Generalized Propagation Channel Model for 2 GHz Low Elevation Links Using a Ray-tracing Method

Unmanned Aerial Vehicles (UAV) will increasingly be used for responding to emergencies or for law enforcement in civil surveillance applications. Transferring the enormous amounts of information from UAV-mounted cameras or sensors will require large bandwidths, unlike the information required for remotely controlling a UAV, thus necessitating higher frequency bands typically in the vicinity of 2 or 5 GHz. Novel hardware developments will need to rely on a versatile propagation channel model for the envisaged scenarios ranging from deep shadow urban areas to open fields. This paper studies more complex intermediate scenarios, which fall between the aforementioned ones, and which are more difficult to model. A semideterministic model, first developed for open, flat areas, has been generalized to accommodate any possible operational scenario and was tested in built-up areas. The model involves a stochastic part and a determinist which is a raytracing based part used to compute the long term mean (LTM) of the signal's coherent component.


Introduction
Unmanned Aerial Vehicles (UAV) will soon be widely used in civil applications as these systems offer a more economical and safer overview to the observer than helicopters or airplanes.By using 2 or 5 GHz high frequency bands, more information can be transferred than at low frequencies which are primarily used for remotely commanding the UAV.However, such high frequency links undergo higher diffraction and shadowing/blockage losses [1], so new hardware is needed to transmit the information from a UAV to the command center ultimately leading developers to seek propagation channel models to define optimized architectures, modulations, coding, etc.
For low elevations between a UAV and the ground station, propagation characteristics lie between those of terrestrial and land mobile satellite links.Generative propagation channel models for land mobile satellite channels are reviewed in [2] while a survey of models for terrestrial propagation can be found in [3].For UAV links, a universal propagation channel model is called for, one which is reliable and precise in all envisaged environments ranging from open to dense urban environments with deep shadowing conditions.A characterization of possible shadowing features, in terms of obstacle sizes and heights, is illustrated in Fig. 1 where buildings, trees, barns and walls are taken into account.Major terrain irregularity effects were not considered in this study as the chosen measurement scenarios were limited to flat areas.
A detailed path loss analysis is performed in [4], [5] and [6].A modeling and experimental study for the open, flat areas was presented in [7] where a 2×2 MIMO semideterministic propagation channel model for UAVs with low elevation was first described.This semi-deterministic model is an evolution of a purely stochastic one developed for deep shadow conditions [8] applying a method from a vehicle-to-vehicle MIMO propagation channel model [9].This paper aims to generalize the semi-deterministic model, originally developed for open areas [7], for more complex, cluttered scenarios such as built-up areas or areas such as those shown in Fig. 1.Contrary to what was observed for significantly deep shadow areas [8] where a purely stochastic approach was sufficient, there is a need for a deterministic, ray-tracing based component which cannot be reproduced by a purely statistical approach in open and cluttered areas.

Measurements
Our measurement campaign was performed in the 2 GHz band using a Multiple Input Multiple Output (MIMO) setup based on criteria laid out in [10] where channel separation was achieved through the use of two nearby carriers within the assumed channel's coherence bandwidth.A number of scenarios, as shown in Fig. 1, were measured [10].However, in this paper attention was focused on a built-up area.

Setup
A remotely controlled airship, simulating a UAV and shown in Fig. 2, carried the transmitter (Tx) with two downward quarter-wave monopole antennas spaced d = 31.78cm (over two wavelengths) apart.Figure 3 shows the static receiver (Rx) which is also composed of two monopole antennas with a four-rod ground plane.The monopoles were placed on a 1.5-m-high tripod with equal separation, d = 31.78cm, as on Tx.A 2x2 MIMO receiver acquired instantaneous power at a 10 kSps (samples per second) rate.The measurement bandwidth of 12.5 kHz accommodated the small Doppler shift, caused by airship motion, and provided a sufficiently small noise floor for a high dynamic range.
The 2×2 MIMO configuration is depicted in Fig. 4. As in [11], the transmit frequencies were extremely close to one another (F 1 = 2001.0666and F 2 = 2000.8666MHz) and within the expected channel's coherence bandwidth, but far enough apart for the receiver's selectivity to separate the signals.
Only received power was measured as no phase information was recorded, i.e. |h| 2 , where h is the channel response at the carrier frequency.3) Computer with software.hence, it was neglected in further analysis.The elevation angle was set from 1° to 3°, in 0.5° increments, resulting in 20 flight paths.By performing ray-tracing, it was verified that all terrain interactions took place in the narrow shaded triangle close to Rx, which means that, in practice, the relevant part of the terrain profile for all flight path transmit points was the same for all Tx positions as shown in Fig. 5.

Versatile Propagation Channel Model
Compared to the open field scenario [7] with two clear coherent contributions (direct and ground reflected rays), cluttered areas introduce more rays subject to diffraction and reflection which make up the coherent or geometry-dependent component of the proposed semi-deterministic model.

Preliminary Requests
In this paper we concentrated on the SISO case and, thus, analyzed one of the four available sub-channels.The others were used for consistency tests in the recorded signal.
Slight modifications to the model parameter extraction procedure used for open areas in [7] were introduced with the received power, P (dBm), acquired at a sampling rate of 10 kSps.The signal was then decimated by a factor of 32 (window 1, W 1 ).The sampling rate was, thus, reduced to 312.5 Sps and yielded a new series, P' (dBm).The line-of-sight (LOS) power, P LOS (dBm), was calculated using the link budget equation and subtracted from all four channels yielding the excess gain, G (dB), given by G(dB) = P' -P LOS .Note that G(dB) = 10 log10|h| 2 .
The method of moments, MoM, [12] was applied to all four channel series.This technique assumes local Rice distributed variations and produces the following parameters: direct signal amplitude, A, and local average multipath power, .A 16-sample window (window 2, W 2 ) was used to extract the coherent component amplitudes A (dB) and the incoherent component average powers  (dB).The same window, W 2, was used for low-pass filtering of the A and  series by computing the running mean.A new series, A' (dB), resulted from subtracting the obtained long-term mean of A, LTM(A), i.e., A'(dB) = A  LTM(A).Similarly, the series '(dB) was obtained from (dB), '(dB) =  -LTM() + <LTM()>, where <LTM()> is the mean value of LTM().
A general model is used to model first-and secondorder characteristics of the propagation channel model for different scenarios.This model is composed of a deterministic part, whose structure changes with the scenarios, and a statistical part, whose structure remains the same with only the parameters being modified.Figure 6 shows the channel model's schematic diagram with greater detail of the model given in [7].The channel model consists of

Geometry-dependent Coherent Component and Simple Ray-tracing Calculation
As there is a deterministic component in the received signal that cannot be reproduced by means of statistical techniques, it was necessary to perform simple ray-tracing to evaluate this coherent component, thus, limiting our analysis to a small number of Rx locations and elevation angles.Figure 7 shows an aerial photograph of Fleming Square, in Prague, with two yellow points indicating the measurement locations.The perimeter of the local environment (an open square in a built-up area) which is most likely to affect the propagation conditions is also shown.Blue and green lines show the paths from the corner points representing the flight path (Fig. 5) to the two Rx locations.The red line demonstrates how the crescent-shaped group of buildings on the right side of the photo of the perimeter cannot contribute side reflections significant enough to affect the received signal.
In this case, the 3D propagation conditions can be simplified to the vertical-plane 2D representation depicted in Fig. 8.As discussed in [8], the closest-to-Rx building's edge influences the received signal the most, hence, buildings beyond this point are neglected.The elements considered in the ray-tracing include a 15-m-high building edge located 100 m from Rx which was placed on a 1.5-m-high tripod sitting on a 1-m-high hill.Behind Rx there is a modern building with a glass surface which is 21 m in height and 55 m away from Rx.We calculated the power as the complex sum of four rays.The variations in each ray, as Tx moves, give rise to signal variations related to the computed value.Such variations were modeled statistically.
Figure 8 shows the magnitudes of the various rays, which were computed as follows: the first ray is a direct path undergoing diffraction; the second is a diffracted ground-reflected ray with a reflection coefficient of ρ 1 = 0.8; the third is a diffracted-reflected ray with the reflection point located on the tinted-glass building behind Rx with a reflection coefficient of ρ 2 = 1; the fourth reaches Rx via a reflection on the glass building (ρ 2 ) and then the ground (ρ 1 ).Due to an extremely low elevation angle, and its relative insignificance, the figure is not drawn in scale.The diffraction loss can be calculated using a simple knife-edge model [13] where the diffraction parameter is given by where h is the difference between edge height and the intersection point of the LOS path with the knife-edge plane,  is wavelength, and d 1 and d 2 are the distances of Tx and Rx from the knife edge.The diffraction loss is F i and is given by where C and S are Fresnel integrals.The total received power, relative to LOS, is given by the complex sum of the four rays, namely which is L = 20·log10(|g|), a diffraction loss in logarithmic units meaning this vector represents LTM (A), the coherent component series.

Stochastic Element of the Coherent Component
The stochastic component of the deterministic part discussed above, LTM(A), is modeled using a normal distribution in dB (log-normal in linear units).The autocorrelation function is approximated by a Gaussian function, where is the correlation length, and v is the airship's velocity.LPF2 (Fig. 5) is an FIR filter with an impulse response such that More details can be found in [7].The zero mean filtered output is multiplied by the standard deviation Σ A (dB), then added to the vector containing the geometry-dependent component and, finally, the result is converted to linear (voltage/field) units, i.e., 20 / ' 10 A a  .

Diffuse Component
The principle for diffuse component generation did not change.The multipath power, ', series generator is also based on filtering normally distributed random time series generated in a similar way as the coherent component.The impulse response of the FIR filter follows the same expression as (5), a detailed extraction of which is described in [4].The output series is multiplied by the standard deviation, Σ Γ (dB), and the mean value, M Γ (dB), is added.Series ', in logarithmic units, is converted to the linear units using

Model Parameters
Model parameters were obtained for two Rx locations at Fleming Square and are summarized in Tab. 1.They are  notably similar as they are almost entirely independent of the elevation angle.The only parameter where the dependency on elevation angle is noticeable is the mean value of Γ (M Γ ) which increases with elevation.

Data Analysis and Discussion
A long pathway with a mean elevation angle of 3.17° is presented.Other series were fit similarly.The measured signal's LTM(A) vector was used in the synthesis to compare the results.The synthetized and measured signals are depicted in Fig. 10.In the deep nulls, the measured signal (blue curve) was clipped by the receiver's dynamic range, while the synthetized signal (red curve) was not clipped.
Figure 11 shows the histograms of the various model parameters extracted using the MoM technique [12].As explained earlier, the signal is divided into a coherent part A and a diffuse part represented by Γ. Parameters A' and Γ', derived from the previous ones, can be approximated by Gaussian distributions.
Vectors LTM(Γ) and LTM(A) were found to be uncorrelated.The behavior of LTM(A) can be described as the combination of four rays which can be identified and quantified using simple ray-tracing.LTM(Γ) was, as in [7], kept constant.

Conclusion
In this paper a semi-deterministic channel model was developed for a built-up area and the obtained parameter set corresponding to the statistical part was computed.The geometry-dependent component was obtained using a simple 2D ray-tracing method.Four main rays were identified.
Values below 121 dBm (121 dBm absolute value 44 dB in Level PLOS ) were clipped during the measurement.In the case of the synthetized signal, there was no need for clipping as shown in Fig. 10.
The model is described with full parametrization for elevations angle from 1 to 3 deg.which supports the general purpose of this model.The model is valid for 1 st -and 2 nd -order characteristics such as CDF and AFD.
The model generality can be seen when the parameter ranges were only adapted in the stochastic part and the principle and schematic were not changed, even though the deterministic part was totally adapted to an urban scenario.This model enables us to synthetize the time series of one representation, so that when many representations are applied, similar statistics to the real measured channel are obtained.

Fig. 1 .
Fig. 1.Classification of studied environments as a function of obstacle size and height.

Figure 5 Fig. 5 .
Figure 5 depicts the airship trajectory with a maximum terrain height difference (without considering buildings) of 38 m.The airship flew along the perimeter of a square with two parallel and two perpendicular flight paths with respect to Rx.The square sides were 200-mlong and the ground distance between Rx and Tx was approximately 2.7 km.The airship speed was 5-8 m/s, so the small Doppler shift was covered by the receiver bandwidth,

Fig. 6 .
Fig. 6.SISO propagation channel model for an urban environment.a coherent component divided into a geometry-dependent (deterministic) part and a slowly varying stochastic term, in addition to an incoherent component (diffuse multipath) representing the diffuse multipath contribution.
the output of the two Gaussian random generators in quadrature to set the appropriate multipath power level.The two Gaussian generator outputs are first filtered to include the Doppler spreading effect.This low-pass Butterworth filter is obtained by a trial-and-error method, with the following specifications: f PASS = 1 Hz; R PASS = 0.5 dB; f STOP = 120 Hz; and R STOP = 40 dB which, together, shape the signal spectrum in the desired way as in the measurements.The output is added to coherent part a to produce the channel's complex envelope time series.

Fig. 12 .
Fig. 12. Measured and synthetized signal a) CDF b) AFD.Finally, Fig. 12 a) shows the cumulative distribution function (CDF) for the measured and synthetized signals.The differences at the tails of the distributions are due to the clipping of the deep nulls in the measurements.Fig. 12 b) shows the average fade duration (AFD) for measured and synthetized signal as having fair agreement.
Model parameter ranges for different elevation angles.