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The Physical Layer

The Physical Layer. The Theoretical Basis for Data Communication. Fourier analysis Niquist chriterium for bandwidth-limited channel Shannon maximum data rate of a noisy channel. Fourier Transform. Periodic signals with period T =2 π / w Non-periodic signals.

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The Physical Layer

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  1. The Physical Layer

  2. The Theoretical Basis for Data Communication • Fourier analysis • Niquist chriterium for bandwidth-limited channel • Shannon maximum data rate of a noisy channel

  3. Fourier Transform • Periodic signals with period T=2π/w • Non-periodic signals

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

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

  6. Bandwidth-Limited Signals Relation between data rate and harmonics.

  7. Band-Limited Channel w 1/Ts 2/Ts -1/Ts • Fourier transform of atypical signal

  8. Power Spectrum Density • Autocorrelation function of signal or noise • Power spectrum density

  9. Filtering • Channel behaves as a filter • When the noise is white (uncorrelated) Gaussian optimum filter has transfer function H(w)=X*(w).

  10. Niquist Theorem • If the signal bandwidth has width of W, then it can be reconstructed by taking 2W samples per second. • Maximum data rate is where V is the number of different symbols

  11. Niquist Chriterium Ts sampling interval, ∆ sampling pulse width

  12. Niquist Chriterium s(t) t t x(t) t

  13. Niquist Chriterium S(f) -W W f X(f) f -2/Ts 1/Ts 2/Ts -1/Ts

  14. Shannon Theorem • If the channel bandwidth has width of W, and S/N is the signal-to-noise ratio, then the maximum data rate is

  15. (a) A binary signal (b) Amplitude modulation (c) Frequency modulation (d) Phase modulation Modulation

  16. Modulation • Signal is located around carrier frequency w0, and its amplitude and phase depend on the data symbol in each time slot

  17. Modulation Schemes (a) QPSK. (b) QAM-16. (c) QAM-64.

  18. Guided Transmission • Twisted Pair • Coaxial Cable • Fiber Optics

  19. Twisted Pair (a) Category 3 UTP 16 MHz. (b) Category 5 UTP 100MHz.

  20. Coaxial Cable A coaxial cable 1GHz.

  21. 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.

  22. Transmission of Light through Fiber Attenuation of light through fiber in the infrared region. Bands 25-30THz, and last two bands have attenuation less than 5%/km

  23. Fiber Cables (a) Side view of a single fiber. (b) End view of a sheath with three fibers, diameter 8-10μm.

  24. Transmission Devices • Light emitting diode (LED) • Semiconductor lasers • Mach-Zehnder external modulator • EDFA • Photodiode

  25. Optical Transmitters A comparison of semiconductor diodes and LEDs as light sources.

  26. Wireless Transmission • Relationship between wavelength and frequency: • 100MHz waves are about 3m long, 1000MHz waves are 0.3m long. • An object distracts those waves, whose length is smaller or equal to the object dimension.

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

  28. 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.

  29. Issues in Wireless Transmission • Radio signals are omnidirectional, and penetrate through objects. Throughput is low. • HF radio and microwave signals are directed. Suffer from multipath fading, and are reflected against the buildings. • Above 4GHz, signals are absorbed by the rain.

  30. Lightwave Transmission Convection currents can interfere with laser communication systems. A bidirectional system with two lasers is pictured here. Fog and rain are disruptive too.

  31. Communication Satellites • Geostationary Satellites • Several kWs. 40 transponders with 80MHz. TDMA. • Medium-Earth Orbit Satellites • 24 GPS satellites. • Low-Earth Orbit Satellites • Iridium project started by Motorola

  32. 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.

  33. Communication Satellites The principal satellite bands.

  34. Frequency Division Multiplexing (a) The original bandwidths. (b) The bandwidths raised in frequency. (b) The multiplexed channel.

  35. Wavelength Division Multiplexing Wavelength division multiplexing.

  36. Time Division Multiplexing The T1 carrier (1.544 Mbps).

  37. Time Division Multiplexing Multiplexing T1 streams into higher carriers.

  38. TDM • US and Japan T1 1.544Mbps • 24 channels one sync. bit • 23 data channels, 7 data bits + 1 signalling bit • Multiplexing degrees 4,7,6 • Others E1 2.048Mbps • 32 channels • 30 data channels, 8 data bits, 1 bit signalling in every sixth frame • Multiplexing degree 4, bit rates: 2.048Mbps, 8.848Mbps,

  39. SONET and SDH • Bellcore and CCITT: Synchronous Optical Networks (SONET), Synchronous Digital Hierarchy (SDH) • Define frames for bit-rates 50Mbps and up

  40. SONET Two back-to-back SONET STS-1 frames comprising 810 bytes

  41. Time Division Multiplexing SONET and SDH multiplex rates.

  42. gK(t) g1(t) g2(t) rK(t) r1(t) r2(t) X X X CDMA – Code Division Multiple AccessIS-95 r(t)

  43. Walsh-Hadamard Sequences

  44. CDMA – Code Division Multiple Access(e.g. IS-95) (a) Binary chip sequences for four stations (b) Bipolar chip sequences (c) Six examples of transmissions (d) Recovery of station C’s signal

  45. 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.

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

  47. Higher Bit-rate Modems • 2400 samples (bauds) per second • V32 to 14.4Kbps, V34 to 33.6Kbps • V90 35Kbps upstream, 56Kbps downstream • V92 48kbps upstream, 56Kbps downstream

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

  49. Digital Subscriber Lines Operation of ADSL using discrete multitone modulation. Up to 8Mbps downstream, and up to 1Mbps upstream. Modulation similar to V34, 15 bits per sample, 4000 bauds per sec

  50. Digital Subscriber Lines A typical ADSL equipment configuration.

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