Introduction Channel Models
Transcript of Introduction Channel Models
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Channel Models
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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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Slow (S) and fast fading (a) inCellular channel
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Propagation mechanisms
CA
D
BReceiverTransmitter
A: free spaceB: reflectionC: diffractionD: scattering
A: free spaceB: reflectionC: diffractionD: scattering
reflection: object is large compared to wavelength
scattering: object is small or its surface irregular
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Radio channel modelling
Narrowband Models• Because the signal
bandwidth is narrow, the fading mechanism will affect all frequencies in the signal passbandequally.
• 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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Comparison
Narrowband modelling Narrowband modelling Wideband modelling Wideband modelling
Deterministic models(e.g. ray tracing,
playback modelling)
Deterministic models(e.g. ray tracing,
playback modelling)
Stochastical modelsStochastical models
Calculation of path loss e.g. taking into account
- free space loss- reflections- diffraction- scattering
Calculation of path loss e.g. taking into account
- free space loss- reflections- diffraction- scattering
Basic problem: signal fading
Basic problem: signal dispersion
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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 interferenceTx
Rx
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Low-pass equivalent (LPE) signal
Real-valued RF signalReal-valued RF signal Complex-valued LPE signalComplex-valued LPE signal
RF carrier frequencyRF carrier frequency
In-phase signal componentIn-phase signal component Quadrature componentQuadrature component
( ) ( ){ }2Re cj f ts t z t e π=
( ) ( ) ( ) ( ) ( )j tz t x t j y t c t e φ= + =
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Fading: illustration in complex plane
in-phase component
quadraturephase
component
Tx
Rx
Received signal in vector form:resultant (= summation result) of “propagation path vectors”
Wideband channel modelling: in addition to magnitudesand phases, also path delays are important.
path delays are not important
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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).
τ
LOS pathLOS path
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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
( )00 0
ja e s tφ τ−
( )11 1
ja e s tφ τ−
( )22 2
ja e s tφ τ−
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
Typical BER vs. S/N curves
S/N
BER
Frequency-selective channel(no equalization)
Flat fading channel
Gaussianchannel(no fading)
In a Gaussian channel (no fading) BER <=> Q(S/N)erfc(S/N)
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BER vs. S/N performance
Typical BER vs. S/N curves
S/N
BER
Frequency-selective channel(no equalization)
Flat fading channel
Gaussianchannel(no fading)
Flat fading: NB channel ( ) ( )BER BER S N z p z dz= ∫z = signal power level
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BER vs. S/N performance
Typical BER vs. S/N curves
S/N
BER
Frequency-selective channel(no equalization)
Flat fading channel
Gaussianchannel(no fading)
Frequency selective fading <=> irreducible BER floor
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Ray-Tracing Propagation Model
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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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• 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.
Generic Model, Continue
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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, ∆θn is a phase displacement due to the motion.
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• 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.
Doppler Shift
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Physical interpretation of Doppler shift
Vαarriving patharriving path
direction of receivermovement
direction of receivermovementRx
cos cosd
Vfν α α
λ= =
Maximum Doppler shiftMaximum Doppler shift
Angle of arrival of arrivingpath with respect to
direction of movement
Angle of arrival of arrivingpath with respect to
direction of movement
V = speed of receiverλ = RF wavelength
V = speed of receiverλ = RF wavelength
Doppler frequency shiftDoppler frequency 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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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, τ2 . . . τn arrival delay times, that define when the signal waves reach the receiver.
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Time-Variant Channels
time t
|h(t,τ) |delay τ
Channel is assumed linear!
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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 ModelsIEEE 802.16 (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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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
• Path loss for unobstructed LOS path• Power falls off :
– Proportional to d2
– Proportional to λ2 (inversely proportional to f2)
d=vt
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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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Simplified Path Loss Model
82,0 ≤≤⎥⎦⎤
⎢⎣⎡= γ
γ
ddKPP tr
• Used when path loss dominated by reflections.
• Most important parameter is the path loss exponent γ, determined empirically.
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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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Simplified indoor modelSIM
• 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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