Introduction to Graphs and their applications. Finite and infinite graphs. History of graph theory. Paths and Circuits. Isomorphism, sub graphs. Walks, paths, and circuits. Hamiltonian paths and circuits. Trees and Fundamental Circuits. Cut-Sets and Cut-Vertices. Connected and disconnected graphs and components. Directed Graphs. Euler graphs. Operations on graphs. Graph-Theoretic Algorithms and Computer Programs. Applications of Graph theory in operations research. Distributed graph algorithms for computer networks. Complex networks.

Graph Theory Preliminaries. Introduction to Complex Networks. Centrality Metrics. Community Detection in Complex Networks. Random Networks. E-R random networks. Properties of Random Network. Real- world examples of random networks. Small- World Networks. Creation of Deterministic Small- World Networks. Anchor Points in a String Topology Small- world Network. Routing in Small-World Networks. The capacity of small-world Networks. Scale-Free Networks. Characteristics of Scale-Free Networks. Real- world examples of Scale-free networks. Preferential Attachment-based Scale-Free Network Creation.

Evolution of the Internet and Big Data. Introduction to the Internet of Things (IoT). The Internet protocol stack. IPv4 and IPv6. TCP and UDP. DNS and the IoT Protocol stack, Layers in the Internet of Things. Sensing and Actuator Layer, Network Layer, and Application Layer. Wireless Sensor Networks. Communication Technologies for the Internet of Things. CoAP, MQTT and HTTP Protocols for IoT. Data aggregation and fusion. Operating Systems for IoT. Contiki OS, Tiny OS, and other IoT OSs. Databases for the Internet of things. Data mining for the Internet of Things.

The need for Software radios and its definition, Characteristics and benefits of Software radio, Design principles of a software radio. Radio Frequency Implementation Issues: Purpose of RF front–end, Dynamic range, RF receiver front –end topologies, Enhanced flexibility of the RF chain with software radios, Importance of the components to overall performance, Transmitter architectures and their issues, Noise and distortion in the RF chain, ADC & DAC distortion, Pre-distortion, Flexible RF systems using micro-electro mechanical systems.

Review of Correlation matrix and its properties, its physical significance. Eigen analysis of matrix, structure of matrix and relation with its Eigen values and Eigen vectors. Spectral decomposition of correlation matrix, positive definite matrices and their properties and physical significance. Complex Gaussian processes.

Information Theoretic aspects of MIMO: Review of SISO fading communication channels, MIMO channel models, Classical. and extended channels, Frequency selective and correlated channel models, Capacity for deterministic and random MIMO channels, Capacity of separately correlated and key hole Rayleigh fading MIMO channels, Ergodic and outage capacity, Capacity bounds and Influence of channel properties on the capacity.

Review of wireless channel characteristics – Multi carrier and OFDM system fundamentals – OFDMsystemmodel-Comparisonwithsinglecarrier-ChannelcapacityandOFDM–FFTimplementation– Power spectrum – Impairments of wireless channels to OFDM signals – Comparison with other multicarrier modulation scheme: MCCDMA. Synchronization in OFDM–Timing and Frequency Offset in OFDM, Synchronization & system architecture, Timing and Frequency Offset estimation–Pilot and Non pilot based methods, Joint Time & Frequency Offset estimation.

Introduction to Wireless Channel and Fading - Rayleigh/Rician Fading, Broadband Wireless Channel Modeling: Introduction to LTV Systems, Channel Delay Spread, Coherence Bandwidth, BER Comparison of Wired and Wireless Communication Systems. Introduction to Diversity, Multi-antenna Maximal Ratio Combiner, BER with Diversity, Spatial Diversity and Diversity Order. ISI and Doppler in Wireless Communications, Doppler Spectrum and Jakes Model. Spread spectrum: PN Sequences, DSSS with BPSK, Signal space dimensionality and processing gain, Frequency-HopSS.

Introduction-Recovery algorithms - greedy and convex-The theory of compressed sensing

Introduction Sparse Signal Recovery via Basis Pursuit with RIP- Sparse Signal Recovery via Basis Pursuit without RIP-Sparse Signal Recovery via Greedy Algorithms- Concentration inequalities

Matrix Completion -Robust PCA-Atomic Norms-new advances and Application

Introduction- Overview of Sampling and Reconstruction. Oversampling techniques. Fundamentals of Multi-Rate Systems-Basic building blocks–Up sampling, down sampling, aliasing. Sampling rate change and filtering, fractional sampling rate change. Inter connection of multirate DSP blocks, Polyphase decomposition, Noble Identities, efficient implementation of sampling rate conversion.