istortion can be in principle compensated by inverting Da(@). If this operation is well conditioned, which is the case in the optical channel, the current after the ideal compensator would be given by (5.46) Technology for Telecommunications: Integrated Optics and Microelectronics where X indicates convolution in the time domain. Sampling at the Nyquist rate and truncating the resulting series to a finite number of terms results in the FFE compensation algorithm (5.47) where d(k) are the coefficients of the FFE filter. The algorithm of Equation 5.47 can be easily implemented by a digital circuit shown in Figure 5.54 that is essentially a set of taps and delay lines. However, Equation 5.47 differs a lot from Equation 5.46 due to the finite number of taps and all the other approximations, thus a simple FFE does not assure a good chromatic dis- persion correction. In order to improve the performance of the compensator generally the FFE is complemented with a DFE. The DFE is essentially another set of delay lines and taps that is put as a feedback to the FFE in order to correct FFE operation. Once the circuit is designed, its effectiveness depends on the choice of the FFE and DFE coefficients and on the number of taps. In practice, five to nine is a feasible number of taps; thus it is required to set up 10 or 18 coefficients to optimize the working of the compensa- tor [71,72]. After initial setting, high-performance FFE-DFE relies on an adaptive coefficient setting algorithm that continuously adjusts the coefficients to optimize the receiver performance. The determination of the FFE-DFE coefficient is in general a process of filter parameters determination in the presence of noise and many FFE-DFE use a least mean square (LMS) algorithm to adapt the coefficient on the grounds of the receiver performances. This solu- tion allows a well-established processing to be used [73]. However, if shot noise cannot be neglected or if amplified optical noise is the dominant noise contribution (see Chapter 6) the noise affecting 