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Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications by Antonio Napolitano

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7.3 Constant Relative Radial Speed

Let ξ(t) be the projection of the vector P R(t) − P T(tD(t)) along the propagation direction ik (oriented from P T(tD(t)) to P R(t)), that is

(7.77) equation

The delay D(t) experienced by the wavefront transmitted at time tD(t) in P T(tD(t)) and received at time t in P R(t) depends on the distance ||PR(t) − PT(tD(t))||. Accordingly with (7.11) we have

(7.78) equation

As observed in Section 7.1.3, |ξ(t)| is the time-varying distance responsible of the Doppler effect, viz, the time-varying delay D(t), and should not be confused with

(7.79) equation

Let us assume that the relative radial speed between P T(tD(t)) and P R(t) is constant within the observation interval. Thus, the projection of the vector P R(t) − P T(tD(t)) along the propagation direction ik is a linear function of t. That is,

(7.80) equation

Furthermore, let us assume that, within the observation interval, RX does not collapse on TX. Thus, ξ(t) does not change sign and it is always img(t, D(t)) > 0. Under ...

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