Dynamically Partitioned Hierarchical Constant Modulus Algorithm for Variable Delay Spread Channels

Abstract

The Constant Modulus Algorithm (CMA) adopts the constant modulus (CM) criterion to minimize the deviation of the equalizer output from a fixed value. However it has two drawbacks: (1) slow rate of convergence (2) the likelihood of getting trapped in a local minimum. The problem gets even worse when the channel delay spread varies rapidly as the filter length cannot match the delay spread. If the filter length is significantly longer than the delay spread, the convergence rate can be slow. In this paper, we improve the performance of the standard CMA by using a dynamically partitioned hierarchical structure to organize the taps of a filter. The filter length is dynamically partitioned according to the delay spread such that they are tightly matched. Preferably, the length of a sub-filter is slightly longer than the delay spread of the channel. The performance evaluation is divided into two parts. In Part I, we do simulation runs for both the cost functions and cost surfaces comparing the standard CMA, where the filter length is significantly longer than the delay spread, and the dynamically partitioned CMA, where the filter length matches the delay spread. In Part II, an analysis is provided to show that the proposed partitioned scheme can speed up the convergence rate and reduce the cost function.