9. parameters of mobile multipath channels

1. WIRELESS COMMUNICATION
SERIES
Parameters of Mobile
Multipath Channels

2. Lecture Videos are available for this slides
at
www.youtube.com/gurukula
Support by Subscribing to my
Channel

3. Definition of Small Scale Fading
Causes of Small Scale Fading
Effects of Small Scale Fading
Factors Influencing the Small Scale Fading
Multipath Propagation
Speed of the Mobile  Gives Raise to Doppler Shifts
Speed of Surrounding
Transmission Bandwidth of the signal

4. Many Multipath channel parameters are derived from the Power
Delay Profile (PDP) Because PDP 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.
PDP of multipath channel is Mathematically expressed as:
Power delay profiles are measured using the Following Techniques
1. Time Dispersion Parameters
2. Coherence Bandwidth
3. Doppler Spread and Coherence Time
Power Delay Profile are 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 .
SIG. FROM
NEARBY
REFLECTORS
SIG. FROM
INTERMEDIATE
REFLECTORS
SIG. FROM
DISTANT
REFLECTORS

5. In order to compare different multipath channels and to develop some general design guidelines for wireless systems,
parameters which grossly quantifies the multipath channel are used.
 Mean Excess Delay (߬):
This is the first moment of Power Delay Profile.
This is calculated by
𝜏 =
𝑘 𝑎 𝑘
2
𝜏 𝑘
𝑘 𝑎 𝑘
2 =
𝑘 𝑝 𝜏 𝑘 𝜏 𝑘
𝑘 𝑝(𝜏 𝑘)
 RMS Delay Spread (𝝈 𝝉):
RMS delay spread is the square root of second
central moment of the power delay profile.
𝜎𝜏 = 𝜏2 − 𝜏2 ; Where 𝜏2 = 𝑘 𝑎 𝑘
2
𝜏 𝑘
2
𝑘 𝑎 𝑘
2 = 𝑘 𝑝 𝜏 𝑘 𝜏 𝑘
2
𝑘 𝑝(𝜏 𝑘)
 Maximum Excess Delay (X in dB):
It is defined as the time delay during which
multipath energy falls to X dB below the Maximum.
𝑋 = 𝜏 𝑥 − 𝜏 𝑜
Where,
𝜏 𝑜= First Arriving Signal
𝜏 𝑥= Maximum delay at which the MPC is
within X dB.

6. It is also important to note that…
1. These delays are measured relative to the first detectable signal arriving at the receiver.
2. The values obtained through the equations do not rely on absolute power level but depends on the multipath
components
3. Typical values of RMS delay spread are on the order of microseconds in outdoor mobile radio channels and on the
order of Nano seconds in indoor radio channels
4. RMS delay spread and mean excess delay are measured for the single power delay profile which is a spatial
average of consecutive impulse response measurements collected and averages over a local area
5. The maximum excess delay defines the temporal extent of the multipath that is above a particular threshold. This value
is sometimes called as excess delay spread of power delay profile.
6. In practice, the values of , ߬,𝝉 𝟐, and 𝝈 𝝉 depends on the choice of noise threshold used to process absolute power
7. The power delay profile and the magnitude frequency response of the channel are related through the Fourier
transform, this enables the analysis of channel in frequency domain also.
8. Coherence bandwidth is used to characterise the channel in frequency domain.
9. Coherence Bandwidth and RMS Delay Spread are inversely proportional to each other.

7. From the power delay profile by applying the Fourier transform, it is possible to obtain the spectrum of the multipath
channel. The frequency response of the channel is shown in the figure.
COHERENCE
BANDWIDTH
(Bc)
Coherence Bandwidth is the
statistical measure of the range of
frequencies over which the channel
can be considered “FLAT”
Meaning: The channel which passes all
spectral components with
approximately equal gain and linear
phase
SIGNAL
BANDWIDTH
(BS)
Case 1: (Bs<Bc)
No attenuation in the Signal.
Called as FLAT Fading Scenario
Case 1: (Bs>Bc)
More Attenuation in the Signal.
Called as Frequency Selective Fading
If the coherence bandwidth is
defined as the bandwidth over
which the frequency correlation
function is above 0.9, and 0.5 then
the coherence bandwidth is
approximately given by
(Respectively )
COHERENCE
BANDWIDTH
(Bc)
SIGNAL
BANDWIDTH
(BS)

8. Doppler Spread (Bd):
 This is the measure of spectral broadening caused by the time rate of change of the mobile radio channel and it is
defined as the range of frequencies over which the received Doppler spectrum is essentially non zero.
 The Doppler spectrum for a sinusoidal signal will have the components (Fc -Fd) to (Fc +Fd). Where Fd is the Doppler
shift.
 This Doppler shift is the function of relative velocity of the mobile, Angle between the direction of motion of mobile
and direction of arrival of scattered waves.
Bs >Bd  Then the Doppler spread are negligible and considered as Slow Fading
Why Doppler Spread?
 Delay Spread and Coherence bandwidth are the parameters which describes the time dispersive nature of the
channel in a local area.
 However they do not offer information about the time varying nature of the channel caused by either relative
motion between the mobile and base station or by the movement of objects in the channel
 Doppler Spread and Coherence Time describes the time varying nature of the channel in a small scale region.

9. Coherence Time (Tc):
 Tc is used to characterise the time varying nature of the frequency depressiveness in the channel in time domain.
 The Doppler spread and Tc are inversely proportional.
Tc ≅ 1/fm (Fluctuations are wider)
 This is a statistical measure of time duration over which the channel impulse response is essentially invariant and
quantifies the similarity of the channel response at different times.
 When the Coherence time is Lesser than the Signal Bandwidth then the channel varies rapidly leading to Fast
Fading Scenario.
Tc ≅ 9/ 16 π fm (Fluctuations are restricted)
 When the Time Correlation Function is above 0.5
Tc ≅ 0.423 / fm (Geometric mean of above 2 eqns.)