Study Of Improved CMA Blind Equalization Algorithm

Blind equalization is a technique for adapting an equalizer without the need of training sequence, only utilizes the statistical character information of input signals to equalize the channel character. It has been becoming a very popular research topic in recent years. With the researching of blind equalization, it has been used in many fields such as digital communication system, radar system, earthquake and image processing system and so on.The constant modulus algorithm (CMA) is one of the first known blind equalization algorithms. This method through adjust equalizer tap gain to make cost function get to least value, which cost function is constituted by the higher-order statistics characteristic of transmitted signal. It has better toughness, and its cost function has only related to the amplitude value of receivedsignal, not the phase. But the algorithm convergence at a low speed, sometimes it makes mistake on convergence, so the application of this method has been restricted.This paper directs toward slow convergence rate of CM blind equalization algorithm, analyses the inherent limitation of CMA, explains relationship between convergence rate and step-size, applies variable step-size theory to CMA, proposes several improved CM blind equalization algorithm. The convergence performance of the proposed algorithms is illustrated by computer simulations.The main works of this paper can be summarized as follows:1. In this paper, the convergence drawback of CMA is analyzed, the variable step-size theory of adaptive filter is applied to CMA, and four variable step size CM blind equalization algorithm are proposed which can overcome the tradeoff in convergence rate, track rate and convergence precision.2. This paper analyses the basic principle of variable step-size in adaptive filter algorithm, applies mean square error (MSE) toimproved Sigmoid function and the non-linear function that controls step-size, achieves two new variable step-size CMA. The convergence performance of the new algorithms is illustrated by computer simulations.3. The kurtosis of equalizer error signal has been applied to improved Sigmoid function and the non-linear function that controls step-size, and two new variable step-size CMA is achieved, computer simulations show that the proposed method gives faster convergence rate and smaller state residual error.