Principles of Digital Communication

COURSE LAYOUT Week 1: Introduction to digital communications: Interfaces and channels for digital communications Week 2: Geometric representation of signals: Geometric representation of signals, Gram-Schmidt orthogonalization, Geometric interpretation of signals Week 3: Review of random variables: Introduction to random variables, joint probability density function, characteristic functions, derived distributions Week 4: Review of random process: Introduction to random processes, Gaussian process, Linear functional of random process, Stationary and wide sense stationary random process, Power spectral density, White Gaussian noise Week 6: Waveform coding: Pulse code modulation, Differential pulse codemodulation, and delta modulation Week 7: Modulation - I: Complex baseband representation, degrees of freedoms, linear modulation, spectral description of linearly modulated signals Week 8: Modulation – II: Nyquist criterion, raised cosine family of pulses, Intersymbol interference Week 9: Modulation - III: Coherent binary modulation formats, e.g., ASK, FSK and PSK, Coherent QAM, M-ary modulation techniques, Orthogonal and biorthogonal modulation Week 10: Hypothesis testing: Optimum decision region in AWGN, Maximum Aposteriori Probability (MAP) and Maximum Likelihood Receiver, Theorem of irrelevance Week 11: Performance analysis of binary and M-ary signaling schemes: Performance analysis of binary signaling schemes, performance analysis of M-ary signaling schemes, bit-level demodulation,Non-coherent communication: Composite hypothesis testing, optimal demodulation for non-coherent communication Week 12: Performance analysis of non-coherent communication: Performance of binary and M-ary non-coherent communication