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Analysis of the Dominant Signal Component of the Air-Ground Channel Based on Measurement Data at C-Band

Operating remotely piloted aircraft is not imaginable without a continuous data exchange between the air vehicle and the remote pilot. This data exchange requires reliable data links. One approach for such a data link discussed in the community is a terrestrial system deployed in C-band. A good knowledge of the physical conditions of the communication channel, in this case the air-ground/ground-air channel, is indispensable for the development of wireless data links. Therefore we carried out a 50 MHz bandwidth channel sounding campaign with a terrestrial transmitter and an airborne receiver. In this paper we give a detailed description of our campaign setup and the processing of the collected data. The campaign covered several flight scenarios, such as take-off, taxiing, and multiple en-route maneuvers. We furthermore present results on the received power and the amplitude distribution of the dominant component of the received signal for the different flight scenarios. We observed significant drops in reception power during certain maneuvers that need to be considered in the design process of a data link for unmanned aviation. Additionally, we show that the amplitude distribution follows the distributions commonly used in statistical channel modeling of wireless channels to some extent. We finally present parameter sets for multiple flight scenarios for scaling the amplitude distributions to allow a statistical channel modeling of the reception power of the first resolvable signal path.


I. INTRODUCTION
M ORE and more Unmanned Aircrafts (UAs) are expected to enter the skies both in the controlled and uncontrolled airspace during the next years. For example, the market for UAs in the European Union is expected to make up to 10% of the European aviation market [1] during the next ten years. The anticipated fields of application are transportation or other logistic tasks, as well as surveillance, exploration, and tasks in the agronomy.
It is ruled out, that these UAs will operate completely autonomously and non-cooperatively. Furthermore, there is also Manuscript  the UA subset of Remotely Piloted Aircraft (RPAS) that do not operate autonomously and require, as the name indicates, a remote pilot. Hence, there is a need for a reliable communication system between the UAs and a central controlling instance and a remote pilot.
In the field of manned aviation, most communication is still performed using analogue voice radio. However, more advanced technologies have been applied during the last years, e. g. Aircraft Communications Addressing and Reporting System (ACARS) or Very High Frequency Data Link (VDL). While these systems are designed as a complement to the still indispensable analogue voice radio, new developments are on their way to provide a more modern communication system. The terrestrial solution is the L-Band Digital Aeronautical Communication System (LDACS) [2], [3]. It provides both voice and data communication, e. g. for the exchange of additional information like flight tracks and telemetric data. Nonetheless, it has not been designed to fulfill the requirements for a Control and Non Payload Communications (CNPC) link for UAs as identified in [4], [5].
The C-Band Digital Aeronautical Communication System (CDACS) is an approach for such a system. It is designed for the frequency range of 5030 MHz and 5091 MHz that is intended for Command and Control (C2) links for UAs [6]. First concepts have been presented in [7], [8]. So far, common channel models have been parameterized based on literature for the C-Band Digital Aeronautical Communication System (CDACS) design, as the knowledge of the physical properties of the wireless communication channel is crucial [9]. The data base for these models was taken from literature, e. g. the model used during the development of Aeronautical Mobile Airport Communication System (AeroMACS) as described in [10] among others. A common procedure to gain knowledge on the communication channel -in case of CDACS, this is the terrestrial ground-air channel in C-band -are channel measurements, often called channel sounding. Based on these measurements, a channel model is developed that is then used to design, evaluate and optimize the wireless waveform. Channel sounding campaigns for the C-band terrestrial ground-air channel have already been performed. The results of a large L-and C-band measurement campaign have been presented in [11]- [14]: While [11] presents the general campaign setup and findings on the channel behavior in over-water scenarios, [12] focuses on the wave propagation in This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ hilly and mountainous terrain. Suburban and near-urban scenarios have been covered in [13]. Finally, the effect of airframe shadowing during flight has been investigated and modeled in [14].
The German Aerospace Center (DLR) performed another measurement campaign to get a better understanding of the C-band air-ground/ground-air channel, especially during flight scenarios not covered by previous campaigns. For example, our campaign mostly contained flight tracks with circular and square shaped flight patterns and the transmitter in the center of the respective pattern. We furthermore flew certain maneuvers close to the transmitter located at a regional airport to investigate the channel behavior in critical situations. The campaign was planned with the experience gained during previous flight measurement campaigns like [15]. A high level overview of the new measurement campaign has already been published in [16].
This paper aims to provide considerably more details on the campaign setup and the data processing. Furthermore, we provide results on the reception of the dominant component received at the transmitter, often misleadingly called the Line of Sight (LOS) component, for different flight scenarios. The dominant component typically contains the actual LOS signal among other signal components that cannot be resolved from the LOS signal due to a limited resolution. Typical examples for non-resolvable components are the signal reflected off the ground and signals reflected or scattered in the vicinity of the transmitter or receiver, respectively.
The sequel of this paper is structured as follows: We describe the overall channel sounding procedure and the used channel sounding waveform in Section II. The hardware setup is presented in Section III. The processing of the collected data of the campaign is explained in Section IV, while the flight routes and performed flight maneuvers are described in Section V. Results covering the received power of the dominant component are presented in Section VI; the distributions of the received amplitudes are presented in Section VII.

II. CHANNEL SOUNDING
The motivation of channel sounding has been described in the previous section. But what is the channel that is actually sounded? Obviously, the desired channel that we are interested in is only the wireless channel between the transmitting and the receiving antennas. However, it is impossible to only measure this channel, since a number of hardware effects influence the signals on both the transmitting and the receiving side. An often applied strategy of minimizing the impact of these effects onto the final channel model is to perform reference measurements. They allow isolating and compensating these hardware effects by appropriate signal processing. Details on how this compensation is applied are given in Section IV.

A. Center Frequency
Although the anticipated frequency band for a C2 link is 5.030 GHz to 5.091 GHz, the center frequency f c used in this campaign is 5.200 GHz. This decision was made due to hardware availability; however, the authors do not expect significant channel deviations between these two bands.

B. Waveform Design
The waveform used in the campaign is a so called multi-tone signal. Multi-tone signals are a popular type of waveform; technologies like Orthogonal Frequency Division Multiplexing (OFDM) are a well-known subclass of these type of signals. Furthermore, multi-tone signals are popular in channel-sounding, however, they suffer from a high Peak-to-Average Power Ratio (PAPR). In communications, a signal with a high PAPR usually requires the High Power Amplifier (HPA) to operate at a significant back-off resulting in an imperfect operating point to avoid distortions or even hardware damage.
The channel sounding signal s CS used in the campaign is generated in two steps: r First, a basic signal is generated according to: where IFFT{.} denotes the inverse Fast Fourier Transform (FFT) and the vector elements have the same absolute value and phases distributed as Newman Phases [17] according to The FFT-length (thus the overall amount of subcarriers) is set to N = 2048, while N G = 5 guard carriers are used to provide guard bands for the expected Doppler shifts.
r In a second step, the PAPR is reduced by iteratively applying clipping and filtering: where Filt{. . .} denotes the application of an ideal Band-Pass (BP) filter, a = 0.95 defines the clipping limit and K = 80 000 defines the iteration limit. The last step of the generation sets s CS = s CS,K and the signal gets upsampled by a factor of f up = 2: s CS,up = UPS f up {s CS }. The upsampling is necessary because of the internal filter design of the Arbitrary Waveform Generator (AWG) used to play the generated signal. The overall bandwidth of the resulting signal sampled at 100 MHz is 49.78 MHz resulting in a spacial resolution of Δr min ≈ 5.994 m. This is the maximum bandwidth achievable with the available hardware.
The signal's PAPR is calculated according to where x * denotes the complex conjugate of x. The PAPR of the channel sounding signal has been determined to be PAPR dB (s CS,up ) ≈ 0.285 dB.  The time-discrete signal s CS,up is replayed in an infinite loop and is converted into the time-continuous transmission signal s Tx (t) according to where mod D (a) denotes the modulo operation on a to basis D and g Tx (t) denotes the transmission filter, i.e. the characteristics of the AWG's Digital-to-Analog Converter (DAC).

III. HARDWARE SETUP
The campaign involved one ground-based transmitting station -in the following: Ground Station (GS) -and one receiving station located onboard a Dassault Falcon 20E aircraft -in the following: Airborne Station (AS).

A. Ground Station
Since the reference measurement procedure described in Section III-C requires the operation of the GS at two different locations, the GS is designed as a portable platform as shown in Fig. 1b). Its block diagram is presented in Fig. 2. All devices are explained in the following.

1) Rubidium (Rb)-Clock and GNSS Receiver:
Together, the Rb-clock 1 and the Global Navigation Satellite System (GNSS) receiver 2 form a GNSS-disciplined oscillator and built the time base of the GS. This is a common approach to benefit from both the short-term clock-stability of Rb-clocks and the long-term clock-stability of the GNSS system at the same time. GNSS data is logged during all measurements and converted into the common RINEX data format afterwards.
2) Arbitrary Waveform Generator (AWG): The pregenerated channel sounding signal s CS is loaded into the AWG 3 and played at 100 MHz in an infinite loop during measurements. The AWG uses the 10 MHz reference signal of the Rb-clock and its average output power is set to −5.5 dBm.
3) High Power Amplifier (HPA) and Filter: The HPA 4 amplifies the AWG's output signal by an average gain of 53.5 dB. An additional BP filter (center frequency at 5.2 GHz, pass-band bandwidth of ∼400 MHz) is connected to the output of the HPA to reduce out-of-band radiation. Due to the losses implemented by the BP filter, cables, and connectors, the average output power of the channel sounding signal coming out of the filter is P out ≈ 47.5 dBm. Thus, the HPA is running with a backoff w. r. t. its 1 dB Gain Compression Point of P 1dB-GCP = 49.5 dBm to avoid nonlinear distortions.

4) Uninterruptible Power Supply (UPS):
All active devices of the GS, except for the HPA, are connected to the Uninterruptible Power Supply (UPS) 5 to allow a mobile operation of the GS for about 12 min. 5) Transmitting Antenna: During the measurement flights, a transmitting antenna was used having an average gain of G Tx ≈ 5 dBi. The antenna characteristics are part of the campaign results. Vertical polarization is used, as this is the common polarization in other aeronautical air-ground communication systems [18], [19].

B. Airborne Station
The receiving equipment onboard the Falcon aircraft was as follows.
1) Rb-Clock and GNSS Receiver: Similar to the GS, these devices form a GNSS-disciplined oscillator to provide a stable clock source through a 10 MHz reference signal. GNSS data is logged during all measurements and converted into the common RINEX data format afterwards.
2) BP Filter and Low Noise Amplifier (LNA): The incoming signal is filtered and amplified by a two-stage Low Noise Amplifier (LNA) and corresponding BP filters. The overall gain including cable and filter losses is ∼14.1 dB.
3) Downconverter: The pre-amplified signal is converted from the incoming carrier frequency f c = 5.2 GHz to an intermediate frequency of f IM = 80 MHz. The mixer inside the device uses the reference signal of the GNSS-disciplined oscillator as a clock basis. The downconverter is equipped with a variable gain G DC that is set by the software of the IQ-recorder via a serial interface.

4) Iq-Recorder:
The IQ-recorder 6 records the incoming signal at a sample rate of f SR = 50 MHz with a resolution of 14 bit for each the real and imaginary part of a sample. Sets of 98 304 kSmpl are stored in a binary file together with a header including the current GNSS-timestamp, the current sample counter value ρ, and the current value of the gain control G DC of the downconverter. The resulting data stream of more than 175 MB/s motivates the usage of a RAID, 7 which is considered as part of the "IQ-Recorder" block in Fig. 3 for the sake of simplicity. The IQ-Recorder uses the reference signal of the GNSS-disciplined oscillator as a clock basis.

5) Video and Inertial Measurement Unit (IMU):
An Inertial Measurement Unit (IMU) 8 is used to record data on the orientation of the aircraft. The data is logged including GNSStimestamps. For documentation, a video camera is filming all flights through the window over the left wing of the Falcon aircraft.
6) Receiving Antenna: A vertical polarized receiving antenna is used. According to the manufacturer's data-sheet, it provides an omnidirectional antenna pattern with an antenna gain of G Rx ≈ 4 dBi. A more precise description of the receiving antenna's pattern is not available. The receiving antenna is mounted at the bottom of the aircraft as shown in Fig. 5 and 6. This location is determined by the architecture of the research aircraft.

C. Measurement Procedure
Each measurement flight consisted of the following steps: 1) Pre-Flight Reference Measurement: The aircraft is on the apron with active Auxiliary Power Unit (APU). The receiver station onboard the aircraft runs on the aircraft's APU power; IQ-sample recording is prepared but paused. The GS is located next to the aircraft on the apron and is connected to the local power supply network as shown in Fig. 4(a) and Fig. 7(a). The Rb-clocks of the GS and the AS have been synchronized via cable. The filter output is connected to the antenna cable of the receiving antenna using a cascade of attenuators. The attenuators provide an overall attenuation of A dB,ref = 90 dB, 6 National Instruments PXI Series, Windows 7 with LabView. 7 National Instruments HDD8265. 8 xSens MTi-100 Series.   corresponding to a Free Space Path Loss (FSPL) of ∼0.15 km for the given f c . The GS starts transmitting the channel sounding signal, the AS starts the IQ-sample recording for about 10 s.

2) Moving the Ground Station:
The GS is moved from the apron into its transmission location on the rooftop of the institute's building. While the HPA is switched off during the relocation, the GNSS-receiver, the Rb-clock, and the AWG are running on the UPS. Once the transmitting location is reached (see Fig. 7(b)), the station is connected to the local power supply network. The filter output is connected to the antenna cable and the HPA is switched on: The transmission of the channel sounding signal is started.
3) Actual Measurement Flight: The receiving antenna of the aircraft is connected to the AS and IQ-sample recording is started in the AS. The aircraft starts taxiing and takes-off. Once the aircraft reached its parking position on the apron after the flight, the recording of the IQ-samples is paused again; all AS devices are kept running on APU power.

4) Moving the Ground Station:
The GS terminates its transmission by shutting down the HPA. The GS is disconnected from the power supply network and moved back from its transmission location to the apron where the aircraft is waiting. Again, the HPA is switched off while the GNSS-receiver, the Rb-clock, and the AWG are running on the UPS.

5) Post-Flight Reference Measurement:
The same procedure as during the pre-flight reference measurement is performed again after each flight. Both measurements are compared during post-processing to get a better understanding of possible hardware drifts during the measurement flight.

A. Received Signal
The signal at the receiver can be described as where * denotes the convolution, h(t) describes the (unknown) channel impulse response and n(t) describes white Gaussian noise. The time-discrete signal s Rx = [s Rx,0 , s Rx,1 , . . .] is created by sampling according to where g Rx (t) is the filter of the Analog-to-Digital Converter and f SR denotes the sample rate.

B. Channel Sounding Signal Processing Concept
The basic idea of the processing is to compare the reference measurement signal s Rx,ref with the signal received during flight s Rx as suggested in [20]. Before the received data of a flight can be processed, the reference signal recorded before (or after) the corresponding flight needs to be loaded.

C. Extracting the Reference Signal
From the properties of the transmission signal (5) and the recording sample rate it follows that a vector of N = 2048 samples of the received IQ data is guaranteed to contain exactly one (circularly shifted) instance of the channel sounding signal s SC . Thus, an arbitrary vector of length N can be chosen from the reference measurement data starting at sample number ρ ref as the reference signal used for evaluation: The logarithmic spectra of three different x ref{0,1,2} with arbitrarily chosen start sample numbers ρ ref{0,1,2} are plotted in Fig. 8. Apparently, the deviations between these three different instances are extremely small and are therefore considered as negligible. 9 Thus, the actual value of ρ ref is free of choice; however, the actual value of ρ ref is later required to determine the time shift when comparing the extracted reference signal with the measurement signal. We define T ref as the time instance of the recording of ρ ref .

D. Hardware Effects
The concept presented in Section IV-B helps reducing the general problem of channel sounding described in Section II by neutralizing most of the hardware effects onto the measurement signal. However, only hardware that is part of both the reference measurement and the actual channel sounding measurement is affected by this neutralization. This was not the case for the following items (also highlighted in Fig. 4): 1) Cable from the BP filter of the GS to the attenuators during the reference measurement a) 2) Cable from the BP filter of the GS to the transmitting antenna during the flight measurement b) 3) Attenuators used during the reference measurement a) 4) Transmitting and receiving antenna during flight measurement b). The cables mentioned in 1) and 2), respectively, were of the same length of 8.40 m and of the same batch of the same manufacturer. Measurements with a Vector Network Analyzer showed that the relevant parameters (group delay, frequency response) do not show any significant variances; consequently, we consider the impaired effects of the different cables as negligible.
While the effects of the attenuators in 3) are also negligible, the antennas in 4) impair more severe effects and are part of the resulting measurement data. However, since most radio hardware (including all active devices and also g Tx (t) and g Rx (t)) are part of both measurements, the most severe effects are fully compensated.

E. GNSS Data and Clock Drift
All GNSS data collected during the campaign was postprocessed by the Precise Point Positioning (PPP) service of the Geodetic Survey of Natural Resources Canada using the SPARK algorithm. The PPP processing provides correction values to compensate clock drifts among other impairments.
The GNSS antenna is mounted at the top of the AS to allow a better reception of the GNSS signals during flight. However, the receiving antenna of the measurement signal is mounted at the bottom of the AS, thus in a different location from the GNSS antenna. The location of the GNSS antenna with respect to the receiving antenna is represented by the vector e GNSS ∈ R 3 given in the North-East-Down (NED) coordinate system as defined in Appendix VIII-C. A similar approach as described in [21] is used to map the measured GNSS data onto the actual receiving antenna's position by applying e GNSS and IMU data. This correction is consequently applied to all location based processing in both the NED system and the East-North-Up (ENU) system as defined in Section VIII-B.
The Rb-clocks of both the GS and the AS are subject to clock drifts. According to the manufacturer, the deployed Rbclocks provide a typical clock stability of 1e-12 in the applied GPS-locked operation mode. However, this value cannot be achieved in a real world scenario where the clocks are subject to vibrations, varying temperatures, and acceleration. The actual clock drifts are therefore expected to be higher than the value given by the manufacturer.
As an example, the clock drifts detected during PPP processing of the GNSS data of both clocks are plotted in Fig. 9. Apparently, the drift of the airborne Rb-clock is greater than the drift of the ground based clock. This difference can be explained by the unstable environmental conditions onboard the aircraft during flight. As the Rb-clocks are always synchronized directly (i.e. a few minutes) before the pre-flight reference measurement of the channel sounding signal as described in Section III-C1, the clock drifts during the reference measurement at T ref are very low.
We explain the small peak of the drift of the GS clock between the pre-flight reference measurement and the takeoff with the relocation of the GS as described in Section III-C2.
The detected clock drifts need to be compensated during the processing of the channel sounding data. We denote the detected clock drifts of the GS and AS as τ GS (t) and τ AS (t), respectively. The overall clock drift compensation τ drift (t) at time instant t is computed according to The campaign took place in July 2018 and consisted of four flights. All flights started and ended at the EDMO airport in Oberpfaffenhofen, Germany, thus close to the location of the GS. While the second flight was a long range flight with a LOS distance of up to 600 km, the remaining flights took place in the area around EDMO (< 60 km). The flight routes of all flights are plotted in Fig. 10; the flight altitude (above mean sea level) is color coded. Flight dates and flight durations are presented in Table II.
All flights ended with a few go-arounds before the actual landing. In aviation, a go-around is initiated when a landing is aborted. 10 A go-around may happen during final approach "whenever landing conditions are not satisfactory" [22]. The go-around scenario, especially the part where the aircraft is above the runway, is dominated by strong multipath components besides the LOS path together with a comparatively high speed of the aircraft resulting in rapidly changing reflections, Doppler shifts, and Doppler spreads.
Furthermore, maneuvers with rolling angles up to ±50 • were flown to investigate the effect of airframe shadowing during banking.

VI. POWER OF THE DOMINANT COMPONENT
We do not consider resolvable multipath propagation effects in this paper, rather we focus on the dominant signal component and evaluate its received power. This signal component is often misleadingly called the LOS signal. In fact, the actual LOS signal component is superimposed to multiple multipath components which cannot be resolved individually.
To calculate the power of this dominant component, the following processing is applied: 1) Blocks of B consecutive channel sounding sequence instances are taken from the received signal s Rx , resulting in a vector of BN samples. Thus, the i-th block can be with ρ i = iBN , where τ 3) The maximum of the PDP denotes the received power of the dominant signal component: P dB,i := max{a i }. 4) As we are often interested in the received power without the effect of the FSPL, we furthermore define where A dB,ref denotes the attenuation used when x ref was recorded during the reference measurement 11 and FSPL i Fig. 11. Color coded received power during strong banking. The background color represents the presence of a LOS path that is determined from the polar angle of a receiver-centered North-East-Down (NED) coordinate system and the aircraft geometry, see Appendix VIII-C; red: "LOS path is blocked," green: "LOS path is present".

A. Banking Angle
The behavior of the received power computed according to (11) during strong banking is given in Fig. 11 providing the rolling angle (see Appendix VIII-C) on the y-axis. Raising the left wing and lowering the right wing indicates a positive rolling angle and vice versa.
By the time the given snapshot was recorded, the LOS distance was 4.6 km at a flight altitude of 1.01 km. The aircraft passed the transmitter from southeast, heading northeast; thus, seen from aircraft, the transmitter was on the left side. Observing the transmitter's position given in NED spherical coordinates (see Appendix VIII-C) allows a precise declaration if airframe shadowing is present (LOS path not available) or not present (LOS path available). In Fig. 11, the background color indicates if the LOS path is available (light green color) or not available (light red color). The presence of the LOS path is determined evaluating the NED angles and the airframe architecture around the receiving antenna as sketched in Fig. 6. For the sake of completeness, we point out that no obstacles around the transmitter are blocking the LOS path for the observed period of time.
The presented rolling angle in Fig. 11 indicates, that the first bank (0.2 s to 5.3 s) leads to a loss of the LOS path since the received power P dB drops down to −30 dB. This statement holds a comparison with the expected presence of the LOS path based on the NED angles. However, the figure shows that the dramatic drop in received power does not happen suddenly, but that a transition from strong reception to low reception is happening. We explain this observation by knife edge diffraction caused by the airframe, most likely the guide rails.
The second bank (5.3 s to 11 s) indicates a bank in the opposite direction, such that the receiving antenna has a direct view to the transmitter without any shadowing due to the airframe or similar. Consequently, the received power is up to 40 dB higher compared to the power received during the first bank.
The third bank starting at 11 s shows the same behavior as the first bank.

B. Takeoff
The received power during takeoff is shown in Fig. 12. All flights started and ended at the EDMO airport, the starting direction was the same for all four flights (heading: south east). The position of the runway and the transmitter is shown in Fig. 15.
While P dB is mostly in the range of -2 dB to 4 dB as long as the aircraft is on the runway, one can observe an intense drop of up to 27 dB during takeoff and climbing. This observation applies to all four takeoffs in a very similar manner, however, the exact position of the strongest drops during climbing varies.
To understand the behavior of the received power, we have to recall that the receiving antenna is located at the bottom of the aircraft and that the aircraft is heading away from the transmitter during takeoff. This results in a complete block of the LOS path as long as the aircraft is climbing with a strong pitch angle in the given direction. Furthermore, no reflector close to the receiving antenna, which could result in a stronger received signal, is present. Nevertheless, the received power varies a bit and was observed to take on values as high as -12 dB. The moderate variations may be caused by signals reflected from buildings and obstacles located behind the runway when seen from the transmitter. Fig. 13 shows the received power during a part of flight II, i.e. the long range flight, vs. the LOS distance. The data shown in Fig. 13 was recorded during a northbound flight at an altitude of 9.3 km, following a radial course away from the transmitter. One can observe a periodically changing received power within a dynamic range of 5 dB. The period is in the range of 11 s, corresponding to a delta of about 1.5 km of LOS distance.

C. En-route (ENR)
These oscillations can be interpreted as large-scale fading and are explained by the Curved-Earth Two-Ray (CE2R) model as described in [11]. This reflection model describes the behavior of the of a received signal which is composed of two signals via superposition: The LOS signal and the signal reflected off the ground. In our case, this composed signal (mostly) defines the dominant component as introduced above. The theoretical signal power based on the CE2R model is also given in Fig. 13. Apparently, the model and the measured received power match quite well. We ascribe the deviations to varying permittivities at the reflection point and a varying relative altitude which is not considered in the given model. The CE2R model can be applied only under the condition that the LOS path and the ground wave path are not resolvable at the receiver, thus that their path lengths differ by less than Δr min . The authors have verified that this condition is fulfilled for the geometry observed in Fig. 13. Fig. 15 shows the received power during eleven go-arounds (see Section V) flown at different altitudes above the runway of the EDMO airport.  The displayed parts of the go-around all have a "U"-shaped flight altitude profile, where the bottom part is flown with different altitudes over the runway ("runway part") as can be seen in Fig. 15(a). During the runway part, the roll, pitch and yaw angles of the aircraft were all kept around 0 • . The received power is comparatively strong (> −5 dB), except for two sections ("drop section") labeled A and B where the received power partially drops down to -22 dB.

D. Go-Around
The position of these drop sections with respect to the transmitter can be identified better in Fig. 15(b), where the received power is plotted in dependency on the azimuth angle ϕ and the polar angle θ according to the East-North-Up (ENU) coordinate system as defined in Appendix VIII-B.
The dependency of the received power on the azimuth angle is clearly visible. The two drop sections A and B are highlighted in both plots and are found to be in the range of 89 • < ϕ < 94 • and 114 • < ϕ < 122 • , respectively. Although the antenna pattern of the transmitter is not considered during data processing, we do not affiliate these significant drops to the antenna, as we do not see a similar power drop at similar azimuth angles in other flight scenarios. As the go-arounds were flown along both directions of the runway, we also consider it as unlikely that the drops can be explained by the receiver's antenna pattern. An analysis of the NED angles and the aircraft's architecture shows that we can also rule out airframe shadowing as the reason for the drops in received power. Therefore, we assume the power drops in A and B are caused by obstacles between the transmitter and the receiver that cause interfering rays (non-resolvable scatter 14 shows that parts of the roof of a hangar building intersect with the ground projection of the LOS path for the corresponding angle range of 89 • < ϕ < 94 • . The authors have verified that this roof does not block LOS path between the transmitter and the receiver for any of the flights observed here. We therefore assume, that these drops are caused by non-resolvable signal components reflected off this roof and reflected off obstacles located on this roof. Apparently, these components are contributing to the dominant component destructively. The condition for a non-resolvable signal path is that the distance between the length of the LOS path and the length of the reflected path is less than Δr min . Considering the location and height of the hangar building, we were able to find reflection points on this roof fulfilling this condition for the specific angle range for all flights. Drop zone A is bounded by higher obstacles located on the roof blocking the path of the reflected signals for greater values of ϕ as it can be verified in Fig. 14.
For drop zone B we have another explanation of the low received power: Fig. 14 reveals that a small radome is located about 15 m southeast of the transmitter. The radome is not that high that it blocks the LOS path for any of the flights, however, its top is high enough to disrupt the estimated first Fresnel Zone of the link between the transmitter and the receiver at least partially for 114 • < ϕ < 122 • . We assume that the radome, therefore, causes the recorded power drops in zone B.
We understand these findings as a hint that the immediate environment of the ground antenna has a strong impact on the resulting channel conditions, especially in critical flight maneuvers like go-arounds. We therefore suggest to carefully choose the ground antenna's location.

VII. AMPLITUDE DISTRIBUTION
In this section, we analyze the distribution of the received amplitudes x for different flight scenarios. In a first step, we apply a Gaussian Kernel Density Estimation (KDE) [23] to visualize the respective amplitude distributions. We then use a Downhill-Simplex based algorithm to find the maximum likelihood parameter estimates for a Rice and a Nakagami PDF which best fit the given data. Both the Rice and the Nakagami distributions are common approaches to model the distribution of received amplitudes when transmitted over a wireless channel. Finally, we use the Mean Squared Error (MSE) between the KDE and the two estimated Probability Density Functions (PDFs) to determine which of the two distributions provides the better fit for the corresponding data set. Although the Nakagami distribution is a more flexible approach providing more degrees of freedom, we observed that it does not substantially outperform the Rice fit in any of the scenarios investigated. We provide both solutions to the reader since the Rice distribution is less complex and its fitting lead, in contrast to the Nakagami fit, to a numerically stable solution for all of the investigated scenarios.
The Nakagami distribution is given by where β is a scaling factor, μ defines the PDF's location, Γ(.) denotes the Gamma distribution, and m denotes the shape parameter. The PDF of the (standardized, i.e. σ = 1) Rice distribution is given by where β and μ again define the distribution's scale and location, respectively, I 0 (.) denotes the modified Bessel function of the 0-th order, and b is the shape parameter. Following the definition above, the well-known K factor describing the power ratio of the LOS component and the multipath components of the Rice PDF is given by K = b 2 . For b → 0, the Rice distribution tends to the Rayleigh distribution.  Table III).
The estimated parameters for the amplitude distributions during the scenarios investigated in the following are given in Table III. The table provides also an estimate of the presence of an unblocked LOS between the transmitter and the receiver (0% corresponding to pure non-LOS, 100% corresponding to pure LOS). These estimates were calculated based on GNSS and IMU data similar to the approach described in Section VI-A.
Please note that the following analysis was performed on the range between the 5th and the 95th percentile of the data to reduce the effect of outliers. The effect of the FSPL was compensated according to (11).

A. Taxiing
The distribution of the received amplitudes during taxiing at the apron is given in Fig. 16. Both the KDE and the fitted Rician and Nakagami PDF are plotted. The MSE of the Nakagami approach is slightly better than the Rician approach, however, the deviation is minimal. Comparing the determined fits to the KDE visually suggest, that the underlying channel observed during the measurement cannot be perfectly represented by just a single PDF. We assume this is caused by changing channel conditions as the aircraft is moving on the apron.
The corresponding data in Table III shows that no LOS was present during taxiing. Nevertheless, in contrast to the takeoff scenario discussed below, the distribution does not tend towards  Table III).  Table III). a Rayleigh distribution. We explain this by the continuous presence of the ground echo during taxiing.

B. Takeoff and Landing
The distribution of the received amplitudes during takeoff of all four flights is given in Fig. 17. The figure shows both the KDE and the PDF of a Rice distribution fitted to the underlying data 12 .  According to the corresponding entry in Table III, the shape parameter b of the Rician PDF is close to zero. As mentioned above, this lets the Rician distribution tend towards a Rayleigh distribution -a common approach to model a non-LOS scenario in wireless communications. Therefore, we state that the receiving antenna at the aircraft is shadowed by the airframe during takeoff for practically all the time. This assumption is supported by the estimated LOS presence of 0%. It can be understood when the geometry of the position of the transmitter, the runway, the starting direction, and the positive pitch angle (i.e. "nose up") of the aircraft during climbing is considered and also matches the findings from Section VI-B.
The amplitude distribution during landing ("final approach") of all four flights is presented in Fig. 18. Both the KDE and the Rice and Nakagami PDF fits are plotted; the latter shows a slightly lower MSE.
The amplitude distribution parameters again reveal a mostly blocked LOS path, however, not as consequent as for the takeoff scenario. In contrast to the takeoff scenario, the aircraft's airframe is not consequently blocking the LOS path during its approach to the runway: It is descending and heading towards the transmitter while still having a mostly non-negative pitch angle. Fig. 19 and 20 show the amplitude distribution during parts of flight I ("circular patterns"). The circles are 23 km ("small") and 62 km ("large") in diameter, respectively, and were flown at different altitudes: 3.2 km ("low") and 10.9 km ("high"). The corresponding flight track is highlighted in a miniaturized map of flight I (compare Fig. 10(a)) in each plot. Fig. 19 compares the distributions of the amplitudes received during the track following the small and the large circle at the low flight altitude. Since the transmitter is located in the center of both circles, the larger diameter corresponds to a larger LOS distance, while the flight altitude above ground is approximately the same. The circular shape of the pattern results in a more or less constant polar angle as defined in Appendix VIII-B for each circle. The different circle diameters lead to a significant difference in the resulting polar angle: While the mean polar angle in Fig. 19(a) isθ ≈ 76 • , it isθ ≈ 84 • in Fig. 19(b). This leads to different conditions of the wireless propagation channel, since the probability of a blocked LOS path is higher in case of a greaterθ. A visual comparison, and the comparison of the corresponding entries in Table III, show that the differences in the channel conditions are also observable in the amplitude distributions. Apparently, the polar angle has a strong influence on the resulting amplitude distribution at the receiver. The distribution parameters from Table III suggest that the scenario in Fig. 19(b) tends closer towards a non-LOS scenario than the scenario presented in Fig. 19(a). This statement is supported by the estimated presence of LOS for the corresponding scenarios (56% and 77%, respectively). Fig. 20 shows a similar flight pattern as described in the previous paragraph, however, at a significantly higher flight altitude of about 10.9 km. This results in smaller polar angles compared to the low flight altitude:θ ≈ 49 • andθ ≈ 71 • for the small and the large circle, respectively. The impact on the amplitude distributions is also clearly visible: Both Fig. 20(a) and Fig. 20(b) show a LOS scenario. Please also note, that the scenarios in Fig. 19(a) and Fig. 20(b), where the mean polar angles are in a similar range, show comparable amplitude distributions. Fig. 21 shows the amplitude distribution during parts of flight III ("square-type patterns") at a flight altitude of roughly 3.2 km 13 . While a small square-type pattern with an edge length of roughly 30 km is flown in Fig. 21(a), a larger square-type pattern with an edge length of about 52 km is flown in Fig. 21(b). Although the flight altitude is kept the same during both flights, the non-circular shape of the flight tracks result in a varying polar angle. However, the average polar angle for the scenario presented in Fig. 21(a) is smaller than the average polar angle in the scenario presented in Fig. 21(b) for the same reasons explained in the previous section.

D. En-route (ENR) -Squares
Similar to the circular pattern, the probability of receiving larger amplitudes for the square-type flight patterns is larger for the smaller square ( Fig. 21(a)) than for the greater square ( Fig. 21(b)). It is also interesting to see that even in the case of the large square, the distribution shows a higher probability for larger amplitudes compared to the large circular pattern at the same flight altitude (Fig. 19(b)). On the one hand, the average polar angle in the large square-type pattern is not as large as in the case of the large circular pattern. However, 13 Please note that only the data recorded while flying along the actual edges of the square-type pattern is discussed here. The parts of the flight where the turns from one edge to the next were flown are skipped, since the channel conditions are not comparable to those during a flight along the edges. this might not be the only reason for the higher probability of receiving a larger amplitude compared to the circular pattern: The pilot of an aircraft flying a circle has to correct the aircraft's heading continuously, which in practice impacts not only the yaw angle, but also the roll angle of the aircraft. Especially in case of a large polar angle, even these minor corrections increase the probability of a blocked LOS path. In contrast, no such continuous heading correction is necessary when flying along the edges of a square.

VIII. CONCLUSION AND OUTLOOK
In this paper we have described a flight campaign investigating the physical properties of the C-band air-ground channel for different flight scenarios. We have furthermore presented first results of the evaluation of the recorded signal. The results presented here focus on the power of the dominant component and the amplitude distribution. We have investigated the received power and the received signal amplitudes and showed their behavior and distribution, respectively. Comparing these results within the different flight scenarios showed significant distinctions. We understand these findings as a motivation to develop an adjustable channel model for the different flight scenarios, as we do not think that the detected distinctions can be covered by just one simple model.
As a next step we will focus on the detection and tracking of the resolvable multipath components during the different flight scenarios.

A. Power Delay Profile (PDP)
The discrete coherent Power Delay Profile function PDP coh : C BN × C N → R f ups N of a vector y ∈ C BN w. r. t. the reference signal x ref ∈ C N is computed as follows: r To simplify the following processing steps, the matrix Y ∈ C N ×B is defined, whose (m, n)-th element is set to y[m + nN ]. r The result is converted to dB-scale: a dB = 20 log 10 {a}

B. Transmitter Centered Coordinate System
We first define a Cartesian coordinate system with the transmitting antenna in its origin: an East-North-Up (ENU) system, where the x-axis shows into the East direction, the y-axis shows into the North direction, and the z-axis shows Up into the sky. More precise: the negative z-axis shows into the center of gravity of the Earth according to the World Geodetic System 1984 (WGS84). We then define the ENU azimuth angle ϕ ENU ∈ [0 • , 360 • ) as the clockwise rotation around the z-axis where ϕ ENU = 0 • indicates the north direction. The polar angle θ ENU ∈ [0 • , 180 • ) is the angle between the LOS and the z-axis, such that all points with θ ENU = 90 • lie in the xy-plane.

C. Receiver Centered Coordinate System
The North-East-Down (NED) coordinate system is a Cartesian coordinate system fixed to the aircraft with the receiving antenna in its origin. The axes are defined as shown in Fig. 6: North (x-axis) is heading into the direction of the aircraft's nose, i.e. towards the viewer, which usually corresponds to the flight direction. East (y-axis) is heading to the left of the figure, which corresponds to starboard during flight. Down (z-axis) is heading downwards, usually towards the ground. Corresponding to the ENU system, we define the angles as follows: The azimuth angle ϕ NED ∈ [0 • , 360 • ) is the positive rotation around the z-axis where ϕ NED = 0 • corresponds to the x-axis. We define the polar angle θ NED ∈ [0 • , 180 • ) as the angle between the LOS and the z-axis, where θ NED = 0 • equals the z-axis and all points with θ NED = 90 • lie in the xy-plane. The transmitter's position given in spherical NED coordinates allows a straight forward analysis whether the LOS connection is blocked by the airframe or not.
We can use the NED system to define the aircraft's rotation axes: Roll is a positive rotation around the x-axis. Pitch is a positive rotation around the y-axis. Yaw is a positive rotation around the z-axis.