Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

7.6 Multipath Doppler Channel

7.6.1 Constant Relative Radial Speeds – Discrete Scatterers

In the case of multiple reflections on point scatterers, propagation can be described by the multipath Doppler channel (Izzo and Napolitano 2002b), (Napolitano 2003), (Izzo and Napolitano 2005), that is a LTV system with impulse-response function

(7.249)

where K is the number of the channel paths.

By double Fourier transforming the right-hand side of (7.249), one obtains the transmission function (see (1.44) and (6.68))

(7.250)

from which, accounting for (4.77a), it follows that the multipath Doppler channel is a FOT deterministic LTV system with Ω = {1, …, K},

(7.251)

(7.252)

Equivalently, accounting for (4.78), we get

(7.253)

(7.254)

The output y(t) corresponding to the input signal x(t) is obtained by substituting (7.249) into (1.41):

(7.255)

7.6.2 Continuous Scatterer

In the case of distributed ...