This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical divisions utilized in this tutorial

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Recent advances in blind identification of fractionally-spaced models for digital communication channels and blind fractionally-spaced equalizer adaptation rely on the assumption that the time span chosen for the fractionally-spaced equalizer exceeds that of the channel. This paper considers time-domain design formulas minimizing the mean-squared symbol recovery error achieved by a finite-length FIR fractionally-spaced equalizer with a time span shorter than the channel impulse response time span for white zero-mean QAM sources in the presence of white zero-mean channel noise. For minimum mean-squared error designs the symbol error rates achievable are plotted versus the ratio of the source variance t o the channel noise variance (with the channel model power normalized to achieve a received signal of unit variance) for different fractionally-spaced equalizer lengths on 64-Q AM for several TIBspaced channel models derived from experimental data. Our intent is to fuel the ongoing debate about fractionally-spaced equalizer length selection.

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