Fractional Order Constant Modulus Blind Equalization Algorithm Under Alpha Stable Distributed Noise

With the development of communication technology,wireless communication plays an important role in the construction of an information society.And channel equalization is one of the important methods to ensure the reliability of wireless communication systems.So it is the hotspots of wireless communication technology research.Constant modulus algorithm(CMA)has many advantages such as simple structure,easy to implement,no training sequence,etc.Therefore,it has been widely used in wireless communication.However,there is alpha stable distribution noise in the actual wireless channel.It causes the performance of CMA to degrade significantly.In order to improve the equalization performance of the blind equalization algorithm in the alpha stable distribution noise,constant modulus algorithm based maximum correntropy criterion(MCC?CMA)is proposed.But this algorithm has the problem of slow convergence speed.It is necessary to speed up the convergence speed of the algorithm without affecting the equalization effect.So this thesis combines the advantages of the maximum correntropy criterion(MCC)and fractional calculus,and makes the following work.First of all,this thesis proposes an algorithm called fractional order constant modulus algorithm based On maximum correntropy criterion(MCC?FOCMA).The MCC is used to optimize the cost function of CMA to ensure that the algorithm can achieve a good equalization effect in the alpha stable distribution noise.Because the fractional gradient contains abundant gradient information.In this thesis,the MCC?FOCMA is proposed by using the fractional gradient to improve the convergence performance of the algorithm.The proposed algorithm can stably converge in alpha stable distribution noise and has high convergence performance.Secondly,the performance of the MCC?FOCMA is analyzed by the energy conservation formula.The classic energy conservation formula cannot be directly applied to the analysis of the MCC?FOCMA because the proposed algorithm uses the MCC and fractional gradient.Therefore,the MCC?FOCMA is simplified using Taylor formula and vector weighted norm.And this thesis derives the steady-state error expression to discuss the influence of step size,kernel width and fractional order on steady-state error.And then give the value range of the step size is given.Third,blind channel equalization system is constructed to verify the performance of the MCC?FOCMA in alpha stable distributed noise and analyze the influence of parameters on the equalization performance.Simulation experiments show that MCC?FOCMA has good stability and equalization performance in alpha stable distributed noise.In addition,MCC?FOCMA can not only has good equalization performance,but also has a faster convergence speed.The two algorithms are compared in the case of sudden channel mutation.The MCC?FOCMA can recover quickly because it has a faster convergence speed.It proves that the MCC?FOCMA has better convergence performance.