THE METHOD FOR OPTIMIZING SIGNAL PARAMETERS USING LAGRANGE MULTI-PLIERS

This article presents a method for optimizing signal parameters using the Lagrange multiplier method to ensure high accuracy of signal reconstruction and interference resilience in cognitive telecommunication networks. The study addresses key challenges related to adapting to dynamic spectral conditions, high levels of interference, and nonlinear signal distortions. Based on an analysis of recent research, the necessity of implementing the proposed method is substantiated. This method considers the orthogonality conditions of Volterra kernel parameters and ensures algorithm stability in dynamic radio environments. The proposed optimization method minimizes the mean squared error (MSE) of signal reconstruction, reduces the influence of nonessential model components, and enhances algorithm stability. Unlike traditional methods, such as Newton’s, Levenberg-Marquardt, and Nelder-Mead methods, the Lagrange multiplier method effectively achieves lower MSE values, particularly at high signal-to-noise ratio (SNR) levels. It has been demonstrated that the implementation of the proposed optimization method significantly improves the efficiency of telecommunication systems for both 4G LTE and 5G NR standards. For 4G LTE, the method ensures stable signal reconstruction even under significant interference. Experiments have shown that the MSE is reduced by 15–20% compared to Newton’s and Levenberg-Marquardt methods and by 40–50% compared to the Nelder-Mead method. For 5G NR, where conditions are significantly more challenging due to dynamic spectral changes and high interference levels, the method demonstrates high efficiency at high SNR values, reducing MSE by 10–15% compared to Newton’s and Levenberg-Marquardt methods. At lower SNR levels, the efficiency of error reduction decreases due to the complex radio environment characteristic of next-generation networks. Experimental evaluation and comparative analysis have confirmed that the Lagrange multiplier method is the most effective for achieving stable signal reconstruction in cognitive networks under high SNR levels. However, further refinement of the method is necessary for 5G NR networks to meet their heightened adaptability requirements and achieve stability comparable to that in 4G LTE.