Chapter 3_ Radio Transmission Theory

Radio Transmission Theory Confidential

Chapter 3 Radio Transmission Theory

3.1 Rationale of Radio Transmission Mobile telecommunications network planning and building, from band determination, frequency assignment, coverage area, telecommunication probability calculation, and electromagnetic interference to the final confirmation of radio equipment parameters, depend on the study and strength forecast of the characteristics of radio transmission. Radio transmission theory is the foundation of system project design and subjects such as spectrum utilization and electromagnetic compatibility.

3.1.1 Radio Transmission Modes

As we know, radio waves can be transmitted from transmitter antenna to receiver antenna through different modes such as line-of-sight transmission, ground wave transmission, troposphere scattering transmission and ionosphere transmission. See Figure 3-1. For electric wave, the easiest transmission from transmitter to receiver is free space transmission. Free space is an isotropic (same attribute in each axial direction) and homogeneous (symmetrical structure) space.

I. Line-of-Sight Transmission

Line-of-sight transmission is a transmission under conditions in accordance with line-of-sight formula (3-14). It usually consists of perpendicular incidence waves and ground reflected waves, and also includes diffraction waves and scattering waves when there are obstructions and scattering objects.

II. Ground Wave Transmission

Ground wave transmission consists of space waves and land surface waves. Land surface waves transmit along the surface of the land. There are only ground waves in places far away from transmitters.

Troposphere scattering transmission is based on the asymmetric scattering of troposphere.

III. Ionosphere Transmission

In ionosphere transmission, the waves reflected from ionosphere may have one or several leaps. See Figure 3-1(e). This kind of transmission is used in shortwave remote telecommunications. Because of the asymmetric refractive

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indexes, scattering also occurs in ionosphere; besides, the meteor track left in ionosphere also leads to scattering waves.

Radio transmission in cellular system is a multipath transmission. It belongs to line-of-sight transmission.

(a) Direct wave transmitting in straight line

(b) Application of Line-of-sight communications

(c) Ground wave transmission

(d) Irregular scattering of radio waves by troposphere

(e) Radio wave reflected by ionosphere

Figure 3-1 Different transmission modes

3.1.2 Reasons for Transmission Study

There are two reasons for transmission study in cellular system design:

It provides necessary tools to calculate the strength covering different cells. The coverage area is usually from hundreds of meters to scores of kilometers and line-of-sight transmission is applicable in such conditions.

It can calculate adjacent channel and co-channel interference.

3.1.3 Signal Strength Forecast Methods

There are three ways to forecast signal strength:



The first one is pure theoretical way which is applicable for separated objects, such as mountains and other solid objects. But this way overlooks the irregularity of earth.

The second way is based on the test in various environments, including irregular terrains and man-made obstructions, especially the high frequency and low mobile station antenna.

The third way combines the above two together and makes certain improvement. It is based on measurement and the consideration of mountains and other obstructions.

3.2 Radio Transmission Environment

3.2.1 Frequency Band Allocation

The frequency range of radio waves is from 3Hz to 3000GHz, divided into 12 bands. See the following table. The frequency in different band has different transmission characteristics. Mobile telecommunications just concern UHF band.

Table 3-1 Radio frequency category

Band Frequency range Wavelength range

Extremely long wave (extremely low frequency, ELF)

3 Hz–30 Hz 105 km–104 km

Specially long wave (specially low frequency, SLF)

30 Hz–300 Hz 104 km–103 km

Ultra long wave (ultra low frequency, ULF)

300 Hz -3000 Hz 103 km–102 km

Very long wave (very low frequency, VLF)

3 kHz -30 kHz 102 km–10 km

Long wave(low frequency, LF) 30 kHz -300 kHz 10 km–1 km

Medium wave(medium frequency, MF)

300 kHz -3000 kHz 103 km–102 m

Shortwave(high frequency, HF) 3 MHz -30 MHz 102 km–10 m

Very short wave(very high frequency, VHF)

30 MHz-300 MHz 10 km–1 m

microwave

Decimeter wave (ultrahigh frequency,

300 MHz-3000 MHz

102 km–10 cm



Band Frequency range Wavelength range

UHF)

Centimeter wave (specially high frequency, SHF)

3 GHz-30 GHz 10 km–1 cm

Millimeter wave (extremely high frequency, EHF)

30 GHz-300 GHz 10 km–1 mm

Submillimeter(ultrahigh high frequency)

300 GHz-3000 GHz 1 km -0.1 mm

Note: The table above is excepted from “Electromagnetic Wave, Antenna and Electric Wave Propagation” written by Pan Zhongying.

3.2.2 Fast Fading and Slow Fading

As described above, in a typical cellular mobile telecommunications environment, the line of sight path is always obstructed by buildings and other objects; therefore, the communications between cellular base station and mobile station is usually carried out through many other paths. In UHF band, the main transmission mode of electromagnetic waves from transmitter to receiver is reflection of buildings or diffraction of natural objects. See Figure 3-2.



① Building reflected wave ② Diffraction wave ③ Line of sight wave ④ Ground

reflected wave

Figure 3-2 Multipath transmission models

I. Fast Fading

2) What is Fast Fading

All signal components combine together and produce an interference wave. Its strength changes according to each component. The synthesized strength reduces by 20–30dB across several bodyworks. The distance between the places where the maximum strength occurs and the minimum strength occurs is about one fourth wavelength.

A large number of transmission paths results in the so called multipath phenomenon. The amplitude and phase of the synthesized wave changes a lot as the mobile station moves, which is usually called multipath fading or fast fading. See Figure 3-1. Multipath fading occurs very fast, which leads to time dispersion. Deep fading points appear in every other half wavelength spatially (17 cm for 900 MHz, 8 cm for 1900 MHz). If the antenna of mobile station happens to be at deep fading point (when a mobile station subscriber in a car



stops at this point because of the red light), certain skills such as frequency hopping can solve the problem of rather low voice quality.

Research shows that if a mobile unit receives wave components with random amplitudes and phases, the probability distribution functions of phase θ and amplitude r of the synthesized signal are as follows:

p 12 0≤≤2 (3-1)

pr r 2 e r2

2 2 r≥0 (3-2)

In the formulae above, σ2 is standard deviation. Phase distributes uniformly

from 0 to 2 and the probability distribution function of amplitude follows

Rayleigh distribution; therefore, multipath fading is also called Rayleigh Fading.

3) How to Deal With Fast Fading

The primary measures to deal with fast fading include time diversity, frequency diversity and space diversity (or polarization diversity):

Time diversity mainly depends on symbol interleaving, error detecting code and error correcting code. Different code has different anti-fading properties. It is also the leading subject in today’s mobile telecommunications study. GSM air channel coding scheme, see the related section in chapter 2.

Frequency diversity theory is based on bandwidth, which means when the difference between two frequencies exceeds certain value, they are regarded as two independent band classes. Sufficient data shows 200 kHz or above difference between two frequencies demonstrates this independency. Frequency diversity mainly takes spread spectrum measures. GSM simply takes frequency hopping to obtain frequency hopping gain, while CDMA itself is a kind of spread spectrum communications with each channel in a relatively broad band class (narrowband CDMA is 1.25 MHz).

Space diversity uses main diversity antenna receiving to solve the problem of fast fading. The base station receiver diversifies and consolidates the signals received through main and diversity channels with maximum likelihood sequence estimation equalizer (MLSE). This main and diversity receiving quality is ensured by the independency of main and diversity receiving antennas. The so called independency means the signals received by main antenna and diversity antenna fade at different time. In space diversity, the distance between main antenna and diversity antenna exceeds ten times of the wavelength of the radio signal. Polarization diversity can also ensure the independency of the main and diversity



antennas. For mobile station, because it has only one antenna, it has no such space diversity function. The equalization of base station receiver to different delayed signals in certain time window is also a kind of space diversity. During the soft handoff in CDMA, mobile station contacts several cell stations at the same time and choose the best signal to send to the switch, which is also a kind of space diversity.

I. Slow Fading

Lots of researches show that the median of received signal strength, except the Rayleigh Fading of transient value, changes slowly with the shift of locations. This kind of phenomenon is called slow fading. See Figure 3-1. Slow fading is caused by shadow effect, so it is also called shadow fading. When the transmission is obstructed by high buildings, forests, fluctuant terrain, electromagnetic shadow occurs. If this happens to the mobile station, the median of the receiving electromagnetic field strength changes. The degree of changes depends on the obstruction and frequency; the change rate depends on both obstruction and speed of vehicles.

Study of this slow fading shows that the change of value follows logarithm logarithmic normal distribution.

The reflection coefficient of electric waves changes because of the change of weather with time and the slow change of vertical slope of air dielectric constant, which results in the slow fading of the median of signal strength with time in the same place.

Statistics shows that the median value follows logarithmic normal distribution in a large scale as time or place changes; therefore, the synthesized value also follows logarithmic normal distribution. In land mobile communications, the degree of median value affected by time is much less than that affected by place, so the influence of time in slow fading can be ignored. But in designated communications, the time factor should be considered in slow fading.

Figure 3-1 Fast fading and slow fading



Generally speaking, two factors influence the cellular system:

The first one is multipath. Signals reflected or diffracted from buildings or other objects show slow fading and move scores of meters. The second one is the slow change of main received signal strength in line of sight path, that is, the long term signal strength change. Which means, signal transmission follows Rayleigh distribution of fast fading and logarithmic normal distribution of slow fading

3.2.3 Transmission Loss

The signal power level received by the receiver is a main characteristic in telecommunications. The decrease of transmission signal due to the influences of transmission path and terrain is called transmission loss.

I. Transmission Loss in Free Space

In electric wave transmission study, the primary task is to research the characteristics of two antennas in free space (Isotropic symmetrical medium with dielectric constant being one and no absorption). Take the ideal omni-directional antenna as example, the path loss in free space is as follows:

Lp 32.4 20 lglg(fMHz ) 20 lglg(d km ) (3-3)

In the formula, f is frequency, d is distance. This formula is inversely proportional to d. when d increases by one time, path loss increases by 6 dB. When wavelength λ decreases, that is, frequency f increases, the path loss increases. The loss can be compensated by radiation increase and receiver antenna gain. When the working frequency is known, the formula above can be rewritten as follows:


Distance (m)

Received power (dBm)

10 20 30

-20

-40

-60

Slow fading

Fast fading


Lp L0 10 lglg(dkm ) (3-4)

In the formula, 2; is path loss gradient. In the actual cellular system, the

range of is between 3 and 5 according to measurement.

II. Transmission Loss in Flat Terrain

With path loss formula, the study of actual transmission between two antennas in flat but not ideal surface is possible. Suppose the surface of the entire transmission path is absolutely flat. The heights of base station antenna and

mobile station antenna are hc and hm respectively. See Figure 3-2.

A

A

A

A'

B

B

B

(a)

(b)

(c)

(a) Multi reflection (b)

Single reflection (c) Imaging to find the difference between line-of-sight and land

reflection

Figure 3-2 Transmission upon flat surface

Compared with the path loss of free space, the path loss of flat ground is as follows:

Lp L0 10 lglgd 20 lglghc 20 lglghm (3-5)



In the formula, 4. It shows the increase of the antenna height by one time can compensate 6 dB’s loss. The receive power of mobile station changes with the fourth power of the distance d, which means if d increases by one time, the received power decreases by 12 dB.

III. Transmission Loss in Complex Terrain

Since terrains and clutters differ greatly, their influences on the loss of electric wave transmission are also complicated. There is no absolutely flat terrain in real life. Complex terrain is usually divided into two types: quasi-flat terrain and irregular terrain.

Quasi-flat terrain is the terrain with mildly fluctuant surface. Its fluctuation height is equal to or less than 20 meters without too much height difference. Okumura defines fluctuation range as the height difference between ten percent height curve and ninety percent height curve within ten square meters in front of mobile station antenna along the transmission direction. CCIR defines it as the height differences between more than ten percent height curve and more than ninety percent height curve within 10–50 square meters in front of the receiver. Ten percent height curve is a horizontal line; the height of ten percent segments in terrain section exceeds this line. Ninety percent height curve has the similar meaning. The rest is irregular terrain that can be divided into highland, isolated mountains, slopes and terraqueous terrain.

IV. Transmission Loss in Urban and Surrounded Areas

As for the transmission loss in urban and surrounded areas, the terrain can be divided into open area, dense city, medium sized city, and suburb according to density of the geographical area.

Diffraction is another factor of transmission loss in mountainous areas or cities with dense skyscrapers. Diffraction loss is a measurement of the height of obstructions and antennas. Compare the height of obstruction with wavelength. The same height of obstructions results in less loss to long wavelength than to short wavelength. In path loss forecast, these obstructions are called sharp obstructions, or “blade shape”. The loss can be calculated with common ways in physical optics. There are two kinds of obstructions in Figure 3-3. In the first case, no obstruction for line-of-sight path at H. in the second case, the obstruction is in transmission path. Suppose the height of obstruction is negative in the first case and positive in the second case. Diffraction loss F can be calculated with diffraction parameter. V is given in the following formula:

v H 2/ 1/d1 1/d2 (3-6)

The approximation of different diffraction loss is as follows:



F0 v 1

20 lglg0.5 0.62v 0 v 1

20 lglg0.5e0.45v 1 v 0

20 lglg0.4 0.12 0.1v 0.382 2.4 v 1

20 lglg 0.225/v v 2.4 (3-7)

(a) Negative height (b) Positive height

Figure 3-3 Radio transmission through blade

3.3 Radio Transmission ModelTransmission model is the basis of mobile transmission network cell planning. Model can guarantee the accuracy and save manpower, costs and time. It is very important to choose independent cell bases in coverage area before cellular system planning in certain area. The only way besides forecast is attempt, through actual measurement. Measure the coverage area of cellular stations and choose the best addressing scheme. This way requires lots of costs and manpower. Take high precision forecast and computing, and then compare and evaluate all the schemes from computer to choose the best one. So the precision of transmission model is of vital importance to the soundness of cell planning and the fact that whether the operator satisfies subscribers with rational investment.

Since China has a vast territory, the transmission environment varies alot in different provinces and cities. For example, cities in highland and plain differ greatly in transmission environment and their transmission models also have great differences. Ignorance of different parameters such as terrains and buildings will definitely results in problems in coverage and quality of network, or the over density of base stations, which is a waste of resources. With the rapid development of mobile network in China, operators pay more and more attention to the match of transmission model and geographical environment.

A good mobile transmission model should be adjustable according to different terrains (plain, highland, valley etc) or different man-made environment (open area, suburb, city etc). These factors concerns lots of important variables. So a good transmission model is very hard to achieve. Model optimization requires lots of statistic data and rectification. For details of model rectification, see 3.4 .



A good model should be simple and usable with clear description, leaving no room for subjective judgment and explanation that always result in different forecasts in the same area. A good model should possess high recognition and acceptability. Since different models may lead to different results, a high recognition is very important.

Most models forecast the path loss of radio wave transmission. Transmission environment plays a key role in model building. The main factors affecting the transmission environment in a certain area are as follows:

Natural terrain (mountain, highland, plain, water area etc) Number, height, distribution and materials of buildings Vegetation Climate Natural and man-made electromagnetic noise

The system working frequency and the motion condition of mobile station also affect the transmission model. In the same area, different working frequency results in different signal fading. The transmission environment of still mobile station also varies a lot from that of mobile station with high translational speed. Transmission models are usually classified as outdoor transmission model and indoor transmission model.

Table 3-1 Several common transmission models

Name Application

Okumura-Hata 150-1000 MHz macro cell forecast

Cost231-Hata 1500-2000 MHz macro cell forecast

Cost231 Walfish-Ikegami 900 MHz and 1800 MHz micro forecast

Keenan-Motley 900 MHz and 1800 MHz indoor environment forecast

ASSET(used in ASSET planning software)

900 MHz and1800MHz macro cell forecast

3.3.1 Macro Cell Model

Okumura-Hata Model and Cost231-Hata Model are built on the data measured in Japan. The median path loss in cities is shown as follows:

Lp 69.55 26.16 lglg f 13.82 lglghb

(44.9 6.55 lglghb ) lglg d AOkumurahm (Okumura-Hata) (3-8-1)



Lp 46.3 33.9 lglg f 13.82 lglg hb

(44.9 6.55 lglghb ) lglgd ACost231hm Cm (Cost231-Hata) (3-8-2)

Lp — path loss from base station to mobile station, unit: dB

f — frequency of carrier, unit: MHz

hb — height of base station, unit: m

hm — height of mobile station antenna, I m to 10 m，average value: 1.5 m, unit: m

d — distance between base station and mobile station, unit: km

Cm — modify in big cities, 0 dB in medium sized cities or suburbs with medium density of trees, 3 dB in big cities

A Okumurahm — modified height of mobile station, (1.1 lgf – 0.7) hm – (1.56 lgf – 0.8)

in medium sized cities, 3.2logloglog11.75hm2 4.97 in big cities ( frequency over than 400 MHz)

ACost231hm＝（1.1 lglg f 0.7）hm (1.56 lglg f 0.8)；In suburbs, the model is revised as follows:

Lps Lp 2[lglg(f /28) ]2 5.4( ci t y) (3-9)

In open areas, the model is revised as follows:

Lpo Lp ( ci ty) 4.78(lglgf)2 18.33 lglgf 40.94 (3-10)

In real transmission environment, terrain and clutter should also be considered. The model of ASSET planning software fully considers all kinds of terrains and clutters and improves the accuracy of coverage forecast.

The model expression is as follows:

Lp K1 K2 lglgd K3(hm ) K4 lglghm K5 lglg(Hb )

K6 lglg(Hb ) lglgd K7 diffn Kclutter (3-11)

The following analysis is applied to macro cells:

K1 — frequency constant

Medium sized cities:

K1=69.55+(26.16+1.56lg(Fc))-0.8 {Fc=150-1000MHz}

K1=46.3+(33.9+1.56)lg(Fc)-0.8 {Fc=1500-2000MHz}



Big cities：K1=69.55+26.16lg(Fc) {Fc=150-1000MHz}

K1=46.3+Cm+(33.9+1.56)lg(Fc)-0.8 {Fc=1500-2000MHz}

Suburbs:

K1=69.55+(26.16+1.56lg(Fc))-0.8 -2(log(Fc/28))2 - 5.4{Fc=150-1000MHz}

K1=46.3+(33.9+1.56)lg(Fc)-0.8 -2(log(Fc/28))2 - 5.4{Fc=1500-2000MHz}

Open areas:

K1=69.55+(26.16+1.56lg(Fc))-0.8-4.78(log(Fc))2+18.33log(Fc)-40.94 {Fc=150-1000MHz}

K1=46.3+(33.9+1.56)lg(Fc)-0.8-4.78[log(Fc)]2+18.33log(Fc)-40.94 {Fc=1500-2000MHz}

K2 — distance attenuation constant

K3、K4 — correction coefficient of height of mobile station antenna

K5、K6 — correction coefficient of height of base station antenna

K7 — diffraction correction coefficient

Kclutter — correction coefficient of clutter attenuation, the signal strength of a given point is modified according to the clutter class at this point and is irrelevant to the clutter class in the transmission path. All losses in the transmission path are included in the median loss.

d — distance between base station and mobile station, unit：km

hm、hb — effective height of antenna in mobile station and base station respectively, unit: m

In radio transmissions, the value of K varies according to terrains, features and environment of cities. Table 3-2 is a list of values of K and attenuation values of some clutters once used for radio transmission analysis in medium sized cities.

Table 3-2 K parameters

K parameter Value

K1 150/900 MHz Urban ,160/1800 MHz Urban

146/900 MHz Large city,163/1800 MHz Large city

K2 44.90

K3 -2.54/900 MHz Urban,-2.88/1800 MHz Urban

0/900 MHz Large city,-2.88/1800 MHz Large city

K4 0.00



K5 -13.82

K6 -6.55

K7 -0.8

Clutter attenuation value

Inland Water -3.00

Wetland -3.00

Open Areas -2.00

Rangeland -1.00

Forest 13.00

Industrial & Commercial Areas 5.00

Village -2.90

Parallel_Low_Buildings -2.50

Suburban -2.50

Urban 0

Dense urban 5

High building 16

Calculate the median loss with these K parameters and modify them according to the complex environment. Building loss should also be considered in indoor cellular mobile system. Building loss is a function of wall structure (steel, glass, brick etc), building height, relative position of buildings to base station, percentage of window areas etc. Because of the complex of variables, building loss can only be forecasted according to the surrounded environment. The following are some conclusions:

Mean building penetration loss in urban areas is greater than that in suburbs and remote areas.

Loss in areas with windows is less than that without windows. Loss in indoor wide area is less than that at indoor wall area with corridor. Loss at street wall with aluminum bracket is greater than that at street wall

without aluminum bracket.



Loss in building with interlayer at ceiling is less than that in building with interlayer both at ceiling and indoor wall.

GSM has two frequency bands: 900 MHz and 1800 MHz. Each band has different transmission characteristics. Long wavelength comes with little diffraction loss and short wavelength comes with little building penetration loss. Indoor wave component is the superimposition of penetration component and diffraction component. Diffraction component constitutes most of the wave component, and therefore, the indoor and outdoor level difference of 1800 MHz is greater than that of 900 MHz. Because of the issues such as complex transmission environment and the direction of incident waves, quantify indoor and outdoor level difference is not very practical. The best way is to carry out level difference test in special environment for planning optimization.

The mean building penetration loss is a function of the height of the building. According to record, the gradient of loss line is -1.9 dB/floor. The mean building penetration loss of the first floor is about 18 dB in urban area and 13 dB in rural area. Tests show that the indoor loss has the characteristics of loss waveguide with attenuation. For example, when the wave transmits along the corridor direction vertical to outdoor window, the loss is about 0.4dB/m.

For the transmission loss in tunnels, the tunnel can be regarded as a waveguide with attenuation. Experiments show that the transmission loss decreases as frequency increases within special distance. The loss curve shows an exponential decrease with working frequency that is less than 2 GHz. For GSM frequency band, the transmission loss shows the fourth power inverse exponential change with distance, that is to say, when the distance between two antennas increases by one time, the transmission loss increases by 12 dB.

In UHF frequency band, tree leaves should also be taken into consideration. Research shows that the transmission loss in summer is usually 10 dB more than that in winter because of the flourishing leaves in summer. In cellular mobile system, vertical polarization is better than horizontal polarization.

3.3.2 COST231 Walfish Ikegami Model

For the network planning in dense cities, the cell radius is much smaller than before, so a micro cell model is necessary, whereas 3G system that is based on CDMA also requires precise RF design to guarantee the result. Most RF designs of this system need a micro cell model in a digital map with building information in it for RF design and emulation.

The preferable city micro cell models at present are COST231 Walfish Ikegami, Volcano and WaveSight. COST231 Walfish Ikegami model includes all the



factors that micro cell model generally considers. The following is a brief introduction to this classic model:

Frequency f: 800 MHz-2000 MHz

Height of antenna Hb: 4 m- 50 m

Height of mobile station Hm: 1 m-3 m

Coverage distance d：0.02 km-5 km

Other parameters

Height of building: Hroof (m)

Width of road: w (m)

Distance between buildings: b (m)

Angle between road direction and perpendicular incidence path：Phi (°)

(1) No perpendicular incidence path between base station and mobile

station (small cells)

Lb = L0 + Lrts + Lmsd (or Lb = L0 for Lrts + Lmsd <= 0) (3-12)

In the formula above：L0 is free space loss：L0 = 32.4 + 20*log (d) + 20*log (f)

Lrts is diffraction loss and dispersion loss between roofs and streets (slow

fading)：Lrts = -16.9 - 10*log (w) + 10 log(f) + 20*log(Hroof - Hm) + Lcri

In the formula above：Lcri = -10 + 0.354*Phi for 0<= Phi < 35°

= 2.5 + 0.075*(Phi-35) for 35<= Phi < 55°

= 4.0 - 0.114*(Phi-55) for 55<= Phi <90 °

Lmsd is multi path loss (fast fading)：Lmsd = Lbsh + ka + kd*log(d) + kf*log(f) - 9*log(b)

In the formula above：Lbsh = -18*log (1 +Hb - Hroof) for Hb > Hroof

= 0 for Hb <= Hroof

ka = 54 for Hb > Hroof

= 54 - 0.8*(Hb - Hroof) for d>= 0.5 and Hb <=Hroof

= 54- 0.8*(Hb-Hroof)*(d/0.5) for d<0.5 and Hb<=Hroof

kd = 18 for Hb > Hroof



= 18 - 15*(Hb - Hroof)/Hroof for Hb <= Hroof

kf = -4 + 0.7*(f/925 - 1) for medium sized cities

= -4 + 1.5*(f/925 - 1) for big cities

(2) With perpendicular incidence path between base station and mobile

station (for example, in the street canyon)

Micro cell (antenna lower than roof), path loss model as follows:

Lb = 42.6 + 26*log(d) + 20*log(f) for d >= 0.020 km (3-13)

3.3.3 Globe Curvature Effect

In broad coverage, such as see area, the globe curvature and refration may influence the transmission loss because of the long distance of perpendicular

incidence. Suppose globe radius is (given that equals the radius of equator,

unit: m), hm、hb are the effective heights of antennas in mobile station and base station respectively, unit: m. According to spherics, line-of-sight distance is:

d 2 hb + 2 hm (m)

Since air pressure, temperature and humidity change with altitude, dielectric constant ξr decreases accordingly and tends to 0 as air attenuates, and therefore, the transmission track of electric wave in troposphere is a curve along globe curvature direction instead of a straight line. Which means, wave refraction occurs in troposphere, refraction coefficient n= (ξr)1/2.

This kind of refraction equals the increase of globe radius, so multiply globe radius by a coefficient k. For standard air pressure refraction, k = 4/3, the

modified formula is shown in (3-14) and the unit of hm、hb is still m.

d0 4.12 hb hm (km) (3-14)

The mobile station beyond the distance calculated from the above formula is considered in the shadow area.

3.4 Transmission Model Rectification

3.4.1 CW Test Theory

Model rectification should be carried out in order to build a radio transmission model in line with local condition and improve the accuracy of coverage forecast for network planning. Continuous wave (CW) test is a necessary step for model rectification. Model rectification data is obtained through CW test and digital map. The longitude and latitude information and received level form the source of model rectification.



According to random theory, the transmission in mobile communications can be represented as the following formula:

r(x) m(x)r0(x) (3-15)

In the formula, x is distance, r(x) is received signal, r0(x) is Rayleigh fading, m(x) is local mean value, the synthesis of long term fading and space transmission loss, which is shown as follows:

m(x) 12L

xL

x L r(y)dy

(3-16)

2L is the average length of sampling intervals, also called intrinsic length.

CW test tries to obtain the local mean value of the geographical position of each point in a certain area and minimize the difference between r(x) and m(x); therefore, local mean value requires removal of the influence of Rayleigh fading. When integrate a group of r(x), if intrinsic length 2L is too short, the influence of Rayleigh fading still exists; if 2L is too long, the shadow fading may also be integrated. The value 2L decides the accordance of data measured and the actual local mean value and the accuracy of the forecast of transmission model rectified by CW test. The famous telecommunication expert Li Jianye proved that in GSM, the difference between measured data and actual mean value is less than 1 dB when the sampling number is 50 and the intrinsic length is 40 times of the wavelength (ignore the error of test equipment and digital map).

3.4.2 CW Test Method

I. Addressing

Decide the address and number of base station before CW test. Generally, in big cities with dense population, the number of test stations should be not less than five; while in small and medium sized cities, one test station is enough. The number of test stations depends on the height of antenna in test station and effective isotropically radiated power (EIRP). The principle of addressing is to cover sufficient clutter classes (from digital map).

In real test, the following criteria help to decide whether the addressing is proper or not:

4) The height of antenna is over 20 meters.5) Antenna exceeds the nearest obstruction by over 5 meters



5mFigure 3-1 Schematic drawing of addressing criteria

The obstruction here mainly refers to the highest building over the roof where antenna locates. The height of the building used as base station should be higher than the average height of surrounding buildings.

II. CW Test Preperation

CW test requires a test station to transmit RF signal, with or without frequency modulation, and then drive test with CW test equipment. Base station system includes transmitter antenna, feeder, high power and high frequency signal. Test system includes test receiver, GPS receiver, range finder, goniometer, test software and portable computer. Test receiver should have a sampling speed as high as possible.

Having installed the test base equipments in the selected place, measure the transmission power and reflection power with power meter and calculate EIRP according to the following formula:

(3-17)

P_forward is forward transmission power; P_reflected is reflection power; Tx_Antenna_Gain is test station transmitter antenna gain (dBi).

Record the antenna gain of test receiver Rx_Antenna_Gain (dBi) and the feeder loss of test receiver Rx_Feeder_Loss for later use.

After Installation and debugging, record the EIRP of the base station. Measure the latitude and longitude of base station with global positioning system (GPS) and the height of building with triangulation method and the tilt angle of antenna with goniometer. The height of antenna is the building height plus mast height and half length of antenna. Sweep frequency with portable tester to make sure normal operation of the equipments and no interfering signal around.

III. CW Test

There are three ways of sampling with professional CW test equipments: samplings according to time, impulse and distance. General test equipment can only do sampling according to time. Sampling according to distance has high



accuracy and can fully meet the requirement of Li Jianye’s theory about 36 to 50 samplings within 40 wavelengths. Distance sampling does not have strict limit on driving speed, but specifies a maximum speed (Vmax). Vmax is relative to the maximum sampling period (Tsample):

Vmaxmaxmax 0.8 /Tsample (3-18)

Choose the paths with various kinds of clutters to do random drive test. When the mobile station is within three kilometers away from test base station, the received signal is greatly affected by the surrounding buildings and the height of antenna. The difference of signal strength between the signal parallel to signal transmission path and the signal vertical to the transmission path is about 10 dB; therefore, when do tests in the streets within this area, take same number of samples in longitudinal streets and lateral streets to remove this influence. Do not choose express highway or broad and flat street but narrow street as test path. For each test base station, take as many data as possible. Test for four hours or above for each station and stop recording at red light.

As the terrain and clutter are relatively fixed during a period of time, the local mean value is definite for a base station in a certain place. This mean value is what the CW test tries to get and also the closest to the forecast.

3.4.3 Transmission Model Rectification with Examples

Model rectification requires a digital map containing terrain height, ground type and other geographical information that influences mobile radio wave transmission. This information is important basic data for planning software to do model rectification, coverage forecast, interference analysis and frequency planning.

Most transmission models used for computer aided analysis from different software developers are based on Okumura model and also provide rectification parameters. The following introduces model rectification method in details on the basis of the planning software ASSET mentioned above. Please note that if the model parameters of a city with similar terrain and clutters are provided, use it directly in planning forecast without the need for CW test and model rectification.

The parameters from K1 to K7 in ASSET model are decided by transmission environment. K(clutter) is the correction coefficient decided y different clutters. These parameters can be fitted from the data in CW test by K parameter testing method or minimum variance method. Most planning software take default model for forecast at first, and then compare the forecast value with drive test data and use their difference to modify model parameters. Keep on doing iterative rectification until the root-mean-square error (RMS Error) of forecast value and drive test data reaches minimum. The parameter values under this circumstance are the required rectification values.



Of all the K parameters, different parameters have different influence on the model. According to analysis, K1 and K(clutter) are constant and irrelevant to transmission distance, antenna height and other factors. K3 and K4 are modifying factors. As the height of mobile station does not change a lot (about 1.5 m), K3

and K4 are regarded as a micro-adjustment in final stage. The adjustment of

K2、K5 and K6 depends on test data and test path. K2 rectification usually comes first, and then comes K(clutter) rectification.

I. K2 Rectification:

6) As Lp = [K1 +K3(Hms) + K4 log(Hms) + K5 log(Hb) + K7 diffn]+[K2+K6log(Hb) ] log(d) + K(clutter) , [K1 +K3(Hms) + K4 log(Hms) + K5 log(Hb) + K7 diffn ] can be regarded as constant. K(clutter) is 0, and Ploss is linearly proportional to log (d).

7) Build a coordinate system with the logarithm of distance as x-axis and signal strength as y-axis.

8) Distribute test data into this coordinate system9) Do linear fitting, and the gradient of the obtained line is K2+K6log(Hb).10) Subtract K6log(Hb) from gradient and the difference is K2.

Planning software does not provide the value of K2 but forecast according to model and obtain the difference between forecast value and test value of each point, and then do linear fitting of the difference. The gradient of the fitted line is the deviation of K2+K6log(Hb). Suppose K6log(Hb) is already a reasonable value, this deviation is the deviation of K2. See Figure 3-1.

II. K1 Rectification:

If Gradient is 0, it means K2 has already been adjusted and the intercept in the coordinate system is the deviation of K1 (Actually, the intercept is the deviation of [K1 +K3(Hms) + K4 log(Hms) + K5 log(Hb) + K7 diffn]. Suppose [K3(Hms) + K4

log(Hms) + K5 log(Hb) + K7 diffn] is constant, and the intercept can be regarded as the deviation of K1). Original K1 plus the intercept is the corrected value of K1. See Figure 3-2.

III. K3 and K4 Rectification

K3 and K4 are relative to the antenna height in mobile station and, because the adjustment is rather tiny, no correction is needed and their changes are made up by K1.

IV. K5 and K6 Rectification

K5 and K6 are relative to the antenna height in base station. If their changes are small and the terrain fluctuation is mild, the changes of K5 and K6 can be replaced by the changes of K1 and K2 and no correction is needed.



V. K7 Rectification

K7 is diffraction parameter and is only effective beyond line-of-sight transmission range. As the current digital map lacks accurate information about building height, K7 is usually not adjusted. Keep its default parameter setting.

VI. K(clutter) Rectification

K(clutter) adjustment is a little complicated. Forecast the transmission loss of a point according to the clutter class and the K(clutter) value of this point. K(clutter) value is the deviation between a particular mean difference (the mean difference between the forecast value and the test value of a point in a particular class of clutter) and the overall mean difference. If the overall mean difference is 0, the mean difference between the forecast value and the test value of each point in a particular class of clutter is the recommended value of K (clutter). Adjustment is an iteration process. Adjusting K(clutter) affects K2 ; readjusting K2 affects K1; adjusting K1 affects K(clutter) . This kind of cyclic iteration is convergent.

Figure 3-1 K2 correction schematic drawing



Figure 3-2 K1 correction schematic drawing

Analyze the accuracy of the model after correction. The accuracy here refers to the accordance of the corrected model to the real test environment. Accuracy is usually evaluated by RMS Error. RMS Error less than 8 dB generally demonstrates the accordance, that is to say, the correction is accurate and can be used in the following planning as reference. RMS Error above 8 shows the corrected model has great difference with the real situation and has no reference meaning. There are four main reasons:

Error occurs in correcting process, such as inaccurate antenna drawing, wrong import of antenna information, no adjustment of map and improper clutter filter setting.

Poor subsequent data processing leads to the filtering of effective data and unfiltering of non-effective data.

Digital map is inaccurate. Improper design of CW test leads to non-effective test data. When RMS

Error>8 dB, check and do re-rectification according to the four reasons above.

If RMS Error>8 dB and no problem is found having checked the four reasons above. It might be because this model is not applicable or because the transmission environment is too complex and the transmission condition is too volatile in this area. Under such circumstances, it is necessary to take field investigation.



3.5 Doppler Effect and Switchover

3.5.1 Doppler Effect and Frequency Change

In GSM, the relationship between Doppler Effect and frequency change can be seen in the following formula:

Base station is the frequency source f, and the received frequency fˊof mobile station is:

fˊ=f(1±V/c) (3-19)

In the formula, v is the translational speed of mobile station; c is the transmission speed of electric waves (3X108 m/s).

Take “+” when mobile station moves to base station and “-” when mobile station moves away from base station.

Mobile station is the frequency source f, and the received frequency fˊof base station is:

fˊ=f/ (1±U/c) (3-20)

In the formula, u is the translational speed of mobile station; c is the transmission speed of signals in the air (3X108 m/s).

Take “+” when mobile station moves to base station and “-” when mobile station moves away from base station.

3.5.2 Discussions in Different situations

Discussions in different situations are as follows:

I. MS Moves to BTS

Mobile station moves to base transceiver station (BTS) at a speed of v. See figure 3-9

f1

f2

f3

V(km /h)

Figure 3-3 MS moves to BTS

The signal frequency of BTS is f1. Through FCCH channel in BCH channel, BTS controls mobile station to synchronize the frequency. Because of Doppler Effect,



the signal frequency that mobile station receives is f2, and then mobile station transmits f2 signal to base station. Because of Doppler Effect, the frequency that BTS receives is f3. According to the formula above, the values of f1, f2 and f3 are as follows:

f2=f1 (1+v/c)

f3=f2/ (1-v/c)

f3=f1 (1+v/c)/(1-v/c)=f1(c+v)/(c-v)

The fractional frequency deviation is：(f3-f1)/f1=2v/(c-v) (3-21)

II. MS Moves Away from BTS

Mobile station moves away from BTS at a speed of v. see Figure 3-4.

f1

f2

f3

V(km /h)

Figure 3-4 Mobile station moves away from BTS

The signal frequency of BTS is f1. Through FCCH channel in BCH channel, BTS controls mobile station to synchronize the frequency. Because of Doppler Effect, the signal frequency that mobile station receives is f2, and then mobile station transmits f2 signal to base station. Because of Doppler Effect, the frequency that BTS receives is f3. According to the formula above, the values of f1, f2 and f3 are as follows:

f2=f1 (1-v/c)

f3=f2/ (1+v/c)

f3=f1 (1-v/c)/(1+v/c)=f1(c-v)/(c+v)

The fractional frequency deviation is (f3-f1)/f1=-2v/(c+v) (3-22)

Since the translational speed of mobile station is much lower than the transmission speed of signal, the relative frequencies in the two situations above are pretty much the same but with opposite directions. In the first situation, the frequency increases; in the second situation, the frequency decreases.

The relation between fractional frequency deviation and translational speed of mobile station is shown in Figure 3-5:



Figure 3-5 Relationship between fractional frequency deviation and translational speed of mobile station

In the figure above, when the translational speed of mobile station is 100 km/h, the fractional frequency deviation is 0.19ppm. The frequency deviations are 171 Hz for 900 MHz and 342 Hz for 1800 MHz.

III. MS Moves Within Two BTSs

Mobile station moves within two base stations at a speed of v as shown in Figure3-6.

The switchover superimposes the two situations above. Mobile station acquires information about neighboring cell BCCH through BA list. Adjust the frequency of mobile station and add several kHz to monitor the level of neighboring cell . Doppler Effect may interferer the normal reception of signals from neighboring cell. For example, in Figure 3-6, mobile station monitors the level of BTS1. The signal f2ˊmobile station receives may appear between the adjusted frequencies of two mobile stations and the mobile station cannot detect the signal level of BTS1.

On the other hand, the Rxlev information reported in SACCH should be sent in every 30s, and such long time may also lead to abnormal monitoring of neighboring cell level and unsuccessful switchover.

The frequency change by Doppler Effect leads to the fact that the base station receives signals with the frequency of f1(c+v)/(c-v) while receives the data according to the sampling clock of f1; therefore, base station receives the wrong data, which also affects the switchover.



f1

f2

f3

V(km /h)

f1'

f2 '

f3 '

BT S1 BT S2MS

Figure 3-6 Mobile station moves within two BTSs

3.6 Fresnel RegionThere are perpendicular incidence wave and reflected wave in the transmission path from transmitter to receiver. When the angel between reflected wave and ground tends to 0, the direction of the electric field of reflected wave is opposite to the original direction with the phase difference of 180. The path difference

between perpendicular incidence wave and reflected wave is 2h thrd and the

phase difference 4 h thr d ; h t and hr represent the heights of transmitter

antenna and receiver antenna respectively; d is the horizon distance between

transmitter antenna and receiver antenna. See Figure 3-7.

Figure 3-7 Schematic

drawing of perpendicular incidence and reflection

Ignore part signals from transmitter to receiver through ground wave (these signals can be ignored in ultrahigh frequency and very high frequency), the square of the ratio of total received field strength to free space field strength (V/m)is as follows:

(3-23)



In the formula above, n is natural number, when equals（2n－1） , the signal

frequency gain is 6 dB; when equals 2n , the two kinds of waves offset each

other. The change of angle may be induced by the height of antenna, the change of

transmission distance, or both. When d < 4h thr

, 2 >

2 ; when d >

4h thr ，

2 < 2 .

In real transmission environment, Fresnel region defines the transmission space of radio wave. In one Fresnel region, the ray path difference is less than half wavelength as shown in Figure 3-8. The first Fresnel region is the main transmission region. If no obstruction occurs in this region, the diffraction loss is

minimal. The radius of Fresnel region of a point (d t away from transmitter, dr

away from receiver) in a path with the length d is as follows:

h0m dtdr

d 548 dtkmdrkmdkmfMHz (3-

24)

Figure 3-8

Radius of first Fresnel region

For example: There is a point in the transmission path of a typical urban base station with coverage of 2 km. Suppose this point is 100 m away from transmitter antenna. For 900 MHz frequency, the radium of the first Fresnel region of this

point is h0 5m.

On the basis of the first Fresnel region, the transmission path in the nth Fresnel region is half wavelength longer than that in the (n-1) th Fresnel region. The radius of the nth Fresnel region is as follows:

hnm ndtdrd 548 ndtkmdrkm

dkmfMHz (3-25)



If line of sight path skip the fluctuant terrain and buildings, reflected wave shows active effect to perpendicular incidence wave; otherwise, it may become a multi-path interference and its destructive effect increases with frequency. Actually, in the line of sight microwave link design, if 55% Fresnel region is unblocked, the rest area will not affect diffraction loss.


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Chapter 3_ Radio Transmission Theory

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