Time variability of the scattering signals from wind turbines may lead to degradation problems on the communication systems provided in the UHF band, especially under near field condition. In order to analyze the variability due to the rotation of the blades, this paper characterizes empirical Doppler spectra obtained from real samples of signals scattered by wind turbines with rotating blades under near field condition. A new Doppler spectrum model is proposed to fit the spectral characteristics of these signals, providing notable goodness of fit. Finally, the effect of this kind of time variability on the degradation of OFDM signals is studied.
Signal variability caused by blade rotation is a critical issue when we are dealing with potential degradations on communications services due to wind farms. For example, in the case of the UHF band, the potential increment on the minimum requirements for quasierrorfree reception of the DVBT service is directly related to the channel time variability [
However, the classical scattering models used for the UHF band are based on worst case assumptions with respect to blade position and do not characterize time variability due to blade rotation [
The study presented in this paper is based on real scattering data obtained from a measurement campaign in the surroundings of a wind farm. Based on these data, the Doppler spectra are estimated. Then a general methodology to characterize these empirical Doppler power spectral densities (PSDs) is proposed, and finally an indepth analysis of the effect of this type of variability on OFDM signals is carried out.
This paper is organized as follows. Section
The following analysis is based on UHF signals scattered by a wind farm which were recorded and postprocessed in order to detect the contributions of each individual wind turbine. Detailed descriptions of the field trials carried out to collect these signals and the methodology to obtain the scattering signals of each wind turbine from the recorded data can be found in previous references from the authors [
More precisely, the source data set is composed of 328 complex scattered signals lasting 10seconds each, and corresponding to four different wind turbines that scattered signals from two nearby located television transmitters. Sampling period is given by the DVBT symbol duration time,
By way of illustration, Figure
Example of the periodic time variability of the scattering signals as blades rotate.
The distances between the transmitter sites and these four wind turbines are in a range from 250 to 950 meters. In the context of signal scattering and for practical measurement situations, near field effects occur when the target is not illuminated by a plane wave, and thus, the phase of the incident wave at the center of the target is different from the phase at its extremes. A widely accepted requirement is to limit the phase deviation to be less than 22.5°, obtaining the condition of far field distance for signal scattering
Taking into account the wind turbine dimensions (a mast of 55 m height and rotor of 52 m diameter), the scattering signals clearly correspond to near field condition. Although the spectral characteristics of the scattered signals will differ from those of the signals scattered under near field condition [
Theoretically, it is enough to apply a discrete Fourier transform to the complex scattered signals along the observation time and take the squared absolute value of the result to obtain the spectral power distribution for the different Doppler frequencies. Nevertheless, as finite time signals are used, the effect is equivalent to multiplying the input signal
Since the spectral characteristic of the windowing function
In order to lessen these effects on the input signal characteristics, there are multiple power spectral estimation methods, normally classified as
Five
The periodogram is defined as [
The
The
In order to reduce the variance of the estimator, the
Finally, Welch’s method proposed two modifications to the Bartlett’s method to reduce the variance without affecting the spectral resolution in the same proportion. First, the temporal segments are overlapped, and second, different windowing functions are applied to the data segments prior to computing the periodogram. The combined use of short data records and nonrectangular windows results in reduced resolution of the estimator, so that a tradeoff between variance reduction and resolution should be taken into account.
The periodic nature of the signals scattered by the wind turbines due to blade rotation makes Welch’s method especially suitable for the Doppler PSD estimation. In fact, the length
Although some references can be found in the literature about the spectral characteristics of the signals scattered by wind turbines [
Prior to the characterization of the obtained Doppler PSDs, the existing Doppler spectrum models should be studied in order to determine their empirical or theoretical basis and their application conditions.
The classical Jakes model is commonly used to characterize propagation for a mobile receiver. It is based on the following assumptions [
Radio waves propagate horizontally, in a twodimensional plane, and the receiver is located in the centre of an isotropic scattering area.
The angles of arrival of the waves arriving the receiving antenna are uniformly distributed in the interval
The radiation pattern of the receiving antenna is omnidirectional.
From these assumptions, the Jakes power spectral density is obtained:
In a threedimensional scenario with isotropic scattering, being the angles of arrival of the waves uniformly distributed for both the horizontal and the vertical plane, the resulting Doppler spectrum is flat, and its PSD is given by (
The Gaussian Doppler spectrum is used to model the multipath components with long delays in UHF communications, in the HF channel and aeronautical communications in the VHF band [
The Rounded Doppler spectrum is proposed in [
As previously observed, the basic parameter to characterize Doppler spectra is the maximum Doppler frequency
For a general bistatic case, the maximum observable frequency depends not only on the blades characteristics and the maximum rotation rate but also on the relative location transmitterwind turbinereceiver and the orientation of the rotor, according to [
Geometry for bistatic Doppler in the horizontal plane.
Therefore, for a certain reception location and considering all the possible rotor orientations, the maximum bistatic Doppler frequency is given by
Bearing this in mind, two examples of estimated Doppler PSDs are shown in Figure
Examples of estimated PSDs corresponding to time variability of the scattering signals as blades rotate.
The spectral characteristics of the estimated PSDs are similar to those of fixed wireless communications where transmitter and receiver are static and the environment is responsible for the time variability of the channel [
These spectral characteristics do not match with the Doppler models presented in the previous section. Therefore, a new model is proposed, which is based on a PSD characterized by a Dirac delta for
For a correct characterization, the estimated Doppler PSDs should be frequency limited to avoid the noise floor being confused with the Doppler spectrum of the received signal. As previously commented, the maximum Doppler shift for a certain reception location depends on the orientation of the rotor against the wind and the rotational speed at that very moment, which is constantly varying and quite difficult to accurately calculate for each specific measurement.
Therefore, after analyzing the exponential decrease of the estimated PSDs and their relation to the noise threshold, the frequency limits of each PSD are calculated according to (
That is to say, using a nonlinear least squares method, the expression in (
The goodness of fit of this Doppler model is evaluated by means of the coefficient of determination
Frequency limits for Example 1.
Frequency limits for Example 2.
Finally, it should be mentioned that for the estimated PSDs featuring wider spectral characteristics, the proposed method can make the calculated frequency limits
Once the frequency limits are established and the noise influence is avoided, a second characterization of the Doppler spectra limited by
The objective of evaluating the influence of the obtained Doppler spectra on OFDM signals is twofold. First, an analysis of the most influential characteristics of the theoretical PSDs on this potential quality degradation is carried out. Second, it is checked whether the estimated spectra and their corresponding fitting expressions behave in a similar manner in terms of quality degradation.
The BER versus SNR curves are obtained using an OFDM software implementation that includes the simulation of configurable Tapped DelayLine (TDL) channel models [
The selected OFDM configuration is close to the DVBT configuration used in Spain [
A TDL channel model is composed of a series of paths, each of them with a certain time delay and mean amplitude, and a Doppler spectrum to account for the channel time variability [
Regarding the Doppler spectra, it is necessary to select, from the 328 obtained samples and their corresponding exponential fittings, a significant number of examples for the simulation. To do so, after an analysis of the typologies of the estimated PSDs, the spectral width and the asymmetry in the power spectral distribution around 0 Hz are considered to be the main characteristics to be studied. Therefore, the following parameters are defined:
Based on these parameters, 24 representative spectrum examples featuring different spectral widths and degrees of symmetry are selected in order to observe their influence on a potential degradation of the OFDM services, and different values of
In order to evaluate the behavior of the different spectra, the SNR values for a BER equal to
The results are classified according to the different factors that are going to be analyzed: the effect of the spectral width and the asymmetry of the Doppler PSD, and the goodness of fit of the proposed exponential fitting.
Figure
BER versus SNR curves for the static case and the empirical Doppler spectra of Examples C and D.
Taken the static channel as a reference, Figure
Difference in SNR values for BER equal to
However, the power spectral density for the highest and lowest frequencies should be also taken into account, as it represents the nonzero Doppler frequency contribution with respect to the zero component power density. To do so, the mean value of the fitting parameters
For instance, Example A (see Table
Parameters of the representative Doppler spectra.
Example 


mean 




A  651.11  0.04  38.06  10.02  0.89  1.57 
B  821.82  0.00  49.16  7.46  0.70  6.39 
C  468.29  0.09  29.96  5.18  0.93  0.22 
D  241.12  0.31  40.32  0.53  0.86  0.13 
E  256.45  0.10  40.66  0.55  0.82  0.16 
F  473.87  0.03  44.60  1.13  0.90  0.06 
G  247.96  0.06  40.47  0.61  0.88  0.02 
This effect is also noticeable when Examples C and F are examined. These two Doppler PSDs have almost equal spectral widths (
For a graphical representation of this issue, data from Figure
Relations between the spectral width, the PSD for the end frequencies, and the SNR difference with respect to the static case.

mean 



any  >1 dB 

≤35  >1 dB 
>35  <1 dB  

any  <1 dB 
Difference in SNR values for BER equal to
Example A: estimated PSD and corresponding exponential fitting (
It can be observed that all the Doppler spectra with spectral widths greater than
Therefore, it can be concluded that the spectral width is a key parameter in order to determine potential degradations on OFDM systems, together with the value of the power spectral density for the highest and lowest frequencies.
The Doppler spectra with the highest grade of asymmetry (highest values of the parameter
Until now, only the results corresponding to the BER versus SNR curves due to the estimated Doppler spectra have been analyzed. However, it is also important to validate the goodness of the proposed exponential fitting, and check the differences in the BER versus SNR curves corresponding to the estimated Doppler spectra and their exponential fittings. To do so, the BER value equal to
From the selected examples, the results of the BER versus SNR curves show that the curves of the exponential fittings with coefficient of determination
More precisely, the difference between the empirical and the fitted curves depends on the additional degradation with respect to the static case due to the empirical Doppler PSD. That is to say, for all the Doppler PSDs whose empirical curves are practically coincident with the static curve, their exponential fitting curves are also coincident even if
It should be noted that the aim of the 24 Doppler spectra used for simulation was to look for critical cases that allowed a thorough study of the potential degradation due to the Doppler PSDs and its connection with the previously commented parameters.
However, these cases of potential degradation are few within the whole available data set. Applying the conclusions from the previous subsections, an estimation of the percentage of cases from the case under study which will be more affecting to OFDM signals can be obtained.
To do so, the Doppler effect is considered to be noticeable when the SNR with respect to static case is
Percentage of the total number of psds according to their degree of degradation due to Doppler effect and goodness of the exponential fit.
Degradation due to Doppler effect ( 
To be considered  9% 
Negligible  91%  
 
Goodness of fit  Acceptable  95% 
Unacceptable  5% 
Fitting parameters of the representative Doppler spectra.
Example 









A  19.72  1.22 · 10^{−2}  38.05  21.42  1.29 · 10^{−2}  38.08  −337.25  313.87 
B  25.50  4.73 · 10^{−2}  51.17  19.40  6.87 · 10^{−2}  47.15  −410.91  410.91 
C  21.98  1.65 · 10^{−2}  30.39  25.09  2.33 · 10^{−2}  29.53  −256.20  212.09 
D  21.72  2.29 · 10^{−2}  42.64  31.74  1.16 · 10^{−2}  37.99  −158.37  82.76 
E  21.36  2.94 · 10^{−2}  41.87  24.45  6.81 · 10^{−2}  39.45  −141.61  114.85 
F  27.01  1.82 · 10^{−2}  44.62  25.49  1.71 · 10^{−2}  44.58  −230.52  243.35 
G  21.21  3.30 · 10^{−2}  40.20  24.65  2.85 · 10^{−2}  40.74  −116.82  131.14 
According to the obtained results, the kind of time variability encountered for a majority of cases will not cause further degradation on OFDM systems with respect to the same propagation channel in static conditions. However, these potentially degrading situations will affect the reception thresholds of digital communication systems and should be taken into account for planning purposes. Apart from that, the proposed exponential model fits the empirical data for a vast majority of cases.
This paper presents the Doppler characterization of the signals scattered by the wind turbines in the UHF band for near field condition in the context of signal scattering. The study is based on empirical data obtained in the surroundings of a real wind farm in Spain. To do so, the Welch’s method with the adaptation of its parameters to the particular conditions of each signal has proved to be suitable for obtaining the Doppler PSDs.
Then, after an evaluation of the existing Doppler spectrum models, it is concluded that none of them applies to the special mobility features of the propagation channel in presence of a wind farm. Therefore, a new exponential model has been proposed. This model is composed of a Dirac delta for the zero Doppler frequency, which corresponds to the static supporting mast of the wind turbine and results in the component of maximum amplitude and side components of decreasing power spectral density for the lowest and highest frequencies, which correspond to the movement of the blades.
This exponential model allows, on a first approach, to limit the Doppler spectra in frequency and filter the noise floor. Then, on a second iteration, this exponential model allows the characterization of the Doppler spectra after the frequency limiting.
In order to analyze the most influential characteristics of the Doppler spectra on OFDM signal degradation, BER versus SNR curves of some representative examples have been carried out. The main conclusion is that one of the most critical parameters is the spectral width, along with the power spectral density values for the end frequencies. The goodness of fit of the proposed exponential fitting has also been proved, because both the empirical spectra and the exponential approximations provide similar BER versus SNR curves for a vast majority of cases.
Finally, it should be noted that the time variability of the scattered signals does not seem to cause further degradation on OFDM signals for a high percentage of cases. Although the probability of time variability causing reception problems is low due to the robustness of digital systems, it should be taken into account in order to estimate the corresponding reception thresholds. To do so, the representative examples of Doppler spectra given by the fitting parameters included in Table
See Table
Example B: estimated PSD and corresponding exponential fitting (
Example C: estimated PSD and corresponding exponential fitting (
Example D: estimated PSD and corresponding exponential fitting (
Example E: estimated PSD and corresponding exponential fitting (
Example F: estimated PSD and corresponding exponential fitting (
Example G: estimated PSD and corresponding exponential fitting (
The authors would like to thank the partners from Iberdrola Renovables for their continuous support and involvement in the study of the wind turbine effects on the radiocommunication services. Special thanks also to Itelazpi and Abertis Telecom for their kind collaboration in this work. This work has been supported in part by the European Union FP7 (Grant Agreement no. 296164), by the Spanish Ministry of Economy and Competitiveness (projects TEC201232370 and TEC200914201), and by the Basque Government (GIC 07/110IT37407, SAIOTEK program and program for the training of the researcher staff BFI08.230).