1. NARROW BAND NOISE UNIT IV Prepared by: D.MENAKA & S.NANDHINI, Assistant Professor, Dept. of ECE, Sri Venkateswara College of Engineering, Sriperumbudur, Tamilnadu.

2. Narrowband Noise Representation The noise process appearing at the output of a narrowband filter is called narrowband noise. With the spectral components of narrowband noise concentrated about some midband frequency as in Figure 1.18a. We find that a sample function n(t) of such a process appears somewhat similar to a sine wave of frequency as in Figure 1.18b. Representations of narrowband noise – A pair of component called the in-phase and quadrature components. – Two other components called the envelop and phase.

3. Representation of Narrowband Noise in Terms of In- Phase and Quadrature Components Consider a narrowband noise of bandwidth 2 B centered on frequency,as illustrated in Figure 1.18. We may represent n(t) in the canonical (standard) form: where, is in-phase component of and is quadrature component of.

4. and have important properties: – and have zero mean. – is Gaussian, then and are jointly Gaussian. – is stationary, then and are jointly stationary. – Both and have the same power spectral density. – and have the same variance as

6. Representation of Narrowband Noise in Terms of Envelope and Phase Components

8. Figure 1.21 Illustrating the coordinate system for representation of narrowband noise: (a) in terms of in-phase and quadrature components, and (b) in terms of envelope and phase.

11. Sine Wave Plus Narrowband Noise

14. : Rician distribution reduced to the Rayleigh distribution The envelope distribution is approximately Gaussian when a is large

15. NOISE IN AM AND FM

16. NOISE IN COMMUICATION SYSTEMS Noise in Communication Systems Signal-to-Noise Ratios Band-Pass Receiver Structures Noise in Linear Receivers Using Coherent Detection Noise in AM Receivers Using Envelope Detection Noise in SSB Receivers Detection of Frequency Modulation (FM) FM Pre-emphasis and De-emphasis Summary and Discussion

17. 17  Noise can broadly be defined as any unknown signal that affects the recovery of the desired signal.  The received signal is modeled as  is the transmitted signal  is the additive noise

18. 18  Lesson 1 : Minimizing the effects of noise is a prime concern in analog communications, and consequently the ratio of signal power is an important metric for assessing analog communication quality.  Lesson 2 : Amplitude modulation may be detected either coherently requiring the use of a synchronized oscillator or non-coherently by means of a simple envelope detector. However, there is a performance penalty to be paid for non- coherent detection.  Lesson 3 : Frequency modulation is nonlinear and the output noise spectrum is parabolic when the input noise spectrum is flat. Frequency modulation has the advantage that it allows us to trade bandwidth for improved performance.  Lesson 4 : Pre-and de-emphasis filtering is a method of reducing the output noise of an FM demodulator without distorting the signal. This technique may be used to significantly improve the performance of frequency modulation systims.

19. 19 Noise in Communication Systems  The mean of the random process  Both noise and signal are generally assumed to have zero mean.  The autocorrelation of the random process.  With white noise, samples at one instant in time are uncorrelated with those at another instant in time regardless of the separation. The autocorrelation of white noise is described by  The spectrum of the random process. For additive white Gaussian noise the spectrum is flat and defined as  To compute noise power, we must measure the noise over a specified bandwidth. Equivalent-noise bandwidth is Fig. 9.1

20. 20 Fig. BackNext

21. 21 Signal-to-Noise Ratios  The desired signal,, a narrowband noise signal,  For zero-mean processes, a simple measure of the signal quality is the ratio of the variances of the desired and undesired signals.  Signal-to-noise ratio is defined by  The signal-to-noise ratio is often considered to be a ratio of the average signal power to the average noise power.

22. 22

23. 23 Fig. 9.2

24. 24 Fig. BackNext

25. 25  If the signal-to-noise ratio is measured at the front-end of the receiver, then it is usually a measure of the quality of the transmission link and the receiver front-end.  If the signal-to-noise ratio is measured at the output of the receiver, it is a measure of the quality of the recovered intormation-bearing signal whether it be audio, video, or otherwise.  Reference transmission model  This reference model is equivalent to transmitting the message at baseband. Fig. 9.3

26. 26 Fig. BackNext

27. 27 1. The message power is the same as the modulated signal power of the modulation scheme under study. 2. The baseband low-pass filter passes the message signal and rejects out-of-band noise. Accordingly, we may define the reference signal-to-noise ratio,, as  A Figure of merit Fig. 9.4

28. 28 Fig. BackNext

29. 29  The higher the value that the figure of merit gas, the better the noise performance of the receiver will be.  To summarize our consideration of signal-to-noise ratios:  The pre-detection SNR is measured before the signal is demodulated.  The post-detection SNR is measured after the signal is demodulated.  The reference SNR is defined on the basis of a baseband transmission model.  The figure of merit is a dimensionless metric for comparing sifferent analog modulation-demodulation schemes and is defined as the ratio of the post-detection and reference SNRs.

30. 30 Band-Pass Receiver Structures  Fig. 9.5 shows an example of a superheterodyne receiver  AM radio transmissions  Common examples are AM radio transmissions, where the RF channels’ frequencies lie in the range between 510 and 1600 kHz, and a common IF is 455 kHz  FM radio  Another example is FM radio, where the RF channels are in the range from 88 to 108 MHz and the IF is typically 10.7 MHz.  The filter preceding the local oscillator is centered at a higher RF frequency and is usually much wider, wide enough to encompass all RF channels that the receiver is intended to handle.  With the same FM receiver, the band-pass filter after the local oscillator would be approximately 200kHz wide; it is the effects of this narrower filter that are of most interest to us. Fig. 9.5

31. 31 Fig. BackNext

32. 32 Noise in Linear Receivers Using Coherent Detection  Double-sideband suppressed-carrier (DSB-SC) modulation, the modulated signal is represented as  is the carrier frequency  is the message signal  The carrier phase  In Fig. 9.6, the received RF signal is the sum of the modulated signal and white Gaussian noise  After band-pass filtering, the resulting signal is Fig. 9.6

33. 33 Fig. BackNext

34. 34  In Fig.9.7  The assumed power spectral density of the band-pass noise is illustrated  For the signal of Eq. (9.13), the average power of the signal component is given by expected value of the squared magnitude.  The carrier and modulating signal are independent  Pre-detection signal-to-noise ratio of the DSB-SC system  A noise bandwidth  The signal-to-noise ratio of the signal is Fig. 9.7

35. 35 Fig. BackNext

36. 36  The signal at the input to the coherent detector of Fig. 9.6  These high-frequency components are removed with a low- pass filter

37. 37  The message signal and the in-phase component of the filtered noise appear additively in the output.  The quadrature component of the noise is completely rejected by the demodulator. Post-detection signal to noise ratio  The message component is, so analogous to the computation of the predetection signal power, the post- detection signal power is where P is the average message power as defined in Eq. (9.16).  The noise component is after low-pass filtering. As described in Section 8.11, the in-phase component has a noise spectral density of over the bandwidth from. If the low-pass filter has a noise bandwidth W, corresponding to the message bandwidth, which is less than or equal to, then the output noise power is

38. 38  Post-detection SNR of  Post-detection SNR is twice pre-detection SNR.  Figure of merit for this receiver is  We lose nothing in performance by using a band-pass modulation scheme compared to the baseband modulation scheme, even though the bandwidth of the former is twice as wide.

39. 39 Noise in AM Receivers Using Envelope Detection  The envelope-modulated signal  The power in the modulated part of the signal is  The pre-detection signal-to-noise ratio is given by Fig. 9.8

40. 40 Fig. BackNext

41. 41  Model the input to the envelope detector as  The output of the envelope detector is the amplitude of the phasor representing and it is given by  Using the approximation Fig. 9.9

42. 42 Fig. BackNext

43. 43  The post-detection SNR for the envelope detection of AM,  This evaluation of the output SNR is only valid under two conditions:  The SNR is high.  is adjusted for 100% modulation or less, so there is no distortion of the signal envelope.  The figure of merit for this AM modulation-demodulation scheme is Fig. 9.10 Fig. 9.11

44. 44 Fig. BackNext

45. 45 Fig. BackNext

46. 46  In the experiment, the message is a sinusoidal wave  We compute the pre-detection and post-detection SNRs for samples of its signal. These two measures are plotted against one another in Fig. 9.12 for.  The post-detection SNR is computed as follows:  The output signal power is determined by passing a noiseless signal through the envelope detector and measuring the output power.  The output noise is computed by passing plus noise through the envelope detector and subtracting the output obtained form the clean signal only. With this approach, any distortion due to the product of noise and signal components is included as noise contribution.  From Fig.9.12, there is close agreement between theory and experiment at high SNR values, which is to be expected. There are some minor discrepancies, but these can be attributed to the limitations of the discrete time simulation. At lower SNR there is some variation from theory as might also be expected. Fig. 9.12

47. 47 Fig. BackNext

48. 48 Noise in SSB Receivers  The modulated wave as  We may make the following observations concerning the in- phase and quadrature components of in Eq. (9.32) : 1. The two components and are uncorrelated with each other. Therefore, their power spectral densities are additive. 2. The Hilbert transform is obtained by passing through a linear filter with transfer function. The squared magnitude of this transfer function is equal to one for all. Accordingly, and have the same average power.

49. 49  The pre-detection signal-to-noise ratio of a coherent receiver with SSB modulation is  The band-pass signal after multiplication with the synchronous oscillator output is  After low-pass filtering the, we are left with

50. 50  The spectrum of the in-phase component of the noise is given by  The post-detection signal-to-noise ratio  The figure of merit for the SSB system

51. 51  Comparing the results for the different amplitude modulation schemes  There are a number of design tradeoffs.  Single-sideband modulation achieves the same SNR performance as the baseband reference model but only requires half the transmission bandwidth of the DSC-SC system.  SSB requires more transmitter processing.

52. 52 Detection of Frequency Modulation (FM)  The frequency-modulated signal is given by  Pre-detection SNR  The pre-detection SNR in this case is simply the carrier power divided by the noise passed by the bandpass filter,; namily, 1. A slope network or differentiator with a purely imaginary frequency response that varies linearly with frequency. It produces a hybrid- modulated wave in which both amplitude and frequency vary in accordance with the message signal. 2. An envelope detector that recovers the amplitude variation and reproduces the message signal. Fig. 9.13

53. 53 Fig. BackNext

54. 54  Post-detection SNR  The noisy FM signal after band-pass filtering may be represented as  We may equivalently express in terms of its envelope and phase as  Where the envelope is  And the phase is Fig. 9.14

55. 55 Fig. BackNext

56. 56  We note that the phase of is  The noisy signal at the output of the band-pass filter may be expressed as  The phase of the resultant is given by Fig. 9.15

57. 57 Fig. BackNext

58. 58  Under this condition, and noting that, the expression for the phase simplifies to  Then noting that the quadrature component of the noise is we may simplify Eq.(9.49) to  The ideal discriminator output

59. 59  The noise termis defined by  The additive noise at the discriminator output is determined essentially by the quadrature componentof the marrowband noise.  The power spectral density of the quadrature noise compinent as follows;

60. 60  Power spectral density of the noise is shown in Fig.9.16  Therefore, the power spectral density of the noise appearing at the receiver output is defined by Fig. 9.16

61. 61 Fig. BackNext

62. 62  Figure of merit  The figure of merit for an FM system is approximately given by

63. 63  Thus, when the carrier to noise level is high, unlike an amplitude modulation system an FM system allows us to trade bandwidth for improved performance in accordance with square law.

64. 64

65. 65

66. 66  Threshold effect  At first, individual clicks are heard in the receiver output, and as the pre-detection SNR decreases further, the clicks merge to a crackling or sputtering sound. At and below this breakdown point, Eq.(9.59) fails to accurately predict the post-detection SNR.  Computer experiment : Threshold effect with FM  Complex phasor of the FM signal is given by  Similar to the AM computer experiment, we measure the pre- detection and post-detection SNRs of the signal and compare the results to the theory developed in this section. Fig. 9.17

67. 67 Fig. BackNext

68. 68 FM Pre-emphasis and De-emphasis  To compensate this distortion, we appropriately pre-distort or pre-emphasize the baseband signal at the transmitter, prior to FM modulation, using a filter with the frequency response  The de-emphasis filter is often a simple resistance-capacitance (RC) circuit with  At the transmitting end, the pre-emphasis filter is Fig. 9.18

69. 69 Fig. 9.18 BackNext

70. 70  The modulated signal is approximately  Pre-emphasis can be used to advantage whenever portions of the message band are degraded relative to others.

71. 71

72. 72 Summary and Discussion  We analyzed the noise performance of a number of different amplitude modulation schemes and found: 1. The detection of DSB-SC with a linear coherent receiver has the same SNR performance as the baseband reference model but requires synchronization circuitry to recover the coherent carrier for demodulation. 2. Non-suppressed carrier AM systems allow simple receiver design including the use of envelope detection, but they result in significant wastage of transmitter power compared to coherent systems. 3. Analog SSB modulation provides the same SNR performance as DSB-SC while requiring only half the transmission bandwidth.  In this chapter, we have shown the importance of noise analysis based on signal-to-noise ratio in the evaluation of the performance of analog communication systems. This type system, be it analog or digital.

73. DISCUSSSION ON NOISE IN DEPTH

74. 74 NOISE

75. 75. Introduction 1. Introduction Noise is a general term which is used to describe an unwanted signal which affects a wanted signal. These unwanted signals arise from a variety of sources which may be considered in one of two main categories:- Interference, usually from a human source (man made) Naturally occurring random noise Interference Interference arises for example, from other communication systems (cross talk), 50 Hz supplies (hum) and harmonics, switched mode power supplies, thyristor circuits, ignition (car spark plugs) motors … etc.

76. 76. Introduction (Cont’d) 1. Introduction (Cont’d) Natural Noise Naturally occurring external noise sources include atmosphere disturbance (e.g. electric storms, lighting, ionospheric effect etc), so called ‘Sky Noise’ or Cosmic noise which includes noise from galaxy, solar noise and ‘hot spot’ due to oxygen and water vapour resonance in the earth’s atmosphere.

77. 77 2. Thermal Noise (Johnson Noise) This type of noise is generated by all resistances (e.g. a resistor, semiconductor, the resistance of a resonant circuit, i.e. the real part of the impedance, cable etc). Experimental results (by Johnson) and theoretical studies (by Nyquist) give the mean square noise voltage as Where k = Boltzmann’s constant = 1.38 x 10 -23 Joules per K T = absolute temperature B = bandwidth noise measured in (Hz) R = resistance (ohms)

78. 78 2. Thermal Noise (Johnson Noise) (Cont’d) The law relating noise power, N, to the temperature and bandwidth is N = k TB watts Thermal noise is often referred to as ‘white noise’ because it has a uniform ‘spectral density’.

79. 79 3. Shot Noise Shot noise was originally used to describe noise due to random fluctuations in electron emission from cathodes in vacuum tubes (called shot noise by analogy with lead shot). Shot noise also occurs in semiconductors due to the liberation of charge carriers. For pn junctions the mean square shot noise current is Where is the direct current as the pn junction (amps) is the reverse saturation current (amps) is the electron charge = 1.6 x 10-19 coulombs B is the effective noise bandwidth (Hz) Shot noise is found to have a uniform spectral density as for thermal noise

80. 80 4. Low Frequency or Flicker Noise Active devices, integrated circuit, diodes, transistors etc also exhibits a low frequency noise, which is frequency dependent (i.e. non uniform) known as flicker noise or ‘one – over – f’ noise. 5. Excess Resistor Noise Thermal noise in resistors does not vary with frequency, as previously noted, by many resistors also generates as additional frequency dependent noise referred to as excess noise. 6. Burst Noise or Popcorn Noise Some semiconductors also produce burst or popcorn noise with a spectral density which is proportional to

81. 81 7. General Comments For frequencies below a few KHz (low frequency systems), flicker and popcorn noise are the most significant, but these may be ignored at higher frequencies where ‘white’ noise predominates.

82. 82 8. Noise Evaluation The essence of calculations and measurements is to determine the signal power to Noise power ratio, i.e. the (S/N) ratio or (S/N) expression in dB.

83. 83 8. Noise Evaluation (Cont’d) The probability of amplitude of noise at any frequency or in any band of frequencies (e.g. 1 Hz, 10Hz… 100 KHz.etc) is a Gaussian distribution.

84. 84 Noise may be quantified in terms of noise power spectral density, p o watts per Hz, from which Noise power N may be expressed as N= p o B n watts 8. Noise Evaluation (Cont’d) Ideal low pass filter Bandwidth B Hz = B n N= p o B n watts Practical LPF 3 dB bandwidth shown, but noise does not suddenly cease at B 3dB Therefore, Bn > B 3dB, Bn depends on actual filter. N= p0 B n In general the equivalent noise bandwidth is > B 3dB.

85. 85 9. Analysis of Noise In Communication Systems Thermal Noise (Johnson noise) This thermal noise may be represented by an equivalent circuit as shown below (mean square value, power) then V RMS = i.e. V n is the RMS noise voltage. A) System BW = B Hz N= Constant B (watts) = KB B) System BW N= Constant 2B (watts) = K2B For A, For B,

86. 86 10. Signal to Noise The signal to noise ratio is given by The signal to noise in dB is expressed by for S and N measured in mW. 11. Noise 11. Noise Factor- Noise Figure Consider the network shown below,

87. 87 12. Noise 12. Noise Factor- Noise Figure (Cont’d) The amount of noise added by the network is embodied in the Noise Factor F, which is defined by Noise factor F = F equals to 1 for noiseless network and in general F > 1. The noise figure in the noise factor quoted in dB i.e. Noise Figure F dB = 10 log10 FF ≥ 0 dB The noise figure / factor is the measure of how much a network degrades the (S/N)IN, the lower the value of F, the better the network.

88. 88 13. Noise Figure – Noise Factor for Active Elements For active elements with power gain G>1, we have F ==But Therefore Since in general F v> 1, thenis increased by noise due to the active element i.e. Na represents ‘added’ noise measured at the output. This added noise may be referred to the input as extra noise, i.e. as equivalent diagram is

89. 89 13. Noise Figure – Noise Factor for Active Elements (Cont’d) Ne is extra noise due to active elements referred to the input; the element is thus effectively noiseless.

90. 90 14. Noise 14. Noise Temperature

91. 91 15. Noise Figure – Noise Factor for Passive Elements

92. 92 16. Review of Noise Factor – Noise Figure – Temperature

93. 93 17. Cascaded Network A receiver systems usually consists of a number of passive or active elements connected in series. A typical receiver block diagram is shown below, with example In order to determine the (S/N) at the input, the overall receiver noise figure or noise temperature must be determined. In order to do this all the noise must be referred to the same point in the receiver, for example to A, the feeder input or B, the input to the first amplifier. oris the noise referred to the input.

94. 94 18. System Noise 18. System Noise Figure Assume that a system comprises the elements shown below, Assume that these are now cascaded and connected to an aerial at the input, with from the aerial. Now, Since similarly

95. 95 18. System Noise 18. System Noise Figure (Cont’d) The overall system Noise Factor is The equation is called FRIIS Formula.

96. 96 19. System Noise 19. System Noise Temperature

97. 97 20. Additive White Gaussian Noise Additive White White noise == Constant Gaussian We generally assume that noise voltage amplitudes have a Gaussian or Normal distribution. Noise is usually additive in that it adds to the information bearing signal. A model of the received signal with additive noise is shown below

98. END OF 4 TH UNIT