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Outline

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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 – PowerPoint PPT presentation

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Title: Outline


1
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)

2
Channel Capacity (Chapter 7) (week 6)
  • Discrete Memoryless Channels
  • Random Codes
  • Block Codes
  • Trellis Codes

3
Channel Models
  • Discrete Memoryless Channel
  • Discrete-discrete
  • Binary channel, M-ary channel
  • Discrete-continuous
  • M-ary channel with soft-decision (analog)
  • Continuous-continuous
  • Modulated waveform channels (QAM)

4
Discrete Memoryless Channel
  • Discrete-discrete
  • Binary channel, M-ary channel

Probability transition matrix
5
Discrete Memoryless Channel
  • Discrete-continuous
  • M-ary channel with soft-decision (analog) output

x0 x1 x2 . . . xq-1
AWGN
y
6
Discrete Memoryless Channel
  • Continuous-continuous
  • Modulated waveform channels (QAM)
  • Assume Band limited waveforms, bandwidth W
  • Sampling at Nyquist 2W sample/s
  • Then over interval of N 2WT samples use an
    orthogonal function expansion

7
Discrete Memoryless Channel
  • Continuous-continuous
  • Using orthogonal function expansion

8
Discrete Memoryless Channel
  • Continuous-continuous
  • Using orthogonal function expansion get an
    equivalent discrete time channel

Gaussian noise
9
Capacity of binary symmetric channel
  • BSC

10
Capacity of binary symmetric channel
  • Average Mutual Information

11
Capacity of binary symmetric channel
  • Channel Capacity is Maximum Information
  • earlier showed

12
Capacity of binary symmetric channel
  • Channel Capacity
  • When p1 bits are inverted but information is
    perfect if invert them back!

13
Capacity of binary symmetric channel
  • Effect of SNR on Capacity
  • Binary PAM signal (digital signal amplitude 2A)

AGWN
14
Capacity of binary symmetric channel
  • Effect of SNR
  • Binary PAM signal (digital signal amplitude 2A)

15
Capacity of binary symmetric channel
  • Effect of SNR
  • Binary PAM signal (digital signal amplitude 2A)

16
Capacity of binary symmetric channel
  • Effect of SNR
  • Binary PAM signal (digital signal amplitude 2A)

Not sure about this Does it depend on bandwidth?
17
Capacity of binary symmetric channel
  • Effect of SNR
  • Binary PAM signal (digital signal amplitude 2A)

18
Capacity of binary symmetric channel
  • Effect of SNR
  • Binary PAM signal (digital signal amplitude 2A)

19
Capacity of binary symmetric channel
  • Effect of SNR
  • Binary PAM signal (digital signal amplitude 2A)

At capacity SNR 7, so waste lots of SNR to get
low BER!!!
20
Capacity of binary symmetric channel
  • Effect of SNRb
  • Binary PAM signal (digital signal amplitude 2A)

21
Channel Capacity of Discrete Memoryless Channel
  • Discrete-discrete
  • Binary channel, M-ary channel

Probability transition matrix
22
Channel Capacity of Discrete Memoryless Channel
  • Average Mutual Information

23
Channel Capacity of Discrete Memoryless Channel
  • Channel Capacity is Maximum Information
  • Occurs for
  • only if
  • Otherwise must work out max

24
Channel Capacity Discrete Memoryless Channel
  • Discrete-continuous
  • Channel Capacity

25
Channel Capacity Discrete Memoryless Channel
  • Discrete-continuous
  • Channel Capacity with AWGN

26
Channel Capacity Discrete Memoryless Channel
  • Binary Symmetric PAM-continuous
  • Maximum Information when

27
Channel Capacity Discrete Memoryless Channel
  • Binary Symmetric PAM-continuous
  • Maximum Information when

28
Channel Capacity Discrete Memoryless Channel
  • Binary Symmetric PAM-continuous
  • Versus Binary Symmetric discrete

29
Discrete Memoryless Channel
  • Continuous-continuous
  • Modulated waveform channels (QAM)
  • Assume Band limited waveforms, bandwidth W
  • Sampling at Nyquist 2W sample/s
  • Then over interval of N 2WT samples use an
    orthogonal function expansion

30
Discrete Memoryless Channel
  • Continuous-continuous
  • Using orthogonal function expansion get an
    equivalent discrete time channel

Gaussian noise
31
Discrete Memoryless Channel
  • Continuous-continuous
  • Capacity is (Shannon)

32
Discrete Memoryless Channel
  • Continuous-continuous
  • Maximum Information when

Statistically independent zero mean Gaussian
inputs
then
33
Discrete Memoryless Channel
  • Continuous-continuous
  • Constrain average power in x(t)

34
Discrete Memoryless Channel
  • Continuous-continuous
  • Thus Capacity is

35
Discrete Memoryless Channel
  • Continuous-continuous
  • Thus Normalized Capacity is
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