1. 1 School of Electrical, Electronics and Computer Engineering University of Newcastle-upon-Tyne Noise in Communication Systems Noise in Communication Systems Prof. Rolando Carrasco Lecture Notes Newcastle University 2008/2009

2. 2 Noise in Communication Systems 1.Introduction 2.Thermal Noise 3.Shot Noise 4.Low Frequency or Flicker Noise 5.Excess Resister Noise 6.Burst or Popcorn Noise 7.General Comments 8.Noise Evaluation – Overview 9.Analysis of Noise in Communication Systems Thermal Noise Noise Voltage Spectral Density Resistors in Series Resistors in Parallel 10.Matched Communication Systems 11. Signal - to – Noise 12. Noise Factor – Noise Figure 13. Noise Figure / Factor for Active Elements 14. Noise Temperature 15. Noise Figure / Factors for Passive Elements 16. Review – Noise Factor / Figure / Temperature 17. Cascaded Networks 18. System Noise Figure 19. System Noise Temperature 20. Algebraic Representation of Noise 21. Additive White Gaussian Noise

3. 3. 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.

4. 4. 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.

5. 5 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)

6. 6 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’.

7. 7 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

8. 8 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

9. 9 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.

10. 10 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.

11. 11 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.

12. 12 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.

13. 13 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,

14. 14 9. Analysis of Noise In Communication Systems (Cont’d) Assume that R 1 at temperature T 1 and R 2 at temperature T 2, then i.e. The resistor in series at same temperature behave as a single resistor Resistors in Series

15. 15 9. Analysis of Noise In Communication Systems (Cont’d) Resistance in Parallel

16. 16 10. Matched Communication Systems In communication systems we are usually concerned with the noise (i.e. S/N) at the receiver end of the system. The transmission path may be for example:- Or An equivalent circuit, when the line is connected to the receiver is shown below.

17. 17 10. Matched Communication Systems (Cont’d)

18. 18 11. 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. 12. Noise 12. Noise Factor- Noise Figure Consider the network shown below,

19. 19 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.

20. 20 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

21. 21 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.

22. 22 14. Noise 14. Noise Temperature

23. 23 15. Noise Figure – Noise Factor for Passive Elements

24. 24 16. Review of Noise Factor – Noise Figure –Temperature

25. 25 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.

26. 26 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

27. 27 18. System Noise 18. System Noise Figure (Cont’d) The overall system Noise Factor is The equation is called FRIIS Formula.

28. 28 19. System Noise 19. System Noise Temperature

29. 29 20. Algebraic Representation of Noise Phasor Representation of Signal and Noise The general carrier signal VcCosWct may be represented as a phasor at any instant in time as shown below: If we now consider a carrier with a noise voltage with “peak” value superimposed we may represents this as: Both Vn and n are random variables, the above phasor diagram represents a snapshot at some instant in time.

30. 30 20. Algebraic Representation of Noise (Cont’d) We may draw, for a single instant, the phasor with noise resolved into 2 components, which are: a) x(t) in phase with the carriers b) y(t) in quadrature with the carrier

31. 31 20. Algebraic Representation of Noise (Cont’d)

32. 32 20. Algebraic Representation of Noise (Cont’d)

33. 33 20. Algebraic Representation of Noise (Cont’d) Considering the general phasor representation below:-

34. 34 20. Algebraic Representation of Noise (Cont’d) From the diagram

35. 35 21. 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

36. 36 School of Electrical, Electronics and Computer Engineering University of Newcastle-upon-Tyne Error Control Coding Error Control Coding Prof. Rolando Carrasco Lecture Notes University of Newcastle-upon-Tyne 2005

37. 37 Error Control Coding In digital communication error occurs due to noise Bit error rate = Error rates typically range from 10 -1 to 10 -5 or better In order to counteract the effect of errors Error Control Coding is used. a) Detect Error – Error Detection b) Correct Error – Error Correction

38. 38 Channel Coding in Communication

39. 39 Automatic Repeat Request (ARQ)

40. 40 Automatic Repeat Request (ARQ) (Cont’d)

41. 41 Forward Error Correction (FEC)

42. 42 Block Codes A block code is a coding technique which generates C check bits for M message bits to give a stand alone block of M+C= N bits The code rate is given by Rate = A single parity bit (C=1 bit) applied to a block of 7 bits give a code rate Rate =

43. 43 Block Codes (Cont’d) A (7,4) Cyclic code has N=7, M=4 Code rate R = A repetition-m code in which each bit or message is transmitted m times and the receiver carries out a majority vote on each bit has a code rate

44. 44 Message Transfer It is required to transfer the contents of Computer A to Computer B. COMPUTER ACOMPUTER B The messages transferred to the Computer B, some may be rejected (lost) and some will be accepted, and will be either true (successful transfer) or false Obviously the requirement is for a high probability of successful transfer (ideally = 1), low probability of false transfer (ideally = 0) and a low probability of lost messages.

45. 45 Message Transfer (Cont’d) Error control coding may be considered further in two main ways 1.In terms of System Performance i.e. the probabilities of successful, false and lost message transfer. We need to know error correcting /detection ability to detect and correct errors (depends on hamming distance). 2. In terms of the Error Control Code itself i.e. the structure, operation, characteristics and implementation of various types of codes.

46. 46 System Performance In order to determine system performance in terms of successful, false and lost message transfers it is necessary to know: the probability of error or b.e.r p. the no. of bits in the message block N the ability of the code to detect/ correct errors, usually expressed as a minimum Hamming distance, d min for the code This gives the probability of R errors in an N bit block subject to a bit error rate p.

47. 47 System Performance (Cont’d) Hence, for an N bit block we can determine the probability of no errors in the block (R=0) i.e. An error free block The probability of 1 error in the block (R=1) The probability of 2 error in the block (R=2)

48. 48 Minimum Hamming distance A parameter which indicates the worst case ability of the code to detect /correct errors. Let d min = minimum Hamming distance l = number of bits errors detected t = number of bit errors corrected d min = l + t + 1with t ≤ l For example, suppose a code has a dmin = 6. We have as options 1) 6= 5 + 0 + 1 {detect up to 5 errors, no correction} 2) 6= 4 + 1 + 1 {detect up to 4 errors, correct 1 error} 3) 6= 3 + 2 + 1 {detect up to 3 errors, correct 2 error}

49. 49 Minimum Hamming distance (Cont’d) Messages transfers are successful if no errors occurs or if t errors occurs which are corrected. i.e. Probability of Success = Messages transfers are lost if up to l errors are detected which are not corrected, i.e Probability of lost = p(t+1) + p(t+2)+ …. p(l) Fortunately, the higher the no. of errors, the less the probability they will occur for reasonable values of p. For option 3 for example, if 4 or more errors occurred, these would not be detected and these messages would be accepted but would be false messages. =

50. 50 Minimum Hamming distance (Cont’d) Message transfers are false of l+1 or more errors occurs Probability of false = p(l+1) + p(l+2)+ …. p(N) = Example Using d min = 6, option 3, (t =1, l =4) Probability of Successful transfer = p(0) + p(1) Probability of lost messages = p(2) + p(3) + p(4) Probability of false messages = p(5) + p(6)+ …….+ p(N)

51. 51 Probability of Error Each bit has a probability of error p, i.e. probability that a transmitted ‘0’ is received as a ‘1’ and a transmitted ‘1’ is received as a ‘0’. this probability is called the single bit error rate or bit error b.e.r. For example, if p = 0.1, the probability that any single bit is in error is ‘1 in 10’ or 0.1. If there were 5 consecutive bits in error, the probability that the 6th bit will be in error is still 0.1, i.e. it is independent of the previous bits in error.

52. 52 Probability of Error (Cont’d) Consider a typical message block below. Error Control Coding Data Information Address bits Synchronization bit pattern The first requirement for the receiver/decoder is to identify the synchronization pattern (SYNC) in the received bit stream and then the address and data bits etc may be relatively easily extracted. Because of errors, the sync’ pattern may not be found exactly.

53. 53 Probability of Error (Cont’d) When synchronization is achieved, the EC bits which apply to the ADD (address) and DATA bits need to be carefully chosen in order to achieve a specified performance. Synchronization is required for Error control coding (ECC ) to be Applied. To clarify the synchronization and ECC requirements, it is necessary to understand the block error rates. For example, what is the probability of three errors in a 16 bit block if the b.e.r is p = 10 -2 ?

54. 54 Probability of Error (Cont’d) Let N be number of bits in a block. Consider N=3 block. Probability of error = p, (denote by Good, G) Probability that a bit is not in error = (1-p), denote by Error, E An error free block, require,G G G i.e, Good, Good and Good. Let R= the number of errors, in this case R=0. Hence we may write Probability of error free block = Probability that R=0 or P(R=0) = P(0) = P (Good, Good and Good)

55. 55 Probability of Error (Cont’d) Since probability of good = (1-p) and probability are independent so, P(0)= p(G and G and G) = (1-p). (1-p). (1-p)= (1-p) 3 P(0) = (1-p) 3 For 1 error in any position Probability of one error P(R=1) = P(1) P(1) = p(1-p) (1-p) + (1-p) p (1-p) + (1-p) (1-p) p P(1) = 3 p (1-p) 2

56. 56 Probability of Error (Cont’d) For 2 errors in combination Probability of one error P(R=2) = P(2) P(2) = p p (1-p) + p (1-p) p + (1-p) p p P(2) = 3 p 2 (1-p) For 3 errors P(3) = p p p = p 3

57. 57 Probability of Error (Cont’d) In general, it may be shown that The probability of R errors in an N bit block subject to a bit error rate p is Where is the number of ways getting R errors in N bits Prob. of (N-R) good bits Prob. of R bits in error No. of ways getting R errors in N bits Prob. of R errors.

58. 58 Probability of Error (Example 1) An N=8 bit block is received with a bit error rate p=0.1. Determine the probability of an error free block, a block with 1 error, and the probability of a block with 2 or more errors. Prob. Of error free block, Prob. of 1 error,

59. 59 Probability of Error (Example 1) Prob. of two or more errors = P(2) + P(3) + P(4)+ ……. P(8) i.e. It would be tedious to work this out, but since

60. 60 Probability of Error (Example 2) A coin is tossed to give Heads or Tails. What is the probability of 5 heads in 5 throws? Since the probability of head, say p = 0.5 and the probability of a tail, (1-p) is also 0.5 and N=5 then Prob. of 5 heads Similarly the probability of 3 heads in 5 throws (3 in any sequence) is

61. 61 Synchronization One method of synchronization is to compare the received bits with a ‘SYNC’ pattern at the receiver decoder. In general sense, synchronization will be successful if the sync bits are received error free, enabling an exact match lost if one or more errors occurs.

62. 62 Synchronization (Cont’d) Let S denote the number of sync bits. To illustrate let S=4 bits and let the sync pattern be 0 1 1 0 The probability of successful sync The probability of lost sync

63. 63 Error Detection and Correction Given that the synchronization has been successful, the message may be extracted as shown below. Probability of successful transfer =

64. 64 Error Detection and Correction (Cont’d) A message, after synchronization contains N=16 bits, with a b.e.r, p= 10 -2. If the ECC can correct 1 error determine the probability of successful message transfer.