*3.1. LPI Waveform Design Considering Radar Detection Performance and the PIS*

The baby-blue dotted lines (only one-sided PSDs are shown) in Figure 1 (experiment 1: white Gaussian noise) and Figure 2 (experiment 2: colored Gaussian noise) are the optimal radar waveforms for target detection proposed by Zhu et al. [12], which place all their power at the frequency where *σ*<sup>2</sup> *<sup>H</sup>*(*f*)/*PN*1(*f*) (denoted by C(*f*)) is maximum. The aim of the proposed LPI waveform design method is to reduce the peak power under a certain loss of radar detection and resolution performance and a fixed transmission power, in order to decrease the interception performance of the PIS. That is, some power will be placed at other frequencies. In this subsection, we first consider radar detection performance, and the combination of radar detection and resolution performance is considered in the next subsection.

**Figure 2.** Optimized LPI radar waveforms under the constraint of the radar detection performance (colored Gaussian noise, *PN*<sup>1</sup> = *PN*2, **Ps** = 5 kw), target-to-noise ratio *σ*<sup>2</sup> *<sup>H</sup>*(*f*)/*PN*1(*f*) of radar, PSD of colored Gaussian noise *PN*2(*f*).

*For experiment 1*, since *PN*2(*f*) is a constant, only by putting some power at the frequency where C(*f*) is the secondary maximum can we furthest reduce the peak power to minimize *D*(**z**; **n**2) under a given radar detection performance constraint *γ*, as the green and red lines show in Figure 1. With the relaxing of constraint *γ*, the power of the optimized LPI waveform will be put at the corresponding frequencies in a descending order of C(*f*) (as the deep blue and purple lines show in Figure 1) until the energy is distributed equally within the whole bandwidth (as the black dotted line shows in Figure 1). *For experiment 2*, since *PN*2(*f*) is not a constant anymore, the frequencies at which the power reduced from the baby-blue dotted line can be placed are related to both C(*f*) and *PN*2(*f*). As the light green and red lines show in Figure 2, the reduced power is first placed at the frequency where *PN*2(*f*) is maximum, which can minimize the *D*(**z**; **n**2) in Equation (10). With the decrease in the value of the radar detection performance constraint *γ*, the optimized LPI waveforms are the result of the combined effects of *PN*2(*f*) and C(*f*) (as the deep blue and purple lines show in Figure 2). When *γ* tends to zero, the optimized waveform is almost completely influenced by *PN*2(*f*), and they have the same shape, as the black dotted line shows in Figure 2.

Since the PIS has no prior information about the transmitted waveform, a reduction in peak power may have a serious effect on its output SNR. In contrast, radar can reduce the effect significantly using the matched filtering technique. As shown in Figure 3, with the decrease in radar detection performance constraint *γ*, the performance degradation *δsnr* gradually increases and remains unchanged in the end. The degradation of radar performance for experiment 1 and 2 stays within 5 dB, while that of the PIS can finally reach 20 dB. As there is such a large performance degradation gap between the radar and the PIS, the optimized radar waveform can achieve a superior LPI performance.

**Figure 3.** Performance degradation versus radar detection performance constraint.
