Underwater Wireless Optical Communication (UOWC) is a key enabling technology for future space-air-ground-sea integrated networks. However, UOWC faces critical hurdles from spatial randomness and stringent energy constraints. These challenges fundamentally limit network lifetime and sustainability. This paper develops a comprehensive stochastic geometry framework to perform a differential energy analysis of UOWC links.Instead of relying on simplified models, we employ a three-dimensional truncated Poisson point process (TPPP) to accurately capture the anisotropic nature of the underwater environment, specifically the disparity between horizontal spread and vertical depth. It incorporates a Lambertian emission pattern, random receiver positions and orientations, and a realistic channel model with extinction effects. Under this model, we derive a full suite of closed-form expressions for key performance indicators. These include the nearest-neighbor distance distribution, expected received power, signal-to-noise ratio (SNR), and bit error rate (BER). A principal and counter-intuitive finding of our analysis is an “offset-pointing” strategy. This strategy involves intentionally misaligning the receiver by a deterministically optimal angle. This approach maximizes the integrated received power across the aperture, contrary to the conventional pursuit of perfect alignment. We formulate and solve an energy-efficiency optimization problem. Our results demonstrate that this strategy enhances system robustness and yields substantial performance gains. Simulation results validate our analytical models. They show that the optimal offset strategy can reduce the required transmit power by nearly 20% to achieve a target BER. This reduction directly translates into extended network lifetime and higher total data throughput. These findings offer a new design paradigm for deploying robust, cost-effective, and sustainable UOWC networks.

In underwater target localization (UTL), the accuracy of distance measurement between anchor nodes and the target is a critical factor that directly affects localization performance. This is especially true for localization methods based on time of arrival (TOA) and time difference of arrival (TDOA), where the acoustic signal propagation time is converted into distance to estimate the target’s position. However, in most existing literature, the distance measurement noise, regardless of whether it is derived from TOA or TDOA, is commonly modeled as Gaussian. In this paper, we propose that the distance noise in UTL is better characterized by a shifted-Gamma distribution. Specifically, we establish a TOA-based UTL model and show that the overall distance error arises from four independent sources: 1) anchor node position error, 2) signal path bending due to refraction, 3) uncertainty in sound velocity, and 4) time synchronization error. Assuming each of these error sources follows a basic Gaussian distribution, we derive the resulting composite distance error, which is then approximated by a shifted-Gamma distribution. Monte Carlo simulation results validate the accuracy of this approximation and reflect its consistency with practical measurement noise. Furthermore, the Cramer–Rao Lower Bound (CRLB) for the UTL accuracy is derived based on the proposed noise model with the derived shifted-Gamma distribution. Across representative geometries and noise ranges, the shifted-Gamma noise model provides tighter Cramér-Rao lower bounds and lower localization error than a Gaussian noise model. The model supports noise-aware estimator design and anchor geometry selection in underwater target localization systems, and improves robustness in environments with strong non-Gaussian disturbances.

Maritime communication demands have surged due to diverse applications such as transoceanic shipping, offshore resource exploration, and emergency rescue. However, current communication systems are unable to meet the diverse data rate demands of maritime applications. In this paper, we propose a space-air-ground-sea integrated network (SAGSIN) that combines onshore base stations, uncrewed aerial vehicles, high-altitude platform stations, and low Earth orbit satellites to provide seamless and reliable communication across vast oceanic regions. Based on stochastic geometry, we model the spatial distribution of network devices on spherical surfaces. The Matérn hard-core point process (MHCPP) is used to model the deployment of both ground and aerial devices, considering the minimum spacing to avoid overdense and collisions. Aerial relays are used to extend the coverage of coastal base stations, with relay selection aimed at maximizing the end-to-end channel capacity. Analytical expressions for the uplink coverage probability are derived by considering the receiver’s decoding threshold. Furthermore, the analysis is extended to the communication probability by incorporating quality of service (QoS) with data rate as the metric. Numerical results validate the accuracy of the proposed model and demonstrate that SAGSIN can effectively extend reliable communication from coastal regions to the deep ocean. Furthermore, dynamic QoS scheduling across heterogeneous links, each with different transmission capabilities, can enhance overall system efficiency to meet diverse QoS demands.

To achieve the Internet of Things (IoT) vision, Mobile Edge Computing (MEC) is a promising technology aimed at providing low-latency computing services to user equipment (UE). However, terrestrial MEC network struggles to provide service to UEs in remote and maritime region. Low Earth Orbit (LEO) satellite networks have the potential to overcome geographical restrictions and provide seamless global coverage for UEs. In this paper, we provide the first attempt to use stochastic geometry to investigate the performance of implementing space caching with LEO satellites (SATs) in the MEC network. We study a LEO satellite-assisted space caching MEC network, and LEO SATs can be equipped with servers to enable space caching, with the advantage of seamless coverage to assist terrestrial CSs for serving UEs in remote or maritime reigon. Using stochastic geometry and queuing theory, we establish an analytical framework for this MEC network. Meanwhile, we develop association strategies for UEs to connect with LEO SATs or CSs and utilize stochastic geometry to derive uplink and downlink coverage probabilities, considering the diversity of task and service types. On this basis, we employ the queuing theory to calculate the average delay to evaluate the system performance. Through Monte Carlo simulations and numerical results, the system performance is evaluated. The results show the potential of SAT spatial caching in improving the performance of the MEC network. Additionally, our results reveal useful insights such as the significant impact of the altitude and number of LEO SATs on the average delay of the network, providing helpful systemlevel recommendations for the design and configuration of the space-caching MEC network.

For next-generation green communication systems, this article proposes an innovative communication system based on frequency-diverse array-multiple-input multiple-output (FDA-MIMO) technology, which aims to achieve high data rates while maintaining low power consumption. This system utilizes frequency offset index realign modulation, multiple-antenna spatial index modulation, and spreading code index modulation techniques. In the proposed generalized code index modulation-aided frequency offset realign multiple-antenna spatial modulation (GCIM-FORMASM) system, the coming bits are divided into five parts: spatial modulation bits by activating multiple transmit antennas, frequency offset index bits of the FDA antennas, including frequency offset combination bits and frequency offset realign bits, spreading code index modulation bits, and modulated symbol bits. Subsequently, this paper utilizes the orthogonal waveforms transmitted by the FDA to design the corresponding transmitter and receiver structures and provide specific expressions for the received signals. Meanwhile, to reduce the decoding complexity of the maximum likelihood (ML) algorithm, we propose a three-stage despreading-based low complexity (DBLC) algorithm leveraging the orthogonality of the spreading codes. Additionally, a closed-form expression for the upper bound of the average bit error probability (ABEP) of the DBLC algorithm has been derived. Analyzing metrics such as energy efficiency and data rate shows that the proposed system features low power consumption and high data transmission rates, which aligns better with the concept of future green communications. The effectiveness of our proposed methods has been validated through comprehensive numerical results.

Received signal strength (RSS)–based cooperative localization has gained significant attention due to its straightforward system architectures and cost-effectiveness. In this paper, we propose Cooperative Localization Techniques (with Unknown Parameters), referred to as CTUP(s), which consider uncertainty in anchor nodes’ locations and assume the transmit power and path loss exponent (PLE) to be unknown. Unlike prior studies, CTUP(s) address unknowns by estimating these parameters, along with the location of target nodes. The non-convex and non-linear nature of the maximum likelihood (ML) estimator of the problem is addressed through relaxation techniques, employing Taylor series expansion, semidefinite relaxation (SDR), and the epigraph method. The resulting problem is solved using semidefinite second-order cone programming (SDP-SOCP), leveraging the precision of SDP and the simplicity of SOCP. We deployed an extensive network comprising 50 BLE nodes covering an area of 640 m$\times 180$m to gather RSS data. The precise location of the nodes is obtained using real-time kinematics global positioning system (RTK-GPS), which is treated as the ground truth. Furthermore, to replicate real-world scenarios, we recorded the positions of the anchor nodes using a standard GPS, thereby introducing uncertainty into the anchor node locations. Extensive simulation and hardware experimentation demonstrate the superior performance of CTUP compared to existing techniques.

Joint sensing and communication (JSAC) is regarded as a promising technology for future networks, which can reuse most devices of the systems in sensing and communication (S&C) and reduces the cost in terms of power and spectrum (P&S) critically. The current research considers the P&S allocation of S&C separately and then discusses the performance from different aspects. However, as an integrated system, the allocation strategy of P&S allocation affects the joint performance significantly. In this article, we use tools from stochastic geometry to study the coverage performance considering the trade-off of P&S allocation for JSAC with the principle requirements of small distance resolution (SDR) in sensing and high data rate (HDR) in communication. In particular, we model the locations of user equipment (UE) and base stations (BSs) as two different Poisson Point Processes and allocate P&S at BSs with two independent ratios. The sensing system will detect the surrounding environment and obtain UE positions. After that, an adaptive beamwidth for beamforming technology is applied in communication, which can save energy effectively. First, we introduce the distance resolution in sensing and special channel models in S&C with a high frequency. Then, considering the proposed system model, we separately model the interference in S&C. Further, the joint coverage probability (CP) of JSAC is derived as a function of densities of UE and BSs, required HDR and SDR, and allocation ratios of P&S. Finally, We draw multiple valuable system-level insights from the proposed analysis. For instance, we show that the SDR and HDR are the two main constraints to the maximum achievable CP with optimized allocations of P&S. Furthermore, we show that different densities of BSs should be considered in various scenarios. The revealed relationship between the densities of UE and BSs can be taken as a reference in practical applications.

Underwater long-distance wireless communication (ULWC) is a critical challenge in many applications, such as marine environmental monitoring, underwater remote control, and underwater navigation, to name a few. However, very little literature focuses on ULWC, especially where the communication distance ups to thousands of kilometers, which is urgently required in the Underwater Internet of Things (UIoT) in the large-scale and deep sea. In this article, to improve the underwater communication capacity at a level of thousands of kilometers, we propose a three-hop underwater wireless acoustic communication (3H-UWAC) structure based on the sound fixing and ranging (SOFAR) channel. The proposed 3H-UWAC consists of transmitters, relay stations (RSs), and receivers. Different from the existing ULWC, 3H-ULWC can improve energy efficiency with a small vertical directivity angle (VDA). Due to the characteristics of UWAC, the straight-line communication link can be realized in the proposed three hops, and the communication distance can be increased to thousands of kilometers. Respecting the randomness of underwater devices, tools from stochastic geometry are used to model the spatial distributions of transmitters’, receivers’, and RSs’ locations. RSs are set on the SOFAR channel at a known depth. In the first hop, the transmitter sends information to the nearest first RS (NFRS) on the SOFAR plane. In the second hop, the NFRS sends information to the nearest RS, which is called the nearest second RS (NSRS), to the receiver on the SOFAR plane. In the third hop, SNFS sends information to the receiver. All three communication hops can be achieved with a narrow beam width, where the energy efficiency is improved critically. With given densities of transmitters, RSs, and receivers, the coverage probabilities (CPs) of the three hops (transmitter to first RS (FRS), FRS to second RS (SRS), and SRS to receiver) are analyzed, and the final CP from a transmitter to a receiver through the 3H link is derived. Insights about the effects of VDAs at the transmitters, FNRS, and SNRS, as well as the depths of transmitters and receivers, are revealed. A rapid optimization method is proposed based on the analytical results. The accuracy of the analysis is verified by Monte Carlo simulations.

Due to its potential to enable global connectivity in remote locations, such as rural areas and islands, Space-Air-Ground networks have become an ambitious solution for terrestrial communication in the sixth generation (6G) wireless communication network. In this paper, we propose a novel structure of Space-Air-Ground-Sea integrated networks (SAGSINs) to study and derive the coverage probability (CP) of users who are annotated as surface stations (SSs) on the far-reaching ocean surface that is far away from the coastline. By incorporating different types of relays such as onshore stations (OSs), tethered balloons (TBs), high altitude platforms (HAPs), and satellites (SATs), communication links between the terrestrial core connected base stations (CCBSs) and SSs are established via one of the four types of relay stations. Considering practical scenarios with a random distribution of SSs, we model the channel using the point-to-area model, which is recommended by ITU (for OSs to SS), the Rician model (for TBs or HAPs to SS), and the Shadowed-Rician model (for SATs to SS). When the SS’s distance from the coastline continues to increase from zero, since different channel models are considered, different relay stations will result in specific received signal strengths at SSs. The most powerful relay station will be chosen as the relay at one time. Hence, as we move away from the coastline, the respective strengths of the different types of relay stations vary, and hence, the association preference (among HAPs, OSs, TBs, and SATs) of the SSs changes leading to a CP value high enough even at locations far away from the coastline into the ocean. We analyze the CP using tools from stochastic geometry. Comparisons of CP between the integrated system with four types of relay stations and the single relay station system (only one type of relay station available) are represented. Numerical results verified by Monte-Carlo simulations reveal insights into the applicability of SAGSINs.

Underwater acoustic communication networks (UACNs) are considered a key enabler to the Underwater Internet of Things (UIoT). UACN is regarded as essential for various marine applications, such as monitoring, exploration, and trading. However, a large part of existing literature disregards the 3-D nature of the underwater communication system. In this article, we propose a$K$-tier UACN that acts as a gateway that connects the UIoT with the space–air–ground–sea integrated system (SAGSIS). The proposed network architecture consists of several tiers along the vertical direction with adjustable depths. On the horizontal dimension, the best coverage probability (CP) is computed and maximized by optimizing the densities of surface stations (SSs) in each tier. On the vertical dimension, the depth of each tier is also optimized to minimize intertier interference and maximize overall system performance. Using tools from stochastic geometry, the total CP of the proposed$K$-tier network is analyzed. For given spatial distribution of UIoT device’s depth, the best CP can be achieved by optimizing the depths of the transceivers connected to the SSs through a tether. We verify the accuracy of the analysis using Monte Carlo simulations. In addition, we draw multiple useful system-level insights that help optimize the design of underwater 3-D networks based on the given distribution of UIoT device’s depths.