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Transcript of 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
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.
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)
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.
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.
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.
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
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 .
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
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.
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
iθ
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
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.
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.
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
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.
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.
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.
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,
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
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.