The wireless channel
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The Wireless Channel. Lecture 3. Area 1. Area 2. Short- term fading. Log-normal shadowing. Transmitter. Large and Small Scale Propagation Models. Wireless Mulipath Channel. Channel varies at two spatial scales: large scale fading small scale fading. Large-scale fading.

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The Wireless Channel

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The wireless channel

The Wireless Channel

Lecture 3


Large and small scale propagation models

Area 1

Area 2

Short-term

fading

Log-normal

shadowing

Transmitter

Large and Small Scale Propagation Models


Wireless mulipath channel

Wireless Mulipath Channel

Channel varies at two spatial scales:

large scale fading

small scale fading


Large scale fading

Large-scale fading

  • In free space, received power attenuates like 1/r2.

  • With reflections and obstructions, can attenuate even more rapidly with distance. Detailed modelling complicated.

  • Time constants associated with variations are very long as the mobile moves, many seconds or minutes.

  • More important for cell site planning, less for communication system design.


Small scale multipath fading

Small-scale multipath fading

  • Wireless communication typically happens at very high carrier frequency. (eg. fc = 900 MHz or 1.9 GHz for cellular)

  • Multipath fading due to constructive and destructive interference of the transmitted waves.

  • Channel varies when mobile moves a distance of the order of the carrier wavelength. This is 0.3 m for Ghz cellular.

  • For vehicular speeds, this translates to channel variation of the order of 100 Hz.


The wireless channel

Plan

  • We wish to understand how physical parameters such as carrier frequency, mobile speed, bandwidth, delay spread impact how a wireless channel behaves from the communication system point of view.

  • We start with deterministic physical model and progress towards statistical models, which are more useful for design and performance evaluation.


Physical models

Physical Models

  • Wireless channels can be modeled as linear time-varying systems:

    where ai(t) and i(t) are the gain and delay of path i.

  • The time-varying impulse response is:

  • Consider first the special case when the channel is time-invariant:


Impulse r response c characterization

Time variations property

t2

t(t2)

t1

t(t1)

Time spreading property

t0

t(t0)

Impulse Rresponse Ccharacterization

  • Impulse response: Time-spreading : multipath

  • and time-variations: time-varying environment


Passband to baseband conversion

Passband to Baseband Conversion

  • Communication takes place at [fc-W/2, fc+ W/2].

  • Processing takes place at baseband [-W/2,W/2].


Baseband equivalent channel

Baseband Equivalent Channel

  • The frequency response of the system

  • Each path is associated with a delay and a complex gain.


Sampling

Sampling


Multipath propagation

Multipath propagation

Signal can take many different paths between sender and receiver

due to reflection, scattering, diffraction

  • Time dispersion: signal is dispersed over time

  • interference with “neighbor” symbols Inter Symbol Interference (ISI)

  • The signal reaches a receiver directly and phase shifted

  • distorted signal depending on the phases of the different parts


The effects of multipath propagation

The Effects of Multipath Propagation

• Due to the different paths taken by the multipath components, they may arrive at different times

• If the symbol period TS is smaller than the delay spread, i.e. TS< Tm, Inter-Symbol Interference (ISI) will occur

• The receiver cannot determine which symbol each multipath component belongs to:


The effects of multipath propagation1

The Effects of Multipath Propagation


Delay spread

Delay Spread

The Delay Spread Tm is defined as the difference between times-of arrival

of the first and last multipath components Typical values are as follows:


Doppler shift

(Doppler shift)


Fading

Fading


Coherence bandwidth

Coherence Bandwidth

  • The Coherence Bandwidth Bcis a statistical measure of the range of frequencies over which the attenuation of the channel is approximately constant

  • Two frequency components f1 and f2 will experience similar attenuation if (f1 – f2) << Bc

  • Coherence Bandwidth is approximately related to the Delay Spread by:

  • Bc(Hz) = 1/Tm

  • e.g. in a particular factory environment,

  • Tm= 120ns, Bc= 1/(120 x 10-9) = 8.33 MHz


Coherence bandwidth 2

Coherence Bandwidth (2)

  • If the transmitted signal has a bandwidth (Bu) much smaller than the Coherence Bandwidth(Bc), i.e. Bu<< Bc, all frequency components will be attenuated similarly.

  • This is called Flat Fading

  • Else, it will undergo Frequency-selective fading, with different components attenuated differently. This causes distortion of the signal


Channel classification

Channel Classification

Based on Time-Spreading

  • Flat Fading

  • BS < BCTm < Ts

  • Rayleigh, Ricean distrib.

  • Spectral chara. of transmitted

  • signal preserved

  • Frequency Selective

  • BS > BC Tm > Ts

  • Intersymbol Interference

  • Spectral chara. of transmitted

    • signal not preserved

  • Multipath components resolved

Channel

Channel

Signal

Signal

BC

BS

freq.

freq.

BS

BC


Channel classification1

Channel Classification

Based on Time-Variations

  • Fast Fading

  • High Doppler Spread

  • 1/Bd@ TC < Ts

  • Slow Fading

  • Low Doppler Spread

  • 1/Bd@ TC> Ts

Signal

Signal

Doppler

Doppler

BD

BS

freq.

freq.

BS

BD


Flat and frequency selective fading channels

Flat and frequency selective fading Channels


Classification of fading channel

Classification of fading Channel


Statistical multipath model

Statistical Multipath Model


The multipath model

The Multipath Model


The tapped delay line model

The tapped delay line model


Time varying impulse response

Time Varying Impulse Response


Linear time varying system

Linear Time Varying System


Received signal characteristics

Received Signal Characteristics


Multipath resolvability

Multipath resolvability


The tapped delay line model revised

The tapped delay line model revised


Narrowband model

Narrowband Model


Statistical models

Statistical Models


Statistical models1

Statistical Models

  • Design and performance analysis based on statistical ensemble of channels rather than specific physical channel.

  • Recall that:


Additive gaussian noise

Additive Gaussian Noise

  • The discrete-time baseband-equivalent model


Rayleigh model

Rayleigh Model

  • Rayleigh flat fading model: many small scattered paths

    Complex circular symmetric Gaussian .

  • Rayleigh PDF:


Typical rayleigh fading envelope @ 900 mhz

Typical Rayleigh fading envelope @ 900 MHz


Rician model

Rician Model

  • Used when LOS or other dominant non fading path exist.

  • Characterized by Rician factor K that compare signal power of the non-fading path to variance of multipath.


Rician rayleigh

Rician Rayleigh


Distributions for rayleigh and rician fading channels

Distributions for Rayleigh and Rician fading channels


Nakagami model

Nakagami model

  • More practical model

Rayleigh fading

Rician fading

No fading, Constant power


More about narrow band channel

More about Narrow band Channel


Wide band channel

Wide band Channel


Inter symbol interference isi

Inter-symbol Interference (ISI)

  • Time domain: dispersion (delay spread Tm)

  • Frequency domain: non-flat response in the band of interest

  • One-tap filter: flat frequency response

  • Multi-tap filter: frequency selective response

  • When symbol time T >> Tm, no ISI (narrowband or low rate)

  • For higher rate, T comparable to Tm , we need to deal with ISI

  • Equalization, OFDM, CDMA with RAKE


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