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)

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

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

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

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

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

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

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:

QAM waveforms QAM orthonormal waveforms:

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

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

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

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

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

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

Channel Modeling Noise Additive White Gaussian Contaminated baseband signal

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

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

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)

Bandwidth required of QAM Bandwidth efficiency of QAM is thus:

Bandwidth required of QAM

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

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

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

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

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

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

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

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

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