## 5 Performance Analysis  
Before performing the BER analysis, we illustrate and define the signal-to-noise ratio (\(SNR\)) parameters in Table 3. The average \(SNR\) can be calculated as shown in (16) below, and the photocurrent at the photodetector output \(I_{P}=\Re\cdot P_{r}\) is the PIN responsivity multiplied by the optical power received. Furthermore, to investigate the effect of irradiance, the instantaneous SNR defined in (17) must be considered in the BER performance analysis. \[SNR=\frac{I_{P}^{2}G^{2}}{2q(I_{P}+I_{D})G^{2}F(G)B_{e}+4K_{B}TB_{e}/R_{L}} \tag{16}\]  
\[SNR_{i}=SNR\cdot I_{r} \tag{17}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Definition** & **Value** \\ \hline \(I_{P}\) & Received photocurrent depends on the PIN & A \\  & photodetector responsivity and optical power received & \\ \(\Re\) & PIN photo-detector responsivity & 0.8 A/W \\ \(F(G)\) & Receiver noise figure & 1.2 \\ \(G\) & Gain of preamplifier receiver & 5 \\ \(I_{D}\) & PIN dark current & 10 nA \\ \(B_{e}\) & Receiver electrical bandwidth & 3.2 GHz \\ \(K_{B}\) & Boltzmann constant & \(1.38\times 10^{-23}\) J/K \\ \(T\) & Receiver temperature & 298 K \\ \(R_{L}\) & Receiver load resistance & 70 K\(\Omega\) \\ \(SNR_{i}\) & Instantaneous SNR & Ratio \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optical receiver parameters used for \(SNR\) calculation. Figure 6: Cross-correlation coefficient between the WMPC sequences \(S_{10}\) and \(S_{41}\). Before calculating the BER performance, we define the values of the transmission parameters, such as the optical power transmitted, transmission efficiencies, operating wavelength range, receiver aperture area, and coding parameters, as listed in Table 4. The chip time was adjusted to 2.6 ps, and the BER performance was calculated several times for prime numbers ranging from 11 to 61. In the BER performance results, we compared different types of water as transmission media according to their chlorophyll concentration, and the OOK modulation scheme was used as a reference to compare the results with those of the proposed M-DPPM scheme. Therefore, the probability of error for both the modulation schemes is illustrated in (18) and (19), as listed below, where \(\gamma_{th}\) is the receiver threshold value that is adjusted using a decision circuit after the correlator, and \(M\) is the system multiplicity according to the M-DPPM modulation scheme [30; 31; 32; 33; 34]. \[\frac{1}{2}erfc\left(\frac{SNR_{i}}{2\sqrt{2}}\right) \tag{18}\]  
\[\frac{1}{M}\left[\frac{1}{2}erfc\left((1-\gamma_{th})\times\sqrt{\frac{M\times SNR _{i}}{8}}\right)+\frac{M-1}{2}erfc\left((\gamma_{th})\times\sqrt{\frac{M\times SNR _{i}}{8}}\right)\right] \tag{19}\]  
When the WMPC is considered, the BER performance is the result of the probability of error of the M-DPPM scheme multiplied by the probability of error owing to the proposed WMPC. For this analysis, we must consider the effect of multiple-user interference when chips from other users interfere with the desired chip owing to multiple access. Table 5 lists the WMPC BER performance parameters used in (21) [35; 36; 37; 38; 39; 40; 41]. \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Name** & **Symbol** & **Value** \\ \hline
1 & Laser peak transmitted power & \(P_{t}\) & 20 dBmW \\
4 & Receiver aperture area & \(A_{r}\) & 0.01 m\({}^{2}\) and 0.05 m\({}^{2}\) \\
5 & Transmitter efficiency & \(\eta_{t}\) & 0.9 \\
6 & Receiver efficiency & \(\eta_{r}\) & 0.9 \\
8 & Divergence angle of laser beam & \(\theta_{d}\) & 60\({}^{\circ}\) \\
9 & Angle between perpendicular of & \(\theta\) & 5\({}^{\circ}\) \\  & transmitter–receiver planes & & \\
10 & Operating wavelength & \(\lambda\) & 400–600 nm \\
11 & Prime number of WMPC & P & 11, 23, 31, 47, 53, 61 \\
12 & Chip time duration & \(T_{C}\) & 2.6 ps \\ \hline \end{tabular}
\end{table} 
Table 4: The values of the transmission and coding parameters used for the BER calculations.