## 2 The Proposed Bi-OCDMA System
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**User No.**} & **Signature** & \multirow{2}{*}{**Data Bit**} & \multicolumn{2}{c}{**Transmitted Optical Polarized Signal**} \\ \cline{3-5}  & **Sequence** & & **H** & **V** \\ \hline \multirow{2}{*}{\#1} & **10111000** & 0 & \(\lambda_{1}\;\lambda_{3}\;\lambda_{4}\;\lambda_{5}\) & \(\lambda_{2}\;\lambda_{6}\;\lambda_{7}\;\lambda_{8}\) \\ \cline{3-5}  & & 1 & \(\lambda_{2}\;\lambda_{6}\;\lambda_{7}\;\lambda_{8}\) & \(\lambda_{1}\;\lambda_{3}\;\lambda_{4}\;\lambda_{5}\) \\ \hline \multirow{2}{*}{\#2} & 01110010 & 0 & \(\lambda_{2}\;\lambda_{3}\;\lambda_{4}\;\lambda_{7}\) & \(\lambda_{1}\;\lambda_{5}\;\lambda_{6}\;\lambda_{8}\) \\ \cline{3-5}  & & 1 & \(\lambda_{1}\;\lambda_{5}\;\lambda_{6}\;\lambda_{8}\) & \(\lambda_{2}\;\lambda_{3}\;\lambda_{4}\;\lambda_{7}\) \\ \hline \multirow{2}{*}{\#3} & 11100100 & 0 & \(\lambda_{1}\;\lambda_{2}\;\lambda_{3}\;\lambda_{6}\) & \(\lambda_{4}\;\lambda_{5}\;\lambda_{7}\;\lambda_{8}\) \\ \cline{3-5}  & & 1 & \(\lambda_{4}\;\lambda_{5}\;\lambda_{7}\;\lambda_{8}\) & \(\lambda_{1}\;\lambda_{2}\;\lambda_{3}\;\lambda_{6}\) \\ \hline \multirow{2}{*}{\#4} & 11001010 & 0 & \(\lambda_{1}\;\lambda_{2}\;\lambda_{5}\;\lambda_{7}\) & \(\lambda_{3}\;\lambda_{4}\;\lambda_{6}\;\lambda_{8}\) \\ \cline{3-5}  & & 1 & \(\lambda_{3}\;\lambda_{4}\;\lambda_{6}\;\lambda_{8}\) & \(\lambda_{1}\;\lambda_{2}\;\lambda_{5}\;\lambda_{7}\) \\ \hline \multirow{2}{*}{\#5} & 10010110 & 0 & \(\lambda_{1}\;\lambda_{4}\;\lambda_{6}\;\lambda_{7}\) & \(\lambda_{2}\;\lambda_{3}\;\lambda_{5}\;\lambda_{8}\) \\ \cline{3-5}  & & 1 & \(\lambda_{2}\;\lambda_{3}\;\lambda_{5}\;\lambda_{8}\) & \(\lambda_{1}\;\lambda_{4}\;\lambda_{6}\;\lambda_{7}\) \\ \hline \multirow{2}{*}{\#6} & 00101110 & 0 & \(\lambda_{3}\;\lambda_{5}\;\lambda_{6}\;\lambda_{7}\) & \(\lambda_{1}\;\lambda_{2}\;\lambda_{4}\;\lambda_{8}\) \\ \cline{3-5}  & & 1 & \(\lambda_{1}\;\lambda_{2}\;\lambda_{4}\;\lambda_{8}\) & \(\lambda_{3}\;\lambda_{5}\;\lambda_{6}\;\lambda_{7}\) \\ \hline \multirow{2}{*}{\#7} & 01011100 & 0 & \(\lambda_{2}\;\lambda_{4}\;\lambda_{5}\;\lambda_{6}\) & \(\lambda_{1}\;\lambda_{3}\;\lambda_{7}\;\lambda_{8}\) \\ \cline{3-5}  & & 1 & \(\lambda_{1}\;\lambda_{3}\;\lambda_{7}\;\lambda_{8}\) & \(\lambda_{2}\;\lambda_{4}\;\lambda_{5}\;\lambda_{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Modified M-sequence codes of length 8 with spectral-polarization coding. First, two CW laser arrays are employed to emit specific wavelengths based on the assigned modified M-sequence codeword, where CW laser array#1 (or #2) sends out the wavelength correlated with chip \"1\" (or \"0\") of the codeword depending on the users' data bit of \"0\" (or \"1\"). As shown in Table 1, because the modified M-sequence codeword \(X_{1}\) = [1 0 1 1 1 0 0 0] is assigned to user#1, the wavelengths of CW laser arrays #1 and #2 are (\(\lambda_{1}\), \(\lambda_{3}\), \(\lambda_{4}\), \(\lambda_{5}\)) and (\(\lambda_{2}\), \(\lambda_{6}\), \(\lambda_{7}\), \(\lambda_{8}\)), respectively. Based on the user data bit, electrical signals are generated by the PSK pulse generator. Because the in-phase output of the PSK pulse generator is \(-1\) and \(1\), electrical bias and electrical gain are utilized to normalize it to \(0\) and \(1\) for the modulating signal of the phase modulator. Next, the electrical signal is sent to the EOM for optical signal modulation. The output optical signals from the phase modulator can be formulated as follows:  
\[E_{out,PM}(t)=E_{in,PM}(t).\exp(j.\Delta Q.X(t)) \tag{7}\]  
where \(E_{in,PM}(t)\) denotes the electrical input signal, \(\Delta Q\) is the phase deviation, and \(X(t)\) is the electrical input. The modulated signals are then distributed to one of the outputs from the optical coupler, depending on the user data bit. The output of the optical coupler can be expressed as:  
\[\left( \begin{array}{c}E_{1 out,C}\\ E_{2 out,C}\end{array} \right)=\left( \begin{array}{cc}\alpha\sqrt{1-c}&pj\sqrt{ c}\\ pj\sqrt{c}&\sqrt{1-c}\end{array} \right)\left(