1. Fading channel

3. OUTLINES 2.2-small scale fading Case 1 Case 2 Case 3
1-multipath fading definition.
2-types of fading.
2.1-large scale fading
2.2-small scale fading
Time-spreading of underlying digital pulses within the signal.
1.Signal Time –spreading viewed In time –delay domain.
2.Signal Time –spreading viewed in the frequency domain.
Time variance of the channel caused by motion.
1.time variance viewed in the time domain.
2.Time variance viewed in the Doppler-shift domain.
3-Mitigation the degradation effects of fading
Case 1
Case 2
Case 3

4. 1-multipath fading definition
In wireless mobile communication system a signal can travel from transmitter to receiver over multiple reflective paths
This phenomena referred to as multipath propagation which can cause fluctuations in the received signal’s amplitude, phase and angle of arrival
Also the signal suffers from reflection, scattering, ISI (intersymbol interference) and weather
condition

5. Multipath Propagation

6. 2-Types of fading

7. 2-1-Large Scale Fading
Introduction
Path loss is caused by dissipation of the power radiated by the transmitter
Shadowing is caused by obstacles between the transmitter and receiver that absorb power.
Since variations due to path loss and shadowing occur over relatively large distances this variation is referred to as large-scale propagation effects.

8. Path loss
linear path loss of the channel is the ratio of transmit power to receive power:
path loss of the channel as the difference in dB between the transmitted and received signal power:

9. 1- Free-Space Path Loss
Consider a signal transmitted through free space to a receiver. there are no obstructions between the transmitter and receiver. the channel is called a line-of-sight (LOS)
The ratio of received to transmitted power is
Pt Transmitted power
Pr Received power
Gl = Gt.Gr
Gt Transmitter antenna gain
Gr Receiver antenna gain
d T-R separation distance
in dBm:

10. Thus, the received signal power falls off inversely proportional to the square of the distance d
the path loss will be:
Pr~1/d2
The free-space path gain is

11. 2-Ray tracing
Due to the objects between the TX and the RX produce reflected , diffracted , or scattered copies of the transmitted signal. These copies called multipath signal components, can be attenuated in power, delayed in time, and shifted in phase or frequency from the LOS.
The multipath and transmitted signal are summed together at the receiver, which produces distortion in the Received signal.

12. I. Two-Ray model.
The two-ray model is used when a single ground reflection dominates the multipath effect. The received signal consists of two rays the LOS ray and a reflected ray.

13. There is a delay in time is delay spread equal the delay between the LOS ray and the reflected ray:
and a path difference also will cause a phase difference:
the two-ray model is the received power of
R: is the ground reflection coefficient.

14. Pr~1/d4 Thus, in large d: & independent of the wavelength λ.
For large d,
the received signal power is approximately
in dB:
Pr~1/d4
Thus, in large d:
& independent of the wavelength λ.

15. We can see that the plot can be separated to three regions:
a. In the first region the path loss is flat.
b. In the second region power falls off -20 dB/decade .
the signal power falls off -40dB/decade
c. In the third region

16. II. Ten-ray model
This model predicts the variation signal propagating along streets with buildings in both sides. So that the rays will be LOS, GR, SW reflected, DW reflected, TW reflected, WG reflected and GW reflected paths . There is two of each type of wall reflected path one for each side of the street so that the total number is ten rays.
the received power:

17. III. General Ray Tracing
GRT can be used to obtain delay and strength signal information for a particular transmitter and receiver configuration. In this model we will take in to consider the effects of the diffraction and scattering beside the reflection.

18. Empirical Path Loss Models
Okumura’s Model
It is one of the most common models for signal prediction.
This model is applicable over distances of Km and frequency ranges of MHz
Okumura used extensive measurements of base station-to-mobile signal attenuation to develop a set of curves, then he make the following path loss formula
d : the distance between transmitter and receiver
L50 : the median value of propagation path loss
Lf : free space path loss
Amu : the median attenuation in addition to free space path loss across
all environment
G(ht) : the base station antenna height gain factor
G(hr) : the mobile antenna height gain factor
GAREA : the gain due to the type of environment.

19. Hata Model valid over the same range of Okumura model (150-1500 MHz)
this model simplifies calculation of path loss and is not based on empirical curves for the different parameters.
The standard formula for median path is:
: Is a correction factor for the mobile antenna height

20. COST 231 Extension to Hata Model
It is extend to hata model Using the following equation
restricted to the following range of parameters:
1.5GHz < fc < 2 GHz, 30m < ht < 200 m, 1m < hr < 10 m, and 1Km < d < 20 Km

21. Walfisch / Bertoni Model
The COST extension to the Hata model does not consider the impact of diffraction from buildings. A model for these effects was developed by Walfisch and Bertoni as following:
P0 :the free space path loss for unidirectional antennas
:reflects the signal power reduction due to buildings that block the receiver at street level
Pl :is based on the signal loss from the building to the street due to diffraction Q2

22. Piecewise Linear (Multi-Slope) Model
A common method for modeling path loss in outdoor channels and indoor channels

23. Small scale fading refer to average power
Results due to small changes in spatial separation between transmitter and receiver
Small scale fading refer to average power
-Also, the signal is travelling and that there are multiple scatter paths
-It is also known as Multipath Fading or Rayleigh Fading

24. Effect of a multipath reflected signal on a desired signal
1-τn(t): time variant propagation delay.
2-αn(t): time variant multiplicative factor.
The received baseband signal Z(t) consists of a sum of time variant phasors having amplitudes αn(t) and phases θn(t)
θn(t)=2π fc τn(t)
Effect of a multipath reflected signal on a desired signal

25. Rician fading
If number of such stochastic component large& none are dominant
The variables xr (t) and yr(t) resulting from their addition.
The received signal =Multiple reflective rays + Significant line-of sight(non-faded) component , Then :
The received envelope amplitude has a Rician pdf
The fading is referred to as Rician fading
A:the peak amplitude of the non fading signal component called ( specular component )
σ2: the predetection mean power of the multipath signal.
I0 : the modified Bessel function of the first kind and zero order.

26. Rayleigh fading
when the magnitude of the specular component approaches zero (A)
The Rician pdf approaches a Rayleigh pdf

27. Small scale fading
Time-spreading of underlying digital pulses within the signal.
2. Time-variant behavior of channel due to motion.

28. Signal time spreading In time –delay domain:
Bello proposed the notion of (WSSUS).
the model treats signals arriving antenna with different delays as uncorrelated.
Bello was able to define function for all time and all frequencies.

29. Delay Spread:
· Mean excess delay
· RMS delay spread
· Excess delay spread
Maximum excess delay is defined as the , where , is the first arriving signal and is the maximum delay at which a multipath component is within X dB of the strongest arriving multipath signal

30. :average received power vary as a function of time delay
Tm : the time between the first and last received component represents the maximum excess delay .
- For typical wireless channel, the received signal usually consists of several discrete multipath component, exhibit multiple isolated peaks.
- For tropospheric scatter channel :received signal continuum of multipath component, smooth(continuous) of multipath.

31. Degradation categories
1-frequncy –selective fading (delay spread> bit duration)
such multipath dispersion of the signal yields the same kind of (ISI) distortion.
The spectral characteristics of the transmitted signal are changed at the receiver as the gain is different for different frequency components.
mitigating the distortion because many of multipath component are resolvable by the receiver but it is difficult.
Tm>Ts

32. Tm<Ts 2-flat fading (delay spread< bit duration)
The spectral characteristics of the transmitted signal are preserved at the receiver.
reduction in SNR.
the mitigation technique called to improve the received SNR.
for digital communication system we use error –correction coding.
Tm<Ts

33. Signal Time –spreading viewed in the frequency domain
A completely analogous characterization of signal dispersion can be specified in the frequency .

34. The channel frequency T.F
Fourier transform

35. What is the correlation between received signals that are spaced in frequency ∆f=f2-f1.
R(∆f)
the correlation between the channel’s response to 2 signals
As afunction of freq. diff. bet. 2 signals

36. Now!!!!!How can we measure R(∆f) for any channel?????
o/p cross-correlating the complex spectra of the two signals
Our channel ⁺
R(∆f)…..made by sinusoidal that is swept in freq. across the band of interest(a wideband signal)

37. Parameters for the channel
{f0 }……………’coherence bandwidth’
1)The range of frequency over which the channel passes all spectral components with approximately equal gain and linear phase.
(i.e)spectral component s affected with the same manner(fading or no fading)
f0 =~1/Tm

38. What is the best indicator for system perform when signals propagate on the channel?????
f0 =~1/Tm
1) Max. excess delay Tm
No the best: as different channels with the same Tm can exhibit very different signal intensity profile over the delay span.
2) r.m.s delay spread

39. 3)By experiment if the channel’s complex frequency T
3)By experiment if the channel’s complex frequency T.F has a correlation at least(0.9)
4)In Mobil radio correlation at least 0.5
5)Involving ionosphere effect
6)The moor popular (correlation at leas0.5)

40. Result
1)Tm &f0 are related to channel’s multipath c/cs. 2)Differing for different propagation paths.

41. Categories due to time-spreading viewed in F.D
Selective fading
flat fading

42. 1)Flat Fading Bwc > Bw(fo>W) Advantages: No ISI
Disadvantage: performance degradation can still be
expected due to the loss in SNR whenever the signal is fading.
all frequency components
of the signal will experience the same
magnitude of fading
affected by the channel
In a similar manner

44. 2) Selective Fading Bwc < Bw(fo<W) ,Complex equalization
Advantages: improved average gain.
Disadvantage: ISI
,Complex equalization
all frequency components
of the signal will experience different
magnitude of fading
not affected equally by the channel

46. IF you insert the change in position
If Mobile radio changes its position
There will be time when received signal experiences frequency _selective distortion even though fo>W

47. IMP…. Result fo To Determine Max. transmission Rate without ISI
NO equalizer in the receiver

48. Direct-sequence spread -spectrum
Examples of Flat fading and frequency selective fading for (DS/SS)system
Direct-sequence spread -spectrum

49. Frequency non selective (slightly selective)
Signal dispersion=~chip time duration Tch=spread spectrum
In typical Ds/ss system fo=1/Tch
Normalized coherence B.W=fo*Tch=1

50. Highly frequency selective
Normalized coherence B.W=fo*Tch=0.25
fo =25% of spread spectrum B.W
Dispersion
ISI

51. Highly frequency selective
fo*Tch=0.1
Dispersion
ISI

52. Representation for fading channel as electronic filter=
The signal spreading of electronic filter
The signal spreading of a fading channel

53. O/p free of distortion in TD& FD
Flat fading channel TD FD
O/p free of distortion in TD& FD

54. Frequency selective channel
There are distortion in both TD & FD

55. Time variance of the channel caused by motion
time variance viewed in the time domain
channel
Time invariant
**if all scatterers making up the channel are stationary ,when ever motion causes the amplitude and phase of the received signal remains constant .
Time variant
**due to motion between transmitter and receiver results from propagation path changes.
**this changes cause variations in the signal amplitude and phase at the receiver.

56. The time duration over which the channel response is time invariant.
R(Δt)
it is the correlation between the channel response to a sinusoid send at time t1 and the response to similar sinusoid sent at time t2 , where Δt= t2- t1 .
Coherence time T0
The time duration over which the channel response is time invariant.
The function R(Δt) and the parameter T0 provide knowledge a bout the fading rapidity of the channel.
For an ideal time invariant channel, the channel’s response will be highly correlated for all values of Δt; thus, R(Δt) as a function of Δt would be a constant.
Motion

57. V Δt is distance traversed.
J is the zero-order Bessel function of the first kind.
V Δt is distance traversed.
V is the mobile constant velocity.
k =2π/λ is the free-space phase constant.
λ is the unmodulated CW signal

58. Fading manifestations
Delay time τ
Observation time t
The interval between antenna position is 0.4λ.
The response pattern differs significantly in, the delay time of the largest signal component, the number of signal copies, their magnitudes, and the total received power.
The sequence of received pulse-power profiles as the antenna moves through a succession of equally spaced position.

59. degradation categories due to time variance, viewed in the time domain
Time-variant nature
Fading rapidity
(or)
Fast fading
Slow fading

60. Fast fading Slow fading
T0 < Ts
The time duration at which the channel behaves is a correlated manner is short compared with the time duration of the symbol .
The fading character of the channel
Will change several times during the time span of a symbol.
fast fading can cause the baseband pulse to be distorted ISI.
Time duration of a transmission symbol
Time duration of a transmission symbol
T0 > Ts
The time duration at which the channel behaves is a correlated manner is long compared with the time duration of the symbol .
The channel state virtually remain unchanged during the time in which a symbol is transmitted.
The propagation symbols will likely not suffer from pulse distortion
Channel coherence time
Channel coherence time

61. Time variance viewed in the Doppler-shift domain
Nature of time variant of the channel can be presented in Doppler-shift (frequency) domain
Doppler shift happen due to motion of transmitter and receiver
The spectrum is centered on the carrier frequency and is zero outside the limits of fc ± fd . Each of the arriving waves has its own carrier frequency (due to its direction of arrival) which is slightly offset from the center frequency. For the case of a vertical 𝜆/4 antenna (𝐺(𝛼) = 1.5), and a uniform distribution 𝑝(𝛼) = 1/2𝜋 over 0 to 2 π .
the output spectrum is given by

62. S(v): Doppler power spectral density(Doppler spectrum)
Frequency shift v in range of f = fc ± fd
Where is Doppler frequency shift also called Doppler spread , fading rate , fading band width or spectral broadening.
is the relative velocity (velocity between transmitter and receiver ) and is signal wave length.

63. In equation if Doppler components arriving at exactly 0°(ahead of antenna) and 180°(behind ) power spectral density is infinite(large value). This is not a problem since 𝛼 is continuously distributed and the probability of components arriving at exactly these angles is zero.
The next Fig shows the power spectral density of the resulting RF signal due to Doppler fading.
Fourier transform

64. Note that the relation between Doppler spread and coherence time is approximately
Before we define that the channel over it is flat(channel response to sinusoid is invariant).

65. Degradation categories due to time variance viewed in Doppler shift domain
fast fading channel
Slow fading channel
W=1/ ts (symbol rate)
Thus to avoid distortion caused due to fast (the channel will change during the transmission of the baseband message) the channel must made slow fading.

66. Analogy for spectral broadening in fading channel
Why the spectral broadening is function of speed motion ? Analogy used to explain this phenomenon
The channel behave like a switch turning the signal on &off.
The greater the rabidity of the change in the channel state the greater spectral broadening.

68. Rayleigh-limit Bit-Error Performance (where (Eb/N0)E(α²)>>1)
Modulation PB
PSK(Coherent)
DPSK(Coherent )
FSK(Coherent)
FSK(Non coherent)
In case AWGN channel α=1
For multipath conditions α is multiplicative factor (Rayleigh distributed random variable) E(α²) is statistical expectation
then the BER expression are given as shown in table .

69. Performance over slow and flat fading Rayleigh channel & AWGN channel
AWGN channel Rayleigh channel

70. Parameters of Mobile Multipath Channels
Conclusion
Coherence bandwidth (𝐵𝑐).
Coherence time (𝑇o ).
Doppler spread (𝑓d ).
Time spread (𝑇m).

71. Classifications of Small Scale Fading Channels
(Based on multipath time delay spread)
Small-Scale Fading
Flat Fading
1. BW of signal < BW of channel
2. Delay spread < Symbol period
2. Delay spread > Symbol period
1. BW of signal > BW of channel
Frequency Selective Fading
(Based on Doppler spread)
Small-Scale Fading
Fast Fading
1. High Doppler spread
2. Coherence time < Symbol period
3. Channel variations faster than
base- baseband signal variations
Slow Fading
1. Low Doppler spread
2. Coherence time > Symbol period
3. Channel variations slower than base-
band signal variations

72. Mitigation the degradation effects of fading
We have three major performance categories in terms of bit error probability versus Eb/No:
The good, the bad and the awful…..as shown in the next figure.

73. Error performance

74. To transit the performance from awful category to the bad curve then it is possible to approach AWGN
If the channel introduce signal distortion as a result of fading, no amount of Eb/No will achieve the desired performance so we must use forms of mitigation to reduce or remove the signal distortion.
Mitigation method depends whether the distortion is caused by frequency selective or fast fading………
Our aim
BUT

75. But actually we have three cases in the previous condition.
We summarize the conditions that must be met so the channel does not introduce frequency selective and fast fading distortion as shown:
In other words , it is desired that the channel coherence bandwidth exceed the signaling rate which in turn should exceed the fading rate of the channel…..
But actually we have three cases in the previous condition.

76. Case 1 fast fading distortion
In this case the signaling rate is less than the
channel fading rate
Mitigation techniques :
1-incorporate sufficient redundancy so that the transmission symbol rate exceeds the channel fading rate but at the same time does not exceed the coherence bandwidth.
2-incorporate error correction coding and interleaving to improve system performance.

77. Case 2 frequency selective fading distortion
In this case the coherence bandwidth is less than the symbol rate ,while the symbol rate is greater than the Doppler spread.
Mitigation techniques:
1-equalization
equalization can mitigate the effects of channel ISI,
Equalizer is an inverse filter of the channel, which may be one of the following: .

78. DFE 1.1 the decision feedback equalizer MLSE
The basic idea is that once an information symbol has been detected, the ISI that is induced on the future symbols can be estimated and subtracted before the detection of subsequent symbols
1.2 a maximum likelihood sequence estimation equalizer
That test all possible data sequences and chooses the data sequence that is most probable the MLSE equalizer was implemented by using the Viterbi decoding algorithm which minimizes the probability of a sequence error, so it is called Viterbi equalizer
MLSE

79. 2-direct sequence spread spectrum techniques The spread spectrum has the capability to reject interference ,but it suffers from loss in energy contains in the multipath components rejected by the receiver. 3-frequency hopping spread spectrum FH systems avoid the degradation effects due to multipath by rapidly changing the carrier frequency band in the transmitter, so interference is avoided by similarly changing the band position in the receiver before the arrival of the multipath signal.
DSSS
FHSS

80. 4-orthognal frequency division multiplexing 5-pilot signal This signal can provide information about the channel state and thus improve performance in fading conditions.
OFDM

81. Case 3 fast fading and frequency selective fading distortion
In this case the channel coherence bandwidth is less than the signaling rate which in turn is less than the fading rate.
Mitigation can be done by the previous techniques.

82. We summarize the mitigation as following

83. Reference Digital Communications ( Fundamentals and Applications)
2nd edition
By BERNARD SKLAR
WIRELESS COMMUNICATIONS
By Andrea Goldsmith
Stanford University

84. Thank you