# Investigation of 2D-WH/TS OCDMA Code Stability in Systems with SOA-Based Device
## 3 Impact of SOA High Bias Current/Gain on 2D-WH/TS OCDMA Prime Code Fidelity  
Here, the investigation was repeated by replacing the DWDM-based OCDMA encoder and decoder with a commercial fiber Bragg grating-based encoder and decoder manufactured by OKL, Japan. The implemented 2D-WH/TS OCDMA carrier-hopping prime code (CHPC) [2] is optimised to ensure that the periodic cross correlation function is at most one [2]. This minimises the multiple-access interference. The encoder/decoder pair uses four wavelength code carriers from a code space (\(w,N\)) = (4, 53), where \(w\) indicates a number of wavelength code carriers with a channel spacing of 100 GHz and \(N\) is the number of chips [3] per the bit period. The code signature (1-\(\lambda_{2}\), 21-\(\lambda_{4}\), 27-\(\lambda_{1}\) \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Description 2** & **Value** \\ \hline \(I\) & Bias current (mA) & 250 \\ \(L\) & Length (mm) & 1 [14] \\ \(W\) & Width (\(\upmu\)m) & 0.4 [22] \\ \(H\) & Height (\(\upmu\)m) & 0.4 [22] \\ \(\alpha_{i}\) & Loss (m\({}^{-1}\)) & 3000 [23] \\ \(g\) & Differential gain (m\({}^{2}\)) & \(3\times 10^{-20}\)[24] \\ \(N_{i}\) & Initial carrier density (m\({}^{-3}\)) & \(3.65\times 10^{24}\)[23] \\ \(\Gamma\) & Optical confinement factor & 0.4 [24] \\ N0 & Carrier density at transparency (m\({}^{3}\)) & \(10^{24}\)[24] \\ \(\alpha\) & Linewidth enhancement factor & 4 [24] \\ \(A\) & Recombination coefficient (s\({}^{-1}\)) & \(10^{8}\)[23] \\ \(B\) & Recombination coefficient (m\({}^{3}\) s\({}^{-1}\)) & \(1.5\times 10^{-16}\)[23] \\ \(C\) & Recombination coefficient (m\({}^{6}\) s\({}^{-1}\)) & \(10^{-40}\)[23] \\ \hline \end{tabular}
\end{table} 
Table 1: Geometrical and material parameters used in the simulation. Figure 6: Wavelength red shift for the SOA biased at 250 mA. The dashed line is simulations and the dots are measured values for \(\lambda_{1}=1550.12\) nm, \(\lambda_{2}=1550.92\) nm, \(\lambda_{3}=1551.72\) nm, and \(\lambda_{4}=1552.52\) nm. 39-\(\lambda_{3}\)) guarantees a minimal separation between adjacent code carriers of more than 30 ps. The SOA bias current/gain and code average/code carriers' peak power at the SOA input were 250 mA/24 dB and 4 mW/57 mW, respectively, resulting in a 100 GHz/0.8 nm code carriers' redshift. The results obtained are shown in Figure 7. Figure 7a is the OCDMA code optical spectrum recorded by the OSA without, and Figure 7b with an SOA being part of the chromatic dispersion compensated transmission link. By comparing both results, it can be observed that wavelength code carriers were red-shifted by 100 GHz/ 0.8 nm. As explained in Section 2, because of this redshift, \(\lambda_{1}\) became \(\lambda_{2}\), \(\lambda_{2}\rightarrow\lambda_{3}\), \(\lambda_{3}\rightarrow\lambda_{4}\), and \(\lambda_{4}\rightarrow\lambda_{5}\). However, the OCDMA fiber Bragg grating (FBG) decoder was designed to handle only (\(\lambda_{1}\), \(\lambda_{2}\), \(\lambda_{3}\), \(\lambda_{4}\)). Therefore, the wavelength \(\lambda_{5}\) that resulted from the \(\lambda_{4}\rightarrow\lambda_{5}\) redshift is'missing' in Figure 7b. As a consequence, the resulting OCDMA autocorrelation height will be reduced by one to its new value \(w-1\). This code weight reduction will decrease the signal-to-noise ratio (SNR) and cause deterioration in the OCDMA system bit-error-rate (BER), which in turn reduces the number of simultaneous users. The performance degradation resulting from the code carriers' red-shifting can be theoretically evaluated using Equation (1) to calculate the probability of error _Pe_. Equation (1) is valid for an OCDMA receiver with hard limiting capabilities [3]. _Pe_ can be used to evaluate the number of simultaneous users (K). \[P_{e}=\frac{1}{2}\sum_{i=0}^{w}(-1)^{w-i}\frac{w!}{[i!\ (w-i)!]}\left(q_{0}+iq_{1} \frac{1}{w}\right)^{k-1} \tag{1}\]  
Here, \(q_{0}=1-q_{1}\), \(q_{1}=\frac{w^{2}}{2 NL}\), \(w\) is the code weight, \(L\) is a number of wavelength code carriers (in this case \(w=L\)), and \(N\) is the number of chips.