For an LFM signal with TB product, the cubic phase predistortion technique can be used to suppress the sidelobe [3, 4]. The signal with little TB product has large ripples in its spectrum band, so widowing is not satisfying for sidelobe suppression. In this situation, the sidelobe suppression can be achieved by suppressing the ripples in band through phase predistortion. This method is easy to implement with surface acoustic wave (SAW) technique.

Suppose the complex expression of the LMF signal to carry out phase predistortion on is

\begin{array}{l}s\left(t\right)=exp\left[j2\pi \left({f}_{0}t+\frac{B}{2T}\xb7{t}^{2}+\phi \left(t\right)\right)\right]\phantom{\rule{0.2em}{0ex}},\\ -T/2-\mathit{\Delta T}\le t\le T/2+\mathit{\Delta T}\end{array}

(2)

where *f*_{0} is the central frequency and *B* is the bandwidth. And the duration of the pulse is *T*. Then the additional phase item can be

\phi \left(t\right)=\left\{\begin{array}{ll}\frac{\mathit{\Delta B}}{3\Delta {T}^{2}}\xb7{\left(-t-T/2\right)}^{3},\hfill & -T/2-\mathit{\Delta T}\le t<-T/2\hfill \\ \frac{\mathit{\Delta B}}{3\Delta {T}^{2}}\xb7{\left(t-T/2\right)}^{3},\hfill & T/2<t\le T/2+\mathit{\Delta T}\hfill \\ 0,\hfill & \mathit{elsewhere}\hfill \end{array}\right.

(3)

where Δ*T* = 1/*B* and Δ*B* = 0.75*B*[3].

The spectrum of the pulse after phase predistortion is shown in Figure 11 and after multiplying a Hamming window, the predistorted spectrum is illustrated as shown in Figure 12.

After matched filtering, the effect of pulse compression is shown in Figure 13.

Figure 13 demonstrated that the sidelobes neighboring to the mainlobe are suppressed well (3–4 dB) through matched filtering after phase-predistortion. But in the positions away from the mainlobe, there are some sidelobe hunches and this may bring range ambiguity of two targets far away from each other.

In ideal situation, the output of the matched filter for an LFM signal has rectangular spectrum. After weighting, the rectangular spectrum becomes a certain window. But when the TB product of the LFM signal is small, its ripples in band are large, so the weighting has little effects for ripple suppression in band. In this case, spectrum modification technique can be resorted to make the processed spectrum approaches ideal window function mostly [5, 6] and to enhance the main-to-side lobe ratio.

Spectrum modification can be implemented by modifying the transfer function of the matched filter. Suppose the spectrum of the LFM signal is *U*(*f*) and the transfer function is *H*(*f*), to make the output of the matched filtering to be a rectangular, it is needed that:

U\left(f\right)H\left(f\right)=I\left(f\right){I}^{*}\left(f\right),I\left(f\right)=\mathit{rect}\left(f/B\right)

(4)

The modified transfer function of the matched filter is

H\left(f\right)={U}^{*}\left(f\right)\left[I\left(f\right){I}^{*}\left(f\right)/{\left|U\left(f\right)\right|}^{2}\right]

(5)

The pulse compression result after using spectrum modification is shown in Figure 14.

From Figure 14, it can be seen that spectrum modification technique has good suppression effect for the sidelobes neighboring the mainlobe. What is the most important, this technique bring a great advantage that suppress the sidelobes far away from the mainlobe to the level under –62 dB.

It is stressed that both phase predistortion and spectrum modification did not spread the mainlobe apparently.