Course Description

The goal of this course is to introduce students to the mathematical theory of communication at the physical layer that deals with designing waveforms for transmission and making decisions on the transmitted bits from the received waveforms. In digital communications, at every time instant, a symbol (group of bits of information) needs to be mapped onto a signal waveform that is then transmitted through a physical channel to the receiver. The physical channel usually places constraints on what kind of waveforms can be transmitted and, further, distorts the transmitted waveforms. At the receiver, given the distorted transmitted waveform, one needs to make a decision on which symbol was most likely to have been transmitted.

Roughly speaking, this course is about how to design good signal waveforms that satisfy constraints imposed by the physical channel, system/application and about how to process the received waveforms at the receiver in order to recover the transmitted information. Both optimal strategies which may not consider complexity issues as well practical design approaches motivated by the limited receiver complexity/cost will be considered. For a given set of signal waveforms and appropriate processing at the receiver, we will discuss techniques to evaluate the performance of these signaling schemes.

Although the course will deal with general design principles and ideas, two types of channels will considered in detail - one is the additive white noise channel and the other is a channel with inter-symbol interference and additive white Gaussian noise.

The course can be thought of as broken in to the following parts – one part deals with sending only one symbol from one user through the channel and making optimal decisions about that symbol from the received waveform. Another part deals with transmitting a sequence of symbols from one user and how decisions can be made about the sequence in the presence of impairments from the channel. If time permits, the design signal waveforms for multiuser communication will be discussed briefly.

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