Steady-state performance analysis of a generalised multimodulus adaptive blind equalisation based on the pseudo Newton algorithm

A generalised modified multimodulus cost function for blind equalisation in digital communication systems is introduced. This generalisation is achieved by dividing the complex plane of modulated signals into several disjoint regions where the regions have different constant modulus. Then an adaptive learning algorithm that employs the pseudo Newton method is presented and based on the predefined generalised cost function its corresponding steady-state mean square error (MSE) is derived. Also, the number of disjoint regions is evaluated so that the minimum of the steady-state MSE is achieved. Here it is proved that the cost function with a single region in the complex plane achieves the minimum MSE. Then the resulting steady-state MSE of pseudo Newton method is compared with the one obtained from stochastic gradient algorithm (SGA). It is concluded that the pseudo Newton method converges to the desired steady-state MSE with a step size larger than the one used in SGA. Additionally, based on the pseudo Newton method and the SGA, a new method is developed that has better convergence speed compared to the other two methods. Finally, various simulation results are presented to verify the previous stated results.