Wireless Transceiver Architecture

Appendix 2 Stationarity

It is often convenient to assume that the processes we are dealing with are stationary. In our system design perspective, this is for instance of interest for the derivation of the power spectral densities of stochastic processes that represent either noises or randomly modulated signals.

In wireless transceivers we have to deal with both bandpass signals, which model for instance the RF signals of interest, and lowpass signals, which model for instance the baseband modulating waveforms. But depending on whether we are dealing with RF bandpass processes that have been generated directly in the RF domain, as may be the case for a thermal noise generated at the early stages of a receiver for instance, or by the frequency upconversion of a stationary lowpass process, as may be the case for all the modulated signals we are dealing with, stationarity is not as obvious a property as it might first appear. It is therefore useful to detail the properties and the conditions associated with such stationarity.

A2.1 Stationary Bandpass Signals

Some of the bandpass RF signals we are dealing with in wireless transceivers are inherently stationary, at least over a characteristic time duration for the wireless link considered. Thus we are already dealing with an approximation as stationarity necessarily requires the process concerned to be spread over an infinite duration [3]. However, we can assume that an RF noise source, linked to thermal noise for instance, is ...