rom (9.68), it is clear that the phase noise presence in the regime of small ratio between the linewidth and the symbol rate has a first effect of creating an additional noise composed of two terms: one proportional to the signal power and the other to the ASE. The noise term proportional to the signal power is particularly dangerous, since its effect cannot be compensated by increasing the transmitted power. As far as the effect on the frequency lock is concerned, Equation 9.41 is substituted in the presence of phase noise with (9.69) SO that, assuming an ideal frequency lock, a simple first order digital filter to limit the lock loop bandwidth and neglecting in conditions of low penalty the unlock probability, the estimated frequency deviation Aw, can be expressed as (9.70) where At is the sampling rate N is the lock loop bandwidth in terms of number of integrated samples SO that the loop bandwidth is B = 1/Nt This error in the estimated angular frequency causes a further element to be added to the photocurrent. In small phase noise regime, Equation 9.69 becomes Telecommunication Networks C1(tj) = (9.71) Since we have assumed to use a small linewidth laser, we can assume that its linewidth is Lorentian with a very good approximation. For a laser with a Lorentian linewidth Av, the following equation holds [31]: Ao=154(0) (9.72) where S(0) is the frequency noise spectrum evaluated for zero frequency (see Chapter 5). Moreover, the following relation exists between the phase noise variance and the fre- quency noise spectrum: (9.73) where Ts is the symbol interval, B is the laser S(a) spectral width (of the order of 2-3 GHz; see Chapter 5) and (9.74) Assuming that both transmitter and LO have the same linewidth, the variance of the phase fluctuations in a bit interval can be expressed as a function of the laser linewidth as follows: (9.75) As far as the angular frequency lock error is concerned it is a Gaussian zero mean process. Its variance can be calculated easily taking into account that the summation can be sim