Performance Analysis Of CMA(p,q) Adaptive Algorithm

When high-speed communication signals pass through the frequency selective channel,they will cause inter-symbol interference due to interference.Blind equalization technology is different from the traditional method of using an equalizer to compensate the channel and using a large number of training sequences.Without passing the training sequence,the parameters can be adaptively adjusted effectively,which can not only eliminate inter-symbol interference,but also It can prevent the traditional method from losing effective information due to the high-speed transmission of the training sequence.In the blind equalization technology,the constant modulus algorithm CMA(p,q)is widely used.The parameters p and q are generally selected as integers 1 and 2.Their performances such as convergence,transient,steady state and tracking have also been extensively studied.In order to be able to adapt to a more general channel environment,the values of parameters p and q must be extended from integers 1 and 2 to ordinary positive real numbers.The main research contents include:(1)Different from the traditional performance analysis method,which is to recurse the covariance matrix of the weight error vector,based on the energy conservation relationship,directly expand the error function by Taylor series,and use the separation assumption principle,and then do not rely on the cycle theorem.The transient performance of CMA(p,q)-type adaptive algorithm is analyzed,and the weighted variance relation and state space equation of CMA(p,q)complex number data and real number data are derived.Then,the theoretical and simulated values of the mean square deviation of the CMA(p,q)with different parameters p,q and non-synchronization length are verified,and they are relatively matched.(2)Based on the weighted variance equation in the transient performance analysis,when the equalizer reaches the steady-state condition,the steady-state closed analytical expressions for the complex and real numbers of CMA(p,q)are derived.Use a computer to perform experiments on CMA(p,q)under the condition of non-synchronization length,and perform theoretical and simulation comparison experiments on the mean square error of CMA(p,q)with the same parameter p and different q and with the same parameter q and different p.Prove the theory right.(3)Combining the random walk model,re-derive the energy conservation relationship with random interference factor terms according to the stochastic gradient iteration formula of CMA(p,q).The separation assumption is made on the estimated error function of Taylor series expansion,and the steady-state tracking performance expression of complex and real numbers with interference factors is derived.Then use MATLAB to compare the theoretical and simulated curves of CMA(p,q)steady-state tracking mean square error.The theoretical and simulated curves are more overlapped.(4)According to the necessary conditions of CMA(p,q)steady-state and tracking performance expressions,establish an ideal mathematical model that is applicable to complex data and real data with respect to the parameters p and q within a certain range.Through theoretical analysis,it is concluded that the deduced theoretical value needs to meet the conditions of an ideal mathematical model.This ideal mathematical model is also suitable for convergent transient performance analysis.