High Resolution Tactical Synthetic Aperture Radar (TSAR) - MATLAB Simulations for Radar Systems Design - page 591

Combining Eq. (12.14) and Eq. (12.13) yields

c
2 R max

------------------------------------

f r max ≤

(12.15)

( – R min )

SAR minimum PRF, , is selected so that Doppler ambiguity is avoided.
In other words, must be greater than the maximum expected Doppler
spread within a footprint. From the geometry of Fig. 12.8, the maximum and
minimum Doppler frequencies are, respectively, given by

f r min

f r min

2 v
λ

θ

--  

f d max = ------ sin sin β ; at t 1

(12.16)

θ
-- 

2 v
λ



f d min = – ------ sin sin β ; at t 2

(12.17)

It follows that the maximum Doppler spread is

∆ f d = f d max – f d min

(12.18)

Substituting Eqs. (12.16) and (12.17) into Eq. (12.18) and applying the proper
trigonometric identities yield

4 v
λ

θ
---

∆ f d = ------ sin sin β

(12.19)

Finally, by using the small angle approximation we get

4 v
λ

θ
---

2 v
λ

∆ f d ≈ ------ sin β = ------ θβ sin

(12.20)

Therefore, the minimum PRF is

2 v
λ

------ θβ

f r min ≥ sin

(12.21)

Combining Eqs. (11.15) and (11.21) we get

c
2 R max

2 v
λ

------------------------------------ ------ θβ

≥≥ f r sin (12.22)

( – R min )

It is possible to resolve adjacent scatterers at the same range within a foot-
print based only on the difference of their Doppler histories. For this purpose,
assume that the two scatterers are within the kth range bin.