## Abstract

This paper studies the robustness properties of the constant modulus (CM) criterion and of its stochastic gradient descent algorithm [the constant modulus algorithm I ('VIA 11 to the sub-optimal but practical situation where the number of fractionally spaced equalizer (FSE) coefficients is less than what is needed to remove all intersymbol interference (ISI). Hence, there necessarily exists an error in the equalized signal. We present original algebraic analysis that describes the deformation of the CM error surface for real-valued, multilevel signaling and the specific case of binary signaling (BPSK). In addition, a truncated (to second order) Taylor series of the binary CM cost function is derived, and a measure of the proximity between Wiener and CM minima is proposed. Our original analysis is evaluated for fractionally sampled channel models derived from empirical digital microwave radio signals. Our main observations based on these practical data sets include the following. i) The deformation in the CM error surface is mild when channel coefficients outside the FSE time span are small. ii) A longer FSE does not always outperform a shorter FSE, due to excess MSE. iii) The Wiener settings of better MSE performance (due to system delay) have CM minima in closer proximity than the Wiener settings of poorer MSE performance.

Original language | English |
---|---|

Pages (from-to) | 541 |

Number of pages | 1 |

Journal | IEEE Transactions on Signal Processing |

Volume | 46 |

Issue number | 2 |

Publication status | Published - 1998 |