Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

7.4 Constant Relative Radial Acceleration

According to notation introduced in Section 7.3, we have

(7.193)

(7.194)

(7.195)

Let us assume that the relative radial acceleration between P _T(t − D(t)) and P _R(t) is constant within the observation interval, that is,

(7.196)

then

(7.197)

(7.198)

where and ξ₀ = ξ(t₀).

Note that motion with constant acceleration is not compatible with the special relativity theory. In fact, from (7.197) it follows that

(7.199)

Consequently, such a motion model can be used provided that the length T of the observation interval is not too large.

Let us assume that TX and RX do not collapse within the observation interval. Then, from (7.194) and (7.198) we have