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1. Chapter 3 – Data Transmission: Concepts and Terminology 1/45

2. TransmissionTerminology • data transmission occurs between a transmitter & receiver via some medium • guided medium • eg. twisted pair, coaxial cable, optical fiber • unguided / wireless medium • eg. air, water, vacuum 2/45

3. TransmissionTerminology • direct link • no intermediate devices • point-to-point • direct link • only 2 devices share link • multi-point • more than two devices share the link 3/45

4. TransmissionTerminology • Simplex transmission • one direction • eg. television • Half-duplex transmission • either direction, but only one way at a time • eg. police radio (walkie-talkie: push-to-talk and release-to-listen) • Full-duplex transmission • both directions at the same time • eg. telephone 4/45

5. Time domain concepts of signals • time domain concepts • analog signal • various in a smooth way over time • digital signal • maintains a constant level then changes to another constant level • periodic signal • pattern repeated over time • aperiodic signal • pattern not repeated over time 5/45

6. Analog and digital signals 6/45

7. Periodic signals • The signal period T is the inverse of signal frequency f : • The signal s(t) is periodic if: • The signal amplitude is denoted by A 7/45

8. Sine wave • Mathematically, the sine wave is given by : • Three parameters : • Peak amplitude (A) • maximum strength of signal • usually measured in volts • Frequency ( f ) • rate of change of signal • measured in Hertz (Hz) or cycles per second • period = time for one repetition ( T ) • T = 1/f • Phase (  ) • relative position in time 8/45

9. Varying Sine Waves 9/45

10. Wavelength (λ) • is the distance occupied by one cycle • assuming signal velocity v, then  =vT • or equivalently f =v, since T=1/f • for the special case when v=c • c = 3*108 m/s(speed of light in free space) • c=λf 10/45

11. Frequency Domain Concepts • signal are made up of many frequencies • components are sine waves • Fourier analysis can shown that any signal is made up of component sine waves • Fourier series of a square wave with amplitudes A and –A : 11/45

12. 12/45

13. Fourier Transform • Mathematical tool that relates the frequency-domain description of the signal to its time-domain description 13/45

14. Time-domain vs frequency-domain Figure 3.5a: frequency domain function for the signal of Figure 3.4c. 14/45

15. Time-domain vs frequency-domain Time-domain Frequency- domain 15/45

16. Spectrum and bandwidth • Spectrum • range of frequencies contained in signal • Absolute bandwidth • width of spectrum • effective bandwidth • often just bandwidth • narrow band of frequencies containing most energy • DC Component • component of zero frequency 16/45

17. Acoustic Spectrum 17/45

18. Analog and digital data transmission • data • entities that convey meaning • signals & signalling • electric or electromagnetic representations of data, physically propagates along medium • transmission • communication of data by propagation and processing of signals 18/45

19. Audio Signals • freq range 20Hz-20kHz (speech 100Hz-7kHz) • easily converted into electromagnetic signals • varying volume converted to varying voltage • can limit frequency range for voice channel to 300-3400Hz 19/45

20. Digital Data • as generated by computers etc. • has two dc components • bandwidth depends on data rate 20/45

21. Analog Signals 21/45

22. Digital signals 22/45

23. Advantages and disadvantages of digital signals • cheaper • less susceptible to noise • but greater attenuation • digital now preferred choice 23/45

24. Transmission Impairments • signal received may differ from signal transmitted causing: • analog - degradation of signal quality • digital - bit errors • most significant impairments are • attenuation and attenuation distortion • delay distortion • noise 24/45

25. Attenuation • where signal strength falls off with distance • depends on medium • received signal strength must be: • strong enough to be detected • sufficiently higher than noise to receive without error • so increase strength using amplifiers/repeaters • is also an increasing function of frequency • so equalize attenuation across band of frequencies used 25/45

26. Delay distortion • propagation velocity varies with frequency • hence various frequency components arrive at different times • particularly critical for digital data • since parts of one bit spill over into others • causing intersymbol interference 26/45

27. Noise • Additional unwanted signals inserted between transmitter and receiver • Thermal • due to thermal agitation of electrons • uniformly distributed • white noise • Interference from other users in a multi-user environment (e.g., mobile environment) 27/45

28. Noise • crosstalk • a signal from one line is picked up by another • impulse • irregular pulses or spikes • eg. external electromagnetic interference • short duration • high amplitude • a minor annoyance for analog signals • but a major source of error in digital data • a noise spike could corrupt many bits 28/45

29. 0 1 +5V -5V Noise: example 29/45

30. Data-rate • Data rate: is the rate, in bits per second (bps), at which data can be communicated 30/45

31. Spectrum, bandwidth and Data-rate • Spectrumof a signal: is the range of frequencies that it contains • Absolute bandwidth: is the width of the spectrum • Effective bandwidth: is a relatively narrow band that contains most signal energy • Any transmission system has a limited bandwidth • Square wave have infinite components and hence infinite bandwidth, but most energy in first few components • Limited bandwidth increases distortion • Limited bandwidth also limit the data rate that can be carried 31/45

32. Bandwidth 32/45

33. Data-rate and bandwidth 33/45

34. Channel Capacity • Channel Capacity: max possible rate at which data can be transmitted over a given communication path, under given conditions • Channel capacity is a function of : • data rate - in bits per second [bps] • bandwidth - in Hertz [Hz] • noise - on communication link • error rate - the rate at which errors occur, reception of 1 when 0 is transmitted, and visa versa 34/45

35. Nyquist Bandwidth • Consider noise free channels • If rate of signal transmission is 2B then we can carry signal with frequencies no greater than B • i.e., given bandwidth B, highest signal rate is 2B • For binary signals (0,1), 2B bps need bandwidth B Hz • Can increase rate by using M signal levels or M symbols (e.g. M=4, Quaternary: 00, 01, 10,11) • Nyquist formula is: • So increase rate by increasing signal levels • at cost of receiver complexity • limited by noise & other impairments 35/45

36. Shannon Capacity Formula • Consider relation of data rate, noise & error rate • faster data rate shortens each bit so bursts of noise affects more bits • given noise level, higher rates means higher errors • Signal-to-Noise Ratio (SNR): • SNR in decibles (dB): • Shannon’s channel capacity (C) in bits/s is related to the channel bandwidth (B) in Hertz and SNR by: • theoretical maximumcapacity • get lower in practise 36/45

37. Nyquit bandwidth and Shannon Capacity • Example: Suppose that the spectrum of a channel is between 3MHz and 4MHz and the SNRdB=24dB. Find: 1. The channel bandwidth (B) 2. The channel capacity (C) 3. Based on Nyquist formula, how many signalling levels are required to achieve the max capacity Solution: 1. B = 4MHz - 3MHz = 1MHz 2. 3. 37/45

38. Decibels and signal strength • It is customary to express gain or loss (attenuation) in decibels: • Logarithmic unit (compressed scale) • Multiplication and division reduce to addition and subtraction • The decibel power gain (GdB): • The decibel power loss (LdB): • The decibel voltage loss: 38/45

39. Decibels and signal strength • Example 1: if a signal with a power level of 10mW is inserted onto a transmission line and the measured power some distance away is 5mW, then the loss can be expressed as: • Example 2: Consider a series of transmission elements in which the input is at a power level of 4mW, the first element is a transmission line with 12dB loss, the second element is an amplifier with 35dB gain, and the third element is a transmission line with 10dB loss. 1. The net gain is -12 + 35 – 10= 13dB 2. The output power (Pout): 39/45

40. Decibels and signal strength • The dBW (decibel-Watt): • Example: a power of 1W is 0dBW, a power of 1000W is 30dBW, a power of 1mW is –30dBW • The dBm (decibel-milliWatt): • Example: a power of 1mW is 0dBm, a power of 30dBm is 0dBW 40/45

41. Example • Given a receiver with an effective noise temperature of 294K and a 10 MHz bandwidth. Find the thermal noise level (N0) at the receiver’s output in units of dBW? 41/45

42. The expression Eb/N0 • The expression Eb/N0 : is the ratio of signal energy per bit (Eb) to noise power density per Hz (N0) 42/45

43. Example • For Binary Phase Shift Keying (BPSK) modulation, Eb/N0= 8.4 dB is required for a bit error rate of 10-4 (one bit error out of every 10000 bits). If the effective noise temperature is 290 K (room temperature) and the data rate is 2400 bps, what received signal power level is required? 43/45

44. Eb/N0 versus SNR • We can relate Eb/N0 to the Signal-to-Noise Ratio (SNR): 44/45

45. Example • Suppose we want to find the minimum Eb/N0 required to achieve a spectral efficiency C/B of 6bps/Hz 45/45