EE 568 is a first graduate level course on Digital Communications. The course has been designed mainly to provide a good understanding of fundamental problems in digital transmission over Additive White Gaussian Noise (AWGN) channels. The course starts with a short review of elements of communication systems and the basic probability and random processes. The later includes a treatment of Markov Processes, chains, state diagrams, trellis, and applications.

Linear bandpass signals and systems, orthogonal expansion, vector representation of signals are discussed. Linear modulation techniques with and without memory are presented. This is followed by illustration of different ways of describing memory, e.g., by state diagram, trellis state transmission matrix,…etc. Nonlinear modulation with memory; CPFSK, full and partial response CPM are detailed.

Power spectral density derivations for all these modulations are presented. General waveform channel synthesis and geometrical representation of signals along with vector recovery by means of a correlator bank are described.

Optimum receiver principles in AWGN channels are discussed; optimum Maximum A-posteriori (MAP) and Maximum Likelihood (ML) decision rules, correlation and matched-filter receivers, SNR, MLSE and its Eucleadian metric are included among other topics.

Performance analysis is presented for all the modulation techniques discussed earlier in terms of average bit error and symbol error probability as a measure of information quality. Both symbol-by-symbol detection as well as sequential detection is examined in detail. Non-coherent and differentially coherent detection methods are discussed.

Carrier and symbol synchronization techniques are discussed. Topics covered include: ML criterion, Carrier phase estimation, data and non-data assisted phase estimation techniques. Phase locked loop (PLL), Equivalent PLL with noise, Linearized PLL, Square-law tracking of phase, COSTAS loop, Symbol timing estimation, Timing recovery circuits, data and non-data assisted timing estimation, ML timing estimation and Early late gate synchronization techniques.