Study On Steady-state Performance Of Multi-modulus Blind Equalization Algorithm

With the rapid development of mobile communications,intersymbol interference and channel interference are still important factors affecting the quality of communications.Blind equalization technology can accurately compensate for the channel characteristics of the transmission channel process,reduce intersymbol interference,improve communication quality,and obtain better equalization effect,and meanwhile,it does not need training sequences which could improve channel efficiency.The constant modulus algorithm is the most commonly used blind equalization algorithm,but it cannot correct the problem of phase rotation.The emergence of multi-modulus algorithm solves this problem.The multi-modulus algorithm is a blind equalization algorithm that divides constant modulus algorithm into real part and imaginary part.Compared with the constant modulus algorithm,it not only has faster convergence speed but also can correct the phase rotation.Based on the energy conservation relation during iteration process of the multi-modulus algorithm,this paper deeply studies the steady-state performance of the multi-modulus algorithm.The main contributions of this paper are as following:(1)The steady-state mean square error of multi-modulus algorithm with p=1 and p=2 are analyzed theoretically,and then the steady-state mean square error expression is deduced.Compared with the constant modulus algorithm with p=1 and p=2,the steady-state mean square error of the multi-modulus algorithm with p=2 is better than the constant modulus algorithm with p=2,but p=1 when it is exactly the opposite.Finally,a large number of simulation experiments verify the correctness of the theoretical analysis.(2)The steady-state tracking excess mean square error of the multi-modulus algorithm with p=1 and p=2 are analyzed theoretically,and then the steady-state tracking excess mean square error,the optimal step size and the minimum steady-state tracking excess mean square error expression are deduced.Compared with the constant modulus algorithm with p=1 and p=2,the tracking performance of the multi-modulus algorithm with p=2 is better than the constant modulus algorithm with p=2,but p=1 when it is exactly the opposite.Finally,a large number of simulation experiments verify the correctness of the theoretical analysis.(3)This paper proposes the multi-modulus-convex blind equalization algorithm and theoretically analyzes the steady-state mean square error of the algorithm.The simulation results show that the convergence speed and steady-state error of the proposed algorithm have a certain improvement,at the same time,it also verifies the correctness of the theoretical steady-state mean squeare error.