1. CSC535 Communication Networks I Chapter 3a: Data Transmission Fundamentals Dr. Cheer-Sun Yang

2. 2 Fundamental of Communications zFourier Series Approximation(section 3.3) zNyquist Theorem(section 3.4) zShannon’s Theorem(section 3.4) zLine Encoding (section 3.5) zModulation and Demodulation (section 3.6)

3. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks3 Receiver Communication channel Transmitter Figure 3.5 A Transmission System....0110101

4. 4 Transmission System Components zTransmitter zReceiver zMedium (physical link) yGuided medium xe.g. twisted pair, optical fiber yUnguided medium xe.g. air, water, vacuum zChannel (Logical Link)

5. 5 Channel Types zDirect link yNo intermediate devices zPoint-to-point yDirect link yOnly 2 devices share link zMulti-point yMore than two devices share the link

6. 6 Signal Classifications zContinuous signal xAmplitude changes in a smooth way over time zDiscrete signal xAmplitude maintains a constant level then changes to another constant level zPeriodic signal xPattern repeated over time zAperiodic signal xPattern not repeated over time

7. 7 Continuous & Discrete Signals

8. 8 Periodic Signals

9. 9 Properties of a Periodic Signal zAmplitude (A) ymaximum strength of signal yunit: volts zFrequency (f) yRate of change of signal yHertz (Hz) or cycles per second yPeriod = time for one repetition (T) yT = 1/f zPhase (  ) yRelative position in time

10. 10 Varying Sine Waves

11. 11 Wavelength zDistance occupied by one cycle zDistance between two points of corresponding phase in two consecutive cycles zRepresented by the symbol zAssuming signal velocity v y = vT y f = v yc = 3*10 8 ms -1 (speed of light in free space)

12. 12

13. 13 Characterizations of Communication Channels zTime Domain Characterization - represents the amplitude s(t) changes of a channel at different time zFrequency Domain Characterization - represents the amplitude s(f) of frequencies of a signal

14. 14 Time Domain Concepts zTime domain characterization of a communication channel reflects the “capability” of carrying an input signal to a long distance. zThe propagation speed of a signal over a channel is reflected by the impulse response at the receiver end.

15. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks15 Channel t 0 t h(t) tdtd Figure 3.17

16. 16 Time Domain Concepts(cont’d) zA very narrow pulse s(t) is applied to the channel at time t = 0. zThe pulse appears at the other end of a channel as an impulse response, h(t). zIdeally, we hope that h(t) = s(t - t d ). zBut, it is impossible to achieve this in real systems.

17. 17 Fourier Transform Jean B. Fourier found that any periodic function can be expressed as an infinite sum of sine function.

18. 18 We can add sines together to make new functions... g 2 (t)=1/3sin(2  ( 3f )t) g 1 (t)=sin(2  f t) g 3 (t)= g 1 (t) + g 2 (t)

19. 19 Addition of Frequency Components

20. 20

21. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks21 1 0 0 0 0 0 0 1... t 1 ms Figure 3.15

22. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks22 Figure 3.16

23. 23 Frequency Domain Concepts zSignal usually made up of many frequencies zComponents are sine waves zCan be shown (Fourier analysis) that any signal is made up of component sine waves zCan plot frequency domain functions

24. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks24 Channel t t A in cos 2  ftA out cos (2  ft +  (f)) A out A in A(f) = Figure 3.13

25. 25 Frequency Domain

26. 26 Signal with DC Component

27. 27 Spectrum & Bandwidth zSpectrum yrange of frequencies contained in signal zAbsolute bandwidth ywidth of spectrum zEffective bandwidth yOften just bandwidth yNarrow band of frequencies containing most of the energy zDC Component yComponent of zero frequency yWhat is the frequency of a function f(t) = 5?

28. 28 Analog and Digital Data Transmission zData yEntities that convey meaning zSignals yElectric or electromagnetic representations of data zTransmission yCommunication of data by propagation and processing of signals zFrom now on, we can assume that a bit stream can be transmitted via a physical link using pulses or sine waves.

29. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks29 communication channel d meters 0110101... Figure 3.10

30. 30 Transmission Speed zAlso known as bit rate with the unit of bits/sec. zWe need to measure how fast a signal can be transmitted by a transmitter: transmission speed zWe also are interested in how fast a signal can be propagated through a physical link: propagation speed

31. 31 Data zAnalog yContinuous values within some interval ye.g. sound, video zDigital yDiscrete values ye.g. text, integers

32. 32 Signals zMeans by which data are propagated zAnalog yContinuously variable yVarious media xwire, fiber optic, space ySpeech bandwidth 100Hz to 7kHz yTelephone bandwidth 300Hz to 3400Hz yVideo bandwidth 4MHz zDigital yUse two DC components

33. 33 Data and Signals zUsually use digital signals for digital data and analog signals for analog data zCan use analog signal to carry digital data yModem zCan use digital signal to carry analog data yCompact Disc audio

34. 34 Analog Signals zDigital computers are incompatible with analog transmission media such as phone lines. zHow can one use analog signals to represent digital data bits? zWe need to convert digital data to analog signal at the sender side and convert analog data back to digital data at the receiver side.

35. 35 Acoustic Spectrum (Analog)

36. 36 Analog Signals Carrying Analog and Digital Data

37. 37 Digital Signals Carrying Analog and Digital Data

38. 38 Analog Transmission zAnalog signal transmitted without regard to content zMay be analog or digital data zAttenuated over distance zUse amplifiers to boost signal zAlso amplifies noise

39. 39 Digital Transmission zConcerned with content zIntegrity endangered by noise, attenuation etc. zRepeaters used zRepeater receives signal zExtracts bit pattern zRetransmits zAttenuation is overcome zNoise is not amplified

40. 40 Advantages of Digital Transmission zDigital technology yLow cost LSI/VLSI technology zData integrity yLonger distances over lower quality lines zCapacity utilization yHigh bandwidth links economical yHigh degree of multiplexing easier with digital techniques zSecurity & Privacy yEncryption zIntegration yCan treat analog and digital data similarly

41. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks41 (a) Analog transmission: all details must be reproduced accurately Sent Received e.g digital telephone, CD Audio (b) Digital transmission: only discrete levels need to be reproduced e.g. AM, FM, TV transmission Figure 3.6

42. 42 Transmission Impairments zSignal received may differ from signal transmitted zAnalog - degradation of signal quality zDigital - bit errors zCaused by yAttenuation and attenuation distortion yDelay distortion yNoise

43. 43 Attenuation zSignal strength falls off with distance zDepends on medium zReceived signal strength: ymust be enough to be detected ymust be sufficiently higher than noise to be received without error zAttenuation is an increasing function of frequency

44. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks44 Amplifier Equalizer Timing Recovery Decision Circuit. & Signal Regenerator Figure 3.9

45. 45 Delay Distortion zOnly in guided media zPropagation velocity varies with frequency

46. 46 Noise (1) zAdditional signals inserted between transmitter and receiver zThermal yDue to thermal agitation of electrons yUniformly distributed yWhite noise zIntermodulation ySignals that are the sum and difference of original frequencies sharing a medium

47. 47 Noise (2) zCrosstalk yA signal from one line is picked up by another zImpulse yIrregular pulses or spikes ye.g. External electromagnetic interference yShort duration yHigh amplitude

48. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks48 SourceRepeater Destination Repeater Transmission segment Figure 3.7

49. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks49 Attenuated & distorted signal + noise Equalizer Recovered signal + residual noise Repeater Amp. Figure 3.8

50. 50 Channel Capacity zData rate yIn bits per second yRate at which data can be communicated zBandwidth yIn cycles per second of Hertz yConstrained by transmitter and medium

51. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks51 f 0 W A(f)A(f) (a) Lowpass and idealized lowpass channel (b) Maximum pulse transmission rate is 2W pulses/second 0W f A(f)A(f) 1 Channel t t Figure 3.11

52. 52 Bandwidth Revisited zA transmission channel can be characterized by the signals within a certain frequency ranges. zIf a channel allows low frequency signals to pass, it is called a low-pass channel. zIf a channel allows high frequency signals to pass, it is called a high-pass channel. zThe bandwidth of a channel is defined as the range of fequencies that is passed by a channel. zFirst major theorem: Nyquist’s Result

53. 53 Bit Rate and Bandwidth zFirst major theorem: Nyquist’s Result zThe bit rate at which pulses can be transmitted over a channel is proportional to the bandwidth. zIn essence, if a channel has a bandwidth W, the narrowest pulse that can be transmitted over the channel has width  = 1/2W seconds. zThus the fastest rate at which pulses can be transmitted into the channel is given by the Nyquist rate: r max = 2W pulses/second.

54. 54 Baud Rate vs. Bit Rate zTransmission speed can be measured in bits per second(bps). zTechnically, transmission is rated in baud, the number of changes in the signal per second that the hardware generates. zUsing RS-232 standard to communicate, bit rate rate = baud rate. zIn general, bit rate rate = N * baud rate, where N is the number of signals in a string.

55. 55 Baud Rate vs. Bit Rate zSender sends the bit string, by b 1 b 2 … b n. zThe transmitter alternately analyzes each string and transmits a signal component uniquely determined by the bit values. Once the component is sent, the transmitter gets another bit string and repeats this process. zThe different signal components make up the actual transmitted signal. The frequency with which the components change is the baud rate. zAt the receiving end, the process is reversed.The receiver alternately samples the incoming signal and generates a bit string.

56. 56 Baud Rate vs. Bit Rate zConsequently, the bit rate depends on two things: the frequency with which a component can change (baud rate) and N, the number of bits in the string. That is why the formula: bit rate = N * baud rate

57. 57 Nyquist Sampling Theorem zDue to Harry Nyquist (1920) zNyquist showed that if F is the maximum frequency the medium can transmit, the receiver can completely reconstruct by sampling it 2ƒ times per second on a perfectly noiseless channel. z In other words, the receiver can reconstruct the signal by sampling it at intervals of 1/(2f) second. z For example, if the max frequency is 4000 Hz, the receiver needs to sample the signal 8000 times per second or using 2ƒ as the baud rate. z Bit rate = 2ƒ * N.

58. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks58 +A+A -A-A 0 T 2T2T 3T3T 4T4T5T5T 111100 Transmitter Filter Comm. Channel Receiver Filter Receiver r(t) Received signal t Figure 3.19

59. 59 Data Rate and Bandwidth zIt looks like that one can increase the bandwidth W of a channel to achieve a higher bit rate r without considering the actual characteristics of a transmission link. zIn fact, any transmission system has a limited band of frequencies. For example, a channel can use +5V as bit 1, -5V as bit 0; a channel may also be able to use +5V as ‘11’, +3V as ‘10’, -3V as ‘01’, and -5V as ‘00’. We are actually dividing the frequency range of F(=1/T) for representing 2 bits into that for representing 4 bits.

60. 60 Data Rate and Bandwidth Question: Can we keep increasing the bandwith or dividing the bandwidth to increase the bit rate?

61. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks61 4 signal levels8 signal levels typical noise Figure 3.22

62. 62 Data Rate and Bandwidth zIn fact, any transmission system has a limited band of frequencies. We cannot increase the bandwidth indefinitely. Signals can be impaired. zWe cannot keep dividing the total frequency range into smaller ranges since the receiver will become harder to distinguish one frequency from another. zThis also limits the data rate a channel can achieve. zThis leads to the second major result: Shannon’s Theorem

63. 63 Any Limit on Bit Rate? z The formula that Bit rate = 2ƒ * N seems to imply that there is no upper bound for the data rate given the maximum frequency. Unfortunately, this is not true for two reasons.

64. 64 How about real hardware? z First, if we used amplitude to represent data bits, each time we separate the amplitude into smaller ranges to represent more data bits, the receiver must be more sophisticated (and more expensive) to be able to detect smaller differences. If the differences become too small, we eventually exceed the ability of a deviec to detect them.

65. 65 How about real hardware? z Second, many channels are actually subject to noise.

66. 66 Limitation on Real Hardware

67. 67 Signal-to-Noise Ratio zElectrical engineers uses S/N to indicate the quality of sound. The higher the ration is, the better the quality is. zB = log 10 (S/N) bels, where B is the quality rate. z S/N is known as the signal-to-noise ratio. z Quality of sound is measured in decibles (abbreviated dB) or bels (1 dB = 0.1 Bel). z If B=2.5 bels, then S = ___________N?

68. Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks68 signal noise signal + noise signal noise signal + noise High SNR Low SNR SNR = Average Signal Power Average Noise Power SNR (dB) = 10 log 10 SNR t t t t t t Figure 3.12

69. 69 Shannon’s Theorem zBit rate = Bandwidth * log 2 (1+S/N) bps. z According to this result, a bit rate around 35,000 bps is an upper limit for conventional modems.

70. 70 Example of Shannon’s Theorem zBandwidth = 3000 Hz, zQuality rate = 35 dB or 3.5 bels, zWhat is the bit rate? zPlease work with your neighbors now. zHint: You must find S/N first.

71. 71 Reading Material zDon’t read sections 3.2 and 3.3 now. You may get confused.