Accurately predicting beam-level reference signal received power (RSRP) is essential for beam management in dense multi-user wireless networks, yet challenging due to high measurement overhead and fast channel variations. This paper proposes Neural Beam Field (NBF), a hybrid neural-physical framework for efficient and interpretable spatial beam RSRP prediction. Central to our approach is the introduction of the Multi-path Conditional Power Profile (MCPP), a learnable physical intermediary representing the site-specific propagation environment. This approach decouples the environment from specific antenna/beam configurations, which helps the model learn site-specific multipath features and enhances its generalization capability. We adopt a decoupled ``blackbox-whitebox" design: a Transformer-based deep neural network (DNN) learns the MCPP from sparse user measurements and positions, while a physics-inspired module analytically infers beam RSRP statistics. To improve convergence and adaptivity, we further introduce a Pretrain-and-Calibrate (PaC) strategy that leverages ray-tracing priors for physics-grounded pretraining and then RSRP data for on-site calibration. Extensive simulation results demonstrate that NBF significantly outperforms conventional table-based channel knowledge maps (CKMs) and pure blackbox DNNs in prediction accuracy, training efficiency, and generalization, while maintaining a compact model size. The proposed framework offers a scalable and physically grounded solution for intelligent beam management in next-generation dense wireless networks.

Collaborative access points (APs) enabled cell-free networks can provide stable and uniform communication services for all user locations, making them a promising network architecture for the sixth-generation (6G) mobile communication systems. While the performance of pure cell-free networks has been extensively studied, it remains unclear whether deploying large-scale cell-free APs in legacy cellular networks can effectively boost communication performance. Besides, the realization of a cell-free network is considered to be a gradual long-term evolutionary process in which APs will be incrementally introduced and form a hybrid communication network with the existing cellular base stations (BSs). Such a collaboration will bridge the gap between the established cellular network and the innovative cell-free network. Therefore, hybrid cellular and cell-free networks (HCCNs) emerge as a feasible solution for advancing cell-free network development, and it is worthwhile to further explore its performance limits. Different from heterogeneous networks or multipoint coordinated networks, the characterization of HCCNs needs to take both inter- and intra-layer collaboration into account. This paper presents a stochastic geometry-based HCCN model to analyze the distributions of signal and interference and reveal their mutual coupling. Specifically, in order to benefit the user equipments (UEs) from both the cellular BSs and the cell-free APs, a conjugate beamforming design is employed, and the aggregated signal is analyzed using moment matching. Then, the coverage probability of the hybrid network is characterized by deriving the Laplace transforms and their higher-order derivatives of interference components. Furthermore, the average achievable rate of the hybrid network over channel fading is derived based on the interference coupling analysis. Simulation results demonstrate that compared to traditional cellular networks, HCCN effectively narrows communication quality differences between different UEs and improves overall communication performance.

Intelligent reflecting surface (IRS) is a promising paradigm to reconfigure the wireless environment for enhanced communication coverage and quality. However, to compensate for the double pathloss effect, massive IRS elements are required, raising concerns on the scalability of cost and complexity. This paper introduces a new architecture of quasi-static IRS (QS-IRS), which tunes element phases via mechanical adjustment or manually re-arranging the array topology. A simple divide-and-assemble (DnA) approach is further proposed, which enables massive production/assembly of purely passive elements without diodes/controllers/bias networks, and thus is suitable for ultra low-cost and large-scale deployment to enhance long-term coverage. To achieve this end, an IRS-aided area coverage problem is formulated, which explicitly considers the element radiation pattern (ERP), with the newly introduced shape masks for the mainlobe, and the sidelobe constraints to reduce energy leakage. An alternating optimization (AO) algorithm based on the difference-of-convex (DC) and successive convex approximation (SCA) procedure is proposed, which achieves shaped beamforming with power gains close to that of the joint optimization algorithm, but with significantly reduced computational complexity.

Aerial base stations (ABSs) mounted on unmanned aerial vehicles (UAVs) are capable of extending wireless connectivity to ground users (GUs) across a variety of scenarios. However, it is an NP-hard problem with exponential complexity in M and N, in order to maximize the coverage rate (CR) of M GUs by jointly placing N ABSs with limited coverage range. The complexity of the problem escalates in environments where the signal propagation is obstructed by localized obstacles such as buildings, and is further compounded by the dynamic GU positions. In response to these challenges, this paper focuses on the optimization of a multi-ABS movement problem, aiming to improve the mean CR for mobile GUs within a site-specific environment. Our proposals include 1) introducing the concept of global connectivity map (GCM) which contains the connectivity information between given pairs of ABS/GU locations; 2) partitioning the ABS movement problem into ABS placement sub-problems and formulate each sub-problem into a binary integer linear programming (BILP) problem based on GCM; 3) and proposing a fast online algorithm to execute (one-pass) projected stochastic subgradient descent within the dual space to rapidly solve the BILP problem with near-optimal performance. Numerical results demonstrate that our proposed method achieves a high CR performance close to the upper bound obtained by the open-source solver (SCIP), yet with significantly reduced running time. Moreover, our method also outperforms common benchmarks in the literature such as the K-means initiated evolutionary algorithm or the ones based on deep reinforcement learning (DRL), in terms of CR performance and/or time efficiency.

Affine Frequency Division Multiplexing (AFDM) is a brand new chirp-based multi-carrier (MC) waveform for high mobility communications, with promising advantages over Orthogonal Frequency Division Multiplexing (OFDM) and other MC waveforms. Existing AFDM research focuses on wireless communication at high carrier frequency (CF), which typically considers only Doppler frequency shift (DFS) as a result of mobility, while ignoring the accompanied Doppler time scaling (DTS) on waveform. However, for underwater acoustic (UWA) communication at much lower CF and propagating at speed of sound, the DTS effect could not be ignored and poses significant challenges for channel estimation. This paper analyzes the channel frequency response (CFR) of AFDM under multi-scale multi-lag (MSML) channels, where each propagating path could have different delay and DFS/DTS. Based on the newly derived input-output formula and its characteristics, two new channel estimation methods are proposed, i.e., AFDM with iterative multi-index (AFDM-IMI) estimation under low to moderate DTS, and AFDM with orthogonal matching pursuit (AFDM-OMP) estimation under high DTS. Numerical results confirm the effectiveness of the proposed methods against the original AFDM channel estimation method. Moreover, the resulted AFDM system outperforms OFDM as well as Orthogonal Chirp Division Multiplexing (OCDM) in terms of channel estimation accuracy and bit error rate (BER), which is consistent with our theoretical analysis based on CFR overlap probability (COP), mutual incoherent property (MIP) and channel diversity gain under MSML channels.

Intelligent Reflecting Surface (IRS) is a promising technology for next generation wireless networks. Despite substantial research in IRS-aided communications, the assumed antenna and channel models are typically simplified without considering site-specific characteristics, which in turn critically affect the IRS deployment and performance in a given environment. In this paper, we first investigate the link-level performance of active or passive IRS taking into account the IRS element radiation pattern (ERP) as well as the antenna radiation pattern of the access point (AP). Then the network-level coverage performance is evaluated/optimized in site-specific multi-building scenarios, by properly deploying multiple IRSs on candidate building facets to serve a given set of users or Points of Interests (PoIs). The problem is reduced to an integer linear programming (ILP) based on given link-level metrics, which is then solved efficiently under moderate network sizes. Numerical results confirm the impact of AP antenna/IRS element pattern on the link-level performance. In addition, it is found that active IRSs, though associated with higher hardware complexity and cost, significantly improve the site-specific network coverage performance in terms of average ergodic rate and fairness among the PoIs as well as the range of serving area, compared with passive IRSs that have a much larger number of elements.

Unmanned aerial vehicles (UAVs) can be utilized as aerial base stations (ABSs) to provide wireless connectivity for ground users (GUs) in various emergency scenarios. However, it is a NP-hard problem with exponential complexity in M and N, in order to maximize the coverage rate of M GUs by jointly placing N ABSs with limited coverage range. The problem is further complicated when the coverage range becomes irregular due to site-specific blockages (e.g., buildings) on the air-ground channel, and/or when the GUs are moving. To address the above challenges, we study a multi-ABS movement optimization problem to maximize the average coverage rate of mobile GUs in a site-specific environment. The Spatial Deep Learning with Multi-dimensional Archive of Phenotypic Elites (SDL-ME) algorithm is proposed to tackle this challenging problem by 1) partitioning the complicated ABS movement problem into ABS placement sub-problems each spanning finite time horizon; 2) using an encoder-decoder deep neural network (DNN) as the emulator to capture the spatial correlation of ABSs/GUs and thereby reducing the cost of interaction with the actual environment; 3) employing the emulator to speed up a quality-diversity search for the optimal placement solution; and 4) proposing a planning-exploration-serving scheme for multi-ABS movement coordination. In particular, the locations of ABSs/GUs are converted into grid pattern representations, whose dimension and associated DNN complexity are invariant with arbitrarily large M and/or N. Moreover, the virtual emulator-planning combined with the actual site-deployment effectively compensates for the prediction errors due to model approximation. Numerical results demonstrate that the proposed approach significantly outperforms the benchmark Deep Reinforcement Learning (DRL)-based method and other two baselines in terms of average coverage rate, training time and/or sample efficiency. Moreover, with one-time training, our proposed method can be applied in scenarios where the number of ABSs/GUs dynamically changes on site and/or with different/varying GU speeds, which is thus more robust and flexible compared with conventional DRL-based methods.

Intelligent reflecting surface (IRS) is regarded as a revolutionary paradigm that can reconfigure the wireless propagation environment for enhancing the desired signal and/or weakening the interference, and thus improving the quality of service (QoS) for communication systems. In this paper, we propose an IRS-aided sectorized BS design where the IRS is mounted in front of a transmitter (TX) and reflects/reconfigures signal towards the desired user equipment (UE). Unlike prior works that address link-level analysis/optimization of IRS-aided systems, we focus on the system-level three-dimensional (3D) coverage performance in both single-/multiple-cell scenarios. To this end, a distance/angle-dependent 3D channel model is considered for UEs in the 3D space, as well as the non-isotropic TX beam pattern and IRS element radiation pattern (ERP), both of which affect the average channel power as well as the multi-path fading statistics. Based on the above, a general formula of received signal power in our design is obtained, along with derived power scaling laws and upper/lower bounds on the mean signal/interference power under IRS passive beamforming or random scattering. Numerical results validate our analysis and demonstrate that our proposed design outperforms the benchmark schemes with fixed BS antenna patterns or active 3D beamforming. In particular, for aerial UEs that suffer from strong inter-cell interference, the IRS-aided BS design provides much better QoS in terms of the ergodic throughput performance compared with benchmarks, thanks to the IRS-inherent double pathloss effect that helps weaken the interference.

Emerged as a promising solution for future wireless communication systems, intelligent reflecting surface (IRS) is capable of reconfiguring the wireless propagation environment by adjusting the phase-shift of a large number of reflecting elements. To quantify the gain achieved by IRSs in the radio frequency (RF) powered Internet of Things (IoT) networks, in this work, we consider an IRS-assisted cellular-based RF-powered IoT network, where the cellular base stations (BSs) broadcast energy signal to IoT devices for energy harvesting (EH) in the charging stage, which is utilized to support the uplink (UL) transmissions in the subsequent UL stage. With tools from stochastic geometry, we first derive the distributions of the average signal power and interference power which are then used to obtain the energy coverage probability, UL coverage probability, overall coverage probability, spatial throughput and power efficiency, respectively. With the proposed analytical framework, we finally evaluate the effect on network performance of key system parameters, such as IRS density, IRS reflecting element number, charging stage ratio, etc. Compared with the conventional RF-powered IoT network, IRS passive beamforming brings the same level of enhancement in both energy coverage and UL coverage, leading to the unchanged optimal charging stage ratio when maximizing spatial throughput.

LoRa networks are pivotally enabling Long Range connectivity to low-cost and power-constrained user equipments (UEs) in a wide area, whereas a critical issue is to effectively allocate wireless resources to support potentially massive UEs while resolving the prominent near–far fairness issue, which is challenging due to the lack of tractable analytical model and the practical requirement for low-complexity and low-overhead design. Leveraging on stochastic geometry, especially the Poisson rain model, we derive (semi-) closed-form formulas for the aggregate interference distribution, packet success probability, and hence, system throughput in both single-cell and multicell setups with frequency reuse, by accounting for channel fading, random UE distribution, partial packet overlapping, and/or multi-gateway (GW) packet reception. The analytical formulas require only average channel statistics and spatial UE distribution, which enable tractable network performance evaluation and incubate our proposed iterative balancing (IB) method that quickly yields high-level policies of joint spreading factor (SF) allocation, power control, and duty-cycle adjustment for gauging the average max–min UE throughput or supported UE density with rate requirements. Numerical results validate the analytical formulas and the effectiveness of our proposed optimization scheme, which greatly alleviate the near–far fairness issue and reduces the spatial power consumption, while significantly improving the cell-edge throughput as well as the spatial (sum) throughput for the majority of UEs, by adapting to the UE/GW densities.

Unmanned aerial vehicles (UAVs), especially fixed-wing ones that withstand strong winds, have great potential for oceanic exploration and research. This paper studies a UAV-aided maritime data collection system with a fixed-wing UAV dispatched to collect data from marine buoys. We aim to minimize the UAV’s energy consumption in completing the task by jointly optimizing the communication time scheduling among the buoys and the UAV’s flight trajectory subject to wind effect. The conventional successive convex approximation (SCA) method can provide efficient sub-optimal solutions for collecting small/moderate data volume, whereas the solution heavily relies on trajectory initialization and has not explicitly considered wind effect, while the computational/trajectory complexity both become prohibitive for the task with large data volume. To this end, we propose a new cyclical trajectory design framework with tailored initialization algorithm that can handle arbitrary data volume efficiently, as well as a hybrid offline-online (HO2) design that leverages convex stochastic programming (CSP) offline based on wind statistics, and refines the solution by adapting online to real-time wind velocity. Numerical results show that our optimized trajectory can better adapt to various setups with different target data volume and buoys’ topology as well as various wind speed/direction/variance compared with benchmark schemes. In particular, our proposed HO2 design can effectively adapt to random wind variations with feasible and robust online operation, and proactively exploit the wind for further energy savings in both single-buoy and multi-buoy scenarios.

Intelligent reflecting surface (IRS) is a new and revolutionary technology capable of reconfiguring the wireless propagation environment by controlling its massive low-cost pas-sive reflecting elements. Different from prior works that focus on optimizing IRS reflection coefficients or single-IRS placement, we aim to maximize the minimum throughput of a single-cell mul-tiuser system aided by multiple IRSs, by joint multi-IRS placement and power control at the access point (AP), which is a mixed-integer non-convex problem with drastically increased complexity with the number of IRSs/users. To tackle this challenge, a ring-based IRS placement scheme is proposed along with a power control policy that equalizes the users' non-outage probability. An efficient searching algorithm is further proposed to obtain a close-to-optimal solution for arbitrary number of IRSs/rings. Numerical results validate our analysis and show that our proposed scheme significantly outperforms the benchmark schemes without IRS and/or with other power control policies. Moreover, it is shown that the IRSs are preferably deployed near AP for coverage range extension, while with more IRSs, they tend to spread out over the cell to cover more and get closer to target users.

Intelligent reflecting surface (IRS) is a new and promising paradigm to substantially improve the spectral and energy efficiency of wireless networks, by constructing favorable communication channels via tuning massive low-cost passive reflecting elements. Despite recent advances in the link-level performance optimization for various IRS-aided wireless systems, it still remains an open problem whether the large-scale deployment of IRSs in wireless networks can be a cost-effective solution to achieve their sustainable capacity growth in the future. To address this problem, we study in this paper a new hybrid wireless network comprising both active base stations (BSs) and passive IRSs, and characterize its achievable spatial throughput in the downlink as well as other pertinent key performance metrics averaged over both channel fading and random locations of the deployed BSs/IRSs therein based onstochastic geometry. Compared to prior works on characterizing the performance of wireless networks with active BSs only, our analysis needs to derive the power distributions of both the signal and interference reflected by distributed IRSs in the network under spatially correlated channels, which exhibit channel hardening effects when the number of IRS elements becomes large. Extensive numerical results are presented to validate our analysis and demonstrate the effectiveness of deploying distributed IRSs in enhancing the hybrid network throughput against the conventional network without IRS, whichsignificantly boosts the signal powerbut results in onlymarginally increased interferencein the network. Moreover, it is unveiled that there exists anoptimal IRS/BS density ratiothat maximizes the hybrid network throughput subject to a total deployment cost given their individual costs, while the conventional network without IRS (i.e., zero IRS/BS density ratio) is generally suboptimal in terms of throughput per unit cost.

Unmanned aerial vehicles (UAVs), especially fixed-wing ones that withstand strong winds, have great potential for oceanic exploration and research. This paper studies a UAVaided maritime data collection system with a fixed-wing UAV dispatched to collect data from marine buoys. We aim to minimize the UAV's energy consumption in completing the task by jointly optimizing the communication time scheduling among the buoys and the UAV's flight trajectory subject to wind effect, which is a non-convex problem and difficult to solve optimally. Existing techniques such as the successive convex approximation (SCA) method provide efficient sub-optimal solutions for collecting small/moderate data volume, whereas the solution heavily relies on the trajectory initialization and has not explicitly considered the wind effect, while the computational complexity and resulted trajectory complexity both become prohibitive for the task with large data volume. To this end, we propose a new cyclical trajectory design framework that can handle arbitrary data volume efficiently subject to wind effect. Specifically, the proposed UAV trajectory comprises multiple cyclical laps, each responsible for collecting only a subset of data and thereby significantly reducing the computational/trajectory complexity, which allows searching for better trajectory initialization that fits the buoys' topology and the wind. Numerical results show that the proposed cyclical scheme outperforms the benchmark oneflight-only scheme in general. Moreover, the optimized cyclical 8-shape trajectory can proactively exploit the wind and achieve lower energy consumption compared with the case without wind.

Unmanned aerial vehicles (UAVs) can be utilized as aerial base stations (ABSs) to assist terrestrial infrastructure for keeping wireless connectivity in various emergency scenarios. To maximize the coverage rate of N ground users (GUs) by jointly placing multiple ABSs with limited coverage range is known to be a NP-hard problem with exponential complexity in N. The problem is further complicated when the coverage range becomes irregular due to site-specific blockage (e.g., buildings) on the air-ground channel in the 3-dimensional (3D) space. To tackle this challenging problem, this paper applies the Deep Reinforcement Learning (DRL) method by 1) representing the state by a coverage bitmap to capture the spatial correlation of GUs/ABSs, whose dimension and associated neural network complexity is invariant with arbitrarily large N; and 2) designing the action and reward for the DRL agent to effectively learn from the dynamic interactions with the complicated propagation environment represented by a 3D Terrain Map. Specifically, a novel two-level design approach is proposed, consisting of a preliminary design based on the dominant line-of-sight (LoS) channel model, and an advanced design to further refine the ABS positions based on site-specific LoS/non-LoS channel states. The double deep Q-network (DQN) with Prioritized Experience Replay (Prioritized Replay DDQN) algorithm is applied to train the policy of multi-ABS placement decision. Numerical results show that the proposed approach significantly improves the coverage rate in complex environment, compared to the benchmark DQN and K-means algorithms.

With growing popularity, unmanned aerial vehicles (UAVs) are pivotally extending conventional terrestrial Internet of Things (IoT) into the sky. To enable high-performance two-way communications of UAVs with their ground pilots/users, cellular network-connected UAV has drawn significant interests recently. Among others, an important issue is whether the existing cellular network, designed mainly for terrestrial users, is also able to effectively cover the new UAV users in the three-dimensional (3-D) space for both uplink and downlink communications. Such 3-D coverage analysis is challenging due to the unique air-ground channel characteristics, the resulted interference issue with terrestrial communication, and the nonuniform 3-D antenna gain pattern of ground base station (GBS) in practice. Particularly, high-altitude UAV often possesses a high probability of line-of-sight (LoS) channels with a large number of GBSs, while their random binary (LoS/non-LoS) channel states and (on/off) activities give rise to exponentially large number of discrete UAV-GBS association/interference states, rendering coverage analysis more difficult. This paper presents a new 3-D system model to incorporate UAV users and proposes an analytical framework to characterize their uplink/downlink 3-D coverage performance. To tackle the above exponential complexity, we introduce a generalized Poisson multinomial (GPM) distribution to model the discrete interference states, and a novel lattice approximation (LA) technique to approximate the nonlattice GPM variable and obtain the interference distribution efficiently with high accuracy. The 3-D coverage analysis is validated by extensive numerical results, which also show effects of key system parameters, such as cell loading factor, GBS antenna downtilt, UAV altitude, and antenna beamwidth.

In conventional terrestrial cellular networks, mobile terminals (MTs) at the cell edge often pose a performance bottleneck due to their long distances from the serving ground base station (GBS), especially in the hotspot period when the GBS is heavily loaded. This paper proposes a new hybrid network architecture that leverages use of unmanned aerial vehicle (UAV) as an aerial mobile base station, which flies cyclically along the cell edge to offload data traffic for cell-edge MTs. We aim to maximize the minimum throughput of all MTs by jointly optimizing the UAV's trajectory, bandwidth allocation, and user partitioning. We first consider orthogonal spectrum sharing between the UAV and GBS, and then extend to spectrum reuse where the total bandwidth is shared by both the GBS and UAV with their mutual interference effectively avoided. Numerical results show that the proposed hybrid network with optimized spectrum sharing and cyclical multiple access design significantly improves the spatial throughput over the conventional GBS-only network; while the spectrum reuse scheme provides further throughput gains at the cost of slightly higher complexity for interference control. Moreover, compared with the conventional small-cell offloading scheme, the proposed UAV offloading scheme is shown to outperform in terms of throughput, besides saving the infrastructure cost.

In conventional terrestrial cellular systems, mobile terminals (MTs) at the cell edge often pose the performance bottleneck due to their long distance from the ground base station (GBS), especially in hotspot areas. This paper proposes a new hybrid network architecture by leveraging the use of unmanned aerial vehicle (UAV) as an aerial mobile base station, which flies cyclically along the cell edge to serve the cell-edge MTs and help offloading the traffic from the GBS. To achieve user fairness, we aim to maximize the minimum throughput of all MTs in a single cell by jointly optimizing the UAV's trajectory, as well as the bandwidth allocation and user partitioning between the UAV and GBS. Numerical results show that the proposed hybrid network with optimized spectrum sharing and cyclical multiple access design significantly improves the spatial throughput over the conventional cellular network with the GBS only.

This paper uses a multi-channel spatial Aloha model to describe a distributed autonomous wireless network where a group of transmit-receive pairs (users) share multiple collision channels via slotted-Aloha-like random access. The design objective is to enable each autonomous user i to select a channel c_i and decide a medium access probability (MAP) q_i to improve its throughput, while providing a certain degree of fairness among the users. Game theoretic approaches are applied, where each user i is a player who chooses the strategy (c_i,q_i) to improve its own throughput. To search for a Nash Equilibrium (NE), a Multi-Leader Stackelberg Game (MLSG) is formulated to iteratively obtain a solution on each dimension of the (c_i,q_i) strategy. Initially, multiple Stackelberg leaders are elected to manage the MAPs of all players. Then under the resulting MAP profile, each player iteratively chooses its channel to improve its throughput. An Oscillation Resolving Mechanism (ORM) is further proposed to stabilize the design in some special cases where the operating points of some players in a local region would oscillate between the two dimensions of the myopic search. Compared to existing methods of pre-allocating MAPs, the MLSG game further improves the overall network throughput by iteratively tuning the MAPs toward max-min throughput in each subnet. Simulation results show that the MLSG game gradually improves the total throughput until reaching a NE, which also provides good throughput fairness for the players.

Aloha games with spatial reuse study the interactions among a group of selfish transmit-receive pairs which share a common collision channel using slotted-Aloha-like protocols. These Tx-Rx pairs are allowed to reuse the channel if they cause negligible interference to each other. Our work in [1] has proved the existence of a Least Fixed Point (LFP) which is the most energy-efficient operating point as well as the unique Nash Equilibrium (NE) in such games. Based on the earlier derived conditions for the stability of this NE and the way to converge to this NE, it is possible to design a self-adaptive algorithm for the players to self-adjust their target rates based on a set of pre-installed rules so that the network always achieves Pareto optimal bandwidth utilization. In this paper, we implement such an algorithm in a fully distributed manner, which requires no information exchange among the players. Each player repeatedly measures its current throughput and uses the measured value to make myopic best response to the current channel idle rate. Our simulations show that the system indeed achieves close to Pareto optimal performance while guaranteeing a certain degree of fairness. The algorithm is robust and can handle various practical issues such as the dynamic arrival/departure of players, parameter estimation errors, etc.

Aloha games study the transmission probabilities of a group of non-cooperative users which share a channel to transmit via the slotted Aloha protocol. This paper extends the Aloha games to spatial reuse scenarios, and studies the system equilibrium and performance. Specifically, fixed point theory and order theory are used to prove the existence of a least fixed point as the unique Nash equilibrium (NE) of the game and the optimal choice of all players. The Krasovskii's method is used to construct a Lyapunov function and obtain the conditions to examine the stability of the NE. Simulations show that the theories derived are applicable to large-scale distributed systems of complicated network topologies. An empirical relationship between the network connectivity and the achievable total throughput is finally obtained through simulations.