Equalization

In a multipath fading scattering environment, the receiver typically detects several constantly changing, delayed versions of the transmitted signal. These time-dispersive channels cause intersymbol interference (ISI) that occurs when symbols received from multiple paths are delayed and overlap in time. ISI causes high error rates because the symbols from multiple received paths interfere with each other and become indistinguishable by the receiver.

Equalizers attempt to mitigate ISI and improve the receiver performance. Equalizer structures are filters that attempt to match the propagation channel response. For time-varying propagation channels, adapting the equalization filter tap weights so that they maintain a match to the channel over time improves the error rate performance.

Equalizer Structure Options

The Communications Toolbox™ includes System objects and blocks to recover transmitted data using by linear, decision-feedback, or maximum-likelihood sequence estimation (MLSE) equalization structures. For more information, see Selected References for Equalizers.

This figure shows the high-level configuration options for each equalization structure.

For each equalizer structure, you can configure structural settings (such as the number of taps and initial set of tap weights), algorithmic settings (such as the step size), and the signal constellation used by the modulator in your design. You also specify adaptability of the equalizer tap weights throughout the simulation.

• Linear and decision-feedback filter equalizer structures adapt tap weights by using the LMS, RLS, or CMA adaptive algorithm. When using these equalizer structures, the number of samples per symbol determines whether symbols are processed using whole or fractional symbol spacing.

  • When using LMS and RLS adaptive algorithms, the equalizer begins operating in tap weights training mode. Configure the equalizer to operate adaptively in decision-directed mode or without further adjustment of taps after training is completed.

  • When using the CMA adaptive algorithm, the equalizer has no training mode. You can configure the equalizer to operate adaptively in decision-directed mode or in nonadaptive mode.

  To explore the linear and decision-feedback filter equalizer capabilities, see Adaptive Equalizers.

• Maximum-Likelihood Sequence Estimation (MLSE) equalizers use the Viterbi algorithm. The MLSE equalization structure provides the optimal match to the received symbols but it requires an accurate channel estimate and is the most computationally complex structure. To explore MLSE equalizer capabilities, see MLSE Equalizers.

The computational complexity of each equalization structure grows with the length of the channel time dispersion. Considering the Doppler and frequency selectivity characteristics of the channel, use the information in this table when selecting which equalization structure to use in your simulation.

Equalizer Structure	Doppler Speed	Is Channel Frequency Selective?	Computational Complexity
Linear RLS	High	No	Medium
Linear LMS	Low	No	Lowest
Linear CMA	Low	No	Lowest
DFE RLS	High	Yes	Medium
DFE LMS	Low	Yes	Lowest
DFE CMA	Low	Yes	Lowest
MLSE	Low	Yes	Highest

Selected References for Equalizers

[1] Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, John Wiley & Sons, 1998.

[2] Haykin, Simon, Adaptive Filter Theory, Third Ed., Upper Saddle River, NJ, Prentice-Hall, 1996.

[3] Kurzweil, Jack, An Introduction to Digital Communications, New York, John Wiley & Sons, 2000.

[4] Proakis, John G., Digital Communications, Fourth Ed., New York, McGraw-Hill, 2001.

[5] Steele, Raymond, Ed., Mobile Radio Communications, Chichester, England, John Wiley & Sons, 1996.