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Chapter 3

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Chapter 3

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  1. Chapter 3 Digital Communication Fundamentals for Cognitive Radio “Cognitive Radio Communications and Networks: Principles and Practice” By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009) 1

  2. Outline • Fundamental of Data Transmission • Digital Modulation Techniques • Probability of Bit Error • Multicarrier Modulation • Multicarrier Equlization • Intersymbol Interference • Pulse Shaping 2

  3. Data Transmission Anatomy of a wireless Digital Comm Sys 3

  4. Data Transmission • Fundamental Limits • Shannon–Hartley theorem S is the total received signal power over the bandwidth (in case of a modulated signal, often denoted C, i.e. modulated carrier), measured in watt or volt; N is the total noise or interference power over the bandwidth, measured in watt or volt; and S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the Gaussian noise interference expressed as a linear power ratio (not as logarithmic decibels). 4

  5. Data Transmission • Source of Transmission Error The linear filter channel with additive noise 5

  6. Data Transmission • Additive White Gaussian Noise (AWGN)‏ • White noise assumption in most situations • Gaussian pdf 6

  7. Data Transmission • Additive White Gaussian Noise (AWGN)‏ Histogram of AWGN superimposed on the probability density function for a Gaussian random variable of N(0,0.25)‏ Power spectral density of AWGN with N(0,0.25)‏ 7

  8. Data Transmission • Nearest neighbor detection AWGN N(0,0.01)‏ AWGN N(0,0.25)‏ 8

  9. Digital Modulation Techniques • Representation of Signals • Euclidean Distance between Signals • Decision Rule • Power Efficiency • M-ary Phase Shift Keying • M-ary Quadrature Amplitude Modulation 9

  10. Representation of Signals 10

  11. Euclidean Distance between Signals • For any two signals and , the Euclidean Distance between them is defined as • Vector form 11

  12. Decision Rule • Nearest neighbor rule: Determine is if is the closest to rewritten as waveform representation 12

  13. Power Efficiency • Measures the largest minimum signal distance achieved given lowest transmit power • Energy per symbol • Energy per bit 13

  14. Power Efficiency • Power efficiency 14

  15. M-ary Phase Shift Keying 15

  16. M-ary Quadrature Amplitude Modulation 16

  17. M-ary Quadrature Amplitude Modulation 17

  18. M-ary Quadrature Amplitude Modulation Receiver Simple receiver structure makes M-QAM popular in digital communication systems. 18

  19. Probability of Bit Error • Also known as bit error rate • Starting from the modulation scheme with two signal waveforms, and • Assuming the noise term has a Gaussian distribution 19

  20. Derivation of BER • Assuming was transmitted, then an error event occurs if • where 20

  21. Derivation of BER • P(error)= • is the noise density • is the correlation between and • Q-function defines the area under the tail of a Gaussian pdf 21

  22. Derivation of BER • When , • and • therefore 22

  23. Upper Bound on BER • At least one error occurs • Therefore 23

  24. Lower Bound on BER • The smaller , the more likely an error happens. • Therefore 24

  25. Multicarrier modulation • Advantages: • Transmission agility • High datarate • Immunity to non-flat fading response. • “divide-and-conquer” channel distortion • Adaptive bit loading 25

  26. Multicarrier modulation • Disadvantages: • Sensitive to narrowband noise • Sensitive to amplitude clipping • Sensitive to timing jitter, delay 26

  27. Multicarrier Modulation Transmitter Receiver 27

  28. Comparison between single carrier and multicarrier • tt 28

  29. OFDM • Orthogonal Frequency Division Multiplexing 29

  30. FB-OFDM • Orthogonal Frequency Division Multiplexing with Filterbank FB-MC subcarrier spectrum employing a seuqre-root raised cosine prototype lowpass filter with a rolloff of 0.25 30

  31. OFDM Transmitter Receiver 31

  32. Multicarrier Equalization • Interference in multicarrier systems 32

  33. Distortion Reduction • Channel coding • Add redundancy to improve recovering 33

  34. Distortion Reduction • Channel equalization Before equalization After equalization 34

  35. Distortion Reduction • Channel equalization • Pre-equalization requires a feedback path from the receiver 35

  36. Intersymbol Interference • Signal being distorted by the temporal spreading and resulting overlap of individual symbol pulses Simplified block diagram for a wireless channel 36

  37. Intersymbol Interference RC-LPF filter response of combined modulation pulses when T=1, A=1 37

  38. Intersymbol Interference • Peak Interference/Distortion • When all symbols before and after have destruct effect on the symbol on cursor 38

  39. Pulse Shaping • Nyquist Pulse Shaping Theory • Time domain condition for zero ISI No ISI if sampling at t=kT 39

  40. Nyquist Pulse Shaping Theory • Nyquist-I Pulse (W=1/(2T))‏ 40

  41. Nyquist Pulse Shaping Theory • Nyquist-II Pulse (W>1/(2T))‏ 41

  42. Nyquist Pulse Shaping Theory • Frequency domain No ISI criterion 42

  43. Chapter 3 Summary • Digital communication theory at the core of cognitive radio operations • Mathematical tools necessary for enabling advanced features • Various modulation schemes can be used for transmission under different constraints and expectations • Bit Error Rate is primarily used to define performance 43