This chapter is from the book
This chapter is from the book
This chapter is from the book
3.5 Chapter Summary
This chapter discussed the principles of modeling channels as random processes. Following is an outline of the major points presented:
-
An autocorrelation function is used to characterize how a random channel evolves in time.
-
Temporal, frequency, and spatial autocorrelation definitions are possible.
-
A wide-sense stationary (WSS) process autocorrelation function depends only on the distance between correlated samples.
-
-
A power spectral density (sometimes called a PSD) measures average spectral power in a random channel.
-
Doppler, delay, and wavenumber spectra are defined.
-
The Wiener-Khintchine theorem states that a PSD and an autocorrelation function are Fourier transform pairs.
-
The scalar spatial channel may be extended to three dimensions by using a vector autocorrelation function and a wavevector spectrum.
-
-
Joint autocorrelation functions and PSDs characterize channels with multiple dependencies. Relationships between numerous dependencies are best viewed on a transform map.
-
The RMS spread is a formal measure of PSD width.
-
Doppler, delay, and wavenumber spreads are defined.
-
RMS fading rates are measures of average channel fluctuation with respect to time, frequency, and space.
-
The fading rate variance and the squared RMS spectrum spread of a channel are proportional.
-
All stochastic modeling of the space–time wireless channel involves a symmetry among dependencies called duality.
-
With the discussions on baseband channel transmission and random channel characterization in our wake, the next step in channel modeling involves the physics of radio wave propagation and the implication for three-dimensional spatial channels. Chapter 4 discusses the unique form and properties that a spatial channel must have to satisfy Maxwell’s equations.