Convergence behavior of the constant modulus algorithm controlled by special stepsize

The constant modulus algorithm (CMA) enjoys widespread popularity as methods for blind beamforming and equalization of communication signals. CMA is straightforward to implement, robust, and computationally of modest complexity. Despite its effectiveness and apparent simplicity, adaptive implementation of the CMA comes along with several complicating factors that have never really been solved. In particular, convergence can be unpredictable and slow depending on the stepsize. In this paper, Convergence behaviors of the constant modulus algorithm based on "1-2" cost function (CMA_1-2) and "2-1" cost function (CMA_2-1) are investigated. We found that certain signals could be quickly removed from the output data choosing special stepsize if at least two signals were of different power. Simulation examples confirm the results.