1. Physical Layer: Channel models and digital modulation techniques
Maria Papadopouli
Department of Computer Science
University of Crete
Thanks to G. Fortetsanakis for generating most of these slides 1

2. Multi-path
A signal transmitted from a transmitter may have multiple copies traversing different paths to reach a receiver
The received signal: sum of all these multi-path signals
The paths traversed by these signals are different (of various length)
The one at the direction of light of signal (LOS) should be the shortest
Channel fading: interaction of these signals with each other:
If signals are in phase, they would intensify the resultant signal
Otherwise, the resultant signal is weakened due to out of phase
This phenomenon is called channel fading.
Criteria to measure channel fading:
Doppler spread
delay spread

3. Delay spread
The signals on shorter paths reach the receiver earlier than those on longer paths
The direct effect of these unsimultaneous arrivals of signal causes the spread of the original signal in time domain
This spread is called delay spread
It constrains the maximum transmission capacity on the wireless channel
If the period of baseband data pulse is larger than the delay spread, inter-symbol interference (ISI) will be generated at the receiver
The data signals on two neighbouring pulse periods are received at the same timethe receiver is unable to distinguish them

4. Channel models Large-scale propagation models
Predict the mean signal strength at large transmitter-receiver distances
Small-scale or fading models
 Characterize the rapid fluctuations of the received signal strength over very short distances or time durations 4

5. Large-scale models Log distance path-loss or in dB
The average large scale path loss is a function of distance
or in dB
d: transmitter-receiver distance
d0: reference distance
n: path loss exponent 5

6. Path loss exponents for different environments6

7. Log-normal shadowing
Surrounding environment varies at different locations
Measured signals are different from the average value predicted by the log-distance model
Path loss is random, distributed log-normally (mean distance-dependent value)
Xσ : zero mean Gaussian distributed random variable (in dB) with standard deviation σ (also in dB) 7

8. Parameter estimation
Parameters n & σ are estimated using linear regression
 The difference between the measured and estimated path losses is minimized in a mean square error sense 8

9. Path loss model for various cities in Germany
Parameters
n=2.7
σ= 11.8 dB
correspond to all cities 9

10. Fading models
Fading describes the rapid fluctuations of amplitudes, phases or multipath delays of a radio signal
Fading is caused by interference between two or more versions of the transmitted signal which arrive at the receiver at different times 10

11. Channel impulsive response
By sending a pulse of very small duration to the channel, the impulsive response can be estimated
 At the output, the duration of the pulse is extended due to multipath
Η έξοδος που παίρνομε όταν βάλομε ως είσοδο ένα παλμό Dirac. 11

12. Analytical expression
If the channel is stationary over a small time interval, the channel impulsive response (h) may be written as:
αi & θi : the amplitude & phase of the ith multipath copy
ti corresponds to the time of arrival of the ith copy 12

13. Time dispersion parameters
Power delay profile: Received power as a function of the excess (additional) delay
Mean excess delay: The first moment of the power delay profile.
It can be expressed as:
P(τi) is the received power at time τi (arrival of the i-th multipath copy).
Excess delay: distasthma pou vlepome isxy ston diaulo (megalyterh diarkeia apo authn pou stelnome ena symvolo). 13

14. Time dispersion parameters (con’td)
rms delay spread: Square root of the second central moment of the power delay profile. It can be defined as:
where
Maximum excess delay (X dB): The time delay during which the multipath energy falls to X dB bellow the maximum. 14

15. Example of Time Dispersion15

16. Flat Channel Definition
When the channel gain remains the same across all the frequencies of the transmitted signal
The channel impulsive response is approximately the same in all the frequencies of the transmitted signal
The “manner” that the transmitted signal fades at each frequency is the same

17. Frequency-selective time-varying fading
Frequency-selective time-varying fading causes a cloudy pattern to appear on a spectrogram
signal strength as grey-scale intensity
Frequency
Time

18. Coherence Bandwidth
The range of frequencies over which the channel is considered flat
The channel passes all spectral components with approximately equal gain
Frequency components have strong potential for amplitude correlation
If the coherence bandwidth is defined as the zone over which the amplitude correlation> 0.9:
If the coherence bandwidth is defined as the zone over which the amplitude correlation> 0.5 :
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19. Flat vs. frequency selective fading
Flat fading:
Bandwidth of transmitted signal < coherence bandwidth (Bs < Bc)
The channel gain is equal for all frequency components of the transmitted signal
Frequency selective fading:
Bandwidth of transmitted signal > coherence bandwidth (Bs > Bc)
 The channel gain may vary for different frequencies of the transmitted signal 19

20. Doppler spread fd: Doppler spread:
When a sinusoidal pulse of frequency fc is transmitted over a multi-path channel, the received spectrum will have components in the range fc- fd to fc- fd
fd: Doppler spread:
v: velocity of the receiver
θ: direction of arrival of the received signal
λ: wavelength 20

21. Coherence time
Definition:
The time interval over which the channel impulsive response is considered stationary
Typical assumption:
Doppler spread and coherence time are related by the formula:
K: constant in the range of 0.25 to 0.5 21

22. Fast vs. slow fading
Fast fading: The symbol duration > the coherence time
(Ts> Tc)
 The channel impulsive response varies during the symbol duration
Slow Fading: The symbol duration is much less than the coherence time (Ts<<Tc)
The channel impulsive response does not change for many symbol intervals 22

23. Fading phenomena Range of frequencies of the transmitted signal
Coherence bandwidth 23

24. Observations
Strong destructive interference is frequently referred to as a deep fade and may result in temporary failure of communication due to a severe drop in the channel signal-to-noise ratio
Since different frequency components of the signal are affected independently, it is highly unlikely that all parts of the signal will be simultaneously affected by a deep fade

25. Rayleigh fading
In flat-fading channels, the envelope of the received signal follows a Rayleigh distribution
σ2 : time averaged power of the received signal before envelope detection 25

26. Ricean fading
When there is a dominant signal component present, such as a line of sight propagation path, the received signal envelope follows the Ricean distribution
A: peak amplitude of the dominant signal
I0(): modified Bessel function of the first kind & zero order 26

27. Digital Modulation Frequency Shift Keying (FSK)
Use of different carrier frequencies to encode the various symbols
Phase Shift Keying (PSK)
Use of a single carrier frequency
The various symbols are encoded by the phase
Quadrature Amplitude Modulation (QAM)
Both phase & amplitude are used for encoding the various symbols

28. FSK modulation An alphabet of M symbols is used (M = 2K for some KN)
Each symbols corresponds to a combination of K bits
ith symbol is mapped to carrier frequency Fi = (n+i)/2T
T: symbol duration, n: an arbitrary integer
To transmit the ith symbol, the following signal is used
E: ενέργεια
amplitude

29. Example BFSK
Bit 0 corresponds to:
Bit 1 corresponds to:

30. FSK demodulation Consider a vector space with base vectors:
The transmitted & received signal correspond to different points on this vector space
This is due to noise & channel gain
The largest coordinate of the received signal corresponds to the transmitted signal with high probability

31. BFSK demodulation Assumptions: When the received signal is
bellow the dashed line, bit 0 is transmitted
Otherwise, bit 1 is transmitted

32. PSK modulation Assume an alphabet of M = 2K different symbols
To transmit the ith symbol, we send the following signal:
Signals Si(t) are linearly dependent & can be represented by linear combination of the vectors:

33. Example BPSK
Bit 0 corresponds to :
Bit 1 corresponds to:

34. QPSK Assumptions: If the received signal lies in the:
1st quadrant, 00 is transmitted
2nd quadrant, 01 is transmitted
etc…

35. 8PSK
If the received signal lies in the first area it is assumed that the combination 000 is transmitted.
If it lies in the second area it is assumed that 001 is transmitted etc.

36. QAM modulation This modulation scheme is an expansion of PSK
Again a single carrier frequency is used (Fc)
Transmitted & received signal are represented as linear combinations of:
Difference: not only the phase but also the amplitude of the carrier signal may vary

37. Example: 16QAM
The constellation point that is closer to the received signal is assumed to correspond to the transmitted bit combination

38. The matched filter
Suppose that r(t) is the received signal which corresponds at a particular symbol interval.
The estimation of the transmitted symbol is done using the matched filter.
r(t) is multiplied with each signal that belongs to the basis of the signal space.
The result of each multiplication is then integrated into the whole symbol interval.
That way the coordinates of the received signal can be estimated.

39. The matched filter for QPSK

40. PDF of the received signal
The probability that the received signal would lie at a particular point is given by a 2-D Gaussian distribution
The probability space of the PDF is the vector space of the signals
The peak of the distribution corresponds to the transmitted signal 40

41. BER calculation
To calculate BER: compute the integral of signal PDF in red zone
For 8PSK: the red zone is larger & yields higher BER
Also the additional red zones in 8PSK have large probability mass which means that the BER is significantly higher than in QPSK 41

42. OFDM Demodulation At the receiver the inverse procedure is followed.
First the signal is brought down to baseband and is converted from analog to digital. Then FFT is performed which produces the estimations of the transmitted symbols.
Finally parallel to serial conversion is performed resulting in an estimation of the transmitted bit stream. 42

43. Orthogonal frequency division multiplexing (OFDM)
When the bandwidth of a communication system is larger than the coherence bandwidth of the channel, ISI is introduced (Frequency Selective Fading)
To reduce the effect of frequency selective fading, we use OFDM
The total available bandwidth is divided into N frequency bins
N is selected such that the channel frequency response is almost constant at each bin (Flat fading)

44. OFDM modulation Bit stream is divided into N parallel sub-flows
Bits of each sub-flow are modulated using MPSK or MQAM
After modulation, symbols are mapped to points on a signal constellation
These points can be represented as complex numbers which are then fed
to the module which performs FFT-1
The resulted signal is
converted from analog to digital
brought to the RF frequencies
fed to the antenna of the transmitter

45. OFDM Demodulation At the receiver the inverse procedure is followed
The signal is brought down to baseband
It is converted from analog to digital
FFT is performed, producing the estimations of transmitted symbols
Parallel to serial conversion is performed resulting in an estimation of the transmitted bit stream

46. References
Theodore S. Rappaport “Wireless communications principles and practice”, Chapters 4,5.
Simon Haykin “Communication systems”, chapter 10.
John G. Proakis Masoud Salehi “Telecommunication systems”, Chapter 8. 46