## 3 Multipath Interference Suppression
 \tag{13}\]

where \(\text{Re}\{L(u)\}\) represents the real part of the LCT of noise, with

\[\text{Re}\Bigg{\{}\int_{-\frac{\Gamma}{2}}^{\frac{\Gamma}{2}}v(t)K_{A}(u,t) dt\Bigg{\}}\sim NORM\Big{(}0,\sigma_{nn}^{2}\Big{)}. \tag{14}\]

In summary, under \(H_{0}\), \(\text{Re}\{L(u)\}\) follows a Gaussian distribution with

\[\text{Re}\{L(u)\}\sim N\Big{(}0,\sigma_{nn}^{2}\Big{)}. \tag{15}\]

In (25), the imaginary part \(\text{Im}\{L(u)\}\) of the LCT under \(H_{0}\) is expressed as

\[\text{Im}\{L(u)\}=\text{Im}\Bigg{\{}\int_{-\frac{\Gamma}{2}}^{\frac{\Gamma}{ 2}}w(t)K_{A}(u,t)dt\Bigg{\}}. \tag{16}\]

Similarly, under \(H_{0}\), \(\text{Im}\{L(u)\}\) follows a Gaussian distribution with

\[\text{Im}\{L(u)\}\sim N\Big{(}0,\sigma_{nn}^{2}\Big{)}. \tag{17}\]

From (15) and (17), the distribution of the sensing statistics based on LCT under the \(H_{0}\) hypothesis is

\[(l|H_{0})\sim CN\Big{(}0,\sigma_{nn}^{2}\Big{)}. \tag{18}\]

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