In the last chapter, algorithms to estimate the combined Fi-Wi channel were described. Once the channel is known, then a suitable equalizer can be devised to cancel out the distortions introduced by the channel. Describing such an equalizer is the focus of this chapter.
This is a very well-investigated topic. Numerous publications are available, with frequency-domain and time-domain equalizers that are optimized to handle different types of wireless channel impairments. Among these, the decision feedback equalizer (DFE) has been a very successful equalizer in mitigating commonly encountered intersymbol interference, which arises typically when the signal bandwidth is higher than the channel coherence bandwidth. In particular, it is robust in mitigating commonly encountered spectral nulls in these frequency-selective fading channels.
It is interesting to note that the basic DFE itself is nonlinear because of the threshold detector and the feedback loop (Fig. 11.1). The DFE removes ISI and noise from the received (analog) symbols and decides the transmitted digital symbol. The feedback loop eases the equalization by using the previous (correct) decisions and cancels post-cursor components. This concept is analogous to an IIR filter, which performs with greater parsimony and fewer parameters than an FIR filter. We can make the following observations about the basic DFE: