**6. Low Velocity Target Suppression: Moving Target Indication (MTI)**

To adapt the scheme to be practicable in the case (2) scenarios above, which resemble a crucially tactical scenario in which targets are blended into a heavy clutter background, integrating efficient clutter suppression schemes into MDSC is a substantial improvement to resolve this ambiguous scene. The techniques for implementing clutter filtering are the basis of the moving-target indication (MTI) scheme, which removes near-zero Doppler clutter spectrum and depth, and the width of the cut-off frequency of the filter is the factor of the number of pulses integrated and weighting coefficients of delay line applied on the pulse train.

Since this study is dealing with pulses transmitted at a pulse repetition frequency (PRF) fr, the received signal, from a given range, consists of one PRI = 1/fr apart. The spectrum of such a signal is folded around fr/2 and centered around zero Doppler repeating every ±n\*fr, n = 0, 1, 2 ... With this zero-Doppler canceling response, the nearly stationary clutters are the subject to be removed out of the non-stationary targets the periodicity in the filter response. The periodic frequency response of the filter resembles a comb; hence it is a so-called comb filter [15].

The two-pulse MIT filter is also called a single delay line canceler which can be implemented as shown in Figure 17. It requires two distinct input pulse to yield out output. These sequential pulse trains are merged into a single pulse by feedback loops of the delay lines with specific coefficients weighing applying on each echo pulse. The output *y*(*t*) is defined as follows [16]

$$y(t) = \mathbb{C}\_1 \mathbf{x}(t) + \mathbb{C}\_2 \mathbf{x}(t - T) \tag{10}$$

where the input *x*(*t*) is an n-pulse pulse train, delay *T* = PRI = (1/fr), and *C*1, *C*<sup>2</sup> the weighting coefficients of each delay-line pulse summation operation.

**Figure 17.** Single delay line canceler for two-pulse moving target indication (MTI).

The impulse response of the canceler is given by

$$h(t) = \mathbb{C}\_1 \delta(t) + \mathbb{C}\_2 \delta(t - T) \tag{11}$$

The double-delay-line cancelers are shown in Figure 18 and it is also called the three-pulse MTI filter. There are three consecutive pulse train the impulse response is given by

$$h(t) = \mathbb{C}\_1 \delta(t) + \mathbb{C}\_2 \delta(t - T) + \mathbb{C}\_3 \delta(t - 2T) \tag{12}$$

**Figure 18.** Double delay line canceler for three-pulse moving target indication (MTI).

The output signal of a three-pulse input signal processed by a double-delay-line canceler is calculated as follows

$$y(t) = \mathcal{C}\_1 \mathbf{x}(t) + \mathcal{C}\_2 \mathbf{x}(t - T) + \mathcal{C}\_3 \mathbf{x}(t - 2T) \tag{13}$$

An MTI filter could be implemented using as little as two pulses and the filter high-pass response is determined by the number of pulses applied and weighting coefficients of the impulse response. Binomial coefficients are applied in the MIT filter frequency responses and a three-pulse delay line canceller is integrated with MDSC schemes to suppress the stationary object distortion to compensate for the ambiguous estimation in this study.

The binomial coefficients of multi-pulse MIT filters are given by

$$\mathbb{C}\_n = \binom{n}{k} \times (-1)^k = \frac{n!}{k!(n-k)!} \times (-1)^k, 0 \le k \le n,\tag{14}$$

where the number of pulse n and the sign of the coefficient is toggled by every *k*th index.

The formula is also called Pascal's rule or Pascal's triangle [17]. The frequency response of the MIT filter with two to four pulses is shown in Figure 19. The zero-Doppler has a deep null point response repeated in multiples of fr = PRF, by which the ambiguous low-velocity target factors are eliminated in the original MDSC. The cut-off bandwidth of near-zero-Doppler in MIT filter frequency response is proportional to the number of canceling line tabs, i.e., the more identical pulse trains integrated, the wider and deeper the cut-off bandwidth. Figure 19 shows the cut-off bandwidth of 2-tab MTI (blue-dash line) < 3-tab MTI (red line) < 4-tab MTI (yellow-dotted-dash line).

**Figure 19.** Frequency response of MTI comb filters applied binomial coefficients with the number of integrating pulses from two to four. The cut-off bandwidths are proportional to the number of delay lines applied.
