# Connexions

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Module by: Ha Ta-Hong, Tuan Do-Hong. E-mail the authorsEdited By: Tuan Do-HongTranslated By: Tuan Do-Hong

There are three basic mechanisms that impact signal propagation in a mobile communication system:

1. Reflection occurs when a propagating electromagnetic wave impinges upon smooth surface with very large dimensions relative to the RF signal wavelength.
2. Diffraction occurs when the propagation path between the transmitter and receiver is obstructed by a dense body with dimensions that are large relative to the RF signal wavelength. Diffraction accounts for RF energy traveling from transmitter to receiver without line-of-sight path. It is often termed shadowing because the diffracted field can reach the receiver even when shadowed by an impenetrable obstruction.
3. Scattering occurs when a radio wave impinges on either a large, rough surface or any surface whose dimension are on the other of the RF signal wavelength or less, causing the energy to be spread out or reflected in all directions.

Figure 2 is a convenient pictorial showing the various contributions that must be considered when estimating path loss for link budget analysis in a mobile radio application: (1) mean path loss as a function of distance, due to large-scale fading, (2) near-worst-case variations about the mean path loss or large-scale fading margin (typically 6-10 dB), (3) near-worst-case Rayleigh or small-scale fading margin (typically 20-30 dB)

Using complex notation

s(t)=Reg(t).ej2πfcts(t)=Reg(t).ej2πfct size 12{s $$t$$ ="Re" left lbrace g $$t$$ "." e rSup { size 8{j2πf rSub { size 6{c} } t} } right rbrace } {}(1)

Where Re.Re. size 12{"Re" left lbrace "." right rbrace } {} denotes the real part of .. size 12{ left lbrace "." right rbrace } {}, and fcfc size 12{f rSub { size 8{c} } } {} is the carrier frequency. The baseband waveform g(t)g(t) size 12{g $$t$$ } {} is called the complex envelope of s(t)s(t) size 12{s $$t$$ } {} and can be expressed as

g(t)=g(t).e(t)=R(t).e(t)g(t)=g(t).e(t)=R(t).e(t) size 12{g $$t$$ = lline g $$t$$ rline "." e rSup { size 8{jφ $$t$$ } } =R $$t$$ "." e rSup { size 8{jφ $$t$$ } } } {}(2)

Where R(t)=g(t)R(t)=g(t) size 12{R $$t$$ = lline g $$t$$ rline } {} is the envelope magnitude, and φ(t)φ(t) size 12{φ $$t$$ } {} is its phase.

In fading environment, g(t) will be modified by a complex dimentionless multiplicative factor α(t).e(t)α(t).e(t) size 12{α $$t$$ "." e rSup { size 8{ - jθ $$t$$ } } } {}. The modified baseband waveform can be written as α(t).e(t).g(t)α(t).e(t).g(t) size 12{α $$t$$ "." e rSup { size 8{ - jθ $$t$$ } } "." g $$t$$ } {}. The magnitude of this envelope can be expressed as follow

α(t).R(t)=m(t).r0(t).R(t)α(t).R(t)=m(t).r0(t).R(t) size 12{α $$t$$ "." R $$t$$ =m $$t$$ "." r rSub { size 8{0} } $$t$$ "." R $$t$$ } {}(3)

Where m(t)m(t) size 12{m $$t$$ } {} and r0(t)r0(t) size 12{r rSub { size 8{0} } $$t$$ } {} are called the large-scale-fading component and the large-scale-fading component of the envelope respectively.

Sometimes, m(t)m(t) size 12{m $$t$$ } {} is referred to as the local mean or log-normal fading, and r0(t)r0(t) size 12{r rSub { size 8{0} } $$t$$ } {} is referred to as multipath or Rayleigh fading.

For the case of mobile radio, figure 3 illustrates the relationship between α(t).m(t)α(t).m(t) size 12{α $$t$$ "." m $$t$$ } {}. In figure 3a, the signal power received is a function of the multiplicative factor α(t)α(t) size 12{α $$t$$ } {}. Small-scale fading superimposed on large-scale fading can be readily identified. The typical antenna displacement between adjacent signal-strength nulls due to small-scale fading is approximately half of wavelength. In figure 3b, the large-scale fading or local mean m(t)m(t) size 12{m $$t$$ } {} has been removed in order to view the small-scale fading r0(t)r0(t) size 12{r rSub { size 8{0} } $$t$$ } {}. The log-normal fading is a relative slow varying function of position, while the Rayleigh fading is a relatively fast varying function of position.

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