# A Distributed Energy-Throughput Efficient Cross-Layer Framework Using Hybrid Optimization Algorithm
###### Abstract  
Magnetic induction (MI)-operated wireless sensor networks (WSNs), due to their similar performance in air, underwater, and underground mediums, are rapidly emerging networks that offer a wide range of applications, including mine prevention, power grid maintenance, underground pipeline monitoring, and upstream oil monitoring. MI-based wireless underground sensor networks (WUSNs), utilizing small antenna coils, offer a viable solution by providing consistent channel conditions. The cross-layer protocols address the specific challenges of WUSNs, leading to improved network performance and enhanced operational capabilities in real-world applications. This work proposes a distributed cross-layer solution, leveraging the hybrid marine predator naked mole rat algorithm (MPNMRA) for MI-operated WUSNs. The solution, called DECMN (distributed energy-throughput efficient cross-layer network using MPNMRA), is designed to optimize the MI communication channels, MI relay coils (MI waveguide), and MI waveguide with 3D coils to fulfill quality of service (QoS) parameters, while achieving energy savings and throughput gains. DECMN utilizes the interactions between various layers to develop cross-layer protocols based on MPNMRA. Simulation results demonstrate the effectiveness of DECMN, offering energy savings, increased throughput, and reliable transmissions within the performance limits. distributed power control; distributed protocol; wireless underground sensor network; NMRA; MPA; MPNMRA; nature-inspired algorithms 2025132244013224013224013224013224013224013224013224013224013240132240132240132240132401322401324013224  
and earthquakes, security and border applications, and many others. Nonetheless, underground environments [2] pose significant obstacles to wireless communication using traditional electromagnetic (EM) waves. Particularly, the key issues associated with EM communication arise from the need for large antenna sizes, the presence of extremely limited communication ranges, and highly unreliable channel conditions. The magnetic induction (MI) technique [2] emerges as a promising wireless communication solution to overcome the challenges encountered in underground environments. This technique utilizes the near magnetic field of coils to transmit information, ensuring consistent channel conditions while employing compact coil sizes. The MI communication method is particularly well-suited for underground settings due to its advantageous characteristics. The research on MI communication encompasses various aspects, such as evaluating the channel capacity between coil transceivers [3], studying the channels formed by magnetically coupled coils in near-field inductive communication systems [4], proposing algorithms for coil deployment in MI-based WUSNs [5], providing models for wireless power system transmission and MI connection budgets [6], enabling efficient wireless energy transmission over longer distances using MI technology [7], discussing bandwidth, connectivity, and signal-to-noise ratio (SNR) in 3D underwater channels from a networking perspective of MI communication [8], enhancing the communication range of MI near-field communication systems with multi-hop relays [9], and employing MI-based sensors for military applications such as underground object discrimination [10]. However, while substantial progress has been made in the physical layer aspects, such as antenna design and signal analysis, there is a lack of protocols specifically tailored for MI-based WUSNs. Future research efforts should focus on addressing this gap and developing protocols that can optimize the performance of MI-based WUSNs, ensuring seamless and reliable communication in challenging underground conditions. By combining advances in both the physical layer and protocol design, MI communication holds the potential to revolutionize wireless communication in underground applications. Cross-layer solutions have been widely recognized as an effective approach for resource-efficient design in WSNs [11].