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Outline. Transmitters (Chapters 3 and 4, Source Coding and Modulation) (week 1 and 2) Receivers (Chapter 5) (week 3 and 4) Received Signal Synchronization (Chapter 6) (week 5) Channel Capacity (Chapter 7) (week 6) Error Correction Codes (Chapter 8) (week 7 and 8)

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Presentation Transcript
outline
Outline
  • Transmitters (Chapters 3 and 4, Source Coding and Modulation) (week 1 and 2)
  • Receivers (Chapter 5) (week 3 and 4)
  • Received Signal Synchronization (Chapter 6) (week 5)
  • Channel Capacity (Chapter 7) (week 6)
  • Error Correction Codes (Chapter 8) (week 7 and 8)
  • Equalization (Bandwidth Constrained Channels) (Chapter 10) (week 9)
  • Adaptive Equalization (Chapter 11) (week 10 and 11)
  • Spread Spectrum (Chapter 13) (week 12)
  • Fading and multi path (Chapter 14) (week 12)
receivers chapter 5 week 3 and 4
Receivers (Chapter 5) (week 3 and 4)
  • Optimal Receivers
  • Probability of Error
optimal receivers
Optimal Receivers
  • Demodulators
  • Optimum Detection
demodulators
Demodulators
  • Correlation Demodulator
  • Matched filter
correlation demodulator
Correlation Demodulator
  • Decomposes the signal into orthonormal basis vector correlation terms
  • These are strongly correlated to the signal vector coefficients sm
correlation demodulator7
Correlation Demodulator
  • Received Signal model
    • Additive White Gaussian Noise (AWGN)
    • Distortion
      • Pattern dependant noise
    • Attenuation
      • Inter symbol Interference
    • Crosstalk
    • Feedback
additive white gaussian noise awgn
Additive White Gaussian Noise (AWGN)

i.e., the noise is flat in Frequency domain

correlation demodulator9
Correlation Demodulator
  • Consider each demodulator output
correlation demodulator10
Correlation Demodulator
  • Noise components

{nk} are uncorrelated Gaussian random variables

correlation demodulator11
Correlation Demodulator
  • Correlator outputs

Have mean = signal

For each of the M codes

Number of basis functions (=2 for QAM)

matched filter demodulator
Matched filter Demodulator
  • Use filters whose impulse response is the orthonormal basis of signal
  • Can show this is exactly equivalent to the correlation demodulator
matched filter demodulator13
Matched filter Demodulator
  • We find that this Demodulator Maximizes the SNR
  • Essentially show that any other function than f1() decreases SNR as is not as well correlated to components of r(t)
the optimal detector
The optimal Detector
  • Maximum Likelihood (ML):
the optimal detector15
The optimal Detector
  • Maximum Likelihood (ML):
optimal detector
Optimal Detector
  • Can show that

so

optimal detector17
Optimal Detector
  • Thus get new type of correlation demodulator using symbols not the basis functions:
alternate optimal rectangular qam detector
Alternate Optimal rectangular QAM Detector
  • M level QAM = 2 x level PAM signals
  • PAM = Pulse Amplitude Modulation
optimal rectangular qam demodulator

Select si for which

Select si for which

Optimal rectangular QAM Demodulator
  • d = spacing of rectangular grid
probability of error for rectangular m ary qam
Probability of Error for rectangular M-ary QAM
  • Related to error probability of PAM

Accounts for ends

probability of error for rec qam
Probability of Error for rec. QAM
  • Assume Gaussian noise

0

snr for m ary qam
SNR for M-ary QAM
  • Related to PAM
  • For PAM find average energy in equally probable signals
snr for m ary qam26
SNR for M-ary QAM
  • Related to PAM

Find average Power

snr for m ary qam27
SNR for M-ary QAM
  • Related to PAM

Find SNR

(ratio of powers)

Then SNR per bit

snr for m ary qam28
SNR for M-ary QAM
  • Related to PAM
snr for m ary qam29
SNR for M-ary QAM
  • Related to PAM
  • Now need to get M-ary QAM from PAM

M½=16

M½=8

M½=4

M½=2

snr for m ary qam30
SNR for M-ary QAM
  • Related to PAM

(1- probability of no QAM error)

(Assume ½ power in each PAM)

snr for m ary qam31
SNR for M-ary QAM
  • Related to PAM

M=