Computational Model

In computation, one of the most important thing is loss model. If the transmitter power is known (say P_T) and SOAs are not there between CO and receivers for which BER is computed, the loss (in dB) between transmitter and receiver assuming that receiver is in i_thgroup starting from CO is given by

$$L_{TR}=L_W + L_{sp} (2 i +5) +i \alpha l + (i-1) L_m +L_{12}$$

$$+ L_i \log_2 n + 10 \log_{10}n.$$ (3)

In the above equation, L_W is insertion loss of wavelength multiplexer at CO, L_sp splice loss, $\alpha$ fiber attenuation per unit length, L the length of fiber between two consecutive OADMs, L_m insertion loss of OADM, L₁₂ insertion loss for drop signal in OADM, L_i insertion loss of $2\times 2$ couplers used for making star coupler, and n the number of users in a group.

The loss (in dB) between transmitter at CO and first OA is used to find the input power to SOA. If the first SOA is placed before the i^thgroup the loss between transmitter and first SOA is given by

$$L_{TA_i} = L_W + 2iL_{sp} + i \alpha L + (i-1) L_m.$$ (4)

If the two consecutive amplifiers are placed before i^th and j^th OADM respectively, then loss (in dB) between them is given by

$$L_{A_iA_j} = 2 (j-i) L_{sp} + (j-i) L_m + (j-i) \alpha L.$$ (5)

Further loss (in dB) between a receiver in l^th branch and nearest amplifier (which is before t^th OADM) is given by

$$L_{A_tR} = \left [ 2 (l-t) +4 \right ] L_{sp} + (l-t) L_m + L_{12} + (l-t) \alpha L$$

$$+ L_i \log_2 n + 10 \log_{10} n \hspace{0.3in} ; t < b$$

$$= \left [ 2 (l-t) + 2 \right ] L_{sp} + (l-t) L_m + (l-t) \alpha L$$

$$+ L_i \log_2 n 10 \log_{10} n \hspace{0.3in}; t = b$$ (6)

Here b is total number of branches in the network.

In order to compute the gain saturation, it is assumed that bits in all the channels are synchronised. In order to find the impact of other channels, two cases have been considered. In one case, average value of saturated gain has been used. In the other case BER for every bit pattern in interefering channels is computed. Thereafter, average BER is computed.