Channel Modeling for Air⁃to⁃GroundWireless Communication

Yingcheng Shi，Di He，Bin Li，and Jianwu Dou

（1.Shanghai Jiao Tong University，Shanghai 200240，China；2.ZTE Corporation，Shenzhen 518057，China）

Channel Modeling for Air⁃to⁃GroundWireless Communication

Yingcheng Shi1，Di He1，Bin Li2，and Jianwu Dou2

（1.Shanghai Jiao Tong University，Shanghai 200240，China；2.ZTE Corporation，Shenzhen 518057，China）

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 pre⁃vious models.We focus on improving this propagation model using the field test data.

air⁃to⁃ground communication；large⁃scale fading model

1 Introduction

R esearch on large⁃scale fading models has a history of about 40 years［1］-［4］.In the 1960s，P.L.Rice and A.G.Longleyet al.proposed the Rice⁃Long⁃ley model，also called the Irregular Terrain Model（ITM），for forecasting the median transmission fading caused by irregular terrain in free space.With this model，transmis⁃sion loss could be computed with respect to parameters such as frequency，antenna height，and transmission distance.How⁃ever，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 transmis⁃sion could be calculated and loss of barrier due to irregulari⁃ties could also be predicted.The model could accurately pre⁃dict the field strength of the signal but not the effect of obsta⁃cles，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 particu⁃larly applicable to cities.However，as urban construction be⁃comes 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 im⁃portant.Our research in this area is based on test data.

2 Large-Scale 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 mo⁃bile station in motion falls under the shadow of an obstacle，shadow fading occurs.Shadow fading is measured in large spa⁃tial scales and mainly depends on the propagation environ⁃ment.Factors such as rolling hills，height distribution of build⁃ings，street direction and position，height of base station anten⁃nas，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：

whereXσis the zero mean standard deviation for a Gaussian random variableσdB with its pdf given by：

whereσis calculated using the linear recursive method to minimize the mean squared error of the measured value and es⁃timated value.

2.1 Okumura Model

The Okumura model is the most widely used model for pre⁃dicting city signals in Japan and has become the standard sys⁃tem 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 applica⁃ble 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 Oku⁃mura model，so a fixed field strength value is set.For an irregu⁃lar terrain，there are several correction factors.By obtaining de⁃tails of the topography and surface of the situation，a more ac⁃curate prediction can be made.

In a quasi⁃smooth terrain，the propagation attenuation val⁃ues 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 direc⁃tion，and more.The attenuation can be expressed as：

whereLFis the free space loss，Amu（f， d）is the relative sp⁃atial attenuation value，G（hb，d）is the base station antenna height gain，G（hm，f）is the terminal antenna height gain，and GAREAis 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 Okumura-Hata Model

The frequency range applicable to the Okumura⁃Hata model is 150-1500 MHz.The formula for urban path loss is：

wherefcis the frequency，hteis the height of transmitting an⁃tenna，andhreis the height of the receiving antenna.The an⁃tenna height correction factor isα（hre）.

The Okumura⁃Hata model makes an accurate prediction in a macro cellular system and also in attenuation.

2.3 Cost231-Hata Model

The COST231⁃Hata model is used on the condition that the carrier frequency is less than 2.5 GHz.This model is a modi⁃fied Hata model that can be applied in urban macro cell，subur⁃ban 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：

wherefis the frequency of transmitting antenna，anddis the distance between transmitting antenna and receiving anten⁃na.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 car⁃ried 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.Fig.1 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.Fig.2 2 shows the fight path of the aircraft.

An air⁃ground channel model has never been built or ap⁃peared 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 COST231-Hata 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，g1are the corre⁃sponding coefficients.Assuming that the total number of re⁃ceived signals is N and the path loss corresponding to the sam⁃pling pointnisL（n），the instantaneous frequency is f（n）.

The minimum mean⁃square error（MMSE）criterion⁃based approach is used to optimize the formula coefficients.The ob⁃jective function can be expressed as：

The partial derivatives of the objective function are ex⁃pressed as：∂F/∂b1，∂F/∂c1，∂F/∂d1，∂F/∂e1，∂F/∂f1，and∂F/∂g1take the same process as∂F/∂a1.

This can be expressed in simplified matrix format：

where M is a7×7dimensional matrix，andare：

To solve（10），we obtain the optimal solution based on the MMSE criterion：

wherea1opt，b1opt，c1opt，d1opt，e1opt，f1opt，g1optare the optimal va⁃lues ofa1opt，b1opt，c1opt，d1opt，e1opt，f1opt，g1opt，respectively.A⁃ccording to the air⁃to⁃ground channel testing，parameters such asfandhteare decided；we reduce the computational com⁃plexity；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 resultusing the testing dataL（n），d（n），hte，f，and（13）can be expressed with.

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 hteare decided，and we record the location information of each sampling point.The result of optimization in a Matlab simula⁃tion is shown in Fig.Fig.3 3.

The formula of air⁃ground channel fading model correspond⁃ing to Fig.3 is：

Using the distance between transmitting antenna and receiv⁃ing antenna，we divide the large⁃scale fading into three differ⁃ent situations（TableTable 1 1）.

▼Table 1.Classification of situations

According to the analysis，we give the air⁃to⁃ground large⁃scale fading model formula and the model formula in different situations（TableTable 2 2）.

▼Table 2.Results of simulation

The formula for the parked situation（Fig.Fig.4 4）is：

The formula for the take⁃off/landing situation（Fig.Fig.5 5）is：

The formula for the cruising situation（Fig.Fig.6 6）is：

The free⁃space propagation，which is based on conventional COST231 model，can be expressed as：

Fig.Fig.7 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 7.1157×104and 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 for2.36 GHz based on COST231⁃Hata，and actual measured data was used.We di⁃ vide 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 ob⁃tained 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.

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Manuscript received：2014⁃11⁃13

Biographiesphies

Yingcheng Shig Shi（yingchengshi@sjtu.edu.cn）received the MS degrees from Shanghai Jiao Tong University 2015.His research interests include air⁃to⁃ground wireless communications，LTE communications，and D2D communications.

Di HeDi He（dihe@sjtu.edu.cn）received the PhD degree in circuits and systems from Shanghai Jiao Tong University in 2002.From 2002 to 2004，he was a postdoctoral fellow in the Department of Electrical and Computer Engineering，University of Cal⁃gary，Canada.From 2004 to present，he has been an associate professor at Shanghai Jiao Tong University.His research interests include wireless communications（par⁃ticularly air⁃to⁃ground wireless communications），LTE communications，cognitive ra⁃dio and long⁃term evolution，nonlinear dynamics and its applications in wireless communications，and satellite communications.

Bin Liin Li（li.bin23@zte.com.cn）received the MSc degree in electronics and computer science from University of Southampton，UK，in 2008.Since 2009，he has been a se⁃nior engineer of the System Simulation Department at ZTE Corporation.His re⁃search interests include signal processing，parameter estimation，and propagation studies of mobile radio channels.

Jianwu Douu Dou（dou.jianwu@zte.com.cn）received the PhD degree from Beijing Univer⁃sity of Technology in 2001.Since 2001，he has been in charge of research and sys⁃tem design of the radio resource management algorithm in UMTS，TD⁃SCDMA and LTEv1 at ZTE Corporation.From 2006，he has also been responsible for system sim⁃ulation of 2G，3G，4G，and WLAN as a director of the department at ZTE.His re⁃search interests include RRM，system simulation，wireless channel sounding and modelling，data mining，high⁃frequency physical⁃layer design，and MTC.

This research work is supported by the ZTE Corporation and University Joint Research Project under Grant No.CON1307100001，and the National High Technology Research and Development Program of China under Grant No.2013AA013602.