# Dynamic Model of Signal Fading due to Swaying Vegetation

- Michael Cheffena
^{1}Email author and - Torbjörn Ekman
^{2}

**2009**:306876

https://doi.org/10.1155/2009/306876

© M. Cheffena and T. Ekman. 2009

**Received: **31 July 2008

**Accepted: **18 February 2009

**Published: **25 March 2009

## Abstract

In this contribution, we use fading measurements at 2.45, 5.25, 29, and 60 GHz, and wind speed data, to study the dynamic effects of vegetation on propagating radiowaves. A new simulation model for generating signal fading due to a swaying tree has been developed by utilizing a multiple mass-spring system to represent a tree and a turbulent wind model. The model is validated in terms of the cumulative distribution function (CDF), autocorrelation function (ACF), level crossing rate (LCR), and average fade duration (AFD) using measurements. The agreements found between the measured and simulated first- and second-order statistics of the received signals through vegetation are satisfactory. In addition, Ricean *K*-factors for different wind speeds are estimated from measurements. Generally, the new model has similar dynamical and statistical characteristics as those observed in measurements and can thus be used for synthesizing signal fading due to a swaying tree. The synthesized fading can be used for simulating different capacity enhancing techniques such as adaptive coding and modulation and other fade mitigation techniques.

## Keywords

## 1. Introduction

In a given environment, radiowaves are subjected to different propagation degradations. Among them, vegetation movement due to wind can both attenuate and cause a fading effect to the propagating signal. Operators cannot guarantee a clear line-of-sight (LOS) to wireless customers as vegetation in the surrounding area may grow or expand over the years and obstruct the path. Fade mitigation techniques (FMTs) such as adaptive coding and modulation can be used to counteract the signal fading caused by swaying vegetation. For example, during windy conditions (high signal fading), power efficient modulation schemes such as BPSK and QPSK (which are less sensitive to propagation impairments compared to high-order modulation schemes) can be used to increase the link availability, while spectral efficient modulation schemes such as 16 QAM and 64 QAM can be applied during calm wind conditions (less signal fading) [1]. An extra coding information can also be added to the channel so that errors can be detected and corrected by the receiver. FMTs need to track the channel variations and adjust their parameters (modulation order, coding rate, etc.) to the current channel conditions. In order to design, optimize, and test FMT, data collected from propagation measurements are needed. However, such data may not be available at the preferred frequency, wind speed conditions, and so forth. Alternatively, time series generated from simulation models can be used. In this case, the simulated time series need to have similar dynamical and statistical characteristics as those obtained from measurements [1].

The signal attenuation depends on a range of factors such as tree type, whether trees are in leaf or without leaf, whether trees are dry or wet, frequency, and path length through foliage [2, 3]. For frequencies above 20 GHz, leaves and needles have large dimensions compared to the wavelength, and can significantly affect the propagation conditions. The ITU-R P.833 [4] provides a model for predicting the mean signal attenuation though vegetation. The temporal variations of the relative phase of multipath components due to movement of the tree result in fading of the received signal as reported in, for example, [5–10]. The severity of the fading depends on the rate of phase changes which further depends on the movement of the tree components. Therefore, for accurate prediction of the channel characteristics, the motion of trees under the influence of wind should be taken into account. This requires the knowledge of wind dynamics and the complex response of a tree to induced wind force. In our previous work, a heuristic approach was used to model the dynamic effects of vegetation [10]. In this paper, we develop a theoretical model based on the motion of trees under the influence of wind, and is validated in terms of first- and second-order statistics using available measurements.

The paper begins in Section 2 by giving a brief description of the measurement setup for measuring signal fading after propagating through vegetation and for measuring meteorological data (wind speed and precipitation). Section 3 discusses the wind speed dynamics. The motion of trees and their dynamic effects on propagating radiowaves as well as the validation of the proposed simulation model are dealt with in Section 4. Finally, conclusions are presented in Section 5.

## 2. Measurement Setup

To characterize the influence of vegetation on radiowaves, measurements were performed in [7] for a broad range of frequencies, including 2.45, 5.25, 29, and 60 GHz, in various foliage and weather conditions. A sampling rate of 500 Hz was used to collect the radio frequency (RF) signals using a spectrum analyzer, multimeter, and a computer with General Purpose Interface Bus (GPIB) interface. In order to understand the behavior of radiowaves propagating through vegetation under different weather conditions, meteorological measurements including wind speed and precipitation were also performed in [7]. The wind speed was recorded every 5 seconds, and the precipitation data every 10 seconds.

Site description [7].

Site | Path length | Foliage depth | Description |
---|---|---|---|

Site 1 | 63.9 m | 14.3 m | 3 foliated maple trees |

7.6 m | 1 foliated flowering crab tree | ||

Site 2 | 110 m | 25 m | Several spruce and one pine tree creating a wall |

## 3. Wind Dynamics

values for different terrain types at 10 meter height [14].

## 4. The Dynamic Effects of Vegetation on Radiowaves

### 4.1. The Motion of Trees

where
is the state vector,
is the input vector, and
is the output vector. The matrices
,
, **C**, and
are obtained from (7); see Appendix B. Note that (9) and (10) are for continuous time and can be converted to discrete time using, for example, bilinear transformation.

### 4.2. Signal Fading due to Swaying Tree

where , , and are as defined in (6), and is obtained from the state-space model in (9) and (10).

The effect of wind speed on the channel statistics can be observed from Figures 11–14 which show comparisons of measured (leaved dry deciduous trees (Site 1) at 29 GHz) and simulated channel statistics during low- and high-wind speed conditions. We can observe from Figure 11 that the probability the received signal is less than a given threshold increases with increasing wind speed. Note also from Figure 12 how fast the ACF decays during high wind speed compared to low wind speed conditions. The increase rate of signal changing activity during windy conditions can be implied from the LCR curves in Figure 13. In addition, the effect of high wind speed which results in deep signal fading with short durations can be observed from the AFD curves shown in Figure 14. The frequency dependency of the channel is evident from Figure 15–18 which show comparisons between measured (leaved dry deciduous trees (Site 1) at 2.45, 5.25, and 60 GHz) and simulated channel statistics during high wind speed conditions ( m/s). The probability that the received signal is less than a given threshold increases with increasing frequency; see Figure 15. We can also observe from Figure 16 that the autocorrelation function decays more rapidly for high frequency compared to low-frequency signals. The increasing rate of signal changing activity and the increasing existence of deep signal fading with increasing frequency can be observed from the LCR and AFD curves shown in Figures 17 and 18, respectively. The frequency dependency of the channel statistics is directly related to the signal wavelength. As the frequency increases, the signal wavelength decreases which results in increasing sensitivity to path length differences caused by swaying tree components. In general, the agreements found between the measured and simulated received signals in terms of both first- and second-order statistics are satisfactory; see Figures 11–18. Moreover, the results shown in Figures 11–18 suggest that the swaying of tree components with wind can highly impact the quality and availability of a given link, and should be considered when designing and evaluating systems at different frequencies.

## 5. Conclusion

In this paper, we use available measurements at 2.45, 5.25, 29, and 60 GHz, and wind speed data to study the dynamic effects of vegetation on propagating radiowaves. A new simulation model for generating signal fading due to a swaying tree has been developed by utilizing a multiple mass-spring system to represent a tree and a turbulent wind model. The model is validated in terms of first- and second-order statistics such as CDF, ACF, LCR, and AFD using measurements. The agreements found between the measured and simulated first- and second-order statistics of the received signals through vegetation are satisfactory. Furthermore, Ricean -factors for different wind speeds are estimated from measurements. In general, the new model has similar dynamical and statistical characteristics as those observed from measurement results and can be used for simulating different capacity enhancing techniques such as adaptive coding and modulation and other fade mitigation techniques.

## Declarations

### Acknowledgments

This work is supported by the research council of Norway (NFR). The authors would like to thank the Communications Research Centre Canada (CRC), especially Simon Perras for providing measurement data. The authors would like also to thank Morten Topland of UNIK for fruitful discussions.

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.