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

The Wireless Channel

Lecture 3

Large and small scale propagation models

Area 1

Area 2






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

  • 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





Time spreading property



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.

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:

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:

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 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











Flat and frequency selective fading channels
Flat and frequency selective fading Channels

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:

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

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