Nonlinear equalizers are used in applications where the channel distortion is too severe for a linear equalizer to handle.
Nonlinear Equalization Methods:
- Decision Feedback Equalization (DFE)
- Maximum Likelihood Symbol Detection
- Maximum Likelihood Sequence Estimation (MLSE)
Decision Feedback Equalization (DFE): The basic idea behind decision feedback equalization is that once an informationsymbol has been detected and decided upon, the ISI that it induces on future symbols can be estimated and subtracted out before detection of subsequent symbols. It consists of a feed forward filter (FFF) and a feedback filter (FBF).
- The DFE can be realized in either the direct transversal form or as a lattice filter as shown in the fig 13.5.below
- The equalizer has N1 N2 1 taps in the feed forward filter and N3 taps in the feedback filter, and its output can be expressed as
- The minimum mean squared error a DFE can achieve is
Advantages of DFE:
- DFE has significantly smaller minimum MSE than an LTE
- the mean squared error of a DFE is much better than a LTE.
- A DFE is more appropriate for severely distorted wireless channels
Predictive decision feedback equalizer
- It also consists of a feed forward filter (FFF) as in the conventional DFE.
However, the feedback filter (FBF) is driven by an input sequence formed by the difference of the output of the detector and the output of the feed forward filter.
- Hence, the FBF here is called a noise predictor because it predicts the noise and the residual ISI contained in the signal at the FFF output and subtracts from it the detector output after some feedback delay.
Maximum Likelihood Sequence Estimation (MLSE) Equalizer :
The MSE-based linear equalizers described previously are optimum with respect to the criterion of minimum probability of symbol error when the channel does not introduce any amplitude distortion.
- Using a channel impulse response simulator within the algorithm, the MLSE tests all possible data sequences (rather than decoding each received symbol by itself), and chooses the data sequence with the maximum probability as the output.
- The MLSE is optimal in the sense that it minimizes the probability of a sequence error.
- The MLSE requires knowledge of the channel characteristics in order to compute the metrics for making decisions.
- The MLSE also requires knowledge of the statistical distribution of the noise corrupting the signal.