1. IMPLEMENTATION OF WIRELESS CHANNEL
MODEL IN MATLAB: SIMPLIFIED
Dr. Rosdiadee Nordin
Wireless Networks and Communications Group MATLAB Workshop, 22nd Dec, 2011
Faculty of Engineering and Built Environment
Universiti Kebangsaan Malaysia

2. LAYOUT
• What is a wireless channel?
• Impairment in wireless
• Basic of channel model
• SISO
• MIMO
• OFDM
• Share of experience

3. What is a wireless channel?
• Performance of wireless comm sys governed by the
wireless channel environment
• Wireless channel is dynamic and
unpredictable, analysis often difficult
• Unique characteristic in a wireless channel is a
phenomenon called ‘fading’  variation of signal
amplitude over time and frequency
• Fading may either be due to multipath
propagation, or shadow fading
• Broadly classified into two different types: (i) large-
scale fading and (ii) small-scale fading

4. What is a wireless channel?
Distortion: amplitude or phase ‘flat’ effect baseband signal variation

5. Impairment in wireless
• Small-scale fading often referred to as fading
• Rapid variation of the received signal level in the short
term as the user terminal moves a short distance
• Multiple signal paths induce interference when arrive
with varying phases in the receive antenna
• Variation of the received signal level depends on the
relationships of the relative phases among the number of
signals reflected from the local scatters
• Small-scale fading is attributed to multi-path
propagation, mobile speed, speed of surrounding
objects, and transmission BW of signal

6. Impairment in wireless
• Characteristics of a multipath fading channel are often
specified by a power delay profile (PDP)
• Useful parameters provide reference of comparison
among the different multipath fading channels:
▫ Mean excess delay
▫ RMS delay spread
• General guideline to design a wireless transmission
system
• Wireless channels characterized by different channel
parameters:
▫ Multipath delay spread: frequency dispersion
(frequency-selective fading)
▫ Doppler spread: time dispersion (time-selective fading)

7. Basic of Channel Models
• Generation of fading channels
▫ LOS (Line-of-Sight): Rician
▫ NLOS (Non Line-of-Sight): Rayleigh
4
x 10
2.5
Rayleigh
Ricean near Rayleigh Rician, K=-40dB
Rician, K=15dB
2
Ricean near Gaussian
1.5
Occurrence
1
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4
x

8. Basic of Channel Models
• Geographical profile: indoor, outdoor, urban, sub-
urban, macro, micro, etc
• Accurate channel model in specific environment,
need knowledge on the characteristics of reflectors,
including situation, movement, and the power of the
reflected signal at any specified time
• Reference to specific channel model that represent a
typical or average channel condition in the given
environment.
• Analysis in static channel: environment in which a
channel condition does not change for the duration
of data transmission at the given time and location

9. Basic of Channel Models
• Complete opposite to time-varying environment, i.e.
objects or people surrounding the transmitter or receiver
are steadily moving even while a terminal is not in
motion
• Degree of time variation in signal strength relative to
symbol duration - relatively small with respect to symbol
duration
• Referred to as a quasi-static channel condition
• Channels usually modeled under the assumption of static
or quasi-static channel conditions

10. SISO
• Can be categorized into:
▫ Indoor channel:
 Small coverage areas inside the building, e.g. office and mall
 Completely enclosed by wall – power azimuth spectrum (PAS)
tends to be uniform, i.e. scattered components will be received
from all directions with same power
 Static due to extremely low mobility of the terminals inside the
building
▫ Outdoor channel:
 Characterized by time variation of the channel gain, subject to
mobile speed of terminals
 Governed by Doppler spectrum – determines time-domain
correlation in the channel gain.
 Channel model can be implemented in both frequency-flat and
frequency-selective channels

11. SISO – Common Implementation
Indoor Outdoor
• Two – ray • FWGN
• Exponential • Clarke/ Gan
• IEEE 802.11 • Jakes
• Saleh-Valenzuela (S-V) • Ray-based
• UWB • Frequency selective fading
• ETSI HiperLAN • Tapped delay line
• Stanford Uni Interim (SUI)

12. SISO (Indoor): Two – ray Channel Model
• Two rays, one for a direct path with
zero delay (t > 0) , and the other for a
2-ray Model
Ideal
0.6
Simulation path which is a reflection with delay of
t1 > 0
0.5
• Delay of second path is the only
Channel Power[linear]
parameter determines the
0.4
0.3
characteristics of model
0.2 • Not accurate: magnitude of second
0.1
path is less than that of the first path
in practice
0
0 20 40 60
Delay[ns]
80 100 120 140
• Acceptable only when there is a
significant loss in the first path

13. SISO (Indoor): Exponential Model
• Average channel power decreases
exponentially with channel delay
1  /  d
P ( )  e (1)
d
• More appropriate for an indoor
channel environment

14. SISO (Indoor): IEEE 802.11
• Representation of 2.4 GHz indoor channel by IEEE
802.11b Task Group
• Channel impulse response can be represented by the
output of finite impulse response (FIR) filter
• Each channel tap is modeled by an independent complex
Gaussian random variable with its average power that
follows the exponential PDP
• Time index of each channel tap by the integer multiples
of sampling periods.

15. SISO (Indoor): IEEE 802.11
• Maximum number of paths determined by the RMS
delay spread,   and sampling period, T s
10 . 
p max  (2)
Ts
• maximum excess delay is fixed to 10 times the RMS
delay spread – as oppose to exponential model (max.
excess delay computed by a path of the least non-
negligible power level)
• In this case, the power of each channel tap is given as
 pT s /  
  0e
2 2
p
(3)

16. SISO (Indoor): IEEE 802.11
• where  0 is the power of the first tap, which is
2
determined so as to make the average received power
equal to one
• Thus: T /
1 e s 
  (4)
2
0  ( p max  1 ) T s /  
1 e
• Sampling period must be at least as small as 1/4

17. SISO (Indoor): IEEE 802.11
Average channel power Channel frequency response
IEEE 802.11 Model,  =25ns, TS=50ns
Frequency response,  =25ns, TS=50ns
1
0
Ideal
0.9 Simulation
0.8 -2
Average Channel Power[linear]
0.7
-4
Channel power[dB]
0.6
0.5 -6
0.4
-8
0.3
0.2
-10
0.1
0 -12
-1 0 1 2 3 4 5 6 7 -10 -8 -6 -4 -2 0 2 4 6 8 10
channel tap index, p Frequency[MHz]

18. MIMO
• Multi-Input and Multi-Output (MIMO) systems:
channel model vary with antenna config
• Different channel model is required to capture their
spatio-temporal characteristics (e.g., correlation
between different paths among multiple transmit
and receive antennas).
• Correlation between transmit and receive antenna is
an important aspect of the MIMO channel.
• Depends on the angle-of-arrival (AoA) of each
multi-path component

19. MIMO
• Two common methods:
▫ I-METRA MIMO
▫ SCM MIMO
• Recall: delay spread and Doppler spread are the
most important factors to consider in characterizing
the SISO system
• MIMO however relies on the correlation between
transmit and receive antenna
• Depends on the angle-of-arrival (AoA) of each
multi-path component
• AoA: azimuth angle of incoming path with respect to
the broadside of the antenna element

20. MIMO

21. MIMO: SCM Channel Model
• Proposed by a joint work of Ad Hoc Group (AHG) in
3GPP and 3GPP2.
• Aimed at specifying the parameters for spatial
channel model and developing a procedure for
channel modeling
• Combination of (sum) the arriving plane waves
• Ray-based channel model, which superposes sub-
ray components on the basis of PDP, PAS, and
antenna array structure
• Model the plane waves incoming from an arbitrary
direction around the mobile terminal - can deal with
the various scattering environments

22. MIMO: SCM Channel Model
• Spatial channel model (SCM) for a MIMO channel in 3GPP is
one of the ray-based channel models
• Channel with the given PAS can be modeled by allocating the
angle and power to each subray in accordance with the PAS.
• Two different methods have been considered:
▫ uniform power subray method
▫ discrete Laplacian method

23. MIMO: SCM Channel Model
• Uniform power subray method allocates the same power
to each subray while arranging the subray angles in a
non-uniform manner
• Given M subrays, each of their angles is determined such
that the area of each section subject to each subray is
equally divided under PAS
• Equal power allocation (EPA) simplifies the modeling
process
• Propagation environments defined in SCM:
▫ Suburban macro
▫ Urban macro
▫ Urban micro

24. MIMO: SCM Channel Model
• Some of the advantages:
▫ Directly models the statistical characteristics of
MIMO channel
▫ Maintains the statistical characteristics in the
time, space, and frequency domains
▫ Simple
▫ Flexibility - various types of PDP and PAS
▫ Supports both LOS and NLOS channels
▫ Effective rank of H depending on the number of
sub-rays in each path, M

25. MIMO: SCM Channel Model
1
0.9
Parameters Urban Micro 0.8
Environment Outdoor urban NLOS 0.7
Normalised power
0.6
Bandwidth 5 MHz
0.5
Excess Delay Spread 923 ns 0.4
0.3
Mean Delay Spread 251 ns
0.2
Carrier Frequency 2 GHz 0.1
200 300 400 500 600 700 800 900 1000
Excess delay (ns)

26. Share of (limited) experience
• Nobody is a great teacher
• Learn from mistakes
• Learn from examples:
• http://www.mathworks.com/matl
abcentral/fileexchange/
• Sharing is caring:
• http://www.edaboard.com/
• Patience is a virtue!

27. THANK YOU &
GOOD LUCK!