High Resolution Tactical Synthetic Aperture Radar (TSAR) - MATLAB Simulations for Radar Systems Design - page 598

Doppler histories

time

0

T ob

Figure 12.10. Doppler histories for several scatterers within the same range bin.

A signal processing block diagram for the range bin is illustrated in Fig.
12.11 . It consists of the following steps. First, heterodyning with the carrier
frequency is performed to extract the quadrature components.

kth

This is followed by LP filtering and A/D conversion. Next, deramping or
focusing to remove the second order phase term of the quadrature components
is carried out using a phase rotation matrix. The last stage of the processing
includes windowing, performing an FFT on the windowed quadrature compo-
nents, and scaling the amplitude spectrum to account for range attenuation and
antenna gain.

The discrete quadrature components are

ô i t n µ i

ô I t () ô I

= () A i = cos [ ( , ) – ξ 0 ]

(12.46)

ô i t n µ i ô Q t () ô Q = () A i = sin [ ( , ) – ξ 0 ]

) ó i t n µ i ô i t n µ i ( , = ( , ) – 2π f 0 t n

(12.47)

and denotes the sampling time (remember that ).
The quadr a ture components after deramping (i.e., removal of the phase
) are given by

t n nth – T ob ⁄ 2 ≤≤ t n T ob ⁄ 2

2

ψπ f 0 = – τ tt t n

ô I ()
ô Q

x I ()
x Q

cos ψ – sin ψ

=

(12.48)

() sin ψ cos ψ ()