but the random behavior of the gain shapes the noise distribution SO that a Gaussian approximation is very near to the reality. Thus, after sampling and bias elimination, the current sample has the following expression: (6.33) where the noise sample Nkj is the sum of all the noise terms and can be considered a Gaussian variable and the dependence of the sample from the polarization induced delay difference is evidenced. Transmission Systems Architectures and Performances Once a value of At is fixed, the BER can be evaluated with the technique that was shown in the previous section, only carefully taking into account that the noise variance is depen- dent on the signal sample. Thus, the following conditional error probability expressions are obtained, the first for an adaptive threshold receiver, the second for a fixed threshold receiver with the threshold at half the detected signal dynamic range: (adaptive threshold) (6.34) (fixed threshold) (6.35) where "er" represents the error event. Thus, applying the Bernoulli theorem, the BER is given by (adaptive threshold) (6.36) (fixed threshold) (6.37) where p(AT) is the distribution of At (see Chapter 4). This technique allows the random effect of the PMD to be incorporated in the evaluation of the error probability. However, besides the average worsening of the BER, the PMD has also another effect. During the random variation of At short periods can happen where the value of the PMD is very high. In this case the system working is completely destroyed even if for a short period. The probability of this event called outage is small; therefore, it does not influence greatly the long-term error probability, but when it happens the system could even go down SO its importance is beyond the pure influence on the long-term error probability. This is the reason why generally also the so-called outage probability is evaluated to characterize the PMD influence on a system in situations of high PMD. We do not detail the evaluation of this parameter in general, encouraging the i