# Fixed Broadband Wireless Communications: Mathematical Tools for Digital Transmission Analysis

## 3.1 INTRODUCTION

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, unwanted signals, and propagation anomalies, (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 characterize mathematically, in the time, frequency, and probability domains,
baseband signals, modulated RF signals, noise, propagation anomalies, and signals corrupted by noise, unwanted signals, and
propagation anomalies. The purpose of this chapter is to review briefly the more prominent of those analytical tools used
in such characterization—namely, spectral analysis and relevant statistical methods. Spectral analysis permits the characterization
of signals in the frequency domain and provides the relationship between frequency domain and time domain characterizations.
Noise and propagation anomalies are random processes leading to uncertainty in the integrity of a recovered signal. Thus no
definitive determination of the recovered signal can be made. By employing statistical methods, however, computation of the
fidelity of the recovered baseband signal is possible in terms of the probability that it's in error. The study of the basic
principles of fixed wireless modulation, covered in Chapter 4, will apply several of the tools presented here. Those readers familiar with these tools may want to skip this chapter and
proceed to Chapter 4.