Module-4

Session wise Topics

Digital Modulation Techniques (Part - 7)

Digital Modulation Techniques (part - 8)

Digital Modulation Techniques (Part - 9)

Digital Modulation Techniques (Part - 10)

Probability of Error Calculation

Calculation of Probability of Error

Calculation of Probability of Error

Equalizers

Page 84 of 103

4.1: NPTEL Video Link

Module-4: Video Lecture number 18 to 25 Sl.

No. Module

No. Lecture

No. Topics covered Video Link

1 Mod 04 Lec-18 FSK scheme.Orthogonal FSK Pulse Position Modulation

http://nptel.ac.in/courses/117101051/18

2 Mod 04 Lec-19 Biorthogonal Signals http://nptel.ac.in/courses/117101051/19

3 Mod 04 Lec-20 Memory less modulation scheme http://nptel.ac.in/courses/117101051/20

4 Mod 04 Lec-21 Eye diagram http://nptel.ac.in/courses/117101051/21

5 Mod 04 Lec-22 Probability of Error http://nptel.ac.in/courses/117101051/22

6 Mod 04 Lec-23 Probability of Error http://nptel.ac.in/courses/117101051/23

7 Mod 04 Lec-24 Probability of Error http://nptel.ac.in/courses/117101051/24

8 Mod 04 Lec-25 Equalizers http://nptel.ac.in/courses/117101051/25

NPTEL Web Link: http://nptel.ac.in/courses/Webcourse-contents/IIT%20Kharagpur/Digi%20Comm/New_index1.html

Page 85 of 103

4.2) Questions:

Questions from Video Lectures of NPTEL

Sl no Questions Video

Number

Time in

Minutes

1 Derive the orthonormal vectors for the two vectors f(t) and g(t) given below:

18 4 - 12

2 Define FSK. Write the pass band representation and complex form of

representation using low pass equivalent signal.

18 13

3 What are the possible values of f in FSK? 18 16

4 Find the inner product of two signals xm(t) and xn(t) in FSK. Plot for the

different values of m and n.

18 17

5 Draw the orthogonal FSK constellation for M=3 with three orthonormal basis

functions.

18 27

6 For a two dimensional signal set, write the constellation of FSK. 18 32

7 What are the properties of orthogonal FSK? 18 33

8 Define Pulse Position Modulation. 18 40

9 Explain the PPM technique with waveforms for the time shifting constant, t

= T/4.

18 42

10 Compare the properties of orthogonal FSK and PPM modulation techniques. 18 46

11 Describe the Bi-orthogonal signals for a set of N-orthogonal signals. 19 3

12 Draw the signal space diagrams for N=2 and N=3 signals. 19 6

13 What are the properties of Bi-orthogonal signals? 19 8

14 Explain the principle of demodulation in bi-orthogonal scheme. 19 13-21

15 Describe how the transmitted signal is estimated using the distance metric

from the received signal vector?

19 24

16 How the N-complex signals are transmitted in 2N dimension considering them

as real signals.

19 28

17 Describe the process of demodulation in bi-orthogonal scheme using

correlation receiver.

19 33-39

Page 86 of 103

18 Describe the matched filter implementation for the demodulation of bi-

orthogonal scheme.

19 42

19 Compare the correlation receiver implementation and matched filter

implementation for Bi-orthogonal schemes.

19 45

20 Derive the matched filter receiver structure in which each signal is matched to

the signal.

19 48

21 Explain the working of receiver using M-matched filter matched directly to

the signal.

20 4

22 With constellation diagram explain the demodulation of PSK signal 20 7

23 With constellation diagram explain the demodulation of 16-QAM signal. 20 11

24 How an FSK signal can be detected using orthogonal signal set. 20 15

25 Explain the detection procedure for Biorthogonal signals 20 17

26 What is equivalence signal set? What is its signification? 20 18

27 With suitable example explain the process of signal translation. 20 20

28 What is the advantage of signal translation? Explain with an example. 20 23

29 Briefly discuss the need of signal rotation in higher modulation scheme. 20 28

30 Explain how a two dimensional FSK signal can be translated and rotated into

one dimension signal set?

20 31

31 Explain how a three dimensional FSK signal can be translated and rotated into

two dimension signal set?

20 32

32 How to choose best transition point in case of signal transition? 20 33

33 What is simplex signal set? Explain with an example. 20 42

34 What are the properties of simplex signal set? Explain with suitable examples. 20 45

35 Explain the effect of channel and receiver on transmitted pulse signal. 21 3

36 Explain why in practice zero ISI is not possible? 21 5

37 Explain the significance of eye diagram to observe ISI 21 10

38 Write the eye diagram for a binary PAM signal and show the optimum

sampling time.

21 12

39 Explain how noise immunity can be calculated in an eye diagram. 21 17

40 Explain how sampling error immunity can be indicated in an eye diagram. 21 19

41 Write the eye diagram for a 4- PAM signal 21 20

42 Explain the working of communication system with channel being continuous

and signal transmitted is discrete.

21 26

43 Briefly discuss the function performed by real time vector discrete-time 21 30

Page 87 of 103

channel

44 What is discrete memoryless channel? Explain its operation. 21 33

45 For M-ary signal write the channel probability transition diagram. 21 36

46 Explain how discrete memory less channel and real vector discrete time

channel are relevant channel models even for continuous time channels.

21 36

47 What is the function performed by the mapper in communication system?

Explain with an example.

21 38

48 What is the advantage of using gray coding while mapping the signals?

Explain how gray coding can be assigned to:

(i) 8-PSK system (ii) 16-QAM system.

21 41

49 What are the criteria’s we should use for designing a mapper? 21 47

50 Explain the trade-off between bandwidth, average energy, bit rate and

probability of error in communication.

21 53

51 With neat diagram explain the working of Matched filter receiver. 22 07

52 What is the function performed by weighting matrix in Matched filter receiver 22 08

53 For a zero mean additive white Gaussian noise with variance N0/2 find the

power spectral density,

22 11

54 Define co-variance of two noise components.ni and nj and derive an

expression for the same.

22 19

55 For 4-PSK write the received signal vector and comment on the effect of noise

on the received vector.

22 29

56 Explain the decision procedure for 4-PSK received signals. 22 30

57 Derive an expression for probability of error for binary PAM. 22 31

58 Define Q-function and what is its significance in finding the probability of

error in communication?

22 37

59 Prove that the Q-function ( ) < / 22 47

60 Explain the procedure to simulate communication using binary PAM through

AWGN discrete-time channel.

22 48

61 Derive an expression for probability of error for any orthogonal signal set. 23 05

62 Derive an expression for probability of error for noise variation in one

dimension only.

23 07

63 Obtain an expression for probability of error for noise variation in two

dimensions only.

23 13

Page 88 of 103

64 Derive an expression for probability of error for noise variation in three

dimensions only.

23 16

65 Obtain an expression for probability of error for noise variation in four

dimensions only.

23 19

66 Write the signal space representation of 16-QAM and derive an expression for

probability of error in case of 16-QAM.

23 22

67 Derive an expression for probability of error for orthogonal signals. 23 40

68 Obtain an expression for probability of error for Bi-orthogonal signals. 24 03

69 Explain the detection rule in case of Bi-orthogonal signals. 24 06

70 What is union Bound on the probability of error? Derive an expression for the

same.

24 16

71 Derive an expression for union bound for orthogonal signal set. 24 20

72 Derive an expression for union bound for Biorthogonal signal set. 24 23

73 What is meaning of modulation with memory, explain with suitable example. 24 33

74 What is baseband modulation? 24 33

75 What are RZ and NRZ representation of binary signals? 24 34

76 Represent binary data 10110001 using NRZ line code without memory. 24 35

77 Represent binary data 10110001 using NRZI line code with memory. 24 36

78 What is differential encoding? What is its significance in modulation? 24 38

79 Explain the working of differential PSK [DPSK] and briefly discuss that DPSK is

a modulation with memory type.

24 43

80 With neat receiver block diagram explain the working of DPSK demodulation

scheme

24 47

81 What is an equalizer? What are the functions performed by an equalizer? 25 03

82 Briefly discuss the criterion for no ISI. 25 05

83 What is ISI? Obtain an expression for ISI at the receiver. 25 09

84 Write the equivalent model of the channel. 25 13

85 What is linear equalizer? Explain its operation. 25 15

86 Explain the function of peak distortion criterion equalizer. 25 19

87 What are the disadvantages of peak distortion equalizer? 25 23

88 Explain the working of MSE criterion equalizer. 25 28

89 Explain the operation of decision feedback equalizer. 25 30

90 What is adaptive equalizer? Explain its role in communication. 25 41

Page 89 of 103

4.3) Quiz Questions

Questions: Fill in the blanks.

Q.

No.

Question Answer

1 All the signals in the orthogonal FSK are __________ to each other. Orthogonal.

2 In orthogonal FSK signal set, the energy of all the signals is _____. same

3 The number of points is ____ to the number of dimension in orthogonal FSK

scheme.

Equal

4 The bandwidth of the FSK signal ______ proportional to the number of

signals in the orthogonal FSK scheme.

Increases.

5 The minimum distance between all pairs of points in FSK is __________. Same.

6 In PPM scheme the pulses are shifted in _________. Time

7 The different pulses used in the PPM scheme are _______ to each other. orthogonal

8 In PPM, Bandwidth increases as the number of points are __________. Increased.

9 FSK and PPM are ______ to each other. Dual

10 Both the orthogonal FSK and PPM schemes have same _____________. Properties

11 In bi-orthogonal scheme as the dimension is increased the bandwidth

requirement __________.

Increases.

12 For PAM we need ______ matched filter for demodulation one

13 There are ______kinds of decision region shapes for 16-QAM reception Three

14 The signal are said to be _________ if the probability of error will not

change either by rotation or translation.

Equivalent

15 During signal transition we choose the signal set which has________

average energy.

Minimum

16 The energy of simplex signal set is __________ original orthogonal signal

set.

Less than

17 The inner product of any pair of simplex signal set is_____ Constant

18 __________ is graphical illustration of ISI. Eye diagram

19 If ISI is present in a channel then we refer it as discrete ________ channel. memory

20 In 16-QAM gray code the difference between adjacent point is ___ bit one

21 The criteria we use for designing a mapper is to give _______ probability of

error

Minimum

Page 90 of 103

22 If the distance between the points increases then the probability of error

_______

decreases

23 If the receiver design is not optimum then probability of error will ________ Increases

24 If the input noise to matched filter is Gaussian then the output noise is

_________

Gaussian

25 The Q-function in terms of cumulative distribution function is Q(x)=_______ Q(x)=1-Fz(x)

26 In case of modulation with memory the current transmitting signal depends

________ transmitted signal also.

Previous

27 The three basic digital modulation schemes are ________ ________ and

______.

ASK, PSK

and FSK

28 In binary PSK the two signals transmitted are called _________ signals. Antipodal

29 Generally in binary FSK the two signals transmitted are ________ signals. Orthogonal

30 The number basis signals required in QPSK scheme is ________. Two

31 For a specified average transmitted power, the system that gives the lowest

probability of error is ______.

PSK

32 For the same bit error and channel noise, the Pe of QPSK is the same as that

of __________.

Binary PSK

33 Spectral efficiency is the ratio of _______ to ______.

Bit

rate/Bandwidth.

34 To reduce the effect of channel noise at receiver we use________ Equalizer

35 In an ideal Nyquist channel of bandwidth of W we can transmit without ISI

at a maximum rate of _________

2W

36 In an eye pattern the maximum opening of eye in the vertical direction

indicates __________

Noise margin

37 The peak distortion equalizer is also referred as ________ equalizer Zero forcing

38 The compensator for ISI is __________ An Equalizer.

39 In a non-ideal channel of bandwidth, W the signal transmission at a symbol

rate exceeding W results in ______.

ISI

40 Two types of linear equalizers used in practical implementation are ___ and

____ equalizers.

Base band and

Pass band.

Page 91 of 103

4.4) True or False:

Q: State whether the following statements are True or False?

Answer 1 FSK signal set is orthogonal if f = k/2T, where k is an integer. T

2 Orthogonal FSK is a constant energy modulation scheme. T

3 The number of points is same as the dimension of the signal space in orthogonal FSK. T

4 In orthogonal FSK, the Bandwidth remains constant when the number of points is

increased.

F

5 The energy of the signal can be constant while increasing the number of points in

orthogonal FSK.

T

6 In PPM method the information is present in the position of the pulse. T

7 In pulse position modulation scheme the information is transmitted by transmitted

the base band pulse at different time instants

T

8 PSK and FSK are constant energy schemes T

9 PAM and QAM are constant energy schemes. F

10 FSK and PPM are orthogonal signaling schemes. T

11 All the signals in Bi-orthogonal signals have constant energy. T

12 Distances between the points in constellation of bi-orthogonal signals are not

uniform.

T

13 QAM technique can be considered as combination of PAM and PSK techniques. T

14 FSK is a nonlinear modulation scheme. T

15 The performance of correlation receiver and matched filter are not same. F

16 The performance of matched filter receiver using N-filters and M-filters are not same,

where M is the number of signals transmitted and N is the number of basis functions

used.

F

17 Bi-orthogonal schemes can be used with FSK. T

18 Bi-orthogonal scheme cannot be used with PPM. F

19 The signal constellation points of a bi-orthogonal scheme for M=4 are (1,0), (-1,0),

(0,1) and (0, -1).

T

20 The signal constellation points of a bi-orthogonal scheme for M=4 are (1,0), (-1,0), F

Page 92 of 103

(1,1) and (1, -1).

21 For QAM demodulator a minimum of two matched filters are used. T

22 For any orthogonal signal set the number of points is same as the dimension of the

signal space,

T

23 For any orthogonal modulation technique the energy of each signal is different. F

24 A good signaling scheme is the one, which gives less probability of error for maximum

energy reception.

F

25 By signal translation we can reduce the average transmission energy of the signal. T

26 By signal translation we can maintain the same probability of error. T

27 By signal rotation the probability of error will change. F

28 One dimensional signal will take less bandwidth compare to two dimensional signals. T

29 We can translate and rotate three dimensional FSK signal into two dimension signal

set

T

30 In signal transition all transition point will have same average energy. F

31 The inner product of simplex signal set is zero. F

32 After signal translation distance between any pair points remains same. T

33 In practice zero ISI is not possible. T

34 It may be expensive to implement pulse p(t) and receiver filter a(t) to avoid ISI

completely.

T

35 In wireless channel the channel behavior is changing. T

36 Detector will pick-up the point nearest to the transmitted vector T

37 In case of real time vector discrete-time channel the input and output signals are not

vectors.

F

38 In a channel if ISI is present then we call it as discrete memoryless channel. F

39 While mapping the error will be maximum with the neighboring point rather than

distant point,

T

40 Gray coding cannot be assigned to 16-QAM F

41 In 16-QAM gray code the difference between vertical adjacent point is not one bit F

42 Gray encoder is the best mapper in communication. T

43 By using grey coding we can achieve the probability of bit errors same as probably of

symbol errors

T

44 For the same data rate to reduce the probability of error we should reduce the F

Page 93 of 103

distance between the points.

45 Upper bound of the probability of error is useful. T

46 Probability of error depends on how we reject the signal at the receiver. T

47 Matched filter is not an optimum receiver. F

48 In Matched filter output is maximum at t=T. T

49 The co variance of ni and nj T

50 For a Gaussian noise the probability of smaller noise is less compared to larger noise. F

51 Biorthogonal signals are symmetric signals. T

52 In case of modulation with memory the current transmitting signal will not depends

on previous transmitted signal also.

F

53 A differential encoded data represents modulation with memory. T

54 A differential PSK [DPSK] represents modulation with memory T

55 In DPSK, no synchronous carrier is needed at the receiver. T

56 In PSK, no synchronous carrier is needed at the receiver. F

57 In FSK, no synchronous carrier is needed at the receiver. F

58 Probability of error in DPSK is higher than PSK receiver. T

59 Among the basic modulation schemes (ASK, FSK and PSK), the probability of error in

PSK is minimum.

T

60 Probability of error in a non-coherent receiver is lower than the coherent receiver. F

61 FSK signaling scheme it is not compulsory to use orthogonal signals. T

62 Equalizers are used to reduce the effect of ISI. T

63 The disadvantage of peak distortion equalizer is it will amplify noise. T

64 The advantage of peak distortion equalizer is it will eliminate ISI completely T

65 In an optimum equalizer the mean square error is always maximum. F

66 A linear equalizer is not the best compensator for the severe ISI. T

67 Decision feedback equalizer is a nonlinear equalizer. T

Page 94 of 103

4.5) Frequently Asked Questions [FAQ]:

Questions Video

No

1 What is the advantage of using orthogonal signals in FSK modulation? 18

2 What is the difference between PPM and FSK schemes? 18

3 What is importance of inner product in the representation of modulation

schemes?

18

4 What is the advantage of bi-orthogonal scheme? 19

5 For bi-orthogonal scheme, which receiver (matched filter or correlation) is

better?

19

6 What are Simplex signals? 20

7 What is meant by memory less modulation technique? 20

8 What is modulation technique with memory? 20

9 What is an Eye diagram? 21

10 How noise margin is measured using Eye diagram? 21

11 What is the importance of a mapper? 21

12 What is the importance of Q-function? 22

13 What is the probability of error? 22

14 What is the difference between Probability of error and Bit error rate? 22

15 What is the importance of dimension of the signal set for the computation of

probability of error?

23

16 What is meant by union bound for signal set? 24

17 What is the difference between memory and memory less modulation

schemes?

24

18 What is an equalizer? What is its importance? 25

19 What is the principle of zero forcing equalizer? 25

20 What is the difference between peak distortion criterion and MSE criterion? 25

21 What is the difference between linear and adaptive equalizer? 25

22 What is meant by Spectral Efficiency?

23 Why Eb/No ratio is preferred for SNR in digital communication?

Page 95 of 103

1.6) Assignment Questions: Sl.

No.

Questions

1

2 Write the signal space diagram of FSK signal set for M=2 and M=3.

3 Show that the inner product of two signals:

xm n -n)].

4 Explain the PPM technique with waveforms for the different time shifting c

Compare them.

5 Derive the pulses for PPM scheme to transmit 8 symbols.

6 Explain the properties of orthogonal FSK and PPM modulation techniques. Compare them.

7 Compare the properties of Bi-orthogonal signals and orthogonal signals.

8 Show that both the correlation receiver and matched filter receivers for the demodulation of

bi-orthogonal signaling scheme produces the same output.

9 Derive an expression for probability of bit error of a coherent binary phase shift keying (PSK)

receiver.

10 Derive an expression for probability of bit error of a coherent binary frequency shift keying

(FSK) receiver considering orthogonal signals.

11

minimum error probability is . . Also determine the probability of error for this choice of

12 What are the properties of simplex signal set? Explain with suitable examples.

13 What is the advantage of using gray coding while mapping the signals? Explain how gray

coding is assigned with examples.

14 With block diagrams, explain the working of QPSK modulator and demodulator.

15 Illustrate the modulation and demodulation process in differential phase shift keying system

considering the binary data 1100101011.

16 Compare the spectral efficiency of the three digital modulation schemes-ASK,PSK and FSK.

17 Binary data having a bit rate of 10kbps is transmitted using binary PAM scheme. Find the

average bit energy and the signal amplitude required to achieve an error probability of 10-5

when the data is transmitted through an AWGN channel with noise power spectral density of

10-8 watts/Hz. Assume Q(4.27) = 10-5.

18 A digital communication system employing frequency shift keying scheme is used for

Page 96 of 103

transmitting information over an AWGN channel having power spectral density 10-9

Watts/Hz. The bit rate used is 2000 bits/sec. Determine the average bit energy and

probability of error when the signal amplitude at input of the receiver is A=10 milli-volts.

19 A coherent FSK system transmits binary data at the bit rate of 3Mbits/sec. In the absence of

the noise, the amplitude of the received signal is 1microvolt. During the transmission, white

Gaussian noise of zero mean and two sided power spectral density 10-20 watts/Hz is added to

the signal. Find the average probability of bit error.

20 A binary receiver system receives a bit rate of 1 Mbps. The waveform amplitude is 6 mV and

the noise power spectral density is 10-11 W/Hz. Calculate the average bit error probability if

the modulation schemes are (i) ASK,(ii)PSK, and (iii)FSK.

21 A binary DPSK system is to have an average probability of error, Pe < 10-4. If the average

transmitted power is 150 milliwatts, the channel attenuation is 80 dB and the additive zero-

mean white Gaussian noise on the channel is having a two-sided PSD of (10-15) W/Hz, find the

maximum allowable bit rate for transmission.

22 Explain the trade-off between bandwidth, average energy, bit rate and probability of error in

communication.

23 In order to transmit at 4.8 kbps over a channel with 3.2kHz bandwidth, which type of M-level

PSK would be most suitable BPSK, QPSK, or 8-PSK. Justify you answer.

24 Derive an expression for error probability of Quadrature Phase Shift Keying (QPSK) system.

Compare its spectral and power efficiency with that of BPSK system.

25 What is an equalizer? What are the functions performed by an equalizer?

26 Explain the role of the equalizer when the channel impulse response h(t) does not satisfy

Nyquist’s first criterion.

27 Compare the linear and adaptive equalizer.

28 Explain the working of decision feedback equalizer?

29 Explain the peak distortion equalizer? Is it same as the zero-forcing equalizer?

30 Determine the tap weight coefficients of a three-tap-zero forcing equalizer if the ISI spans

three symbols and is characterized by the values x(0)=1, x(-1)=0.3, x(1)=0.2. Also determine

the residual ISI at the output of the equalizer for the optimum tap coefficients.

Page 97 of 103

1.7) Test your skill:

Sl.

No.

Questions

1 Verify that the output of a correlator and a matched filter are maximum at t = T, even

though they may differ at other times.

2 Demodulation of binary antipodal signal can be accomplished by an integrate-and-dump

receiver followed by a detector. Determine the SNR at the output of the integrator

sampled at t = T.

3 In PPM method the information is present in the position of the pulse. Justify this

statement.

4 For the binary stream of data 1100100110 draw the waveforms for:

(i) Polar NRZ. (ii) Unipolar RZ code. (iii) Manchester code

5 Derive an expression for the power spectral density of NRZ polar format for the binary

data. Hence explain the bandwidth of the signal.

6 Compare the features orthogonal, bi-orthogonal and simplex signals.

7 A binary communication system employs the on-off signalling for transmission of the

information. The demodulator cross-correlates the received signal r(t) with s1(t) and

sampled the output of the correlator at t = T.

(i) Determine the optimum detector for an AWGN channel and the optimum threshold

assuming the signals are equally probable.

(ii) Find the probability of error as a function of the SNR.

8 The signals 1(t) = A. cos(2 ) and 2(t) = A. sin(2 ), for (0 < t T), where T is the

symbol duration, are used as basis functions for band pass digital modulation. Show that

1(t) and 2(t) are orthogonal over the interval (0 < t T). Assume = 2/ . 9 A binary PAM communication system is used to transmit data over an AWGN channel. The

Prior probabilities for the bits are P(1) = 1/3 and P(0) = 2/3. Find the average probability

of a bit error.

10 A binary signalling scheme uses the Manchester code to describe the symbols 1 and 0.

Assume that the receiver noise is white, Gaussian and zero mean and power spectral

density No/2. Determine the average probability of error when symbols 1 and 0 occur

with equal probability.

Page 98 of 103

11 A 1 Mbps BPSK receiver detects waveforms s1(t) 0t or s2(t)= - 0t with a

matched filter. (a) If A=1mV, what will be the average bit error probability? (b) What

should be the average received signal power to maintain an error probability of 2*10-3?

Assume single sided noise power spectral density to be N0=10-11W/Hz(c) Binary antipodal

signals are used in another scheme with amplitude of ±100V to transmit information over

an AWGN channel at a rate of 105bps. The psd N0/2=0.5*10-2w/Hz. Determine the error

probability achieved.

12 A simple binary communication system model, with additive Gaussian noise, is the

following: S is a binary random variable, representing the message bit sent, taking values

1 and +1 with equal probability. Additive noise is represented by a Gaussian random

variable Z of zero mean and variance 2. The received value is a random variable X = S + Z.

Find the probability density function (pdf) of X.

13 Binary PSK (BPSK) is used for data transmission over an AWGN channel with power

spectral density N0/2 = 10 10 W/Hz. The transmitted signal energy is Eb = A2T/2, where T is

the bit duration and A is the signal amplitude. Determine the value of A needed to achieve

an error probability of 10 6, if the data rate is: (i) 10000 bits/sec (ii) 100K bps.

14 A coherent FSK system transmits binary data at the bit rate of 2Mbits/sec. In the absence

of the noise, the amplitude of the received signal is 1microvolt. During the transmission,

white Gaussian noise of zero mean and two sided power spectral density 10-20 watts/Hz is

added to the signal. Find the average probability of bit error.

15 Determine the reduction in the transmission bandwidth and the average signal energy of

64 QAM and 16 QAM for the same probability of error to be obtained for both.

16 In a digital communication system, using coherent BPSK, it is necessary to keep the

degradation due to phase error to about 0.1 or less. How much of phase error can the

system tolerate?

17 Consider voice transmission using BPSK signaling at a transmission rate of 2400 bps and a

bandwidth efficiency of 1 bps/Hz. It is desired to increase the data rate to 9.6kbps. If the

number of points in the signal constellation is increased until the data rate becomes

9.6kbps while the symbol rate remains at 2400 symbols/sec determine the number of

constellation points.

18 Derive an expression for error probability of Quadrature Phase Shift Keying (QPSK) system.

Compare its spectral and power efficiency with that of BPSK system.

19 In a coherent BPSK system, the correlator in the receiver, to which the received PSK signal

Page 99 of 103

carrier phase. Determine the effect of this phase error

system.

20 The signal constellation diagram for an 8-QAM system is shown below.

(i) Suggest a suitable receiver structure.

(ii) Compute the probability of error for the receiver.

21 What is “Eye pattern”? Explain how it is useful in understanding the ISI problem?

22 Describe the role of the equalizer when the channel impulse response h(t) does not satisfy

Nyquist’s first criterion. Explain how the equalizer known as the linear transversal filter

fulfills this role and provide justification for the “tapped delay” structure of such an

equalizer.

23 Compute the tap weight coefficients of a three-tap-zero forcing equalizer if the ISI spans

three symbols and is characterized by the values x(0)=0.9, x(-1)=0.25, x(1)=0.25. Also

determine the residual ISI at the output of the equalizer for the optimum tap coefficients.

24 Mention the different types of memory less and memory modulation schemes.

25 Explain how storing data on a magnetic or optical disk is equivalent to transmitting a signal

over a radio channel.

26 What are the different types of multiple access schemes used in digital Communication?

Compare their characteristics.

Page 100 of 103

4.8) Additional Links: Module-4 General Links

http://www.youtube.com/watch?v=pZbczyghP8Y http://www.youtube.com/watch?v=2yXQ6VrbpKk http://www.youtube.com/watch?v=a-pjhbYkRFM http://demonstrations.wolfram.com/DigitalModulationQuadraturePhaseShiftKeyingQPSKSignalConstel/ http://freevideolectures.com/Course/2311/Digital-Communication

http://freevideolectures.com/Course/2177/Principles-of-Digital-Communication-II

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-450-principles-of-digital-communications-i-fall-2006/lecture-notes/book_1.pdf

Q Nos

Question Videos Web Link

1 Digital Modulation http://www.youtube.com/watch?v=pZbczyghP8Y http://www.youtube.com/watch?v=2yXQ6VrbpKk

https://www.google.co.in/search?q=Digital+modulation&tbm=isch&tbo=u&source=univ&sa=X&ei=ASQvU-_oKIaNrQfnqYGgBA&ved=0CDIQsAQ&biw=1366&bih=596

http://web.ee.ccu.edu.tw/~wl/wenclass/95/IDCclass/Ch5_Digital.pdf

http://en.wikipedia.org/wiki/Shift_keying#Digital_modulation_methods

2 Shift keying techniques

www.youtube.com/watch?v=5o43sBgDYLA www.youtube.com/watch?v=Ez__KA00hD8 www.youtube.com/watch?v=Cf2hGhs2k-8 www.youtube.com/watch?v=c51oxnOGI5k www.youtube.com/watch?v=

www.ele.uri.edu/Courses/ele436/labs/ASKnFSK.pdf

https://www.fas.org/man/dod-101/navy/docs/es310/.../digicoms.html

http://en.wikipedia.org/wiki/Shift_keying#Digital_modulation_methods

Page 101 of 103

dE_nLy9abaY

www.youtube.com/watch?v=pNkTWgtUjDU

3 ASK, FSK, BPSK

http://www.youtube.com/watch?v=jTzqXywJVlc http://www.youtube.com/watch?v=oUcNdlKioDg http://www.youtube.com/watch?v=iT1GGT5R-9w

http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCcQFjAA&url=http%3A%2F%2Fwww.ni.com%2Fwhite-paper%2F7824%2Fen%2F&ei=dQwzU9_VHcmBrQevgYGYBg&usg=AFQjCNFtohrulplU8kmR0Q4XxoUBQ74q1Q&sig2=NzIO6ljp8NiPJv0eAob-ow&bvm=bv.63738703,d.bmk

http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CDkQFjAC&url=http%3A%2F%2Fwww.slideshare.net%2Folamashaqi%2Fdiditalpres-final&ei=dQwzU9_VHcmBrQevgYGYBg&usg=AFQjCNFffZ-7sCA2m5qD736ZQEqgNT0o5A&sig2=KQw_wxGdZG6IWQJ-Kde9WQ&bvm=bv.63738703,d.bmk

https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0CEIQFjAD&url=https%3A%2F%2Fwww.labvolt.com%2Fdownloads%2Fcwa8087_30.pdf&ei=dQwzU9_VHcmBrQevgYGYBg&usg=AFQjCNEsfULCQqZ0bnyOgfZMGVRA0n57ew&sig2=cFUHlQQXBovoCHNsYneYEg&bvm=bv.63738703,d.bmk

4 Probability of error www.youtube.com/watch?v=PQ48szd9cw0 www.youtube.com/watch?v=UWZZ5Ig3d8M www.youtube.com/watch?v=Dw3UR4-7qMA

www.ece.utah.edu/~npatwari/ece5520/lectureAll.pdf

www.ece.ualberta.ca/~chintha/resources/papers/2005/1431129.pdf

http://en.wikipedia.org/wiki/Bit_error_rate

5 Eye diagram www.youtube.com/watch?v=oBHytOmmiRU http://demonstrations.wolfram.com/DigitalModulationQuadraturePhase

www.engr.sjsu.edu/rmorelos/ee251f06/eyediagram_notes.pdf

http://en.wikipedia.org/wiki/Eye_diagram

Page 102 of 103

ShiftKeyingQPSKSignalConstel/

6 Equalizer http://www.youtube.com/watch?v=a-pjhbYkRFM

http://www.freewebs.com/angsuman/chapter5.pdf

http://en.wikipedia.org/wiki/Equalizer

Page 103 of 103