Modeling and Analysis of Computer Networks (The physical Layer)

1. Modeling and Analysis of Computer Networks (The physical Layer) Ali Movaghar Winter 2009

2. The Theoretical Basis for Data Communication Linear Time-Invariant Filtering Fourier Analysis Bandwidth-Limited Signals Maximum Data Rate of a Channel

3. Linear Time-Invariant Filtering • If input s(t) yields output r(t), then for any τ, input s(t-τ) yields output r(t- τ). • If input s(t) yields output r(t), then for any real number α, αs(t) yields αr(t). • If input s1(t) yields output r1(t) and s2(t) yields output r2(t), then s1(t) + s2(t) yields output r1(t) + r2(t).

4. Example r(t) S(t) T 2T 0 T 0 3T 2T T 5T 0 6T 3T 4T 2T 5T 6T 0 T 4T

5. The convolution integral formula Area ≈ δs(τ+δ) Area ≈ δs(τ) S(t) τ τ+δ Let h(t) be the impulse response of the channel. Then r(t) = s(τ) h(t-τ) dτ

6. Frequency Response (1) Let s(t) = ej2πftwhere j = . Then r(t) = H(f) ej2πft where H(f) = h(τ)e-j2πfτ dτ H(f) above is called the Fourier transform of h(t).

7. Frequency Response (2) Let S(f) be the Fourier transform of s(t). That is S(f) = s(t)e-j2πftdt By inverse Fourier transform, we can write s(t) = S(f)ej2πftdf It follows r(t) = H(f) S(f)ej2πftdf Thus, we get R(f) = H(f) S(f) where R(f) is the Fourier transform of r(t).

8. Fourier Series • Theorem: Let g(t) be a periodic function with period T. Then where f = 1/T is the fundamental frequency, an and bn are the sine and cosine amplitudes of the nth harmonics, c is a constant. We have:

9. Example • Let us consider the transmission of the ASCII character “b” encoded in an 8-bit byte. The pattern that is to be transmitted is 01100010. • The Fourier analysis of this signal yields the coefficients:

10. Bandwidth-Limited Signals A binary signal and its root-mean-square Fourier amplitudes. (b) – (c) Successive approximations to the original signal.

11. Bandwidth-Limited Signals (2) (d) – (e) Successive approximations to the original signal.

12. Bandwidth-Limited Signals (3) Relation between data rate and harmonics.

13. Guided Transmission Data • Magnetic Media • Twisted Pair • Coaxial Cable • Fiber Optics

14. Magnetic Media An industry standard Ultrium tape can hold 200 gigabytes. A box 60 × 60 × 60 can hold about 1000 of these tapes, or 1600 trabits (1.6 petabits). A box of tapes can be delivered anywhere in Iran in 24 hours by “Post-e-Pishtaz”. The effective bandwidth is 166 terabits/86,400 sec, or 19 Gbps.

15. Twisted Pair (a) Category 3 UTP. (b) Category 5 UTP. • Category 3 (16 MHz) Category 5 (100 MHz) • Category 6 (250 MHz) Category 7 (600 MHz)

16. Coaxial Cable A coaxial cable. • Coaxial cable (1GHz)

17. Fiber Optics (a) Three examples of a light ray from inside a silica fiber impinging on the air/silica boundary at different angles. (b) Light trapped by total internal reflection.

18. Transmission of Light through Fiber Attenuation of light through fiber in the infrared region. Attenuation in decibels = 10 log (transmitted power / received power)

19. Bandwidth • f = 1/λ df/dλ = - c/ λ2 • Example: forλ = 1.3 × 10-6 Δλ = 0.17 × 10-6 • We have Δf = 30 THz • For 8 bits/Hz, we get 240Tbps

20. Fiber Cables (a) Side view of a single fiber. (b) End view of a sheath with three fibers.

21. Fiber Cables (2) A comparison of semiconductor diodes and LEDs as light sources. • Light Sources: LEDs and semiconductor diodes • Receiving ends: Photodiodes (1Gbps)

22. Fiber Optic Networks A fiber optic ring with active repeaters.

23. Fiber Optic Networks (2) A passive star connection in a fiber optics network.

24. Wireless Transmission • The Electromagnetic Spectrum • Radio Transmission • Microwave Transmission • Infrared and Millimeter Waves • Lightwave Transmission

25. The Electromagnetic Spectrum The electromagnetic spectrum and its uses for communication.

26. Radio Transmission (a) In the VLF, LF, and MF bands, radio waves follow the curvature of the earth. (b) In the HF band, they bounce off the ionosphere.

27. Politics of the Electromagnetic Spectrum The ISM bands in the United States.

28. Lightwave Transmission Convection currents can interfere with laser communication systems. A bi-directional system with two lasers is pictured here.

29. Communication Satellites • Geostationary Satellites • Medium-Earth Orbit Satellites • Low-Earth Orbit Satellites • Satellites versus Fiber

30. Communication Satellites Communication satellites and some of their properties including altitude above the earth, round-trip delay time and number of satellites needed for global coverage.

31. Communication Satellites (2) The principal satellite bands.

32. Communication Satellites (3) VSATs using a hub.

33. Low-Earth Orbit SatellitesIridium (a) The Iridium satellites from six necklaces around the earth. (b) 1628 moving cells cover the earth.

34. Globalstar (a) Relaying in space. (b) Relaying on the ground.

35. Public Switched Telephone System • Structure of the Telephone System • The Politics of Telephones • The Local Loop: Modems, ADSL and Wireless • Trunks and Multiplexing • Switching

36. Structure of the Telephone System (a) Fully-interconnected network. (b) Centralized switch. (c) Two-level hierarchy.

37. Structure of the Telephone System (2) A typical circuit route for a medium-distance call.

38. Major Components of the Telephone System • Local loops • Analog twisted pairs going to houses and businesses • Trunks • Digital fiber optics connecting the switching offices • Switching offices • Where calls are moved from one trunk to another

39. The Politics of Telephones The relationship of LATAs, LECs, and IXCs. All the circles are LEC switching offices. Each hexagon belongs to the IXC whose number is on it.

40. The Local Loop: Modems, ADSL, and Wireless The use of both analog and digital transmissions for a computer to computer call. Conversion is done by the modems and codecs.

41. Amplitude Modulation (AM) • The (digital) signal s(t) (called the baseband signal) is multiplied by a sinusoidal carrier, say cos(2πf0t), to generate a modulated signal s(t) cos(2πf0t).

42. Amplitude Modulation (AM) • Amplitude modulation. The frequency characteristic of the waveform s(t) is shifted up and down by f0 in frequency.

43. Amplitude Modulation (AM) • At the receiver, the modulated signal is again multiplied by cos(2πf0t), yielding a received signal r(t) = s(t) cos2(2πf0t) =s(t)/2 +1/2 s(t) cos(4πf0t). • AM is rather sensitive to the receiver knowing the correct phase of the carrier. Fore example, if the modulated signal s(t) cos(2πf0t) were multiplied by sin(2πf0t), the low frequency demodulated waveform would disappear.

44. Quadrature Amplitude Modulation (QAM) • This suggest, however, the possibility of transmitting twice as many bits by a technique known as quadrature amplitude modulation (QAM). • Here, the incoming bits are mapped into two baseband signals, s1(t) and s2(t). Then s1(t) is multiplied by cos(2πf0t) and s2(t) by sin(2πf0t); the sum of these products forms the transmitted QAM signal. • The received waveform is separately multiplied by cos(2πf0t) and sin(2πf0t). The first muliplication (after filtering out the high-frequency component) yields s1(t)/2, and the second yields s2(t)/2.

45. Modems (2) cos(2πf0t) s1 Pulse shape Bits to samples X Modulated waveform K bits + Pulse shape s2 X (a) Modulator sin(2πf0t) X Adaptive equilizer s1 cos(2πf0t) Samples To bits Carrier rec. Timing rec. sin(2πf0t) X s2 (b) Demodulator

46. Modems (2) (a) A binary signal (b) Amplitude modulation (c) Frequency modulation (d) Phase modulation

47. Modems (2) (a) QPSK. (b) QAM-16. (c) QAM-64.

48. Modems (3) (b) (a) (a) V.32 for 9600 bps. (b) V32 bis for 14,400 bps.

49. Digital Subscriber Lines Bandwidth versus distanced over category 3 UTP for DSL.

50. Digital Subscriber Lines (2) Operation of ADSL using discrete multitone modulation.