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Abstract
In this paper， we discuss several large?scale fading models for different environments. The COST231?Hata model is adapted for air?to?ground modeling. We propose two criteria for air?to?ground channel modelling based on test data derived from field testing in Beijing. We develop a new propagation model that is more suitable for air?to?ground communication that previous models. We focus on improving this propagation model using the field test data.
Keywords
air?to?ground communication； large?scale fading model
R1 Introduction
esearch on large?scale fading models has a history of about 40 years [1]-[4]. In the 1960s， P. L. Rice and A. G. Longley et al. proposed the Rice?Longley model， also called the Irregular Terrain Model （ITM）， for forecasting the median transmission fading caused by irregular terrain in free space. With this model， transmission loss could be computed with respect to parameters such as frequency， antenna height， and transmission distance. However， only the effect of irregular terrain was taken into account.
The Durkin?Edwards model promoted the development of large?scale modeling. With this model， loss during transmission could be calculated and loss of barrier due to irregularities could also be predicted. The model could accurately predict the field strength of the signal but not the effect of obstacles， such as buildings and trees， on the signal.
The Okumura model was a milestone in large?scale fading modeling. It is the classic model for large?scale fading and the foundation of research on large?scale fading. During testing， the parameters of Okumura model were continually corrected so that the model had strong applicability. However， if the spread of the signal changed faster than that predicted by the model， there would be large errors. Although the model still has some flaws， it works reasonably well. The Okumara?Hata model is now the most widely used model for large?scale fading.
There are two types of fading model for different frequency ranges： Okumura?Hata and COST231?Hata model. The former is based on the Okumura model and mainly used in macro cell systems where the cell radius is greater than 1 km. It is particularly applicable to cities. However， as urban construction becomes denser， the cell radius is no longer greater than 1 km， and a second model， ??COST231?Hata， is used.
In our research， we focus on air?to?ground communication， where the frequency is 2.36 GHz and the maximum height of an aircraft is about 3 km. To the best of our knowledge， no one has proposed air?to?ground channel modeling before. However， with the rapid development of 4G and the deregulation of low?altitude airspace， such modeling has become increasingly important. Our research in this area is based on test data. 2 LargeScale Fading Mechanism
When a signal wave encounters rugged terrain， buildings， vegetation or other obstacles along the propagation path， it casts a shadow on the electromagnetic fields [5]， [6]. If a mobile station in motion falls under the shadow of an obstacle， shadow fading occurs. Shadow fading is measured in large spatial scales and mainly depends on the propagation environment. Factors such as rolling hills， height distribution of buildings， street direction and position， height of base station antennas， and speed of the mobile station all need to be taken into account when determining the extent of shadow fading.
The relationship between shadow fading and propagation distance is：
where [Xσ]is the zero mean standard deviation for a Gaussian random variable [σ]dB with its pdf given by：
where [σ]is calculated using the linear recursive method to minimize the mean squared error of the measured value and estimated value.
2.1 Okumura Model
The Okumura model is the most widely used model for predicting city signals in Japan and has become the standard system model. In Tokyo， it is common to use different frequencies， antenna height， and distance to select a different series of tests [7]. The experience curve constructs the model and is applicable for a frequency of 150 MHz to 3 GHz， a distance of 1 km-100 km， and an antenna height of 30-1000 m.
A city is assumed to be a quasi?smooth terrain in the Okumura model， so a fixed field strength value is set. For an irregular terrain， there are several correction factors. By obtaining details of the topography and surface of the situation， a more accurate prediction can be made.
In a quasi?smooth terrain， the propagation attenuation values ?are also called the basic attenuation values. The model gives a quasi?smooth terrain as well as the family of curves of propagation attenuation values in the urban area.
Within a city， wave propagation attenuation depends on the propagation distance， frequency， base station antenna effective height， mobile antenna height and street width， antenna direction， and more. The attenuation can be expressed as：
where [LF] is the free space loss， [Amuf，d] is the relative spatial attenuation value， [Ghb，d] is the base station antenna height gain， [Ghm，f] is the terminal antenna height gain， and [GAREA] is the environmental gain.
The model is derived from test data and does not provide any analysis or interpretation. It makes the most reliable path?loss prediction and is the most accurate solution for cellular systems and terrestrial wireless systems. The deviation in path loss between the prediction and tested data is about 10-14 dB. 2.2 OkumuraHata Model
The frequency range applicable to the Okumura?Hata model is 150-1500 MHz. The formula for urban path loss is：
where [fc] is the frequency， [hte] is the height of transmitting antenna， and [hre] is the height of the receiving antenna. The antenna height correction factor is [αhre].
The Okumura?Hata model makes an accurate prediction in a macro cellular system and also in attenuation.
2.3 Cost231Hata Model
The COST231?Hata model is used on the condition that the carrier frequency is less than 2.5 GHz. This model is a modified Hata model that can be applied in urban macro cell， suburban macro cell， or microcell city situation [8].
For the urban macro cell， the path loss model is：
For suburbs， the macro cell environment path loss model is：
where [f] is the frequency of transmitting antenna， and [d] is the distance between transmitting antenna and receiving antenna. All the above models are not completely accords with the specific environment of air?to?ground communication.
3 Improved Model Based on Measured Data
On February 27， 2014， low?altitude air?to?ground testing of TD?LTE was carried out in Pinggu District， Beijing. There was one aircraft at an altitude of 300 m-600 m. The testing was carried out in a basin surrounded by mountains on three sides. The height of mountain was about 200 m-300 m. The testing environment is shown in Fig. 1.
The frequency was 2.36 GHz， there were two transmitting and receiving antennas， the maximum altitude of the aircraft was 600 m， and the speed of aircraft was about 150 km/h. Fig. 2 shows the fight path of the aircraft.
An air?ground channel model has never been built or appeared in any of the literature before. Building an air?to?ground channel model based on the test data and optimization methods is a creative job.
3.1 Improved COST231Hata Model Based on MMSE
Criterion
The reason we choose the COST231?Hata model to optimize the air?to?ground channel model is that COST231?Hata model is suitable for macro cells in rural areas， which is similar to the condition of air?to?ground communication.
In the urban macro cell environment， the general COST231?HATA urban path?loss model is [9]：
where[L] is the path loss and [a1，b1，c1，d1，e1，f1，g1] are the corresponding coefficients. Assuming that the total number of received signals is N and the path loss corresponding to the sampling point n is[L（n）]， the instantaneous frequency is[f（n）]. The minimum mean?square error （MMSE） criterion?based approach is used to optimize the formula coefficients. The objective function can be expressed as：
The partial derivatives of the objective function are expressed as：
[?F/?b1，?F/?c1，?F/?d1，?F/?e1，?F/?f1， and ?F/?g1] take the same process as[?F/?a1].
This can be expressed in simplified matrix format：
where [M] is a 7 × 7 dimensional matrix， and [miji，j=1，2，...，7] are：
To solve （10）， we obtain the optimal solution based on the MMSE criterion：
where[a1opt]，[b1opt]，[c1opt]，[d1opt]，[e1opt]，[f1opt]，[g1opt] are the optimal values of [a1opt]，[b1opt]，[c1opt]，[d1opt]，[e1opt]，[f1opt]，[g1opt]， respectively. According to the air?to?ground channel testing， parameters such as [f] and [hte]are decided； we reduce the computational complexity； and （7） can be simplified as：
The objective function （7） has only three variables [a1，b1]：
We obtain the optimal coefficient vector：
where
According to the analysis above， we obtain the result [[a1 b1 ]*opt] using the testing data [L（n），d（n），hte，f]， and （13） can be expressed with [[a1 b1 ]*opt].
4 Optimization Result
According to the analysis and calculation in the last section， we obtain the coefficients a1， b1， and c1. In testing， [f] and [hte] are decided， and we record the location information of each sampling point. The result of optimization in a Matlab simulation is shown in Fig. 3.
The formula of air?ground channel fading model corresponding to Fig. 3 is：
Using the distance between transmitting antenna and receiving antenna， we divide the large?scale fading into three different situations （Table 1）.
According to the analysis， we give the air?to?ground large?scale fading model formula and the model formula in different situations （Table 2）.
The formula for the parked situation （ Fig. 4 ） is：
The formula for the take?off/landing situation （ Fig. 5 ） is：
The formula for the cruising situation （ Fig. 6 ） is：
The free?space propagation， which is based on conventional COST231 model， can be expressed as：
Fig. 7 shows the proposed advanced COST231 model fits the real data better than the conventional COST231 model in （21）. The MMSE of advanced COST231 model is 7.1157×104 and that of the free?space fading model is 6.4546 ×105. The proposed model is more suitable than free?space fading model.
5 Conclusion
In this paper， we have described an air?to?ground wireless communication channel model for 2.36 GHz based on COST231?Hata， and actual measured data was used. We divide it into three situations： parked， take?off/landing， cruising. Based on MMSE/LS criterion， we derived formula of large?scale fading in different situations. Because the data was obtained through real tests， the simulation formula is convincing and helpful for the future research. Therefore， the proposed model describes the air?to?ground situation more accurately. References
[1] Y. R. Zheng and C. Xiao， “Improved models for the generation of multiple uncorrelated Rayleigh fading waveforms，” IEEE Communications Letters， vol. 6， no. 6， pp. 256-258， Jun. 2002. doi： 10.1109/LCOMM.2002.1010873.
[2] B. Roturier et al.， “Experimental and theoretical field strength evaluation on VHF channel for aeronautical mobiles，” AMCP Doc.AMCP/WG?D/7?WP/58， Madrid， Spain， Apr. 1997.
[3] P. Dent and G. E. Bottomley， “Jakes fading model revisited，” Electronics Letters， vol. 29， no. 3， pp.1162-1163， Jun. 1993. doi： 10.1049/el：19930777.
[4] Andrea Goldsmith， Wireless Communications. Cambridge， UK： Cambridge University Press， Aug. 2005.
[5] M. Failli， “Digital land mobile radio communications： final report （14 March 1984?13 September 1988），” Commission of the European Communities， Directorate?General Telecommunications， Information Industries and Innovation， 1989.
[6] W. C. Y. Lee， Mobile Cellular Telecommunication System， Analog & Digital. New York， USA： McGraw Hill， 1995.
[7] G. Dyer and T. G. Gilbert， “Channel sounding measurements in the VHF A/G radio communications channel，” Aeronautical Mobile Communications Panel， Oberpfaffenhofen， Germany， document AMCP/WG?D/8?WP/19， 1997.
[8] Commission of the European Communities and COST Telecommunications， “Digital mobile radio： COST 231 view on the evolution towards 3rd generations systems”， Brussels， Belgium， COST 231 Final report， 1999.
[9] E. Haas， “Aeronautical channel modelling，” IEEE Transactions on Vehicular Technology， vol. 51， no. 2， pp. 254-264， Mar. 2002. doi： 10.1109/25.994803.
Manuscript received： 2014?11?13
In this paper， we discuss several large?scale fading models for different environments. The COST231?Hata model is adapted for air?to?ground modeling. We propose two criteria for air?to?ground channel modelling based on test data derived from field testing in Beijing. We develop a new propagation model that is more suitable for air?to?ground communication that previous models. We focus on improving this propagation model using the field test data.
Keywords
air?to?ground communication； large?scale fading model
R1 Introduction
esearch on large?scale fading models has a history of about 40 years [1]-[4]. In the 1960s， P. L. Rice and A. G. Longley et al. proposed the Rice?Longley model， also called the Irregular Terrain Model （ITM）， for forecasting the median transmission fading caused by irregular terrain in free space. With this model， transmission loss could be computed with respect to parameters such as frequency， antenna height， and transmission distance. However， only the effect of irregular terrain was taken into account.
The Durkin?Edwards model promoted the development of large?scale modeling. With this model， loss during transmission could be calculated and loss of barrier due to irregularities could also be predicted. The model could accurately predict the field strength of the signal but not the effect of obstacles， such as buildings and trees， on the signal.
The Okumura model was a milestone in large?scale fading modeling. It is the classic model for large?scale fading and the foundation of research on large?scale fading. During testing， the parameters of Okumura model were continually corrected so that the model had strong applicability. However， if the spread of the signal changed faster than that predicted by the model， there would be large errors. Although the model still has some flaws， it works reasonably well. The Okumara?Hata model is now the most widely used model for large?scale fading.
There are two types of fading model for different frequency ranges： Okumura?Hata and COST231?Hata model. The former is based on the Okumura model and mainly used in macro cell systems where the cell radius is greater than 1 km. It is particularly applicable to cities. However， as urban construction becomes denser， the cell radius is no longer greater than 1 km， and a second model， ??COST231?Hata， is used.
In our research， we focus on air?to?ground communication， where the frequency is 2.36 GHz and the maximum height of an aircraft is about 3 km. To the best of our knowledge， no one has proposed air?to?ground channel modeling before. However， with the rapid development of 4G and the deregulation of low?altitude airspace， such modeling has become increasingly important. Our research in this area is based on test data. 2 LargeScale Fading Mechanism
When a signal wave encounters rugged terrain， buildings， vegetation or other obstacles along the propagation path， it casts a shadow on the electromagnetic fields [5]， [6]. If a mobile station in motion falls under the shadow of an obstacle， shadow fading occurs. Shadow fading is measured in large spatial scales and mainly depends on the propagation environment. Factors such as rolling hills， height distribution of buildings， street direction and position， height of base station antennas， and speed of the mobile station all need to be taken into account when determining the extent of shadow fading.
The relationship between shadow fading and propagation distance is：
where [Xσ]is the zero mean standard deviation for a Gaussian random variable [σ]dB with its pdf given by：
where [σ]is calculated using the linear recursive method to minimize the mean squared error of the measured value and estimated value.
2.1 Okumura Model
The Okumura model is the most widely used model for predicting city signals in Japan and has become the standard system model. In Tokyo， it is common to use different frequencies， antenna height， and distance to select a different series of tests [7]. The experience curve constructs the model and is applicable for a frequency of 150 MHz to 3 GHz， a distance of 1 km-100 km， and an antenna height of 30-1000 m.
A city is assumed to be a quasi?smooth terrain in the Okumura model， so a fixed field strength value is set. For an irregular terrain， there are several correction factors. By obtaining details of the topography and surface of the situation， a more accurate prediction can be made.
In a quasi?smooth terrain， the propagation attenuation values ?are also called the basic attenuation values. The model gives a quasi?smooth terrain as well as the family of curves of propagation attenuation values in the urban area.
Within a city， wave propagation attenuation depends on the propagation distance， frequency， base station antenna effective height， mobile antenna height and street width， antenna direction， and more. The attenuation can be expressed as：
where [LF] is the free space loss， [Amuf，d] is the relative spatial attenuation value， [Ghb，d] is the base station antenna height gain， [Ghm，f] is the terminal antenna height gain， and [GAREA] is the environmental gain.
The model is derived from test data and does not provide any analysis or interpretation. It makes the most reliable path?loss prediction and is the most accurate solution for cellular systems and terrestrial wireless systems. The deviation in path loss between the prediction and tested data is about 10-14 dB. 2.2 OkumuraHata Model
The frequency range applicable to the Okumura?Hata model is 150-1500 MHz. The formula for urban path loss is：
where [fc] is the frequency， [hte] is the height of transmitting antenna， and [hre] is the height of the receiving antenna. The antenna height correction factor is [αhre].
The Okumura?Hata model makes an accurate prediction in a macro cellular system and also in attenuation.
2.3 Cost231Hata Model
The COST231?Hata model is used on the condition that the carrier frequency is less than 2.5 GHz. This model is a modified Hata model that can be applied in urban macro cell， suburban macro cell， or microcell city situation [8].
For the urban macro cell， the path loss model is：
For suburbs， the macro cell environment path loss model is：
where [f] is the frequency of transmitting antenna， and [d] is the distance between transmitting antenna and receiving antenna. All the above models are not completely accords with the specific environment of air?to?ground communication.
3 Improved Model Based on Measured Data
On February 27， 2014， low?altitude air?to?ground testing of TD?LTE was carried out in Pinggu District， Beijing. There was one aircraft at an altitude of 300 m-600 m. The testing was carried out in a basin surrounded by mountains on three sides. The height of mountain was about 200 m-300 m. The testing environment is shown in Fig. 1.
The frequency was 2.36 GHz， there were two transmitting and receiving antennas， the maximum altitude of the aircraft was 600 m， and the speed of aircraft was about 150 km/h. Fig. 2 shows the fight path of the aircraft.
An air?ground channel model has never been built or appeared in any of the literature before. Building an air?to?ground channel model based on the test data and optimization methods is a creative job.
3.1 Improved COST231Hata Model Based on MMSE
Criterion
The reason we choose the COST231?Hata model to optimize the air?to?ground channel model is that COST231?Hata model is suitable for macro cells in rural areas， which is similar to the condition of air?to?ground communication.
In the urban macro cell environment， the general COST231?HATA urban path?loss model is [9]：
where[L] is the path loss and [a1，b1，c1，d1，e1，f1，g1] are the corresponding coefficients. Assuming that the total number of received signals is N and the path loss corresponding to the sampling point n is[L（n）]， the instantaneous frequency is[f（n）]. The minimum mean?square error （MMSE） criterion?based approach is used to optimize the formula coefficients. The objective function can be expressed as：
The partial derivatives of the objective function are expressed as：
[?F/?b1，?F/?c1，?F/?d1，?F/?e1，?F/?f1， and ?F/?g1] take the same process as[?F/?a1].
This can be expressed in simplified matrix format：
where [M] is a 7 × 7 dimensional matrix， and [miji，j=1，2，...，7] are：
To solve （10）， we obtain the optimal solution based on the MMSE criterion：
where[a1opt]，[b1opt]，[c1opt]，[d1opt]，[e1opt]，[f1opt]，[g1opt] are the optimal values of [a1opt]，[b1opt]，[c1opt]，[d1opt]，[e1opt]，[f1opt]，[g1opt]， respectively. According to the air?to?ground channel testing， parameters such as [f] and [hte]are decided； we reduce the computational complexity； and （7） can be simplified as：
The objective function （7） has only three variables [a1，b1]：
We obtain the optimal coefficient vector：
where
According to the analysis above， we obtain the result [[a1 b1 ]*opt] using the testing data [L（n），d（n），hte，f]， and （13） can be expressed with [[a1 b1 ]*opt].
4 Optimization Result
According to the analysis and calculation in the last section， we obtain the coefficients a1， b1， and c1. In testing， [f] and [hte] are decided， and we record the location information of each sampling point. The result of optimization in a Matlab simulation is shown in Fig. 3.
The formula of air?ground channel fading model corresponding to Fig. 3 is：
Using the distance between transmitting antenna and receiving antenna， we divide the large?scale fading into three different situations （Table 1）.
According to the analysis， we give the air?to?ground large?scale fading model formula and the model formula in different situations （Table 2）.
The formula for the parked situation （ Fig. 4 ） is：
The formula for the take?off/landing situation （ Fig. 5 ） is：
The formula for the cruising situation （ Fig. 6 ） is：
The free?space propagation， which is based on conventional COST231 model， can be expressed as：
Fig. 7 shows the proposed advanced COST231 model fits the real data better than the conventional COST231 model in （21）. The MMSE of advanced COST231 model is 7.1157×104 and that of the free?space fading model is 6.4546 ×105. The proposed model is more suitable than free?space fading model.
5 Conclusion
In this paper， we have described an air?to?ground wireless communication channel model for 2.36 GHz based on COST231?Hata， and actual measured data was used. We divide it into three situations： parked， take?off/landing， cruising. Based on MMSE/LS criterion， we derived formula of large?scale fading in different situations. Because the data was obtained through real tests， the simulation formula is convincing and helpful for the future research. Therefore， the proposed model describes the air?to?ground situation more accurately. References
[1] Y. R. Zheng and C. Xiao， “Improved models for the generation of multiple uncorrelated Rayleigh fading waveforms，” IEEE Communications Letters， vol. 6， no. 6， pp. 256-258， Jun. 2002. doi： 10.1109/LCOMM.2002.1010873.
[2] B. Roturier et al.， “Experimental and theoretical field strength evaluation on VHF channel for aeronautical mobiles，” AMCP Doc.AMCP/WG?D/7?WP/58， Madrid， Spain， Apr. 1997.
[3] P. Dent and G. E. Bottomley， “Jakes fading model revisited，” Electronics Letters， vol. 29， no. 3， pp.1162-1163， Jun. 1993. doi： 10.1049/el：19930777.
[4] Andrea Goldsmith， Wireless Communications. Cambridge， UK： Cambridge University Press， Aug. 2005.
[5] M. Failli， “Digital land mobile radio communications： final report （14 March 1984?13 September 1988），” Commission of the European Communities， Directorate?General Telecommunications， Information Industries and Innovation， 1989.
[6] W. C. Y. Lee， Mobile Cellular Telecommunication System， Analog & Digital. New York， USA： McGraw Hill， 1995.
[7] G. Dyer and T. G. Gilbert， “Channel sounding measurements in the VHF A/G radio communications channel，” Aeronautical Mobile Communications Panel， Oberpfaffenhofen， Germany， document AMCP/WG?D/8?WP/19， 1997.
[8] Commission of the European Communities and COST Telecommunications， “Digital mobile radio： COST 231 view on the evolution towards 3rd generations systems”， Brussels， Belgium， COST 231 Final report， 1999.
[9] E. Haas， “Aeronautical channel modelling，” IEEE Transactions on Vehicular Technology， vol. 51， no. 2， pp. 254-264， Mar. 2002. doi： 10.1109/25.994803.
Manuscript received： 2014?11?13