Closed-form Expressions For Coverage Probability Research Articles

Federated Learning in Small-Cell Networks: Stochastic Geometry-Based Analysis on the Required Base Station Density.

Recently, federated learning (FL) has been receiving great attention as an effective machine learning method to avoid the security issue in raw data collection, as well as to distribute the computing load to edge devices. However, even though wireless communication is an essential component for implementing FL in edge networks, there have been few works that analyze the effect of wireless networks on FL. In this paper, we investigate FL in small-cell networks where multiple base stations (BSs) and users are located according to a homogeneous Poisson point process (PPP) with different densities. We comprehensively analyze the effects of geographic node deployment on the model aggregation in FL on the basis of stochastic geometry-based analysis. We derive the closed-form expressions of coverage probability with tractable approximations and discuss the minimum required BS density for achieving a target model aggregation rate in small-cell networks. Our analysis and simulation results provide insightful information for understanding the behaviors of FL in small-cell networks; these can be exploited as a guideline for designing the network facilitating wireless FL.

Spectrum Sharing Between High Altitude Platform Network and Terrestrial Network: Modeling and Performance Analysis

Achieving seamless global coverage is one of the ultimate goals of space-air-ground integrated network, as a part of which High Altitude Platform (HAP) network can provide wide-area coverage. However, deploying a large number of HAPs will lead to severe congestion of existing frequency bands. Spectrum sharing improves spectrum utilization. The coverage performance improvement and interference caused by spectrum sharing need to be investigated. To this end, this paper analyzes the performance of spectrum sharing between HAP network and terrestrial network. We firstly generalize the Poisson Point Process (PPP) to curves, surfaces and manifolds to model the distribution of terrestrial Base Stations (BSs) and HAPs. Then, the closed-form expressions for coverage probability of HAP network and terrestrial network are derived based on differential geometry and stochastic geometry. We verify the accuracy of closed-form expressions by Monte Carlo simulation. The results show that HAP network has less interference to terrestrial network. Low height and suitable deployment density can improve the coverage probability and transmission capacity of HAP network.

Fairness driven performance analysis for 3-D Poisson Voronoi cell

The requirement of excellent anywhere–anytime data transmission service in future wireless network encourages us to reconsider the fairness among different types of users. To this end, the three-dimensional Poisson point process (PPP) model-based closed-form expressions of coverage probability for both cell-edge user (CEU) and cell inner user (CIU) under multi-user multiple-input multiple-output (MIMO) are derived. It is found that the spectral efficiency of CEU is about 30% of that of CIU under single user scenario. Moreover, when the number of users equals to that of base station (BS) antennas, the difference of coverage probability between CIU and CEU decreases with the number of BS antennas for large signal-to-interference ratio threshold. In addition, for the fixed number of users case, an inverted U-shaped relationship (thereby resulting in a worst case) between the fairness among CEU and CIU, and the number of BS antennas is detected. The impact of massive MIMO on the fairness under the metric of spectral efficiency is also discussed.

On the Optimal Base-Station Height in mmWave Small-Cell Networks Considering Cylindrical Blockage Effects

Small-cell networks (SCNs), especially those operating in millimeter-wave bands, are sensitive to blockages. In this letter, we develop a three-dimensional (3D) SCN model considering blockages to investigate the impact of base-station (BS) height, BS density and blockage density on the downlink coverage probability. More specifically, we model the blockages as cylinders whose locations follow a Poisson point process and model the locations of BSs as a Poisson hole process. We assume that all the BSs are of the same height and the blockage height follows an exponential distribution. Based on the 3D SCN model, we derive the exact integral expression of coverage probability for general SCNs and the closed-form expression of coverage probability for ultra-dense SCNs. Our analytical results are verified to be reliable through simulations. The numerical results quantify the impact of the blockage density and the BS height on the coverage probability. For a small blockage density, elevated BSs always degrade the coverage probability, while the coverage probability first increases and then decreases with the BS height when the blockage density becomes sufficiently large.

Mobility-Aware Access Strategy in Multi-User HetNets

For the user moving with high velocity in heterogeneous networks (HetNets), two aspects that cause performance degradation should be considered, one is the channel aging, the other is the handoffs. Nevertheless, only one of these two aspects is involved for performance evaluation in most of researches. In this letter, the optimal access scheme determination is investigated considering these two aspects caused by user mobility. Firstly, the vertical and horizontal handoff probability in HetNets are analyzed. Then the closed-form expressions of coverage probability considering the channel aging for both open access and closed access are derived. Combining the handoff probability and the coverage probability, a fixed data rate scheme is adopted to determine the optimal access strategy. Numerical results verify our analysis, and show that open access performs better than closed access in dense femto-tier base stations (FBSs), whereas closed access is suggested in relatively sparse FBSs. Further, for a large bias factor, the optimal access strategy depends on both the signal-to-interference ratio threshold and the user velocity.

Coverage and capacity analysis of relay-based device-to-device communications underlaid cellular networks

Coverage and capacity are the key parameters of 4G and beyond wireless networks. These parameters of Long Term Evolution Advanced (LTE-A) networks can be greatly enhanced by enabling device-to-device (D2D) communication. In this paper, full duplex amplify and forward (FDAF) relay nodes (RNs) have been introduced to assisting cellular and D2D communications. The coverage probability (CP) and transmission capacity (TC) for both the cellular and D2D communications have been analyzed with FDAF relay based network. The D2D users can communicate directly or via relaying with FDAF RNs. Cellular users, D2D users and RNs in the network have been modeled using homogeneous spatial poisson point process (SPPP). The closed-form expressions of CP and TC for cellular as well as D2D communications have been derived by using stochastic geometry. The pairing of D2D users is decided by the shortest distance reduced path loss and formed pair either directly or via RN assistance. The approximate complementary cumulative distribution function (CCDF) of the signal to interference plus noise ratio (SINR) for both the cellular users and the D2D users have been derived. The closed form expressions of CP and TC show that coverage and capacity of both the cellular and D2D communications are influenced by various parameters such as D2D user density, relay node density and the distance of D2D pair. Results show the improvement of CP and TC for cellular and D2D communications with the help of RNs.

Coverage analysis of cache-enabled small cell networks with stochastic geometry methods

Caching popular content in the storage of small cells is deemed as an efficient way to decrease latency, offload backhaul and satisfy user's demands. In order to investigate the performance of cache-enabled small cell networks, coverage probability is studied in both single-point transmission and cooperative multipoint (CoMP) transmission scenarios. Meanwhile, the caching distribution modeled as Zipf and uniform distribution are both considered. Assuming that small base stations (SBSs) are distributed as a homogeneous Poisson point process (HPPP), the closed-form expressions of coverage probability are derived in different transmission cases. Simulation results show that CoMP transmission achieves a higher coverage probability than that of single-point transmission. Furthermore, Zipf distribution-based caching is more preferable than uniform distribution-based caching in terms of coverage probability.

Coverage probability analysis for Full-Duplex relay aided Device-to-Device communications networks

The coverage probability of both the cellular users and the Device-to-Device (D2D) users are analyzed. We assume that the cellular users are able to communication with the Base Station (BS) either by relying on the assistance of Full-Duplex (FD) mode relays or via direct user-to-BS links with high-enough Signal-to-Interference-plus-Noise-Ratio (SINR). Note that the FD-mode devices are capable of simultaneously operating in two modes, i.e. the D2D mode and the cooperative relay mode, with the sum power consumption at these devices kept constant. The closed-form expressions for coverage probability of both tier users are derived. After that, numerical analyses are provided, showing that the coverage probability of the both the cellular and the D2D users can be substantially influenced by a variety of parameters, including the power allocation factor of the relays, the density of users, and the self-interference imposed on the FD mode relays, etc. Furthermore, in the D2D enabled networks, it is shown that the FD relay aided transmission is beneficial to enhancing the coverage probability of the cellular users if the target SINR is lower than 5 dB.