IEEE Geoscience and Remote Sensing Magazine - December 2022 - 24

The gaps occur periodically at integer multiples of the PRI,
i.e., at time delays nT· pri
pri
nc /,T 2 where n is an integer.
·
The time at which the SAR Rx is turned off during the
transmit events is known as the blockage time and is denoted
by
b .
xx
bp ,$
x Due to the guard time-the time needed for the
limiter diode in the receive path to recover-the blockage
duration is typically longer than the transmit pulse
as demonstrated in Figure 17. It should be noted that any
transmit event will block all Nel input data streams and all
output beams; thus, for each transmit event ·,fbs
x
samples
will be lost for each channel, which is on the order of a few
thousand samples. Depending on the PRF and the swath
width, each range line may be interrupted several times due
to the multiple transmit events within the echo time Techo.
The average number of gaps within the swath is equal to
,
N
beam 1where
Nbeam
has been introduced earlier in (1)
and represents the average number of beams.
◗ Parameter Values: The reference system images a
swath of 355 km through N
Nadir echo returns may also cause blind ranges, for
corresponding to the slant ranges
which they need to be considered [50]. For reflector-based
SAR, however, the nadir return may be sufficiently attenuated
by the Rx/transmitter (Tx) antenna pattern. Furthermore,
novel techniques for the removal of the nadir echo
within postprocessing based on the alternation of the
transmitted waveform are suggested in [51] and [52]; as an
additional benefit, these techniques allow for relaxing the
PRF constraint.
IMAGING GAP EXTENT
The expression for the imaging gap extent is derived taking
the transmitted signal time-frequency dependency into account
to quantitatively assess the impact on the imaging
performance. Consider a stationary radar, which, without
restriction of generality, is transmitting an up chirp
(pulse 1) of duration
x Take a reference sphere centered
p .
at the antenna that is just large enough to contain the complete
antenna structure. Let t0
p
beam 3= simultaneous
SCORE beams. The diamond diagram in Figure 1 shows
that the swath is interrupted by N 12beam
blockage time b
xn=
x is determined by the pulse duration
p 34 s plus the guard time of 4s .n
-= gaps. The
and t0 + x mark the time
instances where the leading and lagging " edge " of an electromagnetic
wave generated by the transmitted pulse pass
the reference sphere. The corresponding instantaneous frequencies
are fmin and fmax, respectively.
The echo reflected from a point scatter at range r will
intersect the reference sphere at times
tt Tt
=+ D =+ =+ + c
r
00 0
c
and tt
xp
Tpri
Tpri
Tpri
Echo
Time
Gaps
2 22r
(8)
for the leading and lagging pulse edges, respectively. The
term ()/rc2
in the preceding expression, well known from
the radar delay equation, may be rearranged to read /( /).rc 2
It can be deduced that to an observer, the echo appears to
be traveling at /,c 2 which is half the speed of light.
Now, consider a second transmission event occurring
at time t1 that is blocking the Rx for b
x seconds. The
Gap
Ground Range
FIGURE 16. The transmit instances and the received echoes causing
gaps and range ambiguities.
Tpri
(fmax, Rmin) at t1
1
Pulse 1 Echo
Techo
t1
FIGURE 17. The transmit pulse (of duration )p
Time
x and the associated
guard time cause a blockage of the return echo during xb s econd.
To determine the width of the resulting imaging gap, it is necessary
to consider the instantaneous frequencies of the return echo that
are blocked for each range.
24
The preceding expression gives the total slant range extent
of the blockage without considering which frequencies
are blocked at which ranges. The correspondence between
range and frequency is also addressed in the context of dispersive
beamforming in tutorial part 1 [1]. It is crucial to
understand the range-frequency behavior of the blockage,
as detailed in the following.
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2022
2
|x xrb p
=- =+
maxmin
2
RR ().
c
(10)
τp Pulse
τp Blockage
blocked slant range limits are given by the minimum slant
range Rmin of the lagging pulse edge at t1 and the maximum
slant range Rmax of the leading pulse edge at
.
t1 + x With (8), the ranges are determined from the folb
lowing
equations:
()
t ++ =+ =+ (9)xx.
01 01and
2Rmin
pb
c tt c
t
2Rmax
The slant range extent of the gap is obtained by solving for
Rmin and Rmax and forming the difference
t0
t0 + τp
Tx Pulses
t
Rfar
Rnear
IEEE Geoscience and Remote Sensing Magazine - December 2022

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