Large Scale Path Loss 2009

21
EE5401 Cellular Mobile Communications Institute for Infocomm Research 1 National University of Singapore EE5401 Cellular Mobile Communications Dr. Chew Yong Huat Institute for Infocomm Research (I 2 R) (Email : [email protected]) 1 Fusionopolis Way, #21-01 Connexis Singapore 138632 (North Tower Room 10-11) together with Prof. Tjhung Tjeng Thiang (Email : [email protected]) Lecture notes can be downloaded from http://www1.i2r.a-star.edu.sg/~chewyh/ Mainly focus on physical layer issues Requirements: Knowledge on Digital Communications, Probability and Random Processes are required. Quiz – 25% Final Examination – 75% EE5401 Cellular Mobile Communications Institute for Infocomm Research 2 National University of Singapore Subject Outline Introduction to Cellular Mobile Communications Radio Propagation : Large Scale Effects - Path loss prediction models - Shadowing Radio Propagation : Small Scale Effects - Multipath models : Rayleigh, Rician - Doppler effect, power spectra and signal correlation - Coherence time and bandwidth, flat and selective fading channel Modulation Techniques - Constant envelope and phase modulation - QPSK, π /4 QPSK, FSK, GMSK Equalization, Diversity and Coding Techniques - Linear and non-linear equalization - Selection, equal-gain and maximal ratio combining - Interleaving and convolutional coding Multiple Access Techniques - FDMA, TDMA, CDMA, SDMA - Packet radio and random access

Transcript of Large Scale Path Loss 2009

Page 1: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 1 National University of Singapore

EE5401

Cellular Mobile Communications

Dr. Chew Yong Huat Institute for Infocomm Research (I2R)

(Email : [email protected]) 1 Fusionopolis Way, #21-01 Connexis

Singapore 138632 (North Tower Room 10-11)

together with

Prof. Tjhung Tjeng Thiang

(Email : [email protected])

Lecture notes can be downloaded from http://www1.i2r.a-star.edu.sg/~chewyh/

Mainly focus on physical layer issues

Requirements: Knowledge on Digital Communications, Probability and Random Processes are required.

Quiz – 25% Final Examination – 75%

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 2 National University of Singapore

Subject Outline

Introduction to Cellular Mobile Communications

Radio Propagation : Large Scale Effects

- Path loss prediction models - Shadowing

• Radio Propagation : Small Scale Effects

- Multipath models : Rayleigh, Rician - Doppler effect, power spectra and signal correlation - Coherence time and bandwidth, flat and selective

fading channel

• Modulation Techniques

- Constant envelope and phase modulation - QPSK, π /4 QPSK, FSK, GMSK

• Equalization, Diversity and Coding Techniques

- Linear and non-linear equalization - Selection, equal-gain and maximal ratio combining - Interleaving and convolutional coding

Multiple Access Techniques

- FDMA, TDMA, CDMA, SDMA - Packet radio and random access

Page 2: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 3 National University of Singapore

Cellular System Concepts

- Frequency reuse - Channel assignment and control - Cellular traffic - Cellular coverage - System expansion techniques

CDMA Cellular Systems

- Power Control and Interference - Multiuser Detection - Capacity and Enhancement

More Advanced Topics (if time allows)

- Orthogonal Frequency Division Mulitplexing (OFDM) - Multicarrier CDMA System

Speech Coding

Fundamentals of quantization, PCM, Vocoder

Brief Overview of System Standards

GSM, IS-95, IMT2000

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 4 National University of Singapore

References

1. Theodore S Rappaport, Wireless Communications: Principles

& Practice, Prentice-Hall, 2nd Edition.

2. Jon W Mark, Weihua Zhuang, Wireless Communications

and Networking, Prentice Hall.

3. Simon R Saunders, Antennas and Propagation for Wireless

Communication Systems, Wiley.

4. William CY Lee, Mobile Communications Engineering,

McGraw-Hill.

5. JD Parsons, The Mobile Radio Propagation Channel, Wiley,

2nd Edition.

6. Michel Daoud Yacoub, Foundations of Mobile Radio

Engineering, CRC Press. (RBR: TK6570 Mob.Ya)

7. William C Jakes, Microwave Mobile Communications, IEEE

Press.

Page 3: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 5 National University of Singapore

Introduction

The target for mobile communications is to provide communications for anyone, from anywhere, at any time.

A demanding task. Technological challenges include:

1. Time–varying, hostile communication channel.

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 6 National University of Singapore

2. Location and tracking complexities due to mobility.

3. Efficient use of scarce resources such as frequency spectrum ⇒ cellular structure. The amount of interference generated is critical.

4. Power restrictions due to health issues.

The exponential growth of mobile subscribers worldwide is due to the decreasing service charges and diminishing hardware costs. The continuous development of the enabling technologies is the key.

1. RF technologies (such as improved frequency stability in electronics)

For carrier at 100MHz, at year 1940, the stability of oscillator at the base station is more than 100kHz, at year 2000 it is only 10Hz. This is less frequency guard band is needed.

2. IC design (size)

3. Battery technology (weight and size)

Page 4: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 7 National University of Singapore

4. Higher order modulation is made possible due to the use of more sophisticated advanced digital signal processing techniques.

(overhead on guard frequency band, roll-off factor etc.)

5. Speech coding techniques – reduces the required bandwidth per channel.

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 8 National University of Singapore

Cellular system

Example :

1. Consider a system allocated total bandwidth of 12.5 MHz and each voice channel requires a 10kHz slot. We can only support 12.5MHz/10kHz or 1250 simultaneous conversations.

2. Supposing the penetration rate in Singapore is 10%, for a population of 3M+, this is equivalent to 300k users. What happen if 1% of the users making call at the same time? Channels need to be in someway reused or shared?

What can we do? - Frequency bands are reused at different locations. With

this, higher user capacity in the same frequency spectrum can be achieved.

- Technical challenge: interference issue, location tracking, etc., needs to be overcome.

Page 5: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 9 National University of Singapore

- Each cell has a base station (BS), providing the radio interface to the mobile station (MS).

- A sophisticated switching technique called a handover enables a call to proceed uninterrupted across cell boundaries.

- All the BS’s are connected to a mobile switching centre

(MSC) which is responsible for connection users to the public switched telephone network (PSTN).

- Communication between the BS and the mobiles is

defined by a standard common air interface that specifies 4 different physical channels Forward (Downlink) voice/data channel : BS to MS Reverse (Uplink) voice/data channel : MS to BS Forward (Downlink) control channel : BS to MS Reverse (Uplink) control channel : MS to BS

- Control channels transmit and receive data messages that carry call initiation and service requests, and are monitored by mobiles when they do not have a call in progress. ~5% of total available channels.

- A MS contains a transceiver, an antenna and control circuitry. A BS consists of several transmitters and receivers.

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 10 National University of Singapore

Mobile Radio Propagation :

Large Scale Path Loss

The radio propagation channel exhibits many different forms of channel impairments, as a result of time-varying signal reflections, blockage and motion.

Page 6: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 11 National University of Singapore

Continuous measurements made along the radial direction

Short-term and long-term fading

After removing the path loss component, we result in an instantaneous fading signal

)()()( tjetatr ϕ= ,

Measurements made along the tangential direction

The envelope of the signal is given as

)()()( ttmta α=

)(tm and )(tα represent the long-term fading and short-term fading, respectively.

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 12 National University of Singapore

At a given time t, when MS is at physical spot A, y from BS, then

)()()( yymya α=

When no short-term fading, )(yα is a constant, long-term fading are the major factors.

If severe short-term fading is present in the mobile radio environment, then

∫=+

Ly

Lydxx

Lymym )(

2

1)()(ˆ α - )(ym : true local mean

A proper chosen of L between 40λ and 200λ will make

)()(ˆ ymym → or 1)(2

1→∫

+

Ly

Lydxx

Lα .

The fast fading component

)(ˆ)(

)(ym

yay =α or dBdBdB ymyay )(ˆ)()( −=α

Single path fading – the amplitude follows some distributions, such as Rayleigh distribution, Rician distribution, etc.

Page 7: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 13 National University of Singapore

Multipath path fading – in each path, the amplitude follows some distributions. Intersymbol Interference (ISI) is also presence.

Channel impulse response

Instantaneous received signal amplitude changes with time

Non-resolvable multipath resulting in (flat) fading

Resolvable multipath (Frequency selective fading)

Large scale propagation model: predict the mean signal strength for an arbitrary transmitter-receiver (T-R) separation distance. This is useful in estimating the radio coverage area of a transmitter.

- Path loss : attenuation with distance. - Shadowing (long-term fading) : due to the nature of

the terrain, the average received signal is strong when the MS is at the high spot and weak at the low spot, even at the same distance from BS. This average signal is called local mean and is a RV. Its statistics follow the log-normal distribution.

Small scale propagation model : characterize the rapid fluctuations of the received signal strength over short travel distances around a few wavelength or short time duration (short-term fading).

Propagation equation : all terms are in dB scale

dBfadingtermshortdBshadowingdBlosspathdB LLLL , ,, −++=

(what about if all quantities are in linear scale?)

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 14 National University of Singapore

Antenna Theory

A metallic device for radiating or receiving radio waves when carrying a time-varying current.

Coordinate system for antenna analysis

Page 8: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 15 National University of Singapore

- A dipole antenna carrying a sinusoidal current tII ωcos0= . At any point P,

φφθθ aEaEaEE rr ˆˆˆ ++=

φφθθ aHaHaHH rr ˆˆˆ ++=

- Using Maxwell’s equations to solve for the radiation pattern. Solution in free space is given as TEM wave.

An isotropic antenna radiates power uniformly in all directions. Power density at any r is given as:

2)(4 r

PF Tisor π

= W/m2

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 16 National University of Singapore

A directional antenna, like dipole antenna, radiates EM waves more “effectively” in some directions.

- A special type of directional antenna is omnidirectional pattern, in which nondirectional pattern in azimuth plane constant] θφ ),([ f , but directional in the elevation plane constant] φθ ),([g .

Page 9: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 17 National University of Singapore

General directional antenna

Consider an actual antenna such as elementary dipole radiating the same power TP as an isotropic antenna, ie. T

Sr PdSF =∫ ),( φθ , and define

)(

),(),(

isor

rt F

FG

φθφθ = ,

From this definition, the power density at a distance r away from the transmitting antenna having power gain Gt is

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 18 National University of Singapore

tT

r Gr

PF

24π=

As a consequence of reciprocity, the radiation pattern of any antenna is the same for transmitting and receiving.

At the receiving antenna, we define an effective area (or aperture) eA over which the transmitted power density is received. By the Reciprocity theorem, i.e. If G is high (during transmitting), then eA is also high (during receiving).

ee AGGA2

4

λπ

=⇔∝

Received power density at distance r away

trterr PGGr

AFP2

4⎟⎠⎞

⎜⎝⎛==πλ

Page 10: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 19 National University of Singapore

Free Space Propagation Loss

Power levels :

1. dBw= ( )[ ]in Wlog10 10 P

2. dBm= [ ]mW)(in log10 10 P

3. dB is a power ratio, ie. ⎟⎟⎠

⎞⎜⎜⎝

210log10P

P1

( ) ( ) ⎟⎠⎞

⎜⎝⎛+−+=⎟⎟

⎞⎜⎜⎝

⎛πλ

4log20log20 1010 rGG

P

PdBrdBt

dBt

r

The free-space path loss – (show this! take note on the unit used)

( ) 44.32)(log20log204

log20 101010 ++=⎟⎠⎞

⎜⎝⎛−= kmMHzdB rfr

Lπλ

)1( == rt GG

Exercise : An antenna with a gain of 60 dB transmits 2 kW to a satellite at 6 GHz. The satellite is at a distance of 36000 km and receives 5 nW. Determine the satellite antenna gain: (Ans : 23 dB)

This result is only valid in the far-field of the antenna. For distances λ22Ddr f => , where D is the largest physical dimension of the antenna and

λ>>>> ff dDd , .

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 20 National University of Singapore

The received power predicts to fall 6dB when the distance to the transmitter is double (or 20dB per decade). The loss increases by 6dB if the frequency is double.

Different from practical observation! Need to improve the model.

Reflection, diffraction and scattering are the three major causes which impact propagation in a mobile communication system.

Page 11: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 21 National University of Singapore

Reflection

Reflection coefficient of ground (a) vertical polarization (v) or E field in the plane of incidence. (b) horizontal polarization (h) or E field perpendicular to the incident plane

H

E

k

(y)

(z)

(x)

Snell’s law : ri θθ = , 1

2

)90sin(

)90sin(

n

n

t

i =−−θθ

Boundary conditions :

[ ] [ ]//2//1 EE = [ ] [ ]//2//1 HH =

[ ] [ ]⊥⊥ = 2211 EE εε [ ] [ ]⊥⊥ = 2211 HH μμ

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 22 National University of Singapore

Can show that

it

it

i

rv E

E

θηθηθηθη

sinsin

sinsin

12

12

++−

==Γ

ti

ti

i

rh E

E

θηθηθηθη

sinsin

sinsin

12

12

+−

==Γ

where iii εμη = , iii σεμ ,, are the permittivity, permeability and conductance of the media, and

)/( fj iri iπσεεε 20 −= . Other relationships required in

deriving the results : iiin εμ= , iEH η/∝ .

If medium 1 is free space )( 0εε = and medium 2 is an dielectric, then 1,1 −→Γ−→Γ vh regardless of rε if

0→iθ . Ground may be modeled as a perfect reflector (reflection coefficient of unit magnitude) when an incident wave grazes the earth, regardless of polarization or ground dielectric properties.

v

h

A dielectric material is a substance that is a poor conductor of electricity, but an efficient supporter of electrostatic fields.

For earth, at frequency 100MHz

rε range from 4 to 25

σ range from 0.001 to 0.02 S-m

Page 12: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 23 National University of Singapore

Propagation over smooth plane : the received signal is the phasor sum of the direct wave and the reflected wave from the plane (2-ray model).

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 24 National University of Singapore

- Assuming horizontal polarization

⎟⎠⎞

⎜⎝⎛ ′

−−′

=′ )(exp),( 0

c

dtj

d

EtdE cLOS ω

⎟⎠⎞

⎜⎝⎛ ′′

−−′′

Γ=′′ )(exp),( 0

c

dtj

d

EtdE cg ω

- Can show that d

hhddd rt2≈′−′′=Δ ,

d

E

d

E

d

E 000 ≈′′

≈′

if

rt hhd +>> , λ

πφ dΔ⋅=Δ

2. (Note λ

πωλ2cfc == )

- Hence gLOSTOT EEE +=

)exp(1

)(2

exp1

φλπ

Δ+Γ+=

⎥⎦⎤

⎢⎣⎡ ′−′′Γ+=⇒

jE

ddjEE

LOS

LOSTOT

- Power is proportional to square of E field amplitude,

( ) 22

exp1 φΔ⋅Γ+≈= jE

E

P

P

P

P

LOS

TOT

LOS

r

LOS

TOT

- The LOS is itself subject to free space loss

2

4⎟⎠⎞

⎜⎝⎛

′=

dPGGP trtLOS π

λ

- Assuming small incidence angle iθ ( 1−=Γ ), then

( ) ⎟⎠⎞

⎜⎝⎛ Δ

⎟⎠⎞

⎜⎝⎛=Δ−⎟

⎠⎞

⎜⎝⎛=

2sin4

4exp1

42

22

2 φπλφ

πλ

dGGj

dGG

P

Prtrt

t

r

Page 13: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 25 National University of Singapore

- Thus

4

22

d

hhGG

P

P rtrt

t

r = or

( )[ ]rtrtdB GGhhdL 101010 log10)(log20log40 +−=

- Problem : Correctly predicted the 40dB path loss but now path loss is independent of frequency! In actual measurement n

r fP −∝ where 32 << n .

The phase relationship φΔ between the reflected ground wave and the direct wave changes with distance and antenna height. Signal nulls appear if the components are in anti-phase.

( ) 0exp1 2 =Δ− φj (assuming 1−=Γ )

nn πφφ20

2sin2 =Δ⇒=⎟

⎠⎞

⎜⎝⎛ Δ⇒

- Recall that d

hh rt

λπφ ⋅

=Δ4

, so nulls appear at spatial

distances of nd , where

λλππ

n

hhd

d

hhn rt

nn

rt 242 =⇒

⋅= - Fresnel zones

- The mth Fresnel zones is defined as the distance from

the BS where 2λmd =Δ or πφ m=Δ . The first null above corresponds to the second Fresnel zone. The first Fresnel zone distance fD is a useful parameter in

cellular design.

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 26 National University of Singapore

First Fresnel zone

Second Fresnel zone

Third Fresnel zone

Received power in dB

Distance from BS

dB/decade40−

- In practice, zero power is not observed because generally

1<Γ , especially at the higher Fresnel zone. Hence, completely destructive will not be observed. Besides, polarization of wave needs to take into consideration.

Deviate from 4=n

- Modification to 2-ray model : 1−=Γ is not valid

dB/decade40−

dB/decade20−

Received power in dB

Distance from BS

- More than 1 reflected path

- Other consideration such as scattering.

Page 14: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 27 National University of Singapore

Two ray models are only used to understand the path loss mechanism. In general, multiple reflection paths present, and have impact on the path loss, shadowing and short-term fading phenomenon.

In open terrian, actual measured power is normally much higher, ie, 4<n , or log-distance path loss model is generally given as

n

t

r

dP

P⎟⎠⎞

⎜⎝⎛∝

1 , 43 << n .

Reduce the amount of interference on neighboring cells

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 28 National University of Singapore

Diffraction

Diffraction allows radio signals to propagate around the curved surface of the earth, beyond the horizon, and to propagate behind obstacles.

The phenomenon of diffraction can be explained by Huygen’s Principle.

- Each element of a wavefront (a surface of constant phase) at a point in time may be regarded as the centre of a secondary disturbance, which gives rise to spherical wavelets.

- The position of the wavefront at any later time is the envelope of all such wavelets.

Page 15: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 29 National University of Singapore

Estimating the signal attenuation caused by diffraction of radio waves over hills and buildings is essential in predicting the field strength in a given service area. It is mathematically difficult to make very precise estimates of the diffraction losses over complex and irregular terrian. Some cases have been derived, such as propagation over a knife-edge object.

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 30 National University of Singapore

Ideal Knife-edge Scenario

- Can show that path difference ( )

21

212

2 dd

ddhd

+=Δ or

( )21

2122

2

2

dd

ddhd

λπ

λπφ

+=

Δ⋅=Δ

- To take care of antenna having same or different

height, consider only α and assuming that 21,ddh << and λ>>h , then

⎟⎟⎠

⎞⎜⎜⎝

⎛ +=+≈+=

21

21tantandd

ddhγβγβα

Page 16: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 31 National University of Singapore

- Normalize with the dimensionless Fresnel-Kirchoff parameter ν,

)(

2)(2

21

21

21

21

dd

dd

dd

ddh

+=

+=

λα

λν

This leads to 2

2νπφ =Δ

Diffraction losses can be explained by the concept of Fresnel zones.

- Successive regions where secondary waves have excess path lengths of 2/λn . Hence between a transmitter and receiver pair, the nth Fresnel zone is ellipsoid in shape over a three-dimension space, with the location of transmitter and receiver as its focus points.

Any point on an ellipsoid has the same distance from Tx to Rx. The cross section is a circle

- Can show that the radius of the nth Fresnel zone circle is denoted by nr , given by 2/λnd =Δ is given

by 21

21

dd

ddnrn +=

λ.

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 32 National University of Singapore

- Constructive/destructive interference.

Diffraction loss determined by the level of obstructed Fresnel zones.

The electric field strength of a knife-edge diffracted wave is given by

dttjj

FE

Ed ⋅∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛−

+==

ν

πν2

exp2

)1()(

2

0

where 0E is the free-space field strength.

Page 17: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 33 National University of Singapore

1. This integral is known as the complex Fresnel integral 2. The Fresnel integral is a function of the Fresnel-

Kirchoff diffraction parameter ν. 3. The diffraction gain is usually expressed in dB as

( ))(log20)( νFdBGd = 4. The Fresnel integral is commonly evaluated using

tables or graphs for given values of ν.

Using graphical method,

Numerical approximation

0=dG 1−≤ν

( )ν62.05.0log20 10 −=dG 01 ≤≤− ν

( ))95.0exp(5.0log20 10 ν−=dG 10 ≤≤ν

( )210 )1.038.0(1184.04.0log20 ν−−−=dG 4.21 ≤≤ν

( )ν/225.0log20 10=dG 4.2>ν

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 34 National University of Singapore

Multiple Knife-edge diffraction : For the presence of two knife edges, replace it by an equivalent knife edge. One way is as follow.

Scattering

When encountering rough surfaces, reflected energy is spread out in all directions.

It is therefore expected that the received signal is stronger than predicted from reflection and diffraction models alone.

Page 18: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 35 National University of Singapore

Log Distance Path Loss Models

P

oP

0d d

Beyond this point, the relationship not necessary still valid

tP

After considering all these effects, log-distance path loss model is given as

n

r dP ⎟

⎠⎞

⎜⎝⎛∝

1

where n is the path loss exponent. For Free-space propagation model, n=2, and for two-ray model n=4.

At a reference point 0d with received power 0P , can show that

nnr

d

d

d

d

P

P−

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠⎞

⎜⎝⎛=

0

0

0

The path loss from the reference point

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

=

010

0

log10

dB)(in -dB)(in )(

d

dn

PPdL rpath

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 36 National University of Singapore

Need to be careful if you need to extrapolate the curve beyond 0dd < . It could follow another relationship.

rP

1P

1d d

tP

0d

oP

0

0

n

d

d⎟⎟⎠

⎞⎜⎜⎝

⎛ 1

1

n

d

d⎟⎟⎠

⎞⎜⎜⎝

The value of n depends on the amount of clutter in the environment. Usually

Environment n

Free space 2

Urban area cellular radio 2.7 to 3.5

Shadowed urban cellular radio 3 to 5

In building line-of-sight 1.6 to 1.8

Obstructed in building 4 to 6

Obstructed in factories 2 to 3

Sometime different values are used for n depending on the distance from the transmitter.

Page 19: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 37 National University of Singapore

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 38 National University of Singapore

- n does not directly reflect the strength of the received power, for example,

Page 20: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 39 National University of Singapore

Log-normal Shadowing

Two locations at the same distance from the transmitter can experience substantial differences in signal level compared to the expected average value. This phenomenon is caused by large buildings, foliage, etc that obstruct the propagation path and is known as shadowing.

Experimental trails have shown that shadowing effects can be well modeled by a RV with a log-normal distribution.

σXd

dndL shadowingpath +⎟⎟

⎞⎜⎜⎝

⎛⋅⋅=+

010log10)(

Log-normal distribution

1. YX e= where Y is normally distributed.

2. A Gaussian distribution on a log-scale, ie. If sx be the attenuation due to shadowing. Then

sdB xX 10log10= , then

⎟⎟

⎜⎜

⎛−=

2

2

2exp

2

1)(

dBdB X

dB

XdB

XXf

σσπ

The standard deviation dBXσ is known as the shadow

dB spread.

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 40 National University of Singapore

Empirical Models

Many empirical models have been suggested in the literature. Okumura’s model has gained widespread acceptance. This model is based entirely on measurements.

Areartmufreepath GhGhGdfALL −−−+= )()(),(

where muA is the attenuation relative to free space.

G(.) is the antenna height gain factor for the base or mobile station, and

Page 21: Large Scale Path Loss 2009

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 41 National University of Singapore

)200

(log20)( 10t

th

hG = mhm t 101000 <<

)3

(log10)( 10r

rh

hG = mhr 3≥

)3

(log20)( 10r

rh

hG = mhm r 310 >>

AreaG is the gain due to the type of environment.

Other corrections may also be applied to Okumura’s model. Some of the important terrain such as slope of terrain, mixed land-sea parameters,…

Hata’s model : Empirical formulation of Okumura’s model.

[ ] )log()log(55.69.44

)()log(82.13)log(16.2655.69

kmt

rtMHz

dh

hahfL

−+−−+=

For a small/medium city

[ ] [ ]8.0)log(56.17.0)log(1.1)( −−−= MHzrMHzr fhfha

For a large city where MHzfc 300<

[ ] 1.1)54.1log(29.8)( 2 −= rr hha

For a large city where MHzfc 300>

[ ] 97.4)75.11log(2.3)( 2 −= rr hha

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 42 National University of Singapore

Summary

Source

Transmit antenna

Path Loss Shadowing Fast fading Receive antenna

AWGN

Receiver

Additive noise

Multiplicative noise

Useful Reference Source “Antenna and Propagation for Wireless Communication Systems” by Simon R. Saunders – More channel models for pico, micro and macro-cell can be found in the book “Mobile Communications Engineering”, by William CY Lee – More description on the principle behind the channel characterization, and provide with the relevant references.