1. 1 Introduction to Communications Professor R. C. T. Lee Dept. of Information Management Dept. of Computer Science Department of Communications Department of Live Science National Chi Nan University

2. 2 Why do we computer scientists need to know communication technologies?

3. 3 In these days, it is hard to imagine any computer which stands entirely alone. A computer is often connected to others, through communication technologies.

4. 4 Besides, many systems which were traditionally considered as communication systems are actually quite similar to computers. Examples: TV, mobile phone.

5. 5 But, unfortunately, almost all computer scientist students do not understand some very basic communication technologies. Question 1: How is a bit represented when it is transmitted in a wireless environment?

6. 6 We often thought that a bit is represented by a pulse. (1,1,0,0,1)

7. 7 But we cannot send a digital signal in the wireless environment. Question 2: We often mix bits together. An example: In the ADSL system, 256 bits are bundled together.

8. 8 If the bits are represented by pulses, how can they be mixed and later be distinguished. Question 3: We often mix bits by different users together. If the bits are represented by pulses, how can they be distinguished when they are received?

9. 9 A very fundamental problem in communications is to study how digital information is represented, sent and later separated. Fundamental concept: There is no digital signal. Every digital bit is represented by an analog signal. (A quote by Professor R. C. T. Lee, a famous professor. He learned this from one of his students.).

10. 10 Consider the simplest case: There is only one user. We represent bit 1 by and represent bit 0 by. We further require that and are orthgonal.

11. 11 That is, the inner product and for every i..

12. 12 For the receiver, it either receives or. We perform two inner products. Let the sent signal, which is received denoted by. We calculate and If, we conclude that we sent, which is 1(0).

13. 13 There are millions of possible functions for and. We may let and We may also let and We may of course let and.

14. 14 It can be easily seen that We can also prove, for instance, that

15. 15 What we usually do is to find If we conclude that the sent signal is Or, if we conclude that the sent bit is 1(0). and iff

16. 16 We should now always remember that every bit, 1 or 0, is represented by a cosine or a sine function. In the above, we assumed that every bit is sent alone. Can we send two bits together? Yes, we can.

17. 17 Let us assume that we are going to send two bits: Bit 1 and Bit 2. Bit 1 can be 1 or 0 and Bit 2 can also be 1 or 0. We like to mix Bit 1 and Bit 2 together and send the mixed signal out. The important thing is that the receiver must be able to correctly determine what Bit 1 and Bit 2 are.

18. 18 Let Bit 1(Bit 2) be represented by. The value of is determined by the value of Bit 1(Bit 2). We may let be 1(-1) if Bit i is 1(0) for Thus the sent signal is The job of the receiver is to determine the values of for

19. 19 Let denote the sent signal. Then To determine, we perform an inner Product between and Let

20. 20 Similarly, we have

21. 21 If we conclude that User 1 sends 1(0). Similarly, if we conclude that User 2 sends 1(0).

22. 22 We can now see how two bits can be mixed and sent without any trouble. Essentially, we must understand that the digital signals are represented by analog signals which are orthogonal to each other. The receiver uses the property of orthogonality to separate the signals.

23. 23 If we can mix 2 bits together, we can of Course mix 256 bits together. In fact, the ADSL system uses this kind of scheme. This is why the ADSL system is a very fast system.

24. 24 In the ADSL system, each bit i is represented by Thus, each signal is orthogonal to others due to the distinct frequencies. This is why the system is called Orthogonal Frequency Division Multiplexing (OFDM) system.

25. 25 The coding of digital data by analog signals is often called digital modulation. The decoding of analog signals back to digital signals is called demodulation.

26. 26 Let us go one step further by mixing bits from different people. Our trick is the following: A bit of 1 or 0 for User 1 is represented differently from a Bit of 1 or 0 for User 2. Let us consider a simple case: two users.

27. 27 Let the bit of 1 for User 1 be coded as and the bit of 0 for User 1 be coded as Let the bit of 1 for User 2 be coded as and the bit of 0 for User 2 be coded as We may say that User i sends

28. 28 Since and are vectors, we use dot- product as the inner product. We therefore conclude that and are orthogonal to each other.

29. 29 We may mix the bits of User 1 and User 2 and the mixed signal is therefore where or. The job of the receiver is to determine Again, this can be done by using the orthogonality of and

30. 30 To find we calculate Thus can be found similarly.

31. 31 Thus we can see that we can even mix bits of two different users. The main trick is that we represent the bits of different users by vectors and make sure that they are orthogonal to each other. This can be easily extended to more than 2 users.

32. 32 Let us now ask another interesting question. Our cables are often used to transmit digital data. We like our channel to transmit a large amount of bits per second. We are talking about high bit rate systems. Why do we often call these channels broadband system.

33. 33 By By By a broadband system, we mean it can transmit signals with a large range of frequencies. Why is a high bit system also a broadband system? This can be understood only through the knowledge of Fourier transform.

34. 34 A signal

35. 35 The Discrete Fourier Transform Spectrum of the Signal in the Previous Slide

36. 36 A Music Signal Lasting 1 Second

37. 37 A Discrete Fourier Transform Spectrum of the Music Signal in the Previous Slide.

38. 38 Suppose that a bit is a rather wide one, as shown below: Then its Fourier transform spectrum is as follows:

39. 39 Suppose the system is a high bit rate system, the bit length is therefore very very short: Its Fourier transform is as follows:

40. 40 Conclusion: In a low bit rate system, the bit length is very long and it actually contains a narrow band of frequencies. This can be understood by imagining the bit length to be so long that the signal becomes DC. In this case, the only frequency it contains is

41. 41 On the contrary, in a high bit rate system, the bit length is very very short, it contains a wide range of frequencies. The system is consequently called a broadband system because for a wide range of frequencies, it must respond equally well.

42. 42 By using Fourier transform, we can see that the frequency components in our human voice are roughly contained in 3k Hertz.

43. 43 For a signal with frequency f, its wavelength can be found as follows: where f is the velocity of light?

44. 44 If,.

45. 45 It can also be proved that the length of an antenna is around. For human voice, this means that the wavelength is 50km. No antenna can be that long.

46. 46 What can we do? Answer: By amplitude modulation.

47. 47 Let be a signal. The amplitude modulation is defined as follows: where f c is the carrier frequency?

48. 48 What is the Fourier transform of ?

49. 49

50. 50 Fourier transform tells us that every signal contains a bunch of cosine functions. Let us consider.

51. 51 Thus every frequency f is lifted to.

52. 52 The effect of amplitude modulation is to lift the baseband frequency to the carrier frequency level, a much higher one. Once the frequency becomes higher, its corresponding wavelength becomes smaller. An antenna is now possible.

53. 53 After we receive, how can we take out of it? Answer: Multiply by.

54. 54 Thus is recovered.

55. 55

56. 56 Thank You for Your Patience. Good-night and Have a Good Sleep. You will be waken up by Your Wicked Advisers Tomorrow Morning.