# New Approach of Blind Adaptive Equalizer Based on Genetic Algorithms
## 1 Introduction
Among the various techniques for solving stochastic problems, the genetic algorithm (GA) has been a promising option for this purpose. The GA is an evolutionary algorithm that mimics the Darwinian process of natural selection. Due to its stochastic nature, a GA is well suited for the rapid and comprehensive exploration of a large search space to optimize any objective function, and it is independent of the nature of the signal. In the context of data transmission, several approaches using genetic algorithms (GAs) have been proposed in the literature. The work [15] presents a study of the suitability of genetic algorithms for adaptive equalization. The work [16] proposes a GA-based adaptive algorithm for frequency domain equalization of Direct-Sequence Ultra-Wideband (DS-UWB) systems, while the work [17] proposes a GA approach for nonlinear channel equalization. For the particular case of adaptive blind equalization, in general, additional local search techniques are used to improve the convergence of GAs. The work [18] proposes a simple-approach GA, using as the objective function the CMA cost criterion. Like [18], other approaches used GA and the CMA cost criterion as a basis, but also including some local search heuristics [19; 20; 21; 22]. In the context of blind adaptive equalization, a GA is employed for its ability to address optimization challenges in stochastic and dynamic environments effectively. Unlike deep learning methods that often require extensively labeled datasets and significant computational resources, GAs offer a lightweight, flexible approach that does not rely on gradient information or large-scale training. This independence suits GAs for environments with limited data or real-time constraints. Additionally, GAs are inherently robust to local minima and can efficiently explore large search spaces, ensuring effective optimization even in complex communication channels. By leveraging these characteristics, the proposed BLE-GA framework achieves scalable and noise-resilient equalization across high-order modulation schemes, providing a viable alternative to more resource-intensive deep learning approaches [23, 24, 25, 26, 27, 28]. The 5G multimedia communication presents significant challenges due to high data rates, dynamic channel conditions, and complex modulation schemes. To address these challenges, the proposed BLE-GA offers a scalable and robust solution capable of mitigating ISI and optimizing bit error rate performance across various modulation schemes. This work advances adaptive equalization methodologies by addressing the specific demands of next-generation communication systems, focusing on noise resilience and computational efficiency, which are essential for the development and implementation of 5G and beyond [29, 30]. In this paper, a blind equalization scheme is proposed (BLE-GA: Blind Linear Equalizer based on a genetic algorithm): a GA combined with a stochastic linear program cost function used to perform blind equalization. The GA was chosen as the optimization technique due to its fast convergence capacity and robustness to the stochastic nature of the transmitted signal. The contributions of this study to the field of blind adaptive equalization are as follows:  
* The BLE-GA combines a stochastic linear programming cost function with genetic algorithm optimization to address challenges in equalization under stochastic conditions. * BLE-GA demonstrates adaptability across various QAM modulation schemes, including 64-QAM, with improved scalability and efficiency compared to traditional algorithms. * A block-based architecture is introduced, reducing computational requirements while maintaining effective convergence. * Simulations under different noise and inter-symbol interference conditions evaluate and demonstrate the performance of BLE-GA.