Robust direct data domain processing for MTI
2.5 Applications of RD 3 -STAP
2.5.1.3 Case study analysis
The effectiveness of the proposed technique is tested against a simulated dataset, whose main parameters are reported in Table 2.3. Please note that having N ¼5 receiving channels, only up to K1¼2 interferences can be simultaneously suppressed for each Doppler bin. The main aim of this analysis is to verify the effectiveness of the clutter cancellation Doppler bin per Doppler bin, and
Range
processing Range
processing Range
processing Azimuth FFT Azimuth FFT
Azimuth IFFT Target detection
& imaging For different
Vat, Vr
Channel 1 Channel 2 Raw multi-channel SAR data
Channel N
Azimuth FFT
RD3-STAP
Figure 2.12 Block diagram of the integrated technique.2012 IEEE. After [26]
Table 2.3 Case study parameters
Parameter Value
Carrier frequency X-band
Sub-array distance (d) 0.26 m Number of sub-arrays (N) 5 Number of pulses (M) 450 Platform velocity (V) 100 m/s
Random target amplitude (aS;m) 5expðjp=5Þ gðmÞ Target along-track velocity (Vat) 0 m/s
Target radial velocity (Vrad) 3 m/s
Random clutter amplitude (a0;m) 36expðjp=3Þ gðmÞ Clutter dispersion (sD) 1
Thermal noise (rm;n) AWGN, zero mean, unit variance
consequently to verify the target imaging capability. With reference to the block diagram in Figure 2.12, for simplicity, the entire processing is matched to the exact target velocity parameters.
Clutter cancellation
To verify the clutter cancellation capability, two different investigations have been conducted.
In the first analysis, we aimed at comparing the clutter cancellation capability of RD3-STAP in comparison with conventional stochastic STAP, for the case study scenario depicted in Table 2.3. In particular, as conventional stochastic STAP, the single bin post-Doppler technique has been considered because, as the RD3-STAP technique here presented, it allows a partitioning of the overall STAP problem.
Comparison has been conducted in terms of output SINR over normalized target Doppler frequency, and results are reported in Figure 2.13. Both for conventional stochastic STAP and for RD3-STAP, the SINR is measured as the ratio between the adapted patterns (in power) in the target and in the interference directions.
Obviously, for the conventional stochastic STAP, this requires the definition of the corresponding covariance matrix, while for the RD3-STAP, the simple imple- mentation of (2.1) is required. Concerning RD3-STAP, the region of uncertainty is set to one-fifth of the antenna beamwidth, which is a reasonable value in target tracking or confirmation cases. Performance of conventional stochastic STAP filter is evaluated under the clairvoyant hypothesis of known covariance matrix, and for the more realistic case of a very limited sample support for interference covariance
0
–10
–20
Normalized SINR [dB]
–30
–40
–50
–60 –0.45 –0.3 –0.15 0
Normalized Doppler frequency (fD/PRF) 0.15 0.3
RD3-STAP conv. STAP (KCM) conv. STAP (estimated)
0.45
Figure 2.13 Comparison of normalized SINR [dB].2012 IEEE. After [26]
matrix estimation. In particular, only five homogeneous range gates have been used, and diagonal loading has been applied to robustify matrix estimation. As is apparent, conventional STAP is theoretically able to outperform RD3-STAP, but only if a fine estimation of the interference is conducted, otherwise adaptivity losses have to be accepted. Please note that the scenario here considered is actually favourable for conventional STAP (over RD3-STAP), since a sample support (although small) is still available. By further reducing such sample support, additional instabilities are expected up to the situation where covariance matrix estimation is not possible anymore. Concerning the achievable performance of RD3-STAP, the following considerations are in order. The width of the clutter filter notch is directly introduced by the robustness constraint in (2.15) which preserves target self-nulling in case of target parameter mismatch. Apart from this, consistent degradations are also experienced nearby the central blind zone. These degrada- tions simply represent the limit of a single snapshot clutter cancellation. In other words, they have to be accepted if no covariance matrix can be estimated due to extremely fast varying interference characteristics. Alternatively, a double canceller RD3-STAP approach such as the one in (2.25) can be exploited.
The second analysis, aimed at evaluating the behaviour of RD3-STAP in the SAR case. To this end, following the procedure described in the preceding sections, the weight vector wðfDÞobtained by solving (2.15) has been evaluated for every Doppler bin independently, for a region of uncertainty corresponding to the antenna main beamwidth. After applying a FFT in the spatial domain, the RD3-STAP filter transfer function is obtained, see Figure 2.14. For convenience the behaviours of
0 0.1 0.2 0.3 0.4 0.5
Normalized Doppler frequency (fD/PRE) 0.6 0.7 0.8 0.9
–0.05 0
θ (rad) θs(fD)
θi(fD)
0.05
0 –10 –20 –30 –40 –50 –60 –70
Figure 2.14 RD3-STAP transfer function [dB].2012 IEEE. After [26]
qSðfDÞ (solid line) and of qiðfDÞ (i¼1;2) (two adjacent dashed lines) are also reported. As is apparent, the RD3-STAP filter maintains over Doppler a constant unitary gain in the target direction, while strong depressions are always ensured to adequately mitigate the interferences. Please note that the two green dashed lines in Figure 2.14 represent the clutter ridge. While all interfering signals along this line are constantly present at the same time, the target signal is moving along the red solid line over slow-time. For this reason and due to the clutter Doppler decoupling, if target parameters are known with some acceptable level of accuracy, the RD3-STAP filter has to cope, Doppler bin per Doppler bin, only with the few interferences associated with the corresponding target Doppler location.
In Figure 2.15, the output of the RD3-STAP filter is reported as a function of the Doppler frequency, that is yðfDÞ. Specifically, the first sub-plot reports the amplitude ofyðfDÞ, while the phase is shown in the second sub-plot. As one can see, the amplitude ofyðfDÞnicely replicates the behaviour of the antenna pattern over Doppler or equivalently ofaSðfDÞ(superimposed markers), while the linear phase of yðfDÞ clearly shows that the phase locking of wðfDÞ to aðfDÞ automatically compensates the moving target phase history. Finally, also note the smooth beha- viour of the RD3-STAP filter transfer function in the surroundings of the target position in Figure 2.14. Such smooth behaviour is the peculiar characteristic of the robust implementation of the D3-STAP filter. In fact, it allows proper reconstruc- tion of the behaviour ofaSðfDÞeven in presence of mismatch between the nominal and the true target DOA (here not considered). Even in normal STAP applications
60
y(fD) amplitude [dB]y(fD) phase [rad]
40 20 0 –20
4
2
0 –2
0 0.25 0.5
Normalized Doppler frequency (fD/PRF)
0.75 1
0 0.25 0.5 0.75 1
Figure 2.15 Filter output yðfDÞin amplitude and phase.2012 IEEE. After [26]
[e.g. with short coherent processing intervals (CPIs)], this is an important feature since it allows to prevent target self-nulling effects (see [13]), but in the SAR case, it becomes an extremely important feature since a trusty reconstruction ofaSðfDÞis necessary to avoid distortions in the following imaging step.
Moving target imaging
Following the previous considerations, the imaging of the moving targets after the application of the RD3-STAP filters in the Doppler domain simply requires an IFFT. The obtained pulse response, for the sample case study under analysis, is reported in Figure 2.16. The remaining noise level is well below the values here shown (compare also markers and solid line in the upper sub-plot of Figure 2.15), so that the behaviour looks noise free but it is not. The obtained azimuth resolution is about 46 cm, which agrees with the target Doppler bandwidth shown in Figure 2.15. The sidelobe level is also increased with respect to the conventional 13 dB of a sinc function due to the azimuth antenna taper.