1. Data Communication lecture10
Channel Models
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2. Data Communication lecture10
Introduction
Propagation models are fundamental tools for designing any broadband wireless communication system.
A propagation model basically predicts what will happen to the transmitted signal while in transit to the receiver
Traditionally, ‘propagation models’ is the term applied to those algorithms and methods used to predict the median signal level at the receiver.
Such models include signal level information, signal time dispersion information and, in the case of mobile systems, models of Doppler shift distortions arising from the motion of the mobile.
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Fading
Fluctuation in the strength of signal, because of variations in the transmission medium.
Fading is a broad term applied to a wide range of variation in the signal amplitude, phase, and frequency characteristic.
For example, the term ‘shadow fading‘ is used to describe the decrease in signal strength that is observed when a mobile terminal is behaind a building.
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4. Slow (S) and fast fading (a) in Cellular channel
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5. Propagation mechanisms
A: free space
B: reflection
C: diffraction
D: scattering
A: free space
B: reflection
C: diffraction
D: scattering
reflection: object is large compared to wavelength
scattering: object is small or its surface irregular
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6. Radio channel modelling
Narrowband Models
Because the signal bandwidth is narrow, the fading mechanism will affect all frequencies in the signal passband equally.
So, a narrowband channel is often referred to as a flat-fading channel.
Wideband Models
The bandwidth of the signal, sent through the channel is such that time dispersion information is required.
Time dispersion causes the signal fading to vary as a function of frequency, so wideband channels are often called frequency-selective fading channels.
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7. Comparison Narrowband modelling Wideband modelling
Calculation of path loss e.g. taking into account
- free space loss
- reflections
- diffraction
- scattering
Deterministic models
(e.g. ray tracing, playback modelling)
Stochastical models
Basic problem: signal fading
Basic problem: signal dispersion
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8. Signal fading in a narrowband channel
magnitude of complex-valued radio signal
distance
propagation paths
fade <=> signal replicas received via different propagation paths cause destructive interference Tx Rx
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9. Low-pass equivalent (LPE) signal
RF carrier frequency
Real-valued RF signal
Complex-valued LPE signal
In-phase signal component
Quadrature component
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10. Fading: illustration in complex plane
Received signal in vector form: resultant (= summation result) of “propagation path vectors”
quadrature phase component
path delays are not important Rx Tx
in-phase component
Wideband channel modelling: in addition to magnitudes and phases, also path delays are important.
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11. Generic Wideband Channel Model
Wideband generally indicates those channels in which time dispersion and frequency-selective fading have a significant impact on the signal being transmitted.
For signals whose occupied bandwidth is narrow compared to the correlation bandwidth of the channel, the generic wideband model simplifies to a narrowband model in which many elements of the wideband model may be discarded.
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If the channel is considered as a filter with some low-pass impulse response, then that impulse response would be given by:
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A sinewave signal at frequency ω leaving the transmitting antenna would arrive at the receiver reduced in amplitude by factor A, shifted in phase by θ, and delayed by τ seconds.
Such a model of the transmission channel is applicable for free-space propagation conditions in which signal energy arrives at the receiver directly (via one path) from the transmitter.
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If the channel consisted of two transmission paths for the transmitted energy to arrive at the receiver (for example, with the addition of a single ground reflection), the channel impulse response would be the sum of the effect of the two paths:
This is the impulse response of the so-called ‘two-ray’ channel model.
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For N possible transmission paths, h(t) becomes:
This is the channel impulse response to a particular point p2(x2, y2, z2) from a transmitter located at point p1(x1, y1, z1).
LOS path 
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16. Example: multipath signal
The received multipath signal is the sum of N attenuated, phase shifted and delayed replicas of the transmitted signal s(t) T : Tm
Normalized delay spread D = Tm / T
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Important Note:
The normalized delay spread is an important quantity.
When D << 1, the channel is
- narrowband
- frequency-nonselective
- flat
and there is no intersymbol interference (ISI).
When D approaches or exceeds unity, the channel is
- wideband
- frequency selective
- time dispersive
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BER vs. S/N performance
In a Gaussian channel (no fading) BER <=> Q(S/N)
erfc(S/N)
Typical BER vs. S/N curves
BER
Frequency-selective channel
(no equalization)
Gaussian
channel
(no fading)
Flat fading channel
S/N
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BER vs. S/N performance
Flat fading: NB channel
z = signal power level
Typical BER vs. S/N curves
BER
Frequency-selective channel
(no equalization)
Gaussian
channel
(no fading)
Flat fading channel
S/N
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BER vs. S/N performance
Frequency selective fading <=>
irreducible BER floor
Typical BER vs. S/N curves
BER
Frequency-selective channel
(no equalization)
Gaussian
channel
(no fading)
Flat fading channel
S/N
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21. Ray-Tracing Propagation Model
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22. Measured power delay profile.
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RMS Delay spread
A common measure of the amount of time dispersion in a channel is the RMS delay spread.
The RMS delay spread can be found from the power delay profile:
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24. Generic Model, Continue
The more general impulse response can thus be written as:
Here, the number, amplitude, phase, and time delay of the components of the summation are a function of the location of the transmit and receive antenna points in the propagation space.
This equation is for a single static point in space.
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For mobile communication, the receiver is often moving.
That motion can affect the phase relationship of the components of this equation, in a way that may be important to data symbols being transmitted.
This motion will result in a frequency or Doppler shift of the received signal, which will be a function of speed and direction of motion, and the angle of arrival (AOA) of the signal energy.
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Modification to include the Doppler shift:
Here, Δθn is a phase displacement due to the motion.
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Doppler Shift
For a mobile receiver:
φn is the arrival angle of the nth component, v is the speed of motion, φv is the direction of motion, and λ is the wavelength.
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28. Physical interpretation of Doppler shiftV
arriving path 
direction of receiver movement Rx
Doppler frequency shift
V = speed of receiver
l = RF wavelength
Angle of arrival of arriving path with respect to direction of movement
Maximum Doppler shift
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In general, the amplitudes An and phase shifts θn, will be functions of the carrier frequency ω, thus:
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30. Time-Variant Channels
To deal with a time-variant channel, we define the input delay-spread function h(t, τ ).
This is the low-pass response of the channel at some time t to a unit impulse function input at some previous time τ seconds earlier.
Note that this delay τ is different from the discrete τ1, τ τn arrival delay times, that define when the signal waves reach the receiver.
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31. Time-Variant Channels
Channel is assumed linear!
 h(t,) 
delay 
time t
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32. Time-Variant Channels
The output of the channel y(t) can then be found by the convolution of the input signal um(t) with h(t, τ ) integrated over the delay variable τ:
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Some Notes
Using an impulse response from a ray-tracing propagation model, and convolving it with a raised cosine symbol pulse, the result is a time signature of the channel.
The variations in signatures are due to the relative phase changes, and not changing amplitudes.
By taking the Fourier Transform of the time signatures, it is possible to created spectrum signatures.
The nonuniform frequency response, represents the frequency-selective nature of the channel.
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Path Loss Modeling
Maxwell’s equations
Complex and impractical
Physical Models
Free space path loss model
Too simple
Ray tracing models
Requires site-specific information
Empirical Models
Don’t always generalize to other environments
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Empirical Models
Commonly used in cellular system simulations
Are based on observations or measurements.
measurements are typically done in the field to measure path loss, delay spread, or other channel characteristics.
Site and field dependent
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Empirical Models
IEEE (SUI) model
where d is the distance in meters, d0 = 100 meters,
hb is the base station height above ground (10m < hb < 80 m)
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41. Some Other Empirical Models
Okumura model
Empirically based (site/freq specific)
Hata model
Analytical approximation to Okumura model
Cost 136 Model:
Extends Hata model to higher frequency (2 GHz)
Walfish/Bertoni:
Cost 136 extension to include diffraction from rooftops
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Physical Models
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Free Space (LOS) Model
d=vt
Path loss for unobstructed LOS path
Power falls off :
Proportional to d2
Proportional to l2 (inversely proportional to f2)
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Two Path Model
Path loss for one LOS path and 1 ground (or reflected) bounce
Ground bounce approximately cancels LOS path above critical distance
Power falls off
Proportional to d2 (small d)
Proportional to d4 (d>dc)
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45. Simplified Path Loss Model
Used when path loss dominated by reflections.
Most important parameter is the path loss exponent g, determined empirically.
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46. Ray Tracing Approximation
Represent wavefronts as simple particles
Geometry determines received signal from each signal component
Typically includes reflected rays, can also include scattered and defracted rays.
Requires site parameters
Geometry
Dielectric properties
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General Ray Tracing
Models all signal components
Reflections
Scattering
Diffraction
Requires detailed geometry and dielectric properties of site
Similar to Maxwell, but easier math.
Computer packages often used
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51. Simplified indoor model SIM
An effort to provide a fast and simple model that predicts indoor signal levels.
Worksin the area of 2.4 GHz Wi-Fi or 5.7 GHz U-NII band systems, intended to work over short ranges, especially indoors through walls and floors.
SIM makes use of four basic propagation primitives: line-of-sight rays, wall transmission loss, corner diffraction, and attenuation due to partial Fresnel zone obstruction
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