## 3 System Model
### Communication Model  
Denote the independent information and jamming signal as \(s\sim\mathcal{CN}(0,1)\) and \(a\sim\mathcal{CN}(0,1)\), respectively, so that the signal transmitted from BS can be denoted as  
\[\mathbf{x}=\mathbf{v}_{1}s+\mathbf{v}_{2}a. \tag{5}\]  
Assuming that BS has a maximum transmit power \(P_{max}\), then we have \(\mathbf{v}_{1}^{H}\mathbf{v}_{1}+\mathbf{v}_{2}^{H}\mathbf{v}_{2}\leq P_{max}\). We assume that the UE and Eves are each equipped with \(J\) receive antennas and a single RF receive chain. The final signal received by UE and the Eves can be denoted as  
\[y_{l}=\mathbf{W}_{l}^{H}\mathbf{H}_{l}\mathbf{M}(\mathbf{v}_{1}s+\mathbf{v}_{ 2}a)+\mathbf{W}_{l}^{H}\mathbf{z}_{l},\quad l\in\{u,e_{k}\}, \tag{6}\]  
Figure 2: Reconfigurable holographic surface.  
where \(\mathbf{W}_{l}\) is a \(J\times 1\) RF combiner at UE and each Eve, implemented by using phase shifting such that \(\left|\mathbf{W}_{l}(j)\right|^{2}=1\). In this research, we have simplified it to a uniform linear phased array for convenience, so \(\mathbf{W}_{l}=\left[1,e^{\mathrm{i}k_{f}d_{s}\sin\phi_{l}},\cdots,e^{\mathrm{ i}k_{f}(J-1)d_{s}\sin\phi_{l}}\right]^{T}\), where \(\phi_{l}\) is the angle of signal arrival to the antenna array in reserve, and \(d_{s}\) is the distance between the antennas of the receivers. The matrix \(\mathbf{M}\in\mathbb{C}^{XY\times K}\) is composed of \(\left\{M_{x,y}\cdot e^{-\mathrm{i}\mathbf{k}_{x}\cdot\mathbf{r}_{x,y}^{k}}\right\}\), where \(e^{-\mathrm{i}\mathbf{k}_{x}\cdot\mathbf{r}_{x,y}^{k}}\) is the phase of the reference wave, and \(\mathbf{z}_{l}\sim\mathcal{CN}\left(0,\sigma^{2}\mathbf{I}_{I}\right)\) is the additive white Gaussian noise. The matrix \(\mathbf{H}_{l}\in\mathbb{C}^{J\times XY}\) is the complex equivalent channel between RHS and UE or Eves. The matrix \(\mathbf{M}\) can be decomposed into \(diag(\mathbf{m})\Theta\), where \(\mathbf{m}=\left[M_{1,1},\cdots,M_{x,y},\cdots,M_{X,Y}\right]^{T}\), \(0\leq M_{x,y}\leq 1\), and \(\Theta\) is the matrix of the phase \(e^{-\mathrm{i}\mathbf{k}_{x}\cdot\mathbf{r}_{x,y}^{k}}\). By changing variables as \(\mathbf{W}_{l}^{H}\mathbf{H}_{l}diag(\mathbf{m})\Theta=\mathbf{m}^{H}\mathbf{ \hat{H}}_{l}\), where \(\mathbf{\hat{H}}_{l}=diag(\mathbf{W}_{l}^{H}\mathbf{H}_{l})\Theta\), the signal-to-interference plus noise ratio (SINR) at UE or Eves can be derived as  
\[\gamma_{l}=\frac{\left|\mathbf{m}^{H}\mathbf{\hat{H}}_{l}\mathbf{v}_{1}\right| ^{2}}{J\sigma^{2}+\left|\mathbf{m}^{H}\mathbf{\hat{H}}_{l}\mathbf{v}_{2} \right|^{2}},\quad l\in\{u,e_{k}\}. \tag{7}\]  
In our research, the propagation environment between the BS and receivers is modeled as a sparse millimeter-wave channel with \(I\) paths. We assume that all channel state information (CSI) is known at the BS to characterize the optimal performance of the considered RHS-assisted secrecy communication system. Therefore, the achievable rate of UE or Eves can be denoted as  
\[R_{l}=\log_{2}\left(1+\frac{\left|\mathbf{m}^{H}\mathbf{\hat{H}}_{l}\mathbf{v }_{1}\right|^{2}}{J\sigma^{2}+\left|\mathbf{m}^{H}\mathbf{\hat{H}}_{l}\mathbf{ v}_{2}\right|^{2}}\right),\quad l\in\{u,e_{k}\}. \tag{8}\]