## 3 SM and MP-WFRFT Aided Scheme Based On FDA  
### The Architecture of System with Cooperative LUs  
The traditional PA-DM schemes and even the AN-aided PA-DM synthesis schemes cannot achieve range dependence, and so these schemes cannot prevent eavesdroppers from intercepting messages and recognize private users in same direction. Therefore, we depart from PA and apply FDA into our DM implementations because of its extra range dimension dependence rather than simply angle dependence. In this paper, the line-of-sight (LoS) channel, far-field communication, and Gaussian wiretap channel are considered. As shown in Figure 2, the system consists of a legitimate transmit  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Bits Block** & **LUs Numbers** & \(\mathbf{u(\emph{t})}\) & **Bits Block** & **LUs Numbers** & \(\mathbf{u(\emph{t})}\) \\ \hline
00000 & 1,2,3 & \([-1,-1,-1,0]\) & 10000 & 1,3,4 & \([-1,0,-1,-1]\) \\
00001 & 1,2,3 & \([-1,-1,+1,0]\) & 10001 & 1,3,4 & \([-1,0,+1,-1]\) \\
00010 & 1,2,3 & \([-1,+1,-1,0]\) & 10010 & 1,3,4 & \([-1,0,-1,+1]\) \\
00011 & 1,2,3 & \([+1,-1,-1,0]\) & 10011 & 1,3,4 & \([+1,0,-1,-1]\) \\
00100 & 1,2,3 & \([-1,+1,+1,0]\) & 10101 & 1,3,4 & \([-1,0,+1,+1]\) \\
00101 & 1,2,3 & \([+1,+1,-1,0]\) & 10110 & 1,3,4 & \([+1,0,+1,-1]\) \\
00111 & 1,2,3 & \([+1,+1,+1,0]\) & 10111 & 1,3,4 & \([+1,0,-1,+1]\) \\
00111 & 1,2,3 & \([+1,+1,+1,0]\) & 10111 & 1,3,4 & \([+1,0,+1,+1]\) \\
01000 & 1,2,4 & \([-1,-1,0,-1]\) & 11000 & 2,3,4 & \([0,-1,-1,-1]\) \\
01001 & 1,2,4 & \([-1,-1,0,+1]\) & 11001 & 2,3,4 & \([0,-1,-1,+1]\) \\
01010 & 1,2,4 & \([-1,+1,0,-1]\) & 11010 & 2,3,4 & \([0,-1,+1,-1]\) \\
01011 & 1,2,4 & \([+1,-1,0,-1]\) & 11011 & 2,3,4 & \([0,+1,-1,-1]\) \\
01100 & 1,2,4 & \([-1,+1,0,+1]\) & 11100 & 2,3,4 & \([0,-1,+1,+1]\) \\
01101 & 1,2,4 & \([+1,-1,0,+1]\) & 11101 & 2,3,4 & \([0,+1,-1,+1]\) \\
01110 & 1,2,4 & \([+1,+1,0,-1]\) & 11110 & 2,3,4 & \([0,+1,-1,-1]\) \\
01111 & 1,2,4 & \([+1,+1,0,+1]\) & 11111 & 2,3,4 & \([0,+1,+1,+1]\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: SM map.  
station, \(K\) LUs whose information can be shared with each other, and \(J\) passive Eves whose locations are unavailable to transmitter station.  
A uniform \(N\) elements linear array with a spacing \(d\) is utilized for the transmitter. The transmitting frequency at the \(n-th\) (n = 1, 2,..., N) antenna is designed as \(f_{n}=f_{c}+\Delta f_{n}\), where \(f_{c}\) is the carrier wave frequency and \(\Delta f_{n}\) is the frequency increment. Here, we propose RFDA whose beam pattern is angle-range independent without coupling. Therefore, \(\Delta f_{n}\) can be replaced as \(\Delta f_{n}=\lambda_{n}\Delta f\), where \(\Delta f\) refers to a fixed frequency increment, and \(\lambda_{n}\) represents a random variable.  
For an arbitrary receiver at \((r,\theta)\), the normalized steering vector is denoted by  
\[\mathbf{h}(\theta,r,t,\mathbf{f})=\frac{\rho(r)}{\sqrt{N}}\left[e^{- \beta 2\pi f_{1}\left(t-\frac{r}{c}\right)},e^{-\beta 2\pi f_{2}\left(t-\frac{r-d\sin\theta}{c}\right)}\right.\,,\ldots,e^{-\beta 2\pi f_{N}\left(t-\frac{r-(N-1)d\sin \theta}{c}\right)}\right]^{T} \tag{6}\]  
where \(c\) denotes light speed, \(\rho(r)\) refers to the path loss factor due to the free space propagation.  
The location of LU \(K\) is \((r_{l_{k}},\theta_{l_{k}})\), and for simplicity \(\mathbf{h}(t)_{l_{k}}\stackrel{{\Delta}}{{=}}\mathbf{h}_{L_{k}}(r,\theta,t,\mathbf{f})\) is the normalized steering vector of LU \(K\). Furthermore, we use the steering matrix \(\mathbf{H}_{L}(t)\) to denote steering vectors of all LUs, i.e.,  
\[\mathbf{H}_{L}(t)\stackrel{{\Delta}}{{=}}[\mathbf{h}_{L_{1}}(t), \mathbf{h}_{L_{2}}(t),\cdots,\mathbf{h}_{L_{k}}(t),\cdots,\mathbf{h}_{L_{K}}(t )], \tag{7}\]  
where \(\mathbf{h}_{L_{k}}(t)\) is the instantaneous normalized steering vector of \(k\)-th LU at \((r_{L_{k}},\theta_{L_{k}})\).