To appear as a chapter in Unsupervised Adaptive Filtering, Ed. Simon Haykin,
New York, NY: Wiley, 1999.
The Core of FSE-CMA Behavior Theory
by C.R. Johnson, Jr., P. Schniter, I. Fijalkow, L. Tong, J.D. Behm,
M.G. Larimore, D.R. Brown, R.A. Casas, T.J. Endres, S. Lambotharan,
H.H. Zeng, A. Tounzi, J.R. Treichler, and M. Green
Abstract
This chapter presents the basics of the current theory regarding the
behavior of blind fractionally-spaced equalizers (FSE) adapted via the
constant modulus algorithm (CMA). The constant modulus algorithm, which
was developed in the late 1970s and disclosed in the early 1980s,
performs a stochastic gradient descent of a cost function that penalizes
the dispersion of the equalizer output from a constant value.
This cost function leads to a blind algorithm because evaluation at the
receiver of the constant modulus cost does not rely on access to a
replica of the transmitted source, as in a scenario with training.
The capability for blind start-up makes certain communication systems
feasible in circumstances that do not admit training.
The theory-enabling feature of fractionally-spaced realization of a
linear equalizer is the potential for perfect equalization in the
absence of channel noise given a finite impulse response equalizer of
time span matching that of the finite impulse response channel.
The conditions for perfect equalizability coupled with some mild
conditions on the source can be used to establish convergence to
perfect performance with FSE parameter adaptation by CMA from any
equalizer parameter initialization. The FSE-CMA behavior theory
presented here merges the taxonomy of the behavior theory of trained
adaptive equalization and recent robustness analysis of FSE-CMA with
violation of the conditions leading to perfect equalization and global
asymptotic optimality of FSE-CMA.
