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. Transmitters (week 1 and 2)
Information Measures
Vector Quantization
Delta Modulation
QAM

3. Digital Communication System:
Information per bit increases
Bandwidth efficiency increases
noise immunity increases
Transmitter
Receiver

4. Transmitter Topics Increasing information per bit
Increasing noise immunity
Increasing bandwidth efficiency

5. Increasing Noise Immunity
Coding (Chapter 8, weeks 7 and 8)

6. Increasing bandwidth Efficiency
Modulation of digital data into analog waveforms
Impact of Modulation on Bandwidth efficiency

7. QAM modulation Quadrature Amplitude Modulation
Really Quadrature Phase Amplitude modulation
Amplitude and Phase modulation
g(t) is a pulse waveform to
control the spectrum,
e.g., raised cosine

10. QAM waveforms
To construct the wave forms we need to know fc, g(t), Amc, and Ams
However, we can write sm(t) as an linear combination of orthonormal waveforms:

11. QAM waveforms
QAM orthonormal waveforms:

12. QAM signal space
sm1
sm2
QAM wave form can be represented by just the vector sm
(still need fc, g(t), and g to make actual waveforms)
Signal space Constellation determines all of the code vectors

13. Euclidean distance between codes
Is the Energy of the signal
Is the cross correlation of the signals

14. Euclidean distance between codes
Signals of similar energy and highly cross correlated have a small Euclidean separation
Euclidean separation of adjacent signal vectors is thus a good measure of the ability of one signal to be mistaken for the other and cause error
Choose constellations with max space between vectors for min error probability

15. Rectangular QAM signal space
sm1
sm2
Minimum Euclidean distance between the M codes is?

16. Rectangular QAM signal space
Euclidean distance between the M codes is:

17. Rectangular QAM signal space
sm1
sm2
Minimum euclidean distance between the M codes is:

18. Channel Modeling Noise Additive White Gaussian
Contaminated baseband signal

19. Baseband Demodulation
Correlative receiver
Matched filter receiver
64-QAM Demodulated Data

20. Bandwidth required of QAM
If k bits of information is encoded in the amplitude and phase combinations then the data rate:
Where 1/T = Symbol Rate = R/k

21. Bandwidth required of QAM
Can show that bandwidth W needed is approximately 1/T for Optimal Receiver
Where M = number of symbols
(k = number of bits per symbol)

22. Bandwidth required of QAM
Bandwidth efficiency of QAM is thus:

23. Bandwidth required of QAM

24. Actual QAM bandwidth Consider Power Spectra of QAM
Band-pass signals can be expressed
Autocorrelation function is
Fourier Transform yields Power spectrum in
Terms of the low pass signal v(t) Power spectrum

25. Actual QAM bandwidth Power Spectra of QAM
For linear digital mod signals
Sequence of symbols is
For QAM

26. Actual QAM bandwidth Assume stationary symbols Where
Time averaging this:
Fourier Transform:

27. Actual QAM bandwidth G(f) is Fourier transform of g(t)
is power spectrum of symbols

28. Actual QAM bandwidth
G(f) is Fourier transform of g(t)

29. Actual QAM bandwidth
G(f) is Fourier transform of g(t)

30. Actual QAM bandwidth power spectrum of symbols
Determined by what data you send
Very random data gives broad spectrum

31. Actual QAM bandwidth
White noise for random
Symbol stream and QAM?

32. Channel Bandwidth 3-dB bandwidth Or your definition and justification
g(t) =
Modulated 64-QAM spectrum