the noise level because of the strong blockage effect. Nevertheless, the level of the blockage is different near the front and the rear bumper because of, probably, distinguishing bumper geometry. It can be recognised by depth and width of the blue region along D1 or D2. Meanwhile, the maximum value of the total received power was identified at 2–3 m of D1 or D2. At these distance ranges, the blockage effect is negligible, as a predicted priori. These preliminary results are quite encouraging, and therefore additional measurements are required to deepen the observed relationships. FIGURE 4Open in figure viewerPowerPoint Measured total received power as a function of D1 and D2 at H = 0.3 m. The small figure precises the measured data in the range D1 = D2 = 1–4 m It is evident that the most interesting region for further investigation is the transition from strong (blue colour in Figure 4) to weak (deep red colour in Figure 4) obstruction. These distances are D1 = 1–4 m and D2 = 1–4 m. Additionally, step Δmeas. was reduced down to 0.2 m to improve the measurement accuracy. The results of these additional 225 (15 for D1 and 15 for D2) measurements at H = 0.3 m are illustrated in the small Figure 4. Based on this, the next set of outcomes might be delivered. Indeed, the symmetry of the blue regions of D1 = D2 in Figure 4 was not reached again (as in Δmeas. = 1.0 m). On the contrary, the blue-to-red transition region of interest becomes less sharp: some intermediate colours appeared in the small figure. It is notable in Figure 4 and Table 1 that the front bumper is more ground-close than the rear one. Therefore, it blocks the near-ground signal stronger, which affects the difference of the blue zones along D1 and D2. Moreover, based on Table 1, the c > b rule is typically satisfied for all the listed and, probably, most of the existing vehicles. Meanwhile, the position of data points, referencing the maximum total received power in the communication scenario, is localised in the range of 2–4 m. To explain this phenomenon, two-dimensional plots, comparing the P tot com ${P}_{\text{tot}}^{\text{com}}$ with the theoretical FE as a function of total distance between antennas D1 + D2 + L and H were derived from the originally measured data. Specifically, Figure 5a,b relate to H = 0.3 m and H = 0.5 m, accordingly. In both graphs, the measured values are denoted as red circles, while the black solid line represents FE. The introduced made-by-sight dashed lines A and B bound the measured data and will help to explain the observed relationships in the following sections. These lines are shown for better visualisation. FIGURE 5Open in figure viewerPowerPoint Measured (red circles) and modelled (black crosses) total received power as a function of D1 + D2 + L at (a) H = 0.3 m and (b) at H = 0.5 m When antennas are next to the blocking car (i.e. D1 + D2 + L = 7 m in Figure 5a and D1 + D2 + L = 10 m in Figure 5b), the signal is strongly obstructed, and contribution to the P tot com ${P}_{\text{tot}}^{\text{com}}$ is almost zero. As soon as D1 + D2 + L starts gradually increasing, the P tot com ${P}_{\text{tot}}^{\text{com}}$ begins proportionally raising along the dashed line A as well, due to the diminishing role of the blockage effect. On the contrary, the growth of the total received power along the dashed line A goes slower for heights H = 0.5 m. This observation is quite intuitive: the
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