**7. Two-Target, Clutter-Suppressed Multi-Doppler-Shift-Compensation (CS-MDSC)**

The ambiguous scenario with one near-stationary target has been discussed in Section 5 case (2). Figure 20 shows a typical unresolvable scenario to MDSC, which contains two targets at the same range cell with extremely velocity difference the target-one is stationary with zero-Doppler offset at the center, whereas the target-two velocity difference is at 15 Mach, which introduces a 102 kHz Doppler shift at S-band. The pulse compressed echo of up-down chirp LFM waveform has two peak values due to the Doppler shift at range cell ±6.25.

**Figure 20.** Pulse compressed echo of two overlapped targets. Target-one is zero Doppler, while target-two velocity is at Mach 15.

For an MIT comb filter application, Figure 21 demonstrates a three-pulse LFM echo with two targets with such extreme location and velocity conditions described above with fd/PRF = 0 and 0.32, respectively. The frequency response of three-pulse MTI filter is shown in Figure 19; the target-1 echo with fd1/PRF = 0 gets suppressed significantly while that of target-2, fd2/PRF = 0.32, is in the passband of the filter.

**Figure 21.** A 3-pulse LFM echo of two overlapped targets. Target-one is zero Doppler, while target-two velocity is at Mach 15.

Figure 22 displays the MTI processed echo of Figure 20, the zero-Doppler clutter is eliminated while the Mach 15 moving target echo remains, which leaves no ambiguity of the correctly pairing estimation.

**Figure 22.** A 3-pulse MTI filtered echo of two overlapped targets. Target one is zero Doppler, while target two is at fd2/PRIL = 0.32.

Another case study of a slow-moving target overlapping with a high-velocity target, which is also an ambiguous scenario for MDSC, is shown in Figure 23. Both moving targets introduce a pair of detection peaks with range offset after PC of the LFM waveform. The slow-moving target resembles a near-zero-Doppler clutter, such as cloud or sea with the fd1/PRF = 0.072, while the second target resembles a high-velocity target, fd2/PRF = 0.32, travelling across this strong clutter background. Figure 19 shows that the near-zero-Doppler clutter also suffers significant attenuation at fd1/PRF = 0.072 for about 26 dB, whereas the second target with high velocity retains a strong response level at fd2/PRF = 0.32.

**Figure 23.** Pulse compressed echo of two overlapped targets. Target-one is Near-zero-Doppler, while target-two velocity is at 15 Mach.

Figure 24 shows the three-pulse MTI filtered echo of Figure 23. The −26 dB frequency response substantially drops down the target-one energy at fd1/PRF = 0.072. Since the outcome energy of target-one, which is implied as a low velocity clutter at range cell = ±0.037, has been significantly deteriorated and leaves 16 dB power difference between the detection pairs of two targets, this artifact signal can be removed completely by setting up a reasonable detection threshold, such as a constant false alarm rate threshold. Therefore, with the prior state of a properly designed clutter suppression scheme, the remaining detection pair at range cell ±6.2 can resolve the target-two range and velocity information unambiguously.

**Figure 24.** A 3-pulse MTI filtered echo of two overlapped targets. Target one is near-zero-Doppler, while the target-two velocity is at Mach 15.

To compensate the inapplicable scenarios of MDSC, a two-target, clutter suppression multi-Doppler-shift-compensation (CS-MDSC) workflow is illustrated in Figure 25. The process procedures begin with:

	- i. If the detection count is greater than two, then process MDSC to find the correct detection pair of LFM waveform for resolving these two targets' locations and velocity.
	- ii. If the number of detection is less than and equal to two due to the clutter suppression process, then there is no ambiguity on finding the right pair of the target. The location and velocity information of the moving target can be resolved by the remaining two or one detected signals.

**Figure 25.** Clutter-suppression, multi-Doppler-shift-compensation (CS-MDSC) workflow.
