A linear equalizer can be implemented as an FIR filter, otherwise known as the transversal filter.This type of equalizer is the simplest type available
Structure of a linear Equalizer:
- linear transversal equalizer: In such an equalizer, the current and past values of the received signal are linearly weighted by the filter coefficient and summed to produce the output, as shown in Figure 13.2
- The output of this transversal filter before decision making (threshold detection) is given
- Cn*represents the complex filter coefficients or tap weights,
- d k is the output at time index k,
- y i is the input received signal at time t 0 iT,
- t 0 is the equalizer starting time ,N= N1 N2 1 is the number of taps
- ,N1&N2 denotes the number of taps in forward and reverse portion of the equalizer respectively.
The minimum mean squared error E [│e (n)│2] that a linear transversal equalizer can achieve is
where│F(ejwt)│2 is the frequency response of the channel, and N0 is the noise spectral density.
A lattice filter:The linear equalizer can also be implemented as a lattice filter.
- Each stage of the lattice is then characterized by the following recursive equations
- Where Kn(k) is the reflection coefficient for the it th stage of the lattice
- Output of the equalizer is given by
- Two main advantages of the lattice equalizer is its numerical stability and faster convergence.
- The unique structure of the lattice filter allows the dynamic assignment of the most effective length of the lattice equalizer.