Mathematical Tools for Digital Transmission Analysis

The study of digital wireless transmission is in large measure the study of (a) the conversion in a transmitter of a binary digital signal (often referred to as a baseband signal) to a modulated RF signal, (b) the transmission of this modulated signal from the transmitter through the atmosphere, (c) the corruption of this signal by noise and other unwanted signals, (d) the reception of this corrupted signal by a receiver, and (e) the recovery in the receiver, as best as possible, of the original baseband signal. In order to analyze such transmission, it is necessary to be able to characterize mathematically the time, frequency, and probability domains, baseband signals, modulated RF signals, noise, and signals corrupted by noise. The purpose of this chapter is to briefly review the more prominent analytical tools used in such characterization, namely, spectral analysis and relevant statistical methods.