1. BASEBAND DATA
TRANSMISSION
by Dr. Uri Mahlab
Dr. Uri Mahlab

2. Communication system
Dr. Uri Mahlab

3. Block diagram of an Binary/M-ary signaling
scheme +
Channel noise +
Dr. Uri Mahlab

4. Block diagram Description
{dk}={1,1,1,1,0,0,1,1,0,0,0,1,1,1}
For Tb
For Tb
Dr. Uri Mahlab

5. Block diagram Description (Continue - 1)
{dk}={1,1,1,1,0,0,1,1,0,0,0,1,1,1}
Dr. Uri Mahlab

6. Block diagram Description (Continue - 2)
{dk}={1,1,1,1,0,0,1,1,0,0,0,1,1,1}
100110
Dr. Uri Mahlab

7. Block diagram Description (Continue - 3)
{dk}={1,1,1,1,0,0,1,1,0,0,0,1,1,1} Tb
Timing
100110 t t
Dr. Uri Mahlab

8. Block diagram Description (Continue - 4)
Timing
HT(f)
HR(f)
(X(t
Information
source
Pulse
generator
Trans
filter +
Receiver
filter
Channel noise n(t) Tb
2Tb
5Tb
6Tb t
3Tb
4Tb t t
Dr. Uri Mahlab

9. Block diagram Description (Continue - 5)Tb
2Tb
5Tb
6Tb t
3Tb
4Tb t t
Dr. Uri Mahlab

10. Block diagram of an Binary/M-ary signaling
scheme
Timing + +
Dr. Uri Mahlab

11. Block diagram DescriptionTb
2Tb
5Tb
6Tb t
3Tb
4Tb t t t
Dr. Uri Mahlab

12. Typical waveforms in a binary PAM system
Dr. Uri Mahlab

13. Block diagram of an Binary/M-ary signaling
scheme
Timing + +
Dr. Uri Mahlab

14. Explanation of Pr(t)
Dr. Uri Mahlab

15. The element of a baseband binary PAM system
Dr. Uri Mahlab

16. Analysis and Design of Binary Signal
Dr. Uri Mahlab

17. For and is the total time delay in the system, we get.
The input to the A/D converter is
For and is the total time delay in the system, we get. t t t2 t3 t tm t1
Dr. Uri Mahlab

18. tm =mTb+td t t The output of the A/D converter at the sampling time t2
Dr. Uri Mahlab

19. ISI - Inter Symbol
Interference t2 t3 t tm t1
Dr. Uri Mahlab

20. Explanation of ISI t t f f
Dr. Uri Mahlab

21. Explanation of ISI - ContinueTb
2Tb
5Tb
6Tb t
3Tb
4Tb
Dr. Uri Mahlab

22. Dr. Uri Mahlab

23. -The pulse generator output is a pulse waveform
If kth input bit is 1
if kth input bit is 0
-The A/D converter input Y(t)
Dr. Uri Mahlab

24. Dr. Uri Mahlab

25. 5.2 BASEBAND BINARY PAM SYSTEMS
- minimize the combined effects of inter symbol interference and noise in order to achieve minimum probability of error for given data rate.
Dr. Uri Mahlab

26. 5.2.1 Baseband pulse shaping
The ISI can be eliminated by proper choice of received pulse shape pr (t).
Doe’s not Uniquely Specify Pr(t) for all values of t.
Dr. Uri Mahlab

27. To meet the constraint, Fourier Transform Pr(f) of Pr(t), should
satisfy a simple condition given by the following theorem
Theorem
Proof
Dr. Uri Mahlab

28. Which verify that the Pr(t) with a transform Pr(f)
Satisfy ______________
Dr. Uri Mahlab

29. 1 The condition for removal of ISI given in the theorem is called
Nyquist (Pulse Shaping) Criterion 1
-2Tb
-Tb Tb
2Tb
Dr. Uri Mahlab

30. The Theorem gives a condition for the removal of ISI using a Pr(f) with
a bandwidth larger then rb/2/.
ISI can’t be removed if the bandwidth of Pr(f) is less then rb/2. Tb
2Tb
5Tb
6Tb t
3Tb
4Tb
Dr. Uri Mahlab

31. Particular choice of Pr(t) for a
given application p
(t) r
Dr. Uri Mahlab

32. A Pr(f) with a smooth roll - off characteristics is preferable
over one with arbitrarily sharp cut off characteristics.
Pr(f)
Pr(f)
Dr. Uri Mahlab

33. In practical systems where the bandwidth available for transmitting data at a rate of rb bits\sec is between rb\2 to rb Hz, a class of pr(t) with a raised cosine frequency characteristic is most commonly used.
A raise Cosine Frequency spectrum consist of a flat amplitude portion and a roll off portion that has a sinusoidal form.
Dr. Uri Mahlab

34. raised cosine frequency characteristic
Dr. Uri Mahlab

35. Summary The BW occupied by the pulse spectrum is B=rb/2+b.
The minimum value of B is rb/2 and the maximum value is rb.
Larger values of b imply that more bandwidth is required for a
given bit rate, however it lead for faster decaying pulses, which
means that synchronization will be less critical and will not cause
large ISI.
b =rb/2 leads to a pulse shape with two convenient properties.
The half amplitude pulse width is equal to Tb, and there are zero
crossings at t=3/2Tb, 5/2Tb…. In addition to the zero crossing
at Tb, 2Tb, 3Tb,…...
Dr. Uri Mahlab

36. Optimum transmitting and receiving filters
5.2.2
Optimum transmitting and receiving filters
The transmitting and receiving filters are chosen to provide
a proper
Dr. Uri Mahlab

37. Where td, is the time delay Kc normalizing constant.
-One of design constraints that we have for selecting the filters is the relationship between the Fourier transform of pr(t) and pg(t).
Where td, is the time delay Kc normalizing constant.
In order to design optimum filter Ht(f) & Hr(f), we will assume that Pr(f), Hc(f) and Pg(f) are known.
Portion of a baseband PAM system
Dr. Uri Mahlab

38. If we choose Pr(t) {Pr(f)} to produce Zero ISI we are left
only to be concerned with noise immunity, that is will choose
Dr. Uri Mahlab

39. Noise power Spectral Density - Channel transfer function -
Noise Immunity
Problem definition:
For a given :
Data Rate -
Transmission power -
Noise power Spectral Density -
Channel transfer function -
Raised cosine pulse -
Choose
Dr. Uri Mahlab

40. Error probability Calculations
At the m-th sampling time the input to the A/D is:
We decide:
Dr. Uri Mahlab

41. The noise is assumed to be zero mean Gaussian at the receiver input
A=aKc
The noise is assumed to be zero mean Gaussian at the receiver input
then the output should also be Zero mean Gaussian with variance No
given by:
Dr. Uri Mahlab

42. b
Dr. Uri Mahlab

43. Dr. Uri Mahlab

44. -A A
Dr. Uri Mahlab

45. Dr. Uri Mahlab

46. Q(u)
dz= U
Dr. Uri Mahlab

47. Hence we need to maximize the signal to noise Ratio
Perror decreases as
increase
Hence we need to maximize the signal
to noise Ratio
Thus for maximum noise immunity the filter transfer functions HT(f)
and HR(f) must be xhosen to maximize the SNR
Dr. Uri Mahlab

48. Optimum filters design calculations
We will express the SNR in terms of HT(f) and HR(f)
We will start with the signal:
The PSD of the transmitted signal is given by::
Dr. Uri Mahlab

49. And the average transmitted power ST is
The average output noise power of n0(t) is given by:
Dr. Uri Mahlab

50. The SNR we need to maximize is
Or we need to minimize
Dr. Uri Mahlab

51. Using Schwartz’s inequality
The minimum of the left side equaity is reached when
V(f)=Const*W(f)
If we choose :
Dr. Uri Mahlab

52. The filter should have a linear phase response in a total time delay of td
Dr. Uri Mahlab

53. Finally we obtain the maximum value of the SNR to be:
Dr. Uri Mahlab

54. Rectangular pulse can be used at the input of HT(f).
For AWGN with
and
pg(f) is chosen such that it does not change much over the bandwidth of interest we get.
Rectangular pulse can be used at the input of HT(f).
Dr. Uri Mahlab

55. 5.2.3 Design procedure and Example
The steps involved in the design procedure.
Example:Design a binary baseband PAM system to transmit data at a a bit rate of 3600 bits/sec with a bit error probability less than
The channel response is given by:
The noise spectral density is
Dr. Uri Mahlab

56. If we choose a braised cosine pulse spectrum with
Solution:
If we choose a braised cosine pulse spectrum with
Dr. Uri Mahlab

57. We choose a pg(t)
We choose
Dr. Uri Mahlab

58. Plots of Pg(f),Hc(f),HT(f),HR(f),and Pr(f).
Dr. Uri Mahlab

59. For Pr(f) with raised cosine shape
To maintain a
For Pr(f) with raised cosine shape
And hence
Which completes the design.
Dr. Uri Mahlab

60. DUOBINARY BASEBAND PAM SYSTEM
5.3
In order to transmit data at a rate of rb bits/sec with zero ISI PAM data transmission system requires a bandwidth of at least rb /2 HZ. +
Binary PAM data transmission at a rate of rb bits/sec with zero ISI
1.such filters are physically unrealizable
2. Any system with this filters will be extremely sensitive to perturbations.
Dr. Uri Mahlab
204

61. Dr. Uri Mahlab

62. The duobinary signaling schemes use pulse spectra Pr(f):
The duobinary scheme utilizes controlled amounts of ISI for transmitting data at a rate of rb /2 HZ The shaping filters for duobinary are easier to realize than the ideal rectangular filters.
The duobinary signaling schemes use pulse spectra Pr(f):
The pulse response Pr(t):
Dr. Uri Mahlab

63. use of controlled ISI in duobinary signaling scheme
5.3.1
The output Y(t) of the receive filter can be written as:
If the output is sampled at tm= mTb/2+ td than it is obvious that in the absence of noise:
The Am' s can assume one of two values +/-A depending on whether the m th input bit is 1 or 0. Since Y(tm) depends on Am & Am-1 assuming no noise :
+2A if the m th and (m-1st)bits are both 1's
0 if the m th and (m-1st)bits are different
-2A if the m th and (m-1st)bits are both zero
Y(tm) =
Dr. Uri Mahlab

64. Transmitting and receiving filters for optimum performance
5.3.2
The receiving levels at the input to the A/D converter are 2A, 0, and -2A with probabilities 1/2, 1/ The probability of bit error pe is given by:
Since no is a zero mean Gaussian random variable with a variance No we can write pe as:
For the direct binary PAM case :
Dr. Uri Mahlab

65. The integral can be evaluated as :
Where /2=Gn(f) is the noise power spectral density the probability of error is:
The integral can be evaluated as :
Dr. Uri Mahlab

66. M-ARY SIGNALING SCHEMES
5.4
M-ARY SIGNALING SCHEMES
In baseband binary PAM we use pulses with one of 2 possible amplitude, In M-ary baseband PAM system we allowed M possible levels (M>2) and there M distinct input symbols.
During each signaling interval of duration the source is converted to a four-level PAM pulse train by the the pulse generator.
The signal pulse noise passes through the receiving filter and is sampled by the A/D converter at an appropriate rate and phase.
the M-ary PAM scheme operating with the preceding constraints can transmit data at a bit rate of rs log2M bit/sec and require a minimum bandwidth of rs/2 HZ.
Dr. Uri Mahlab

67. MISCELLANEOUS TOPICS
Eye Diagram
The performance of baseband PAM systems depends on the amount of ISI and channel noise.
The received waveform with no noise and no distortion is shown in Figure 5.20a the “open” eye pattern results
Figure 5.20b shows a distorted version of the waveform the corresponding eye pattern.
Figure 5.20c shows a noise distorted version of the received waveform and the corresponding eye pattern.
Dr. Uri Mahlab

68. Dr. Uri Mahlab

69. In the figure 5.21 we see typical eye patterns of a duobinary signal
Dr. Uri Mahlab

70. If the signal-to-noise ratio at the receiver is high then the following observations can be made from the eye pattern shown simplified in Figure 5.22:
Dr. Uri Mahlab

71. 5. The sampling time is midway between zero crossing.
1. The best time to sample the received waveform is when the eye is opening is largest.
2. The maximum distortion is indicated by the vertical width of the two branches at sampling time.
3. The noise margin or immunity to noise is proportional to the width of the eye opening.
4. The sensitivity of the system to timing errors is revealed by the rate of closing of the eye as sampling time is varied.
5. The sampling time is midway between zero crossing.
6. Asymmetries in the eye pattern indicate nonlinearities in the channel.
Dr. Uri Mahlab

72. synchronization
5.7.2
Three methods in which this synchronization can be obtained are:
1. Derivation of clock information from a primary or secondary standard.
2. Transmitting a synchronizing clock signal.
3. Derivation of the clock signal from the received waveform itself.
An example of a system used to derive a clock signal from the received waveform is shown in figure 5.23.
To illustrate the operating of the phase comparator network let us look at the timing diagram shown in figure 5.23b
Dr. Uri Mahlab

73. Dr. Uri Mahlab

74. Scrambler and unscrambler
5.7.3
Scrambler and unscrambler
Scrambler: The scrambler shown in figure 5.24a consists a “feedback” shift register.
Unscrambler:The matching unscrambler have a ”feed forward” shift register structure.
In both the scrambler and unscrambler the outputs of several stages of of shift register are added together modulo-2 and the added to the data stream again in modulo-2 arithmetic
Dr. Uri Mahlab

75. Dr. Uri Mahlab

76. Scrambler affects the error performance of the communication system in that a signal channel error may cause multiple error at the output of the unscrambler.
The error propagation effect lasts over only a finite and small number of bits.
In each isolated error bit causes three errors in the final output it must also be pointed out that some random bit patterns might be scrambled to the errors or all ones.
Dr. Uri Mahlab