ECE 5654 Digital Communications II: Advanced Theory and Analysis | ECE | Virginia Tech


Course Information


Fundamentals of the theory, design, and analysis of modern digital communication systems. Representation of signal in digital form. Design and analysis of digital modulation formats and receivers using signal space techniques. Combining error correction techniques with digital modulation. Viterbi algorithm for maximum likelihood sequence estimation. Equalization and adaptive equatlization. Fading channels and diversity techniques.

Why take this course?

There is a set of fundamental principles that are at the core of the design and analysis of modern communication systems. These principles include:

  • The design and analysis of modulation formats using signal space techniques (Gramm-Schmidt orthogonalization procedure, bandwidth and power spectrum analysis, optimal MAP receiver design, probability of error analysis for generalized signal constellations)
  • The use of error correction in the design of communication systems (analysis of communication systems with block and convolutional codes, hard and soft decision decoding, combined coding and modulation, selection of error correction techniques for communication system design). The use of the Viterbi algorithm for maximum likelihood sequence estimation such as the decoding of convolutional codes. )
  • The use of equalization for high data rate systems, particularly adaptive equalization techniques. )
  • The impact of multipath fading channels and diversity techniques to overcome fading channels.
  • Students need an understanding of this material to work in the field of modern communication system design, to take more advanced courses in satellite and wireless communications, simulation, and information theory, and to conduct research in communications.


    Prerequisites: 4634, 5605

    There are two prerequisites for this course:

  • ECE 4634 Introduction to Digital Communications. In order to treat the material at a high conceptual level it is necessary for students to have previous experience in understanding the basic blocks that make up a communication system and the terminology associated with communication systems. Such knowledge could be obtained through ECE 4634 at Virginia Tech. It is anticipated that many, but not all, new graduate students may have taken a similar senior level communications elective at a previous university.
  • ECE 5605 - Stochastic Signals and Systems I. A knowledge of stochastic processes is required both for obtaining the spectral properties of different signal and modulation formats and for carrying out a probability of error analysis for different communication systems. Such knowledge could be obtained through ECE 5605 at Virginia Tech.
  • Major Measurable Learning Objectives

    • Identify the major blocks of a digital communication system and explain their relationships
    • Represent QAM, PSK, FSK, and other modulation formats using a signal space representation
    • Determine a signal space representation for an arbitrary signal set using the Gramm-Schmidt orthogonalization procedure.
    • Use signal space representations to design digital modulation formats which achieve a desired combination of energy and bandwidth efficiency
    • Design an optimal coherent receiver for an arbitrary digital modulation format in Guassian noise
    • Analyze the bit, symbol, and frame error probabilities for any arbitrary digital modulation format
    • Analyze the error probability of any combination of modulation format and block or convolutional error correction code
    • Design an appropriate combination of modulation format and error correction code for bandwidth-limited and power-limited applications
    • Implement the Viterbi algorithm for maximum likelihood sequence estimation
    • Analyze the performance of the Viterbi algorithm for maximum likelihood sequence estimation
    • Implement an adaptive equalizer for frequency selective channels
    • Determine the impact that multipath fading will have on digital modulation and design counter-measures to improve link performance.

    Course Topics


    Percentage of Course

    Signal Space Approach to Modulation 30%
    Signal Space Representation of Signals 7.5%
    Optimum Coherent Receiver Design 7.5%
    Probability of Error Analysis for Coherent Receivers 5 %
    Optimum Noncoherent Receiver Design 5%
    Probability of Error Analysis for Noncoherent Receivers 5%
    Integration of Modulation and Error Correction 35%
    Encoding and Decoding of Block Codes 5%
    Encoding of Convolutional Codes 5%
    Probability of Error Analysis for Error Correction
    Codes with Modulation 10%
    Maximum Likelihood Sequence Estimation - Viterbi Algorithm 5%
    Combined Coding and Modulation - Trellis Codes 5%
    Turbo Coding 5%
    Advanced Digital Communications Concepts 35%
    Equalization 10%
    Continuous Phase Modulation 5%
    Advanced modulation concepts (e.g., OFDM) 5%
    Fading channels and countermeasures 10%
    Multiple access 5%