A Novel Godard Algorithm Based On Convex Combination Pair Structure

The constant modulus algorithm (CMA) in the form of convex combination with different step sizes shows its advantages in terms of convergence speed and steady-state error performance, but the performance of the algorithm is poor in the case of Gaussian noise and non-Gaussian noise. However, the Godard algorithm is widely used in practical applications because of its ability to suppress noise to a certain extent. In order to combine the advantages of the two algorithms perfectly, based on the form of combination pairs, this paper combines a pair of CMA algorithms with different step size convex combinations and a pair of Godard algorithms with different parameter convex combinations to obtain a Godard algorithm based on a convex combination pair structure (CCPS-GA), and applies it to different noise environments. In the aspect of performance analysis, the expression formula of the steady-state performance of the new algorithm is derived by using energy conservation formula, Taylor expansion formula, separation hypothesis and other methods. By comparing the obtained results with simulation values, the correctness of the derived formulas is verified. From the simulation curve, it can be seen that the combined algorithm not only perfectly inherits the advantages of each blind equalizer, but also has better convergence speed, steady-state residual error, anti-Gaussian noise and anti-non-Gaussian noise ability than the known singlepath algorithm and the convex combination algorithm, which is a relatively ideal blind equalization algorithm at present.