effects. These values are input to a set of digital filters with transfer functions hre(j) and hjm(j). The resulting in-phase and quadrature drive voltages d1 and d2 are then obtained by complex-summing the outputs of the filters as shown in the figure. The equalizer resulting from the composition of digital filters and look-up table is poten- tially very efficient, requiring a much smaller memory table with respect to a direct appli- cation of the look-up table method. Nevertheless, the great potentialities of this equalization method are not free from chal- lenges that have to be solved for a practical implementation. The first challenge is the complexity of the electronic circuitry with respect to a simple FFE-DFE post-processing. In the mixed solution represented in Figure 5.64, the set of lin- ear filters consume alone about two times a traditional FFE-DFE filter. In addition, there is the look-up table. Finally there is the real-time adaptive algorithm that is needed to adapt equalization to the channel fluctuations. The implementation of this algorithm is another challenge: if all the equalizer param- eters have to be adapted to channel variations, the adaptive algorithm results in being quite complicated and a lot of design work is needed to implement it in a practical circuit. Last, but not least, the adaptive algorithm needs a return channel from the receiver to the transmitter to drive transmitter-adaptive evolution with the received pulse shape. Thus, the receiver also must sample at a very high speed the incoming pulses to feed the trans- mission-adaptive procedure. A complete study of the back-propagation algorithm in case of the adoption of a scalar propagation model and of the efficiency and complexity of this method is reported in [90]. Filters Serializer Modulator table FIGURE 5.64 Scheme of an electronic pre-compensator that combines the look-up table technique with a further compensa- tion through digital filtering. (After Killey, R.I. et al., Electronic dispersion compensation by signal predi