# Visible-Light CDMA Communications Using Inverted Spread Sequences
## 3 MUI Cancellation Schemes with Inverted MPSC
### EWO Scheme with Inverted MPSC  
In the EWO scheme with an inverted MPSC, two codewords, \(\mathbf{w}^{\prime}_{k,0}\) and \(\mathbf{w}^{\prime}_{k,1}\), are assigned to the \(k\)th user (\(k=0,\ 1,\ \cdots,\ N_{\text{max}}\)-1), where \(N_{\text{max}}=q\lfloor q/2\rfloor\) and \(\mathbf{w}^{\prime}_{k,I}\) is an inverted sequence of \(\mathbf{w}_{k,I}\) for the conventional EWO scheme (\(I\in\{0,\ 1\}\)). An example of codeword assignment for this scheme is shown in Table 4.  
The encoder of this scheme is also illustrated by Figure 1(a), where the sequences \(\mathbf{w}_{k,1}\) and \(\mathbf{w}_{k,0}\) are replaced with \(\mathbf{w}^{\prime}_{k,1}\) and \(\mathbf{w}^{\prime}_{k,0}\), respectively. We also note that an all-one sequence is transmitted constantly when the user is not active in the EWO and the other two schemes using an inverted MPSC. Figure 4 shows an example of multiplexing sequences in the EWO scheme with an inverted MPSC with \(q=4\), \(N_{\text{L}}=8\), and \(N=4\). In Figure 4, (a) shows the two sequences encoded by the inverted codewords \(\mathbf{w}^{\prime}_{2,0}\) and \(\mathbf{w}^{\prime}_{2,1}\), which are assigned to the second user; (b) shows the sequences transmitted simultaneously by four active users, who are the first, second, fifth, and seventh users transmitting data 1, 0, 0, and 1, respectively; and (c) shows the multiplexed sequence of the eight sequences including all-one sequences transmitted by four non-active users. We can see that the multiplexed sequence in Figure 3(c) is equal to the sequence subtracting the multiplexed sequence in Figure 3(c) from the constant-level sequence whose level is the maximum light intensity of \(N_{\text{L}}\) light sources. It is shown that the average light intensity of the multiplexed sequence in Figure 3(c) is much higher than that of the multiplexed sequence in Figure 3(c).  
The \(k\)th user's decoder, also illustrated by Figure 1(b), computes two correlations between the received sequence \(\mathbf{r}^{\prime}\) and the two sequences \(\mathbf{w}_{k,0}\) and \(\mathbf{w}_{k,1}\), where \(\mathbf{w}_{k,0}\) and \(\mathbf{w}_{k,1}\) are non-inverted MPSC codewords. Therefore, the two correlators, Correlator 1 and  
Figure 4: Examples of signal sequences for the EWO scheme with an inverted MPSC.  
Correlator 0, are exactly the same as those in the decoder for the conventional EWO scheme. \(\Gamma^{\prime}{}_{1}\) and \(\Gamma^{\prime}{}_{0}\) are outputs of Correlator 1 and Correlator 0, respectively, and are represented by  
\[\Gamma^{\prime}{}_{1}=\Gamma\left(\dot{\mathbf{r}},\mathbf{w}_{k,1}\right), \tag{10}\]  
\[\Gamma^{\prime}{}_{0}=\Gamma\left(\mathbf{r}^{\prime},\mathbf{w}_{k,0}\right). \tag{11}\]  
The only precaution that needs to be taken is to calculate the difference \(\Gamma^{\prime}{}_{0}-\Gamma^{\prime}{}_{1}\) before the decision circuit, while \(\Gamma_{1}-\Gamma_{0}\) is calculated by the conventional EWO decoder. If the difference \(\Gamma^{\prime}{}_{0}-\Gamma^{\prime}{}_{1}\) is greater than or equal to the threshold _zero_, the decoder outputs \(\hat{I}=1\) as a decoded datum. Otherwise, the decoder outputs \(\hat{I}=0\).  
For an ideal link, \(\Gamma^{\prime}{}_{1}\) and \(\Gamma^{\prime}{}_{0}\) are equal to \(qN_{\mathrm{L}}-\Gamma_{1}\) and \(qN_{\mathrm{L}}-\Gamma_{0}\), respectively, where \(\Gamma_{1}\), \(\Gamma_{0}\), \(\Gamma^{\prime}{}_{1}\), and \(\Gamma^{\prime}{}_{0}\) are given by Equations (4), (5), (10), and (11), respectively. Therefore, the difference \(\Gamma^{\prime}{}_{0}-\Gamma^{\prime}{}_{1}\) is equal to \(\Gamma_{1}-\Gamma_{0}\) in the conventional EWO scheme. This means that the EWO scheme with an inverted MPSC can cancel MUI completely without estimating the received light intensity and that its decision distance is \(2q\).