The Wireless Channel Propagation

The Wireless Channel: Propagation
and Fading
Jay Chang
1

2
Large-Scale Fading
Small-Scale Fading
Agenda

3
Radio propagation
Reflection is the physical phenomenon that occurs when a propagating electromagnetic wave impinges upon an object with very
large dimensions compared to the wavelength, for example, surface of the earth and building. It forces the transmit signal power
to be reflected back to its origin rather than being passed all the way along the path to the receiver.
Diffraction refers to various phenomena that occur when the radio path between the transmitter and receiver is obstructed by a
surface with sharp irregularities or small openings. It appears as a bending of waves around the small obstacles and spreading
out of waves past small openings. The secondary waves generated by diffraction are useful for establishing a path between the
transmitter and receiver, even when a line-of-sight path is not present.
Scattering is the physical phenomenon that forces the radiation of an electromagnetic wave to deviate from a straight path by
one or more local obstacles, with small dimensions compared to the wavelength. Those obstacles that induce scattering, such as
foliage, street signs, and lamp posts, are referred to as the scatters.
Fading
Fading the variation of the signal amplitude over time and frequency.
The fading phenomenon can be broadly classified into two different types: large-scale fading and small-scale fading.
Large-scale fading occurs as the mobile moves through a large distance, for example, a distance of the order of cell size. It is
caused by path loss of signal as a function of distance and shadowing by large objects such as buildings, intervening terrains, and
vegetation.
• Shadowing is a slow fading process characterized by variation of median path loss between the transmitter and receiver in
fixed locations.
• In other words, large-scale fading is characterized by average path loss and shadowing.
Small-scale fading refers to rapid variation of signal levels due to the constructive and destructive interference of multiple signal
paths (multi-paths) when the mobile station moves short distances.
• Depending on the relative extent of a multipath, frequency selectivity of a channel is characterized (e.g., by frequency-
selective or frequency flat) for small-scaling fading.
• Depending on the time variation in a channel due to mobile speed (characterized by the Doppler spread), short term
fading can be classified as either fast fading or slow fading.

4
Fig. Classification of fading channels.
Large-scale fading is manifested by the mean path loss
that decreases with distance and shadowing that
varies along the mean path loss. The received signal
strength may be different even at the same distance
from a transmitter, due to the shadowing caused by
obstacles on the path.
Furthermore, the scattering components incur small-
scale fading, which finally yields a short-term variation
of the signal that has already experienced shadowing.

時間選擇性衰落(快衰落)
頻率選擇性衰落
5
1
coherent
Doppler
T
f
∝
∆
1
: BW .
: ( )
coherent
spread
coherent
spread
B
t
B
t h t
∝
相干帶寬在該內信道衰落基本不變
時延擴展信道沖激響應持續時間
Small-scale fading 2個重要觀念個重要觀念個重要觀念個重要觀念
• Doppler spread causes → frequency dispersion → Ɵme-selective fading
• Multipath delay spread causes → time dispersion → frequency-selective fading

6

7
0
1
0.2 0.4 0.6
2 3 4
0.8 1.0
5
t / s
d / m
/dB
-30
-20
-10
0
10 快衰落快衰落快衰落快衰落
慢衰落慢衰落慢衰落慢衰落
相對電平相對電平相對電平相對電平/dB
慢衰落: 慢衰落指的是接收信號強度隨機變化緩慢, 具有十幾分鐘或幾小時的長衰
落週期.
快衰落: 接收信號強度隨機變化較快, 具有幾秒鐘或幾分鐘的短衰落週期。
典型信號衰落特性典型信號衰落特性典型信號衰落特性典型信號衰落特性

8

9
多徑傳播信道的衝激响應模型
( ) ( ) 1 2 3
1
,
L
i i L
i
h aτ δ τ τ τ τ τ τ
=
= − ≤ ≤ ≤ ≤∑ ⋯
對上式進行FT得到信道多徑環境下的頻率响應(傳輸函數)
( ) ( )
1
i
L
jj
i
i
H h e d a e ωτωτ
ω τ τ
∞
−−
−∞
=
= = ∑∫
( ) ( ) 1 2 3
1
,
L
i i L
i
y t a s t τ τ τ τ τ
=
= − ≤ ≤ ≤ ≤∑ ⋯
假設假設假設假設
)(ts
t
)(ty
t
時延擴展時延擴展時延擴展時延擴展
i ia τ和是每路信號的強度和到達時間L是所有傳播路徑的數目
( ) ?s t設發射信號為則接收到的信號是經多徑傳播後的總和

10
V0
V0
時時時時延延延延t0
時時時時延延延延t0＋＋＋＋τ
＋＋＋＋
)(ts )(ty
)(ωH
0
ω
τ
π
τ
π2
τ
π3
τ
π4
02V
0 0
0 0
0 0 0 0
( )
0 0
2
0 0
( ) ( ) ( )
( ) ( ) ( )
( ) (1 ) 2 cos
2
j t j t
j
j t j tj
y t V s t t V s t t
Y V S e V S e
H V e e V e e
ω ω τ
ωτ
ω ωωτ
τ
ω ω ω
ωτ
ω
− − +
−
− −−
= − + − −
= +
= + =
2
cos2)( 0
ωτ
ω VH =

11
• 信道的多徑數目為7, 信號經7條不同
路徑到達時的幅度和時間是隨機選
擇的.
( )
1 1
( ) ,
( ) ( )i i
j t
L L
j t j j t j t
i i
i i
s t e
y t a e a e e H e
ω
ω τ ωτ ω ω
ω− −
= =
=
= = ⋅ =∑ ∑
若發射信號則接收到的信號為

12
Large-Scale Fading
Small-Scale Fading
Agenda

13
General Path Loss Model
L = 1
Gt = Gr = 1
Fig. Free-space path loss model.

14
More generalized form of the path loss model can be
constructed by modifying the free-space path loss with the
path loss exponent n that varies with the environments.
This is known as the log-distance path loss model, in which the
path loss at distance d is given as
Log-distance path loss model

15
A log-normal shadowing model is useful when dealing with a
more realistic situation. Let Xσ denote a Gaussian random
variable with a zero mean and a standard deviation of σ.
Then, the log-normal shadowing model is given as
This particular model allows the receiver at the same distance
d to have a different path loss, which varies with the random
shadowing effect Xσ.
Log-normal shadowing model

16
Different types of model
https://gist.github.com/oklachumi/6fe737b8f99c12edfe619d152469d114

17
Okumura/Hata Model
Okumura model has been obtained through extensive experiments to compute the antenna height and coverage area for mobile
communication systems.
It is one of the most frequently adopted path loss models that can predict path loss in an urban area. This particular model
mainly covers the typical mobile communication system characteristics with a frequency band of 500–1500MHz, cell radius of 1–
100 km, and an antenna height of 30 m to 1000 m.
The path loss at distance d in the Okumura model is given as:
Hata model is currently the most popular path loss model. For the height of transmit antenna, hTX [m], and the carrier frequency
of fc [MHz], the path loss at distance d [m] in an urban area is given by the Hata model as:

19https://github.com/oklachumi/octave-in-communications

20
IEEE 802.16d Model
IEEE 802.16d model is based on the log-normal shadowing path loss model.
There are three different types of models (Type A, B, and C), depending on the density of obstruction between the transmitter
and receiver (in terms of tree densities) in a macro-cell suburban area. Table below describes these three different types of
models in which ART and BRT stand for Above-Roof-Top and Below-Roof-Top.
IEEE 802.16d path loss model is given as:
Types of IEEE 802.16d path loss models.
Parameters for IEEE 802.16d type A, B, and C models.
hTX is the height of transmit antenna (typically, ranged from 10mto 80 m). Furthermore, Cf is the correlation coefficient for the
carrier frequency fc [MHz], which is given as

21
modified IEEE 802.16d model follows

23
Large-Scale Fading
Small-Scale Fading
Agenda

24
Small-Scale Fading
Small-scale fading is often referred to as fading in short. Fading is the rapid variation of the received signal level in the short term
as the user terminal moves a short distance.
Small-scale fading is attributed to multi-path propagation, mobile speed, speed of surrounding objects, and transmission
bandwidth of signal.
Characteristics of a multipath fading channel are often specified by a power delay profile (PDP).
Power delay profile: example (ITU-R Pedestrian A Model).
Mean excess delay and RMS delay spread are useful channel parameters that provide a reference of comparison among the
different multipath fading channels.

時間選擇性衰落(快衰落)
頻率選擇性衰落
25
1
coherent
Doppler
T
f
∝
∆
1
: BW .
: ( )
coherent
spread
coherent
spread
B
t
B
t h t
∝
相干帶寬在該內信道衰落基本不變
時延擴展信道沖激響應持續時間
Small-scale fading 2個重要觀念個重要觀念個重要觀念個重要觀念

26
Time-Dispersive vs. Frequency-Dispersive Fading:
Fading Due to Time Dispersion: Frequency-Selective Fading Channel
Fading Due to Frequency Dispersion: Time-Selective Fading Channel
Fig. Characteristics of fading due to time dispersion over multi-path channel
signal bandwidth is narrow signal bandwidth is wide
BW of the wireless channel Bc > signal BW Bs,
maintaining a constant amplitude and linear phase
response within a passband.
Constant amplitude undergone by signal bandwidth
induces flat fading = frequency-non-selective fading.
Symbol period Ts > delay spread τ, current symbol does
not affect the subsequent symbol imply ISI is not
significant.
BW of the wireless channel Bc < signal BW Bs.
Symbol period Ts < delay spread τ, ISI significant.
A channel is typically classified as frequency selective
when στ (RMS delay spread) > 0.1Ts.
sT τσ<

27
Time-Dispersive vs. Frequency-Dispersive Fading:
Fading Due to Time Dispersion: Frequency-Selective Fading Channel
Fading Due to Frequency Dispersion: Time-Selective Fading Channel
• Coherence time Tc, is inversely proportional to doppler spread (maximum Doppler shift fm).
• The bandwidth of Doppler spectrum, denoted as Bd, is given as Bd = 2fm.
• Derived under the assumption that a Rayleigh-faded signal varies very slowly.
The transmit signal is subject to fast fading.
The transmit signal is subject to slow fading.
In the case where the coherence time is defined as a
bandwidth with the correlation of 0.5 or above
The most common definition of coherence time is to use the geometric mean of above two equations
Fast or slow fading does not have anything to do with time dispersion-induced fading.
Frequency selectivity of the wireless channel cannot be judged merely from the channel characteristics of fast or slow fading.
Because fast fading is attributed only to the rate of channel variation due to the terminal movement.

28
Statistical Characterization of Fading Channel
The amplitude of the received signal, over the multipath channel subject to numerous scattering
components, follows the Rayleigh distribution.

29
The power spectrum density (PSD) of the fading process is found by the Fourier transform of the autocorrelation function
Called classical Doppler spectrum
If some of the scattering components are much stronger than most of the components, the fading process no longer follows
the Rayleigh distribution. In this case, the amplitude of the received signal
follows the Rician distribution and thus, this fading process is referred to as Rician fading.

30
Generation of Fading Channels
Fig. Non-LOS and LOS propagation environment.
Fig. can be represented by a complex Gaussian random variable, W1 + jW2, where W1 andW2 are the independent and
identically-distributed (i.i.d.) Gaussian random variables with a zero mean and variance of σ2.
X denote the amplitude of the complex Gaussian random variable W1 + jW2,
X is a Rayleigh random variable with the following probability density function (PDF):
In the LOS environment where there exists a strong path which is not subject to any loss due to reflection, diffraction, and
scattering, the amplitude of the received signal can be expressed as X = c + W1 + jW2.
X is the Rician random variable with the following PDF:
• K = 0, no LOS component → Rayleigh PDF
• K increases → Gaussian PDF.
• Generally, K ~ -40 dB for the Rayleigh fading channel.
• K > 15 dB for the Gaussian channel.
Rician distributionRayleigh distribution

31
Distributions for Rayleigh and Rician fading channels
https://github.com/oklachumi/octave-in-communications/blob/master/plot_Ray_Ric_channel.m

The Wireless Channel Propagation

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