Global convergence of a single-axis constant modulus algorithm

Abstract

We propose a modification to the Constant Modulus Criterion for real valued sources processed with a complex valued receiver. Our modification is called Single-Axis Constant Modulus Criterion (SA-CM) because it operates solely on the real component of the complex equalizer output. We show that under idealized conditions, a finite length, baudspaced, complex valued equalizer minimizing the SA-CM criterion admits only desirable global minima settings that are ISI-free. A single-axis receiver architecture is compared to other receiver architectures for real valued sources and staggered modulation schemes. Simulation examples using vestigal sideband (VSB) signaling verify our methods.

On the Misbehavior of Constant Modulus Equalizers for Improper Modulations

“…(15)] for the case of an infinite-length CM equalizer, under the simplifying assumption of BPSK symbols with unitary variance. Finally, it is noteworthy that with reference to real-valued symbols (i.e., ), it was shown in [12] that the undesired minima (8) and (9) disappear by minimizing the CM cost function (2), provided that the equalizer output is not a strictly linear function of ; namely, . More generally, if the transmitted symbols are improper complex, one has to use widely linear equalizing structures [5], where the equalizer output is given by and the CM cost function is minimized with respect to both and , where is not necessarily constrained to be equal to .…”