Digital Communication SPPU _Unit II.pptx

1. Faculty Orientation Program on TE (E&TC) Revised Syllabus 2019 Course under the aegis of Board of Studies E&TC, SPPU, Pune July 22, 2021 Digital Communication Dr Mrs P Malathi Professor & HOD E&TC DYPCOE, Akurdi, Pune

2. Unit II Digital Modulation-I (07 Hrs.) Baseband Signal Receiver: Probability of Error, Optimal Receiver Design. Digital Modulation: Generation, Reception, Signal Space Representation and Probability of Error Calculation for Binary Phase Shift Keying (BPSK), Binary Frequency Shift Keying (BFSK), Quadrature Phase Shift Keying (QPSK), M- ary Phase Shift Keying (MPSK). CO2: Understand and explain various digital modulation techniques used in digital communication systems and analyze their performance in presence of AWGN noise.

3. Text Books: Taub, Schilling and Saha , “Principles of Communication Systems”, McGraw-Hill, 4 th Edition, B.P. Lathi, Zhi Ding , “Modern Analog and Digital Communication System”, Oxford University Press, 4th Edition. Reference Books: Bernard Sklar , Prabitra Kumar Ray, “Digital Communications Fundamentals and Applications”, Pearson Education, 2nd Edition Wayne Tomasi , “Electronic Communications System”, Pearson Education, 5th Edition A.B Carlson, P B Crully , J C Rutledge, “Communication Systems”, Tata McGraw Hill Publication, 5t h Edition Simon Haykin , “Communication Systems”, John Wiley & Sons, 4th Edition 5. Simon Haykin , “Digital Communication Systems”, John Wiley & Sons, 4 th Edition. MOOC / NPTEL Courses: 1. NPTEL Course on “Digital Communications” Link of the Course: https://nptel.ac.in/courses/108/102/108102096/ Learning Resources

4. Objectives To understand base band receiver design and analysis of performance parameter probability of error. To study generation and reception of digital modulation methods of BPSK, BFSK, QPSK and M- ary PSK. To study signal space representation and its significance for various digital modulation techniques. Derive mathematical expression for Probability of digital modulation techniques BPSK, BFSK, QPSK and M- ary PSK.

5. Outcomes [Contributing to Placement, Higher Education, Entrepreneurship] Students Will Able to analyze baseband receiver for digital communication system. Compute probability of error for optimum filter Appraise the concept of generation and reception of different digital modulation techniques such as BPSK, BFSK, QPSK, MPSK. Understand significance of signal space representation and power spectral density of BPSK, BFSK, QPSK, MPSK. Compute probability of error for digital modulation techniques.

6. Base Band Receiver

7. 7 Detection of Binary Signal in Presence of Noise For any binary channel, the transmitted signal over a symbol interval (0,T) is: The received signal r(t) degraded by noise n(t) and possibly degraded by the impulse response of the channel h c (t), is Where n(t) is assumed to be zero mean AWGN process For ideal distortion less channel where h c (t) is an impulse function and convolution with h c (t) produces no degradation, r(t) can be represented as:

8. 8 Detection of Binary Signal in Presence of Noise The recovery of signal at the receiver consist of two parts Filter Reduces the effect of noise (as well as Tx induced ISI) The output of the filter is sampled at t=T. This reduces the received signal to a single variable z(T) called the test statistics Detector (or decision circuit) Compares the z(T) to some threshold level  , i.e., where H 1 and H 2 are the two possible binary hypothesis

9. Optimum Filter It is used for detecting baseband signals Requirements of signal receivers must have Improved SNR Checked at instant in bit period when SNR is Maximum Minimum Pe Decision Threshold in Optimum Filter Let us assume that received signal is binary waveform & is represented in Polar NRZ signaling For Binary 1 : S 1 (t) = +A for T duration For Binary 0 : S 2 (t) = -A for T duration

10. Optimum Filter Thus the input signal can either be S 1 (t) or S 2 (t) depending upon the polarity of NRZ Signaling In absence of Noise, receiver output is r(T) = S 01 (T) if s(t) = s 1 (t) r(T) = S 02 (T) if s(t) = s 2 (t) Thus in absence of noise, decisions are taken clearly.

11. In presence of noise Select S 1 (t) if r(T) is closer to S 01 (T) than S 02 (T) Select S 2 (t) if r(T) is closer to S 02 (T) than S 01 (T) Therefore the decision boundary will be the midway between S 01 (T) & S 02 (T) i.e. decision boundary = (S 01 (T) + S 02 (T))/2 Optimum Filter

12. Probability of Error for Optimum Filter Suppose that S 2 (t) was transmitted, but S 01 (T) is greater than S 02 (T). If noise n o (T) is positive & larger in magnitude then the voltage difference [(S 01 (T)+S 02 (T))/2] - S 02 (T) then incorrect decision will be taken. Error will be generated if n o (T) ≥ [(S 01 (T) + S 02 (T))/2]-S 02 (T) n o (T) ≥ [(S 01 (T) - S 02 (T))/2] …………… 1

13. Similarly, Suppose that S 1 (t) was transmitted, but S 02 (T) is greater than S 01 (T). Incorrect decision will be taken if n o (T) ≤ [(S 02 (T) - S 01 (T))/2] …………….. 2 Probability of error for S 1 (t) & S 2 (t) are obtained on evaluating Probability of equation 1 & 2 respectively. Probability of Error for Optimum Filter

14. Probability of Error for Optimum Filter P[n0(t)]=(S01(T)-S02(T))/2

15. Probability of Error for Optimum Filter Gaussian Noise: pdf of a Gaussian distributed function for random variable x is given by, To calculate pdf of a white Gaussian noise we replace x = n o (T) & zero mean, i.e. m=0

16. Probability of Error for Optimum Filter P[no(T) ≥ [(S 01 (T) - S 02 (T))/2] ] = To solve the above integral Put So integrals will change to

17. Probability of Error for Optimum Filter We use the standard erfc function Probability of Error for Optimum Filter is given by Optimum Filter has to maximize the ratio in such a way that Pe becomes maximum

18. 18 An optimum filter yields a maximum ratio is called a matched filter when the input noise is white. In other words the matched filter is the optimal filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive white Noise. So the noise spectral density will be . Transfer function of matched filter is given by The impulsive response of the filter can be calculated by taking inverse Fourier transform of H(f). = X Transfer Function of Matched filter   Matched Filter

19. 19 The impulse response of a filter producing maximum output signal-to-noise ratio is the mirror image of message signal s(t), delayed by symbol time duration T. The filter designed is called a MATCHED FILTER   Matched Filter

20. 20 Realization of Matched filter A filter that is matched to the waveform s(t) , has an impulse response h(t) is a delayed version of the mirror image of the original signal waveform   Signal Waveform Mirror image of signal waveform Impulse response of matched filter

21. In correlator the received signal plus noise n(t) is multiplied by a locally generated waveform s1(t)-s2(t). The output of the multiplier is passed through an integrator whose output is sampled at t=T. This type of receiver is called a correlator since we are correlating the received signal and noise with the waveform s1(t) –s2(t). The output signal and noise of the correlator shown - ]dt where Si(t) is either S1(t) ot S2(t) - ]dt   Correlator

22. Correlator The matched filter and correlator are not simply two distinct, independent techniques which happen to yield the same result. In fact they are two techniques of synthesizing the optimum filter h(t).

23. Digital Modulation

24. Digital modulation and demodulation: Modulation maps the digital information into an analog waveform appropriate for transmission over the channel. Examples: ASK, FSK, PSK In CW modulation , PM and FM signals are difficult to distinguish. In PSK and FSK both have constant envelope while ASK does not. Demodulation recover the baseband digital information from a bandpass analog signal at a carrier frequency that is very high compared to the baseband frequency.

25. Digital Modulation Techniques Modulation involves operations on one or more of the three characteristics of a carrier signal: Amplitude, Frequency and Phase . The three basic modulation methods are: Amplitude Shift Keying (ASK) Phase Shift Keying (PSK) –Frequency Shift Keying (FSK) These could be applied to binary or M-ary signals.

26. Waveforms for the three basic forms of signaling binary information (a) Amplitude-shift keying. (b) Phase-shift keying. (c) Frequency-shift keying with continuous phase.

27. In BPSK the transmitted signal is a sinusoid of fixed amplitude. It has one fixed phase when the data is at one level and when the data is at other level the phase is different by 180 degree. Binary Phase-Shift Keying (BPSK) 0 1 1 0 1 0 0 1

28. Binary Phase-Shift Keying (BPSK) BPSK equation can be written as Where b(t) will be either 1 or -1   , , bit duration : carrier frequen c y , c ho s en to be for s o m e fi x ed integer : t transmitted signal energy per bit, i.e. The pair of signals differ only in a relative phase shift of 180 degrees or f c   1 / T b “1” “0”

29. BPSK Transmitter

30. BPSK Receiver

31. Spectral Density of BPSK  

32. PSD of NRZ Data b(t) & Binary PSK BW= 2fb

33. T he r e i s on e bas i s f unc ti o n o f un i t ene r gy Then A binary PSK system is therefore characterized by having a signal space that is one-dimensional (i.e. N=1), and with two message points (i.e. M = 2) s 1 s 2 Signal Space Representation for BPSK

34. Decision rule of BPSK Decision rule: Signal s 1 (t) (or binary 1) was transmitted if the received signal point r falls in region R 1 Signal s 2 (t) (or binary 0) was transmitted otherwise s 1 s 2 Assume that the two signals are equally likely, i.e. P(s 1 ) = P(s 2 ) = 0.5. Then the optimum decision boundary is the midpoint of the line joining these two message points Region R 2 Region R 1

35. The conditional probability of the receiver deciding in favor of symbol s 2 (t) given that s 1 (t) is transmitted is r Probability of Error for BPSK

36. Probability of Error for BPSK BPSK signal for 1 and 0 Probability of Error function for Optimum Filter Maximum Signal to noise ratio of Optimum filter. PSD of White noise input is S ni (f)=N0/2

37. Probability of Error for BPSK X(t)=s1(t)-s2(t) Probability of Error for BPSK is given by

38. Quadrature Phase Shift Keying (QPSK) PSK that uses phase shifts of 90º= π /2 rad 4 different signals generated, each representing 2 bits Advantage: higher data rate than in PSK (2 bits per bit interval), while bandwidth occupancy remains the same 4-PSK can easily be extended to 8-PSK, i.e. n-PSK However, higher rate PSK schemes are limited by the ability of equipment to distinguish small differences in phase

39. Mathematical Representation of QPSK  

40. QPSK Waveforms

41. QPSK Transmitter

42. QPSK Receiver

43. Signal Space Representation

44. Signal Space Representation

45. p. 45

46. PSD of QPSK p. 46 In QPSK M=4  

47. Probability of Error for QPSK Error Probability of QPSK is given by Pe QPSK = 2 x Pe BPSK In QPSK each symbol is of 2 bit duration long so E=2Eb Therefore probability of error for QPSK is

48. M ary PSK (MPSK) In M- ary data transmission, it sends one of M possible signals during each signaling interval T. M=2^n and T= nTb , where n is an integer. Each of the M signals is called as symbol. In MPSK the phase of the carrier takes on M possible values.

49. M ary PSK (MPSK) The mathematical equation for MPSK is given by

50. MPSK Transmitter

51. MPSK Receiver

52. Signal Space Representation

53. Signal Space Representation

54. Power Spectral Density of MPSK

55. Probability of Error for MPSK Probability of MPSK is given by

56. Binary Frequency Shift Keying 0 1 1 0 1 0 0 1 The output of a FSK modulated wave is high in frequency for a binary High input and is low in frequency for a binary Low input. The binary 1s and 0s are called Mark and Space frequencies.

57. Binary Frequency Shift Keying  

58. Two balanced modulators are used one with carrier W H and one with carrier W L . The voltage values of P H (t) and P L (t) are related to the voltage values of d(t) in the following manner d(t) P H (t) P L (t) +1 V +1V 0V -1V 0V +1V Binary Frequency Shift Keying

59. Binary FSK Transmitter

60. Non Coherent BFSK Receiver

61. Coherent Binary FSK Receiver

62. Power Spectral Density of BFSK  

63. Power Spectral Density of BFSK  

64. PSD of BFSK BW= 4fb

65. Unlike BPSK, here two orthogon normal basis functions are required to represent s 1 (t) and s 2 (t). S i gna l spac e represent a ti on Signal Space for BFSK

66. S i gna l spac e d iagra m f o r b inar y FS K Message point Message point

67. Decision Regions of Binary FSK The receiver decides in favor of s 1 if the received signal point represented by the observation vector r falls inside region R 1 . This occurs when r 1 > r 2 When r 1 < r 2 , r falls inside region R 2 and the receiver decides in favor of s 2 M e ss ag e po i nt M e ss age po i nt D e c i s i o n bounda ry R 1 R 2

68. Probability of Error for Binary FSK The binary FSK signal is represented as For binary 1 For binary 0 Probability of Error function for Optimum Filter Error Probability of BPSK is given by Non-orthogonal FSK Orthogonal FSK

69. Probability of Error and the Distance Between Signals Parameters BPSK QPSK BFSK d 12 2 E b 2 E b 2E b P e ½ erfc ( E b /N o ) erfc ( E b /N o ) ½ erfc ( 0.6E b /N o ) Bandwidth requirement 2f b f b 4f b Modulation Linear Linear Non linear

70. Applications QPSK is used in various cellular wireless standards such as GSM, CDMA, LTE, 802.11 WLAN, 802.16 fixed and mobile WiMAX , Satellite and CABLE TV applications.   BPSK modulation is a very basic technique used in various wireless standards such as CDMA, WiMAX (16d, 16e), WLAN 11a, 11b, 11g, 11n, Satellite, DVB, Cable modem etc.  Telephone line modem use FSK to transmit 300 bits/sec at two frequencies 1070Hz & 1270 Hz

71. Digital Communication Lab

72. List of Laboratory Experiments based on Unit-II Group A 1 Study of BPSK transmitter & receiver using suitable hardware setup/kit. 2 Study of QPSK transmitter & receiver using suitable hardware setup/kit 3 Study of BFSK transmitter & receiver using suitable hardware setup/kit 4 Study of Baseband receiver performance in presence of Noise using suitable hardware setup/kit. Group C 5 Simulation study of Performance of M- ary PSK 6 Simulation Study of performance of BPSK receiver in presence of noise

73. Study of BPSK transmitter & receiver

74. Study of QPSK transmitter & receiver

75. Study of BFSK transmitter & receiver

76. Study of Baseband receiver performance in presence of Noise

77. Simulation Study of performance of BPSK receiver in presence of noise % Initialization of Data and variables clc ; clear all ; close all ; nr_data_bits =8192; b_data=(randn(1,nr_data_bits))>.5; b=[ b_data ]; d=zeros(1,length(b));

78. Generation of BPSK for n=1:length(b) if (b(n)==0) d(n)=exp(j*2*pi); end if(b(n)==1) d(n)= exp(j*pi); end end disp (d) bpsk =d;

79. Plotting of BPSK Data figure(1); plot( d, 'o ' ); axis([-2 2 -2 2]); grid on ; xlabel ( 'real' ); ylabel ( ' imag ' ); title( 'BPSK constellation' );

80. Addition of Noise SNR=0:24; BER1=[]; SNR1=[]; for SNR=0:length(SNR ); sigma=sqrt(10.0^(-SNR/10.0)); snbpsk =(real( bpsk )+sigma.* randn (size( bpsk )))+ i .*( imag ( bpsk )+sigma* randn (size( bpsk )));

81. Plotting of BPSK data with Noise figure(2); plot( snbpsk , 'o' ); axis([-2 2 -2 2]); grid on ; xlabel ( 'real' ); ylabel ( ' imag ' ); title( ' Bpsk constellation with noise' );

82. Recovering of Data %receiver r= snbpsk ; bhat =[real(r)<0]; bhat = bhat (:)'; bhat1= bhat ; ne=sum(b~=bhat1); BER=ne/nr_data_bits; BER1=[BER1 BER]; SNR1=[SNR1 SNR]; end

83. Plotting of BER graph of BPSK figure(3); semilogy (SNR1,BER1, '-*' ); grid on ; xlabel ( 'SNR=Eb/No( db )' ); ylabel ( 'BER' ); title( 'Simulation of BER for BPSK ' ); legend( 'BER-simulated' );

84. Thank You….. !!