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Propagation Mechanisms

●Communication is possible even when there is no line of sight between sender and receiver due to reflection, scattering, and diffraction.



Reflection

●Reflection occurs when an electromagnetic wave impinges upon an object which has dimensions greater than the wavelength of the wave.
●Reflection occurs from the surface of the earth, buildings and walls.
●180 degree phase shift occurs after reflection.
●When a radio wave propagating in one medium impinges upon another medium having different electrical properties, the wave is partially reflected and partially transmitted.
●The electric field intensity of the reflected and transmitted waves may be related to the incident wave through the Fresnel reflection coefficient.
●Fresnel reflection coefficient depends on the material which is reflecting the wave.
●Electromagnetic energy cannot pass through a perfect conductor. A plane wave incident on a conductor has all of its energy reflected back.

Diffraction

●Diffraction occurs when an electromagnetic wave is obstructed by a surface that has sharp edges.
●Diffraction occurs when a wave passes through a narrow slit.
●Diffraction phenomena can be explained by huygens’ principle which states that all points on a wave front can be considered as point sources for the production of secondary wavelets.
●At high frequency, diffraction depends on the geometry of objects as well as amplitude, phase, polarisation of the incident wave.

Scattering

●Scattering occurs when the medium through which the wave travels consists of objects with dimensions that are small compared to the wavelength of the wave.
●It causes the transmitter energy to be radiated in many directions.
●High frequency waves are scattered more.
●Scattered waves are produced by rough surfaces, small objects or by other irregularities in the channel.
●E.g. foliage, street signs, lamp posts, etc.



Friis Free Space Propagation Model



●It is also called the path loss model.
●The free space propagation model is used to predict received signal strength when the transmitter and receiver have a clear, line-of-sight ( LOS ) path between them i.e. no obstacles between them.
●Eg: satellite communication systems, microwave radio link.


Free Space Loss 

●Consider a sphere of radius d.
●If the Tx antenna radiates isotropically, the power density is Pt / 4πd2 
●Then the received power is Pr(d) = Pt / 4πd2 * Ae where Ae is the effective area of the Rx antenna and is given by Gr λ2 / 4π.
●If the Tx antenna is not isotropic then Pr(d) = Pt Gt Gr λ2 / ( 4πd )2 the received power as a function of distance d in free space is known as Friss law.
●Free space loss factor = ( 4πd / λ )2 = ( 4πd f / c )2 i.e. attenuation in free space increases with frequency.


Free Space Model

●The power received by a receiver antenna which is separated from a radiating transmitter antenna by a distance d is given by Friss free space equation



Pr( d ) = Received Power
Pt = Transmitted Power
Gr = Receiving Antenna Gain
Gt = Transmitting Antenna Gain
d = distance between transmitting and receiving antenna
L = System Loss Factor ( L >= 1 ) caused due to filter loss, antenna loss

●Gain of antenna is related to effective aperture Ae and is given by 



●The effective aperture Ae is related to the physical size of an antenna.

●An isotropic radiator is an ideal antenna which radiates power with unit gain uniformly in all directions, and is used to reference antenna gains in wireless systems. The effective isotropic radiated power ( EIRP ) is defined as EIRP = PtGt


Path Loss

●Path loss is the difference between the effective transmitted power and the received power. 
●It represents the signal attenuation and is measured in dB.
●The path loss for the free space model is given by



●If antenna gains are excluded, path loss is given by






Fraunhofer Distance ( df )

●The friis free space model is only valid for values of d which are in the far field of the transmitting antenna. 
●The far-field of a transmitting antenna is defined as the region beyond far field distance df, which is given by


		D is the largest physical linear dimension of the antenna

	Additionally to be in the far field region df must satisfy df >> D and df >> 𝛌 

  d0 ≥ df
	Where d0 is the reference distance




Ground Reflection ( 2-Ray ) Model

●Free space propagation model is inaccurate when used alone. In line-of-sight scenarios the reflection from the ground is also important. The Two-Ray model assumes both Line-of-sight and reflected signal from the ground for calculating the path loss.



ht = Height of Transmitting Antenna
hr = Height of Receiver Antenna
ELOS = E Field of LOS Signal
Eg = E Field of Reflected Signal
d = Tx-Rx Separation

Assumptions
●Tx-Rx separation distance is in kilometres.
●Earth is assumed to be flat.
●Height of the antennas are larger than the wavelength of the propagating wave. i.e. ht . hr >> 𝜆
●Height of the antennas are lesser than the Tx-Rx separation. ht . hr << d


Parameters to be Estimated
●E-Field of Both Rays ELOS & Eg
●Path Difference ( 𝝙 )
●Phase Difference ( 𝜽𝚫 )
●Time Delay ( 𝜏d )









Indoor Propagation Model

●Indoor propagation models are used to understand the path loss because of the internal structures of the building.
●The indoor radio channel differs from the outdoor radio channel in two aspects- 
○The tx-rx distance is very less.
○The variability of the environment is greater due to partitions.

Partition Losses ( same floor )

●Buildings have partitions and obstacles which form the internal and external structure.
●Eg: Windows, concrete walls, wooden frames, etc.
●Partitions that are part of the buildings are called hard partitions. They are immovable.
●Partitions which are not rising up to the ceiling and are movable are called soft partitions.

Material Type	Loss ( dB )
All Metals	26
Concrete Block Wall	13

Partition Loss between floor

●The losses between the floors of a building are determined by materials of the buildings, type of floors and the external surroundings.
●FAF = Floor Attenuation Factor

Log Distance Path Loss Model

●It is given by equation-



n = path loss exponent
d0 = reference distance 
d = Tx-Rx separation
X𝜎 = zero-mean gaussian distributed random variable with standard deviation 𝜎



Attenuation Factor Model

●When we use the Attenuation factor model, path loss comes down to a very low value. 
●It reduces the standard deviation between measured and predicted path loss to around 4 dB, as compared to 13 dB in case of a log-distance model.
●It is given by equation-


		
		nSF = path loss exponent value for same floor
FAF = Floor attenuation factor
PAF = Partition attenuation factor

●FAF can be replaced by an exponent which already considers the effects of multiple floor separation.



nMF = path loss exponent value for multiple floors




Outdoor Propagation Model

●Radio transmission often takes place over irregular terrains. The terrain profile of a particular area needs to be taken into account for estimating the path loss.
●The terrain profile may vary from a simple curved earth profile to a highly mountainous profile.
●The presence of trees, buildings and other obstacles also must be taken into account.


Okumura Model

●It is the widely used model for signal prediction in urban areas.
●This model is applicable for -
○Frequencies in the range 150 MHz to 1920 MHz 
○Distances of 1 km to 100 km
○Base station antenna heights ranging from 30 m to 1000 m


Okumura Path Loss Equation

L50 ( dB ) = LF + Amu ( f, d ) - G( ht ) - G( hr ) - GArea

L50 ( dB ) = median value of propagation path loss
LF = free space path loss
Amu = Attenuation with respect to free space 
G ( ht ) = Gain factor for base station antenna height 
G ( hr ) = Gain factor for receiver base station
GArea = Correction gain factor









Small Scale Fading

●Small scale fading is the rapid fluctuations in the amplitude when the distance between Tx and Rx is very small. It is caused by the interference between two or more versions of the transmitted signal which arrive at the receiver at slightly different times.

●In case of large scale fading, Tx-Rx separation is in the order of kilometres whereas here the separation will be in the terms of metres.

●Multipath propagation in wireless channels causes small scale fading effects. The time dispersion  caused by multipath propagation delays. There are multiple paths, some paths are shorter and other paths are longer hence the signal reaches at different durations of time. So there are various versions of the signal in time delays. 

●Fading may also occur because the height of the base station antenna is very much higher than the height of the mobile stations and height of mobile stations are less than the surrounding structures. Hence there is no line of sight path present between the mobile station and the base station. 

●Even when there is a Line of sight path present it is also possible that the wave may hit the ground and then get reflected. When the wave hits the ground there are various versions of the signal created because there are various points on the ground from where the wave gets reflected. As a result the incoming radio waves arrive from different directions with different time delays.


Factors Influencing Small Scale Fading

Multipath Propagation

●In multipath propagation, the signal reaches the receiver from multiple paths as a result receiver receives various versions of the same signal and finally we combine all the versions together to form the actual signal.

Speed of Mobile

●The relative motion between the base station and the mobile station results in random frequency modulation due to different doppler shifts on each of the multipath components. Doppler shift will be positive or negative depending on whether the mobile receiver is moving toward or away from the base station.

Speed of surrounding objects

●If the objects in the radio channel are in motion, they induce a time varying doppler shift on multipath components. If the surrounding objects move at greater rate than the mobile, then this effect dominates small scale fading.

Transmission bandwidth of signal

●If the transmitted signal bandwidth is greater than the bandwidth of the channel, the received signal will be distorted. 



Doppler Shift



●Car is moving from point X to point Y at a constant velocity v.
●Distance between point X and point Y is d.
●Source S is constantly transmitting the information to the mobile phone in the car.
●Difference in the path length when the mobile phone is at X and Y is Δl.

Δl = d cos 𝛉 = v Δt cos 𝛉

●The phase change in the received signal due to the difference in the path length is therefore



●Hence, the apparent change in frequency, or doppler shift is given by fd



●If the mobile is moving towards the direction of arrival of the wave, the doppler shift is positive. 
●If the mobile is moving away from the direction of arrival of the wave, the doppler shift is negative.



Parameters of Mobile Multipath Channels

●Many multipath channel parameters are derived from the Power Delay Profile ( PDP ) because it gives the intensity of a signal received through a multipath channel as a function of time delay.
●The time delay is the difference in travel time between multipath arrivals.

Power Delay Profile is generally represented as the Plots of Relative received power as a function of Excess delay with respect to fixed time delay reference.

A typical power delay profile of Outdoor and Indoor channels are depicted in the Figure.



Time Dispersion Parameters

●The transmitted signal arrives at the mobile station from different paths. Since each path has a different path length, the time of arrival for each path is different. This effect spreads out the signal in the time domain. This is called delay spread.



●Mean Excess Delay = This is the first moment of power delay profile.
●RMS Delay Spread = This is the square root of the second central moment of the power delay profile.
●Maximum Excess Delay = It is defined as the time delay during which multipath energy falls to X dB below maximum.



Coherence Bandwidth ( Bc )

●It is the range of frequencies over which the channel can be considered flat i.e. all the frequency components within this bandwidth have approximately the same gain and linear phase.

●Two signals with frequency separation greater than Bc are affected differently by the channel.

●Coherence bandwidth is a range of frequencies over which two frequency components have a strong potential for amplitude correlation.

●If the frequency correlation function is above 0.9, then the coherence bandwidth is approximately 



●If the frequency correlation function is above 0.5, then the coherence bandwidth is approximately



●The exact relationship between coherence bandwidth and rms delay spread does not exist.



Doppler Spread ( BD )

●It is a measure of spectral broadening caused by the time rate of change of the mobile radio channel.

●It is defined as the range of frequencies over which the received doppler spectrum is non zero.

●If we are transmitting a signal of frequency fc the received signal spectrum is called doppler spectrum which have frequencies in the range from (fc - fd) to (fc + fd) where fd is the Doppler Shift.

●The amount of spectral broadening depends on Doppler Shift ( fd ) which depends on
○Relative velocity of mobile phone
○Angle between direction of motion of mobile and direction of arrival of scattered wave




Coherence Time ( Tc )

●Doppler spread and coherence time are inversely proportional to one another.

Tc ∝ 1 / fm

●It is the time duration over which the channel impulse response is invariant. 

●It is the time duration over which two received signals have a strong potential for amplitude correlation.

●Two signals arriving with a time separation greater Tc are affected differently by the channel. 

●If the coherence time is defined as the time over which the time correlation function is above 0.5, then the coherence time is approximately

Tc = 9 / 16 fm

	fm is maximum doppler shift given by v / 𝛌

●In modern digital communication, coherence time is defined as the geometric means of the above two equations.
	
Tc = 0.423 / fm




Fading

●Fading refers to the variations in signal strength caused by constructive or destructive interference of multipath signals. 
●It affects the performance of wireless communication systems.


Large Scale Fading

●Variations occur over large distance i.e. several 100s or 1000 metres
●Path Loss and Shadowing
●It is caused by the mobile unit moving into the shadow of surrounding objects.
●It affects the entire signal.
●Reduces overall received signal power.
●It can be mitigated by - power control, antenna placement, diversity methods.


Small Scale Fading

●Signal variation occurs over a few distance ( cms to metres )
●Multipath and Doppler Spread
●It is caused by the multipath propagation.
●It affects the individual symbols.
●It causes interference and distortion.
●It can be mitigated by - equalisation, diversity, adaptive mechanisms.



Types of Small Scale Fading








Rayleigh Distribution

●Rayleigh distribution is used to describe the time varying nature of the received envelope of a flat fading signal.

●The probability density function ( pdf ) of Rayleigh distribution is given by



●The cumulative distribution function ( CDF ) of Rayleigh distribution is given by 


●rmean of rayleigh distribution is given by 




Rician Distribution

●When there is a dominant signal component present, such as a line-of-sight propagation path, the small-scale fading envelope distribution is Ricean. 

●Rician distribution degenerates down to a Rayleigh distribution when the dominant component fades away.

●The probability density function ( pdf ) of Rician distribution is given by



A = Peak amplitude of dominant signal
	I0 = Bessel function of the first kind and zero-order

●The Rician distribution is often described in terms of a parameter K ( Rician Factor ) .



●As A→ 0, K → -∞ , the Rician distribution degenerates to a Rayleigh distribution.