# SIC-Free Based Indoor Two-User NOMA-VLCP System
## 2 System Module and Optimization Algorithm
\(\theta_{1}(n)\) and \(\theta_{2}(n_{1},n_{2})\) represent the first and second order Volterra kernels, respectively. The demodulated signal using the AFT algorithm of user \(i\) can be shown as:  
\[S_{\text{AFT},i}=f_{\text{AFT}}(S_{\text{rvol},i}) \tag{14}\]  
where \(f_{\text{AFT}}(\cdot)\) denotes the baseband signal demodulation algorithm based on AFT. This algorithm is a dynamic decision algorithm without SIC. Two users generate a training sequence and obtain the initial decision threshold. In a symbol period of each user, the weighted summation and averaging operation is performed on the signal within the period to achieve demodulation of the two user signals and update the decision threshold [31]. In this paper, SINR is used as a measure of communication performance to participate in the optimization operation. In the system proposed in this paper, the SINR when two user signals are demodulated is expressed as:  
\[\text{SINR}_{1,\text{AFT}}=\frac{\rho_{1}P_{\text{t}}}{\frac{B_{1}}{B_{2}} \Big{(}\rho_{2}P_{\text{t}}+N_{0}\Big{)}}=\frac{R_{2}(1+\beta_{2})\rho_{1}P_{ \text{t}}}{R_{1}(1+\beta_{1})\Big{(}\rho_{2}P_{\text{t}}+N_{0}\Big{)}} \tag{15}\]  
\[\text{SINR}_{2,\text{AFT}}=\frac{v\rho_{2}P_{\text{t}}}{\lambda\rho_{1}P_{ \text{t}}+vN_{\text{c}}} \tag{16}\]where \(\lambda\) represents the power compression factor of the volterra equalizer, \(v\) represents the compression parameters related to \(B_{1}\), \(B_{1}\) and \(\lambda\):  
\[v=\frac{B_{2}-(1-\lambda)B_{1}}{B_{2}} \tag{17}\]  
To optimize the system performance containing the user fairness, the PSO algorithm is used to optimize the user power allocation factor \(\rho_{i}\) and the SRRC roll-off coefficient \(\beta_{i}\) under the premise of both the communication and positioning performance. The PSO algorithm mathematical expression and objective function are set as [33]:  
\[V_{\text{M}}^{(u+1)}=V_{\text{M}}^{u}+q1\times p1\big{(}Xv_{\textit{{{pbest}}} }-Xv_{\text{M}}^{k}\big{)}+q2\times p2\big{(}Xv_{\textit{{{Gbest}}}}-Xv_{\text {M}}^{k}\big{)} \tag{18}\]  
Due to the characteristics of PSO being easy to implement and having a high degree of parallelism, the PSO algorithm is used to optimize the system parameters. The parameters in the optimization process are set as follows: the  
demodulation algorithm to avoid EP. The structure of the proposed system is compared with that of the traditional VLCP system with SIC. The system proposed has a rate of 1 Mb/s for user 1 and 20 Mb/s for user 2. The following studies are based on this rate. The system is deployed in the indoor space of 5 m \(\times\) 5 m \(\times\) 25 m, where the LED coordinates are (2.5 m, 2.5 m, 2.5 m), and the emitting power of LED, area of the PD and related parameters are shown in Table 1.  
To reflect the characteristics of the superimposed signals in the power domain of the system, the time domain characteristics of the superimposed signals, after filtered by SRRC, are shown in Figure 2a, and the total time length of the signals is 500 us. Figure 2b displays the spectrum of the originating signal in the proposed system. The red spectrum represents the user 1 signal, the blue spectrum represents the user 2 signal, and the green spectrum represents the superimposed Gaussian white noise. Each user's signal is processed separately by the SRRC. User 1 has a bandwidth of approximately 0.6 MHz, while User 2 has a bandwidth of approximately 18 MHz There is a significant bandwidth gap between the users, which helps to reduce user interference. Figure 3 shows the convergence curves of the objective function, SINR, and positioning accuracy of the system using PSO. The PSO algorithm was limited to a total of 60 iterations during the simulation. Figure 3a shows that the objective function converges with acceptable fluctuation. The optimization algorithm for this system has an upper limit of 10 cm positioning error. It can be attributed to the compensation factor \(\chi\) providing higher sensitivity. Figure 3b displays the optimization targets of the communication and positioning services.