(ATBD) SMAP Level 1 Radar Data Products - NASA

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and R(t) indicates that the range is a function of time because of spacecraft motion.
By including the time dependence of R, the Doppler frequency shift of the
echo waveform due to the motion of the spacecraft relative to the surface point is
automatically included. The received waveform (V rf in volts) is then given by
V rf (t) = As rf (t − 2R(t)/c)
= Au p (t − 2R(t)/c − iτ pri )cos(2πf cg (t − 2R(t)/c − iτ pri ) + 2πf u (t − 2R(t)/c)
+ πK 1 (t − 2R(t)/c − iτ pri ) 2 ) + φ u + φ cg )
(19)
The received RF signal is first mixed down with another continuous running sinousoid
at frequency f d = m d f ctu .
s d (t) = cos(2πf d t + φ d ) (20)
where φ d is an arbitary starting phase for the mixdown signal. To deliver an intermediate
frequency of 90 MHz regardless of the transmit tuning, the value of m d
is chosen from the range [903, 965] synchronized by index with the values of m cg
used by f cg . The result of multiplying s rf and s d and taking the lower sideband is
V if (t, i) = Au p (t − 2R(t)/c − iτ pri )cos(2πf cg (t − 2R(t)/c − iτ pri ) + 2πf u (t − 2R(t)/c) − 2πf d t
+ πK 1 (t − 2R(t)/c − iτ pri ) 2 ) + φ u − φ d + φ cg )
(21)
As shown in Fig. 6, the IF signal centered at 90 MHz is sampled at 40 MHz which
undersamples the signal. The IF signal is 5 MHz wide and includes the H-pol, noise
channel, and V-pol band passes spaced 1.5 MHz apart. Aliasing will cause the IF
signal to show up in the 20 MHz bandwidth of the ADC samples centered at 11.5
MHz for H-pol data, 10.0 MHz for noise only data, and 8.5 MHz for V-pol data.
The final filtering and IQ demodulation for each of the three channels is performed
digitally in the radar FPGA. The filtering is done by high order FIR digital
filters that offer a sharp cutoff and a bandwidth of about 1.1 MHz for each channel.
The demodulation and aliasing can be modeled as another mixdown with the
mixdown frequency chosen to match each channel IF center frequency. Here it is
assumed that the demodulation mixdown starts from zero phase for each pulse just
like the chirp generator
s demod (t, i) = s demod (t − iτ pri ) = cos(2π(f cg + f u − f d )(t − iτ pri )) (22)
Multiplying s if by s demod and taking the lower sideband gives the final complex
basebanded point target response
V bbpt (t, i) = Au p (t − 2R(t)/c − iτ pri )exp(j2π(f u − f d )iτ pri − j4π(f cg + f u )R(t)/c
+ jπK 1 (t − 2R(t)/c − iτ pri ) 2 ) + j(φ u − φ d + φ cg ))
(23)