Course Objectives

At the end of this course, students should be able to:

  • Understand the function of the basic blocks in a typical digital communication system and the advantages of such an architecture.
  • Find baseband representations for passband signals and understand the relationship between them and also understand the relationship between baseband signal processing and passband signal processing.
  • Find signal space representations for a general digital modulation format, i.e., find a set of basis functions and represent the different waveforms as vectors in this basis.
  • Devise a receiver structure for optimally detecting the transmitted symbols from the received analog waveform for additive white noise channels, simplify this for the Gaussian noise case.
  • Compute either the exact probability of error (if possible) or reasonable bounds on the probability of error for a given digital modulation format when used over additive white noise channels. The student should recognize the difference between the union bound, nearest neighbor union bound, lower bounds based on the minimum distance. Student should also realize that it is possible to get approximations to the probability of errors that may not be valid upper or lower bounds, for example the nearest neighbor union bound.
  • Compute the spectrum of digitally modulated signals for linear modulation formats for a given pulse shape, modulation format and transmitted rate in bauds.
  • Implement base band synchronization algorithms in software
  • Design a non-coherent detector and compute the probability of error or bounds on the probability of error for a non-coherent detector
  • Design pulses that will not result in inter-symbol interference for an ideal bandlimited channel of bandwidth W when the desired data rate is R. Understand why excess bandwidth is used in practical systems.
  • Implement a sequence-wise optimal receiver (ML receiver) for an ISI channel in software
  • Design an optimal linear equalizer in the MMSE sense of a given length for a given ISI channel impulse response and compute the error probability for high SNRs.
  • Design an optimal DFE in the MMSE sense of a given number of feedforward and feedback taps for a given ISI channel impulse response and compute the error probability for high SNRs.
  • Understand the advantages of OFDM as a complexity reduction technique to deal with ISI and be able to implement an OFDM system in software.
  • Understand how continuous phase modulation systems work and the structure of the optimal detector for AWGN channels
  • Simulate a digital communication system in baseband in software for a given modulation format, pulse shape, transmission rate, channel and be able to implement receiver processing algorithms in software to deal with ISI, phase errors. Be able to obtain a plot of bit error versus signal to noise ratio for such a communication system through simulations.

Comments: when I say the student should be able to simulate certain things in software, it doesnt mean that we have to actually give homeworks or exams to test this, rather I mean that the student should get a detailed understanding (rather than just an overall picture) of the issues to a point that the student can perform the simulation if asked to.

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