Robust direct data domain processing for MTI
2.4 Results of RD 3 -STAP
Doppler frequency is shown in Figure 2.4, where the nominal target position is marked with a white ‘x’, while the real target position is marked with an ‘o’. For convenience, in Figure 2.4, also the jammer and clutter contributions have been highlighted with black lines.
Table 2.1 Case study parameters
Parameter Value
Wavelength (l) 0.03 m
Antenna element distance (d) l=2
PRF (fr) 1,550 Hz
Number of channels (N) 11
Kn 6
Number of pulses (M) 65
Km 25
Target qNs ¼ 0.1 rad;qTs¼ 0.1 rad
fsN¼100 Hz;fsT¼120 Hz as¼12:8ej0:67
Jammer q1¼ 0.6 rad
a1¼51ej1:37
Clutter qi¼[0.2, 0.2] rad
fi¼[220, 220] Hz ai¼42ej0:78
Thermal noise (rm;n) AWGN, zero mean, unit variance
300
True 60 Nominal
50 40 30 20 10 0 –10
Doppler frequency [Hz]
200
100
0
–100
–200
–300
–1 –0.5 0
θ (rad)
0.5 1
Figure 2.4 Input signal power spectrum (x: nominal target position; o: true target position) in dB.2012 IEEE. After [13]
The output signal power spectrum obtained by applying the conventional D3-STAP filter is shown in Figure 2.5. As is apparent, deep notches are placed both at the jammer DOA and along the clutter ridge. However, the target self- nulling effect can be clearly seen. That is the slight mismatch in target Doppler frequency knowledge causes the synthesis of a notch in the real target position (black circle).
A different result is obtained by applying the RD3-STAP approach. In this case, the adaptive filter pulse response is designed to tolerate a maximum mismatch in the target Doppler frequency knowledge of 25 Hz.
As a consequence, the output signal power spectrum shows no target self- nulling effect, as is clearly visible in Figure 2.6. The real target position (black circle) is now preserved, while strong depressions are synthesized to suppress both jammer and clutter.
2.4.2 Application of RD3-STAP filter to real data
The RD3-STAP approach is here applied to a real multi-channel data set acquired with the experimental radar system PAMIR developed at Fraunhofer FHR [21].
Experimental data have been acquired during a flight campaign in 2008. PAMIR main system parameters used in the acquisition are reported in Table 2.2. During the experiment, two signal repeaters have been used to emulate the echoes of two different targets whose characteristics are described in Table 2.2.
300
200
100
Doppler frequency [Hz] –100
–200
–300–1 –0.5 0
θ (rad)
0.5 1
0
True
60 50 40 30
10 0 –10 –20 20 Nominal
Figure 2.5 D3-STAP output signal power spectrum (x: nominal target position;
o: true target position) in dB.2012 IEEE. After [13]
The range-Doppler map of the sum channel is reported in Figure 2.7. The zoom in Figure 2.8 highlights the positions of the two targets just at the edge of the main clutter region.
300
200
100
Doppler frequency [Hz] –100
–200
–300–1 –0.5 0
θ (rad)
0.5 1
0
True
60 50 40 30
10 0 –10 –20 20 Nominal
Figure 2.6 RD3-STAP output signal power spectrum (x: nominal target position;
o: true target position) in dB.2012 IEEE. After [13]
Table 2.2 Main PAMIR parameters
Parameter Value
Wavelength (l) 0.03 m
Sub-array distance (d) 0.26 m
PRF (fr) 1,550 Hz
Signal bandwidth Lowered to 38 MHz
Number of channels (N) 3
Kn 2
Number of pulses (M) 51
Km 26
Target 1 (strong) qTs ¼0 rad fsT¼165 Hz RCS¼100 m2 Range¼2,664 m Target 2 (weak) qTs ¼0 rad
fsT¼165 Hz RCS¼10 m2 Range¼2,694 m
1,600
60 50 40 30 20 10 0 –10 –20 1,800
2,000 2,200 2,400
Slant range [m]
2,600 2,800 3,000 3,200 3,400 3,600
–600 –400 –200 0 200
Doppler frequency [Hz]
RD-map sum channel [dB]
400 600
Figure 2.7 Range/Doppler map of the sum channel [dB].2012 IEEE. After [13]
2,550
2,600
2,650
2,700
Slant range [m]
2,750
2,800
0 50 100 150 200
Doppler frequency [Hz]
RD-map sum channel (zoom) [dB]
Target 1
60 50 40 30 20 10
–10 –20 0 Target 2
250 300 350
Figure 2.8 Zoom of the range/Doppler map of the sum channel over the two targets [dB].2012 IEEE. After [13]
In order to test the effectiveness of the RD3-STAP approach in this real situation, some uncertainty in the knowledge of the target parameters has been emulated. In particular, given the limited number of spatial DOFs, only an error in the target Doppler frequency has been assumed of half a Doppler bin (fe¼fr=ð2MÞ ¼16 Hz), leading to a nominal Doppler frequency offsN 150 Hz for both targets. In the following analysis, the RD3-STAP approach will be com- pared with both conventional D3-STAP and with stochastic STAP. In particular, the adjacent bin post-Doppler STAP technique [2] will be considered, applied with all available receiving channels and with three Doppler bins. The interference covar- iance matrix is estimated by means of local learning strategy, using 36 range gates (twice the number required by the RMB rule). The strong target is analysed first, by extracting from the PAMIR data cube the corresponding space–time data snapshot.
D3-STAP and RD3-STAP filters have then been applied to the input data snapshot of the strong target, leading to the output signal spectra reported in the upper sub-plot of Figure 2.9. For comparison, the input signal power spectrum is reported as well. As one can see, the target is strong and separated from the clutter contribution at 0 Hz so that it is visible even after D3-STAP filtering. However, by applying the D3-STAP filter, some residual clutter is still present in the output signal due to the presence of high sidelobes in the pulse response. In particular, a residual clutter contribution at about 40 Hz is still visible after D3-STAP filtering, which is not present if the RD3-STAP filter is applied.
100 50
20
–20 –40 0
Power [dB]SCNR [dB]
–800 –600 –400
STAP Input signal
Output signal D3-STAP Output signal RD3-STAP
–200 0 150
Doppler main cut
Doppler frequency [Hz]
400 600 800
–800 –600 –400 –200 0 150 400 600 800
0
Figure 2.9 Output signal spectrum [dB] – target 1 range gate.2012 IEEE.
After [13]
Observing Figure 2.9, one can see that the residual clutter contribution in the D3-STAP output signal spectrum is due to the presence of a high sidelobe in the corresponding pulse response located at the same Doppler frequency. This does not occur if the RD3-STAP filter is applied, due to the low sidelobes shape of the pulse response. This property directly originates from the solution of the convex mini- mization problem in (2.15) (see [13] for more details). In the second sub-plot of Figure 2.9, the Doppler cut of the strong target range gate is reported after the application of the adjacent-bin post-Doppler STAP filter. Please note that the out- put signals obtained after D3-STAP filtering are not normalized to the interference power, thus leading to a different scaling of theyaxis with respect to the stochastic STAP filter output, and hence requiring the use of two different sub-plots for proper comparison. The normalization to the interference power has not been performed in order to show the unit gain of the two D3-STAP filters at the nominal target Dop- pler frequency. As mentioned before, the stochastic STAP filter is made adaptive by estimating the interference covariance matrix of the target range gate using secondary data taken from range gates close to the CUT. Due to the vicinity of the two targets, the secondary data corresponding to one target range gate include also the range gate of the other target, thus determining inter-target nulling. This effect is only partly visible when the strong target range gate is considered. In fact, the presence of the weak target in the secondary data has only a limited effect on the strong target detection. In contrast, the inter-target nulling is much more evident when the weak target range gate is considered. In this latter case, the presence of the strong target polarizes the statistics of the secondary data, making them similar to the range gate under test and making the weak target detection more difficult (if not even impossible).
This effect is shown in the range-Doppler map after stochastic STAP filtering reported in Figure 2.10, where the output power has been normalized to the aver- age interference power. As is apparent, the strong target is clearly detectable, with an estimated signal-to-interference-plus-noise ratio (SINR) of about 15 dB. On the other hand, the weak target is completely nulled by the presence of the strong target in the corresponding secondary data. It is clear that an inter-target nulling effect is intrinsically impossible when D3-STAP or RD3-STAP filtering is applied.
As a consequence, we expect it to be able to detect the weak target. To verify this, the previous analysis has been repeated extracting the weak target range gate from the PAMIR data cube. The corresponding Doppler main cut of the input signal spectrum is reported in the upper plot Figure 2.11. We can easily observe how the target detection is now more challenging with respect to the strong target range gate case.
In particular, the clutter is now mainly characterized by three different contributions located at about100, 30 and 120 Hz. In particular, the latter clutter contribution is close to the target position. The first sub-plot in Figure 2.11 reports also the output power spectra after the application of D3-STAP and RD3-STAP filtering. As one can see, when the D3-STAP filter is applied, the sidelobe level is unacceptable for reliable target detection, whereas a much better result is obtained when the RD3-STAP filter is considered.
2,550
2,600
2,650
2,700
Slant range [m]
2,750
2,800
0 50 100 150 200
Doppler frequency [Hz]
Range-Doppler map after conventional STAP [dB]
Target 1 Target 2
20 18 16 14 12 10 8 6 4 2 0 –2 250 300 350
Figure 2.10 Range/Doppler map after stochastic STAP (zoom) [dB].
2012 IEEE. After [13]
100 Input signal
Output signal D3-STAP Output signal RD3-STAP 50
20 0 –20 –40 Power [dB]SCNR [dB] 0
–800 –600 –400 –200 0
Doppler main cut
Doppler frequency [Hz]
150 400 600 800
–800 –600 STAP
–400 –200 0 150 400 600 800
Figure 2.11 Output signal spectrum [dB] target 2 range gate.2012 IEEE.
After [13]
The second sub-plot of Figure 2.11 reports, for comparison, the output power spectrum after adjacent-bin post-Doppler STAP filtering normalized to interference power level. As is apparent, the weak target is completely cancelled due to the inter-target nulling effect.