Mathematical basics
Gaussian random variables
Gaussian random processes
Specification, correlation function, stationarity and power spectra
Optimum receiver principles
Optimum receiver design for AWGN channels
Vector channels - decisions regions
Waveform channels - waveform synthesis, geometric interpretation of signals, irrelevant data
Receiver implementation - correlation and matched filter receiver
Probability of error - rectangular and orthogonal signal sets
Concept of union bound
Signal space representation
Gram-Schmidt orthogonalization
Efficient signaling for message sequences
Bit-by-bit signaling
Block orthogonal signaling
Probability of error comparison
Modeling of real bandpass and equivalent complex baseband signals
Power spectral density (PSD) of different modulation schemes
Transmit signal design for desired PSD
Necessary condition for symbol clock recovery
Asynchronous digital communication systems
Random amplitude and phase
Receiver design and error performance
Carrier frequency and phase estimation
Digital transmission over bandlimited channels
Nyquist criteria for zero ISI and pulse shaping
Rectangular and raised cosine pulses
Partial response signalling
Duo-binary case
Practical digital transceiver design
Elements of noise figure, link budget margin and receiver sensitivity
Transceiver architectures - Heterodyne, homodyne and digital-IF
Case study - Phillips’ GSM transceiver