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, 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.
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