Signal Processing in Communications

The lecture focuses on the practical use of vectors and matrices in the description of telecommunication systems. Digital transmission is based on the transformation of physical signals into matrices. This may be done by using a sampling operation or by applying a bank of correlators. Simple preliminaries presented within the lecture result in mathematical descriptions which simplify and explain some of the algorithms used in telecommunications.

The methods discussed in the first part of the lecture are the basis for multiple algorithms in digital communication. Many methods can be reduced to the same mathematical principle, e.g., detection, multi-user separation and filter optimization. Thus, for a deeper understanding, the basic ideas are more important than a detailed knowledge of individual realizations. In order to demonstrate the elaborated principles, the simplified methods resulting from the mathematical description are applied to up-to-date topics in communications, e.g., problems arising in estimation theory, matched filter whitening, diversity techniques, multiuser detection, MIMO transmission and equalization.