Lecture Lecture 2. Frequencies for communication

Propagation CharacteristicsLecture 2

Frequencies for communication

Frequencies and regulations

Signal propagationPropagation in free space always like light (straight line)Receiving power proportional to 1/d² (d = distance

between sender and receiver)Receiving power additionally influenced byFading (frequency dependent)ShadowingReflection at large obstaclesRefraction depending on the density of a mediumScattering at small obstaclesDiffraction at edges

Signal propagation

Real world example

Free space loss, ideal isotropic antenna

Pt = signal power at transmitting antennaPr = signal power at receiving antennaλ = carrier wavelengthd = propagation distance between antennasc = speed of light (3x108 m/s)where d and λ are in the same units (e.g., meters)

Free Space LossFree space loss equation can be rewritten:

Free Space LossFree space loss accounting for gain of other antennas

Gt = gain of transmitting antennaGr = gain of receiving antennaAt = effective area of transmitting antennaAr = effective area of receiving antenna

Isotropic ant : Gt=1, Gr=1

Free Space LossFree space loss accounting for gain of other

antennas can be recast as

Propagation modelPath loss: function of distance between TX and RX

d0 : close-in distance, received power reference point, commonly 1Km usedd :T-R separation: distancen: path loss exponentLog-normal shadowing: amplitude has a log-normal PDF

Addition of random variable

Xσ : zero-mean Gaussian distributed random variable (in dB) with standard deviation σ

Path loss model parameter

Path loss model parameter

Two values arecomputed frommeasured data,using linearregression method

Empirical ModelsOkumura model

Empirically based (site/freq specific)Awkward (uses graphs)

Hata modelAnalytical approximation to Okumura model

Cost 231 Model: Extends Hata model to higher frequency (2

GHz)

Walfish/Bertoni:Cost 231 extension to include diffraction from

rooftopsCommonly used in cellular system simulations

(Okumura) model

Hata modeldhhahfdBL trtcp log)log55.69.44()(log82.13log16.2655.69][

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Propagation CharacteristicsPath Loss (includes average shadowing)Shadowing (due to obstructions): reflection, refraction, diffractionMultipath Fading

Pr/Pt

d=vt

PrPt

d=vt

v Very slow

SlowFast

Channel characteristicsChannel characteristics change over time and locationsignal paths changedifferent delay variations of different signal partsdifferent phases of signal partsquick changes in the power received (short term fading)

Additional changes indistance to senderobstacles further awayslow changes in the average powerslow changes in the average term fading received (long term fading)

Combined Path Loss & Fading

Path Loss ModelingMaxwell’s equations

Complex and impracticalFree space path loss model

Too simpleRay tracing models

Requires site-specific informationSimplified power falloff models

Main characteristics: good for high-level analysis

Empirical ModelsDon’t always generalize to other environments

Small Scale fadingVariations due to shadowing occur over relatively

large distances– often many meters

Signals in multipath environments also undergo small scale fading – variations that occur over the wavelength of the signal

This is due to the different multipath components combining either constructively or destructively

Small-scale fading (2)Offset of only a fraction of a wavelength can lead to large change in signal level:

Multipath propagationSignal can take many different paths between sender and receiverdue to reflection, scattering, diffraction

Time dispersion: signal is dispersed over timeinterference with “neighbor” symbols Inter Symbol Interference (ISI)

The signal reaches a receiver directly and phase shifteddistorted signal depending on the phases of the different parts

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 Propagation

Delay SpreadThe Delay Spread Tm is defined as the difference between times-of arrivalof the first and last multipath components Typical values are as follows:

(Doppler shift)

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change Phase

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Fading

Coherence Bandwidth The Coherence Bandwidth Bc is 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)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