7.2 Constant Velocity Vector

In this section, the case of constant velocity vector is analyzed. The relative radial speed is not necessarily constant.

7.2.1 Stationary TX, Moving RX

By specializing (7.34) with

(7.67)

with i ₁ ⊥ i ₂ (without lack of generality) and ||i ₁|| = ||i ₂|| = 1, we get (Figure 7.5)

(7.68)

where the first equality is due to (7.35). RX is moving with constant velocity vector . The (non-constant) radial speed is

(7.69)

and it results that

(7.70)

Figure 7.5 Constant velocity vector: TX stationary, RX moving

7.2.2 Moving TX, Stationary RX

By specializing (7.37) with

(7.71)

with i ₁ ⊥ i ₂ (without lack of generality) and ||i ₁|| = ||i₂|| = 1, we get (Figure 7.6)

(7.72)

Figure 7.6 Constant velocity vector: TX moving, RX stationary

From (7.38) we have

(7.73)

That is,

(7.74)

Hence

(7.75)

with B² − 4AC ≥ 0 since . Thus,

(7.76)

where the solution with “+” sign provides a positive delay D(t). This result is in accordance with (Quinn and Hannan 2001).