Analysis of the Effect of the Lagrange Multipliers on the Estimation Algorithm Convergence of the Parameters M-QAM Signal Based on Method of Moments

This paper proposes an algorithm of M-QAM signal parameters estimation with interference with lognormal amplitude distribution and with uniform phase distribution. The synthesis of algorithm is based on method of moments which leads to improperly posed problem. Modified method of least mean square (LMS) in the form of Tikhonov A.N. functional was used to solve the problem. As a result of this approach, a recurrent procedure for finding estimates was obtained, which consists of processing of an entire test signal with a fixed size. Also, the recurrent expression for Lagrange multipliers was found. During a computational experiment, the convergence of the algorithm was analyzed using the recurrent estimation procedure, both with and without a regularization parameter in the form of a Lagrange multiplier. It was shown that an introduction of the regularization allows to increase the accuracy of unknown signal parameters estimation (amplitude, frequency shift and phase) and exclude the recurrent procedure convergence with some sample sizes being processed. The comparison of the algorithm based on method of moments with a procedure of nonlinear recurrent Stratanovich filtering with first Taylor approximation (extended Kalman filter). Here is shown in case with the same estimation accuracy filtering requires a larger sample size of information than an algorithm presented in this paper and in case with small sample size filtering has bigger value of mean-squared error (MSE) than the procedure based on method of moments.