# SIC-Free Based Indoor Two-User NOMA-VLCP System
## 2 System Module and Optimization Algorithm  
Figure 1 shows the proposed dual-user NOMA VLCP system without SIC where data from each user is passed through a square root-derived cosine filter (SRRC), maximal ratio combining (MRC) and Volterra equalizer. This system uses a single LED as the signal transmitter, placed in the center of the ceiling. Since there is spectrum overlap between two users in the baseband NOMA system and a SIC-free decision method is used at the receiving end, the receiver only needs to process the light intensity information without considering frequency, phase, and other information, each will be coded signal using on-off keying (OOK) modulation.To reduce inter-user interference and improve communication and positioning performance, particle swarm optimization (PSO) algorithm was used to optimize the system parameters. During the optimization process, the signal bandwidth changes due to the change of the roll-off factor, the bit rate of each user satisfies \(R_{1}<R_{2}\), Bitstream undergoes shaping through an SRRC filter, the shaping function for user \(i\) being [28]:  
\[h_{\text{SRRC},i}(t)=\frac{\sin\Bigl{(}\frac{\pi t}{t_{i}}(1-\beta_{i})\Bigr{)} +\frac{4\beta_{i}t}{T_{i}}\cos\Bigl{(}\frac{\pi t}{t_{i}}(1+\beta_{i})\Bigr{)} }{\frac{\pi t}{T_{i}}\biggl{(}1-\Bigl{(}\frac{4\beta_{i}t}{T_{i}}\Bigr{)}^{2} \biggr{)}} \tag{1}\]  
where \(T_{i}=1/R_{i}\) is the duration of a single code element for user \(i\), \(\beta_{i}\) is the SRRC filter roll-off coefficient corresponding to the user \(i\). After applying the SRRC filter, the signal transmitted by user \(i\) is represented as:  
\[S_{\text{t},i}(t)=2\sqrt{\rho_{i}P_{i}}\sum_{k}S_{i}(k)h_{\text{SRRC},i}\left( t-\frac{k}{R_{i}}\right) \tag{2}\]  
where \(S_{i}(k)\) is the signal after modulation by OOK, \(\rho_{i}\) is the power allocation factor of user \(i\) and \(0<\rho_{i}<1\), \(k\) is the number of bits in the data stream after encoding for each user. Superimposed in the power domain and adding a DC bias to drive the LED, the emitted signal \(S_{\text{t}}\) can be expressed as:  
\[S_{\text{t}}=\sum_{i=1}^{M}S_{\text{t},i}(t)+\text{D} \tag{3}\]  
where M is the total number of subscribers in a single cell, and D is the LED DC bias. According to the Lambertian radiation model, the channel gain of the line-of-sight (LOS) link can be expressed as [29]:  
\[H=\frac{A(m+1)}{2\pi d^{2}}\cos^{m}(\Phi)\cos(\Psi)T_{s}(\Psi)G(\Psi) \tag{4}\]  
where \(m\) is Lambertian radiation coefficient, \(A\) is the physical area of the detector for PD, \(d\) is the transmission distance from the LED light source to each photodetector, The angle of radiation and the angle of incidence is denoted as \(\Phi\) and \(\Psi\), \(T_{s}(\Psi)\) and \(G(\Psi)\) are the gain of the optical filter and concentrator. Through the LOS channel, the received signal of the \(j\)-th PD is referred to as:  
\[S_{r,j}(t)=HR_{\text{PD}}S_{\text{t}}(t)+n(t) \tag{5}\]  
where \(R_{\text{PD}}\) is the responsiveness of the PD, \(n(t)\) is Gaussian white noise. The receiver uses one horizontal PD and four oblique PDs to form a common receiver, and the signal received by the \(j\)-th PD is filtered by SRRC to obtain the signal of user \(i\) expressed as:  
\[S_{r,i,j}=\sum_{k}S_{r,j}(k)h_{\text{SRRC},i}\left(t-\frac{k}{R_{i}}\right) \tag{6}\]MRC is suitable for optimal combining in independent additive Gaussian white noise channels, which is widely used in VLC systems [30]. For the VLC system proposed in this letter, the receiving end consists of one horizontal PD and four inclined PDs.