## 1 Introduction
Therefore, communication is restricted to adjacent layers. Conversely, the cross-layer technique allows any layer to utilize services from any other layer. This interaction between different layers of the network protocol stack enhances WSN performance. Cross-layer designs have identified six options based on potential interactions between the routing, MAC, physical, and application layers [18]. In terms of optimization, this paper employs Grey Wolf Optimization (GWO) at the network layer to identify better clustering. Numerous studies have highlighted the benefits of integrating GWO in WSNs. For instance, [PERSON] et al. [19] propose a hybrid GWO algorithm with a golden ratio mechanism for mobile target tracking in WSNs. This combination enhances both global search capabilities and local search precision, leading to improved tracking accuracy and energy efficiency. The method dynamically adapts to changes in the network, ensuring robust real-time tracking performance. GWO also finds applications in various domains requiring efficient optimization. [PERSON] et al. [20] introduce the SSGWO algorithm, which combines GWO with simulated annealing and B-spline curves for UAV path planning in complex environments. This approach balances local and global searches using a nonlinear convergence factor, resulting in superior path quality and reduced energy consumption. Simulations demonstrate the effectiveness of SSGWO in generating efficient paths. Additionally, [PERSON] et al. [21] applied an improved GWO (IGWO) with Support Vector Regression for estimating knee joint extension force from mechanomyography signals. The IGWO incorporates a dimensional learning strategy, enhancing convergence speed and prediction accuracy, outperforming standard GWO and other techniques in force estimation. This paper makes several key contributions to the field of WSN clustering:  
* Designed a novel cross-layer protocol targeting the MAC and network layers;
* Optimized clustering using GWO to identify optimal CHs based on residual energy, intra-cluster distances, and inter-cluster distances;
* Implemented a robust objective function for CH selection;
* Utilized Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) and Network Allocation Vector (NAV) for active mode/sleep mode management;
* Highlighted the effectiveness of cross-layer designs in peer protocols and identified key strategies from these protocols to inform the development of our own;
* Conducted extensive simulations comparing our protocol with peers;
* Demonstrated superior performance of EOAMRCL in terms of overall network remaining energy, number of dead nodes, and total data received at the BS and network lifetime;
* Validated the effectiveness of our cross-layer approach in reducing energy consumption and enhancing network performance. Table 1 provides a comprehensive list of acronyms used throughout the paper for ease of reference and clarity. The remainder of the paper is structured as follows: Section 2 reviews related works and discusses the incorporation of OSI layers in WSN clustering. Section 3 details the integration of WSN node sleep scheduling into the CSMA/CA mechanism. Section 4 introduces the fundamentals of the GWO algorithm and its application in optimization. Section 5 outlines our proposed Energy Optimization Approach based on MAC/Routing Cross-Layer (EOAMRCL). Section 6 evaluates the performance of the proposed approach through simulation results and analysis. Finally, Section 7 concludes the study with final remarks and future perspectives.