Meta Distribution Research Articles

Meta Distribution Analysis in Finite Blocklength Communications

Meta Distribution Analysis in Finite Blocklength Communications

MetaFed: Federated Learning Among Federations With Cyclic Knowledge Distillation for Personalized Healthcare.

Federated learning (FL) has attracted increasing attention to building models without accessing raw user data, especially in healthcare. In real applications, different federations can seldom work together due to possible reasons such as data heterogeneity and distrust/inexistence of the central server. In this article, we propose a novel framework called MetaFed to facilitate trustworthy FL between different federations. obtains a personalized model for each federation without a central server via the proposed cyclic knowledge distillation. Specifically, treats each federation as a meta distribution and aggregates knowledge of each federation in a cyclic manner. The training is split into two parts: common knowledge accumulation and personalization. Comprehensive experiments on seven benchmarks demonstrate that without a server achieves better accuracy compared with state-of-the-art methods e.g., 10 %+ accuracy improvement compared with the baseline for physical activity monitoring dataset (PAMAP2) with fewer communication costs. More importantly, shows remarkable performance in real-healthcare-related applications.

Finite Blocklength Regime Performance of Downlink Large Scale Networks

Some emerging 5G and beyond use-cases impose stringent latency constraints, which necessitates a paradigm shift towards finite blocklength performance analysis. In contrast to Shannon capacity-achieving codes, the codeword length in the finite blocklength regime (FBR) is a critical design parameter that imposes an intricate tradeoff between delay, reliability, and information coding rate. In this context, this paper presents a novel mathematical analysis to characterize the performance of large-scale downlink networks using short codewords. Theoretical achievable rates, outage probability, and reliability expressions are derived using the finite blocklength coding theory in conjunction with stochastic geometry, and compared to the performance in the asymptotic regime (AR). Achievable rates under practical modulation schemes as well as multilevel polar coded modulation (MLPCM) are investigated. Numerical results provide theoretical performance benchmarks, highlight the potential of MLPCM in achieving close to optimal performance with short codewords, and confirm the discrepancy between the performance in the FBR and that predicted by analysis in the AR. Finally, the meta distribution of the coding rate is derived, providing the percentiles of users that achieve a predefined target rate in a network.

Communication-Computation-Aware User Association in MEC HetNets: A Meta-Analysis

The stochastic geometry-based modeling and analysis of large-scale mobile edge computing (MEC) networks are vital for the effective configuration of MEC networks. In this paper, we develop a meta-analytical framework for MEC-enabled heterogeneous networks with the communication-computation-aware (CCA) user association mechanism. Compared with the communication-based user association mechanisms in most existing works, the CCA user association mechanism can capture the impacts of network computation capability on the association process between the user and MEC access point, at the expense of dealing with the more complex coupling of communication and computing. Given the need for interference characterization, we first derive the essential prerequisite quantities (i.e., per-tier association probability, link distance distribution, interferer process intensity, etc.) to represent the computation-dependent interference model. Further, the moment and the meta distribution of the task success offloading probability are derived, based on which we investigate the task execution latency performance, including the communication latency, local computing latency, and edge computing latency. By theoretical analysis and simulation results, it is demonstrated that the proposed analytical framework can provide accurate fine-grained network information for the MEC-enabled HetNets. Moreover, we elaborate on the impacts of the edge computation capability on the network performance and reveal important tradeoffs of the performance metrics.

Assessing the Spectrum Needs for Network-Wide Ultra-Reliable Communication With Meta Distributions

Identifying and assessing the spectrum needs for ultra-reliable communication are key to enabling ultra-reliable communication services in the next generation of mobile networks. This article proposes a framework to assess the spectrum required to support ultra-reliable communication services network-wide. Using meta distributions, we derive expressions that reveal a simple relationship between spectrum needs and reliability requirements. Broadly speaking, each “nine” in reliability (e.g., five-nines in 99.999%) maps onto one order of magnitude of additional bandwidth. Numerical evaluations indicate that the bandwidth required for ultra-reliable communication can be up to hundreds of gigahertz, beyond what is available in today’s networks.

A Dominant Interferer Plus Mean Field-Based Approximation for SINR Meta Distribution in Wireless Networks

This paper proposes a novel approach for computing the meta distribution of the signal-to-interference-plus-noise ratio (SINR) for the downlink transmission in a wireless network with Rayleigh fading. The novel approach relies on an approximation mix of exact and mean-field analysis of interference (dominant interferer-based approximation) to reduce the complexity of analysis and enhance tractability. In particular, the proposed approximation omits the need to compute the first or the second moment of the SINR that is used in the beta approximation typically adopted in the literature but requires of computing the joint distance distributions. We first derive the proposed approximation based on a Poisson point process (PPP) network with a standard path-loss and Rayleigh fading and then illustrate its accuracy and operability in another four widely used point processes: Poisson bipolar network, Matérn cluster process (MCP), <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -tier PPP and Poisson line Cox process (PLCP). Specifically, we obtain the SINR meta distribution for PLCP networks for the first time. Even though the proposed approximation looks simple but it shows good matching in comparison to the popular beta approximation as well as the Monte-Carlo simulations, which opens the door to adopting this approximation in more advanced network architectures.

Spatio-Temporal Analysis of D2D Networks in Finite Areas

This correspondence investigates the spatio-temporal performance of device-to-device (D2D) networks in finite areas. The locations of transmitters are modeled as a binomial point process with dedicated receivers at fixed distance. The evolution of discrete-time packets at each D2D pair is modeled as a Bernoulli process. Using the tools from stochastic geometry and queuing theory, we analyze the interactions between the spatial locations of nodes and their temporal traffic dynamic. We first derive the distance-dependent meta distribution of signal-to-interference-plus-noise ratio for both reference receiver and random receiver, based on which the packet throughput and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -stability region are obtained. Simulations validate the analytical results and reveal the existence of an optimal number of D2D pairs that maximizes the packet throughput.

On the Uplink SINR Meta Distribution of UAV-Assisted Wireless Networks

This letter studies the signal-to-interference-plus-noise (SINR) meta distribution of uplink transmission of UAV-enabled wireless networks with inversion power control. Within a framework of stochastic geometry, the Matern cluster process (MCP) is used to model the locations of users and UAVs. Conditional success probability and moments are derived to compute the exact expression and moment matching approximation of SINR meta distribution (beta approximation). Specifically, the effect of the power control compensation factor and UAV altitude are studied. Our numerical results show that UAV altitude has a higher impact on the system reliability than transmit power at low values of SINR threshold since users benefit more from establishing line-of-sight (LoS) links with UAVs.

The Meta Distribution of SINR in UAV-Assisted Cellular Networks

Mounting compact and lightweight base stations on unmanned aerial vehicles (UAVs) is a cost-effective and flexible solution to provide seamless coverage on the existing terrestrial networks. While the coverage probability in UAV-assisted cellular networks has been widely investigated, it provides only the first-order statistic of signal-to-interference-plus-noise ratio (SINR). In this paper, to analyze high-order statistics of SINR and characterize the disparity among individual links, we provide a meta distribution (MD)-based analytical framework for UAV-assisted cellular networks, in which the probabilistic line-of-sight channel and realistic antenna pattern are taken into account for air-to-ground transmissions. To accurately characterize the interference from UAVs, we relax the widely applied uniform off-boresight angle (OBA) assumption and derive the exact distribution of OBA. Using stochastic geometry, for both steerable and vertical antenna scenarios, we obtain mathematical expressions for the moments of condition success probability, the SINR MD, and the mean local delay. Moreover, we study the asymptotic behavior of the moments as network density approaches infinity. Numerical results validate the tightness of the theoretical results and show that the uniform OBA assumption underestimates the network performance, especially in the regime of moderate altitude of UAV. We also show that when UAVs are equipped with steerable antennas, the network coverage and user fairness can be optimized simultaneously by carefully adjusting the UAV parameters.

Rate Meta Distribution of Downlink Base Station Cooperation for Cellular-Connected UAV Networks

This letter studies the downlink rate meta distribution of a typical UAV under base station (BS) cooperation in a cellular-connected UAV network. An analytical model is derived for the meta distribution of the downlink transmission rate of a typical UAV by using a standard beta distribution approximation, taking into account the LoS probability and Nakagami-m fading of a downlink. Based on the derived model, the impacts of relevant parameters on the rate meta distribution are investigated. The derived analytical model can be used to provide a reference for the setting of relevant parameters in the design of a BS cooperation strategy.

On the Deployment of Clustered Power Beacons in Random Wireless Powered Communication

Wireless powered communication (WPC) is able to provide wireless devices (WDs) practically infinite energy by using the radio frequency energy harvesting technique. The electricity of WDs for the wireless information transmission (WIT) is converted from the received electromagnetic signals of wireless energy transfer (WET). Power beacon (PB) is usually deployed as the dedicated energy source in WPC networks and the performance of WET is sensitive to the path-loss effect. Thus, both WET and WIT are significantly influenced by the locations of the PBs. To enable efficient transmission in WPC, this paper analytically investigates the impact of the PB deployment strategies on the WPC performance when WDs are clustered around the access points (APs). Specifically, we propose the PB deployment strategy based on the truncated Poisson cluster process (PCP) model. The distribution of PBs is correlated to the locations of WDs by choosing APs as their common parent points. Then, we derive the semi-closed form expressions for the energy outage probability and the transmission success probability. We further present the expressions of the meta distributions of WET and WIT, and investigate the proportion of the WDs in one cluster that achieves successful transmission while satisfying the reliability constraint. Moreover, the distance distribution between the WD and the intra-cluster PBs is analytically derived for the proposed correlated PCP model. By comparing the performance with other deployment strategies, it is shown that the preference of the PB deployment strategy depends on the PB density. The analytical and numerical results can provide insightful guidelines for designing practical WPC systems.

Performance Analysis of Location-based Base Station Cooperation for Cellular-Connected UAV Networks

This paper studies the downlink performance analysis of a Unmanned aerial vehicles (UAV) in a cellular-connected UAV network with a location-based base station (BS) cooperation strategy. In the network, a UAV in a non-cooperation area is provided its downlink by the closest ground BS (GBS) while a UAV in a cooperation area is provided its downlinks by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> closest GBSs. To more comprehensively measure the performance of BS cooperation, we use a refined metric, meta distribution, to reflect more fine-grained information on the transmission performance of a UAV in addition to traditional metrics, coverage probability and local delay. Correspondingly, we derive performance models for investigating the impacts of the BS cooperation level, UAV altitude, and GBS density on the coverage probability, meta distribution, and local delay of a UAV, taking account of the line-of-sight (LoS) probability of the downlink between a GBS and a UAV, and the small-scale fading of a channel following a Nakagami-m distribution. Simulation results show that the derived performance models are effective, and can be used to provide a theoretical reference for the design of a BS cooperation strategy for a cellular-connected UAV network.

Performance Analysis of Directional Ultra-Dense Networks with Dynamic Spectrum Partition Strategy

Intercell interference coordination (ICIC) plays a significant role in strengthening ultra-dense network (UDN) downlink coverage. From a statistical average perspective, a user is primarily interfered by its adjacent base station (BS), especially the second nearest BS. By modeling BSs equipped with directional antennas as a Poisson point process (PPP), this paper proposes a dynamic spectrum resource allocation strategy mainly about users’ service BS and its nearest interference BS, where the subchannel assigned by the typical (served) user is interlaced from the channel simultaneously occupied by users within the effective radiation range of its second nearest BS. To fully explore this scheme for directional networks, we develop analytical expressions in terms of success probability and ergodic rate for the typical user based on the techniques of stochastic geometry, taking into account the fading of directional BS radiation angle. Then, we derive the meta distribution of the signal-to-interference ratio (SIR) for capturing individual link performance changes of users. Simulations verify the correctness of numerical results, and it is revealed that this strategy is in favor of users alleviating interference from their second nearest BSs and the performance advantages of the proposed ICIC strategy are better than those of the traditional directional UDNs.

SINR Meta Distribution for mmWave Heterogeneous Networks Under Varying Queue Status: A Spatio-Temporal Analysis

A fine-grained analysis of network performance is crucial for system design. In this paper, we focus on the meta distribution of the signal-to-interference-plus-noise-ratio (SINR) in the mmWave heterogeneous networks where the base stations (BS) in each tier are modeled as a Poisson point process (PPP). By utilizing stochastic geometry and queueing theory, we characterize the spatial and temporal randomness while the special characteristics of mmWave communications, including different path loss laws for line-of-sight and non-line-of-sight links and directional beamforming, are incorporated into the analysis. We derive the moments of the conditional successful transmission probability (STP). By taking the temporal random arrival of traffic into consideration, an equation on the meta distribution is formulated and its solution is obtained in a recursive manner. The critical arrival rate for a fraction of the queues at the BSs to be stable is provided. In addition, the mean delay is obtained. The numerical results reveal the impact of the key network parameters, such as the blockage parameter, the bias factor, the number of antenna elements and the BS density, on the network performance. Specifically, offloading the users from the macro BS tier to the small BS tier by biasing can reduce the performance fluctuation while only causing a slight degradation of the overall network performance.

The Meta Distribution of Task Offloading in Stochastic Mobile Edge Computing Networks

The stochastic geometry modeling and analysis of mobile edge computing (MEC) networks contribute to the effective network configuration. Most prior works investigate the MEC network performance by spatial averaging the topological randomness, which can hide the differences among users and result in inaccurate analytical results. To address this limitation, an analytical framework is developed to study the meta distribution of the task offloading performance. We consider the Poisson MEC network where the users with dynamic task requests offload the tasks to the MEC server. Given the model, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$b$</tex-math></inline-formula> -th moment and the meta distribution of the success task offloading probability are first analyzed. Further, the exact yet convenient approximation of the MEC computing load is derived, based on which the edge computing delay is obtained. Our results demonstrate that the proposed meta-analytical framework allows tractable yet accurate analytical results, and provides additional fine-grained information about MEC-network planning.

An Analysis of Distributed Joint Spectrum Resource Allocation With Power Control in Ultra-Dense Cellular Networks

In the view of spatial statistical average, when users are associated with their nearest small base stations (SBSs), they are mainly interfered by their second closest SBSs, especially for edge users. To reduce inter-cell interference (ICI) caused by the second closest SBSs, a distributed joint spectrum resource allocation strategy with power control in the downlink of one-tier ultra-dense networks (UDNs) is proposed in this paper. According to the distance from users to their nearest SBSs, users are divided into inner users and edge users. We then try to make the subchannel randomly allocated so they be different from that of edge users of their second closest SBS. Meanwhile the transmission power of SBSs on different subchannels is adjusted. Using stochastic geometry we derive the analytical expressions of the meta distribution of signal-to-interference ratio (SIR) to obtain more fine-grained information such as the mean and variance of conditional success probability, the local delay. Furthermore, we revise and redefine the area spectrum efficiency (ASE) and energy efficiency (EE) to accurately evaluate the benefits. Compared with the traditional random resource allocation strategy, which does not exploit resource allocation and interference coordination scheme, the proposed strategy can balance the performance of users and improve the whole network EE. Our analytical results are validated through simulation.

Coverage and Meta Distribution Analysis in Ultra-Dense Cellular Networks With Directional Antennas

This article proposes a one-tier ultra-dense cellular network framework based on the characteristics of directional beamforming to explore the downlink signal-to-interference ratio (SIR) performance. The features of the proposed cellular network include: small base stations (SBSs) are equipped with directional antennas; the beam boresight directions of antennas are adaptively adjusted with the locations of users on the two-dimensional horizontal plane while the boresight directions are perfectly aligned with their associated users. In addition, an angle fading model, which follows from the exponential distribution, is developed to simulate the signals attenuation of interference links. The angle fading of the interference signals depends on the angle offset between the locations of users and the beam boresight directions of their interfering SBSs. With the assistance of stochastic geometry, the analytical expressions of coverage probability and average ergodic rate are derived by combining with the probability density function of angle offset variable. Then, the meta distribution of SIR is obtained to capture the performance changes of individual links for users. The numerical results indicate that the performance advantages of the proposed directional network obviously exceed that of the conventional isotropic antennas case. Monte-Carlo simulations validate the correctness of numerical results.

Performance Analysis of Distance-Based D2D Matching Mechanism

The traditional cellular architecture where devices connect to their service base station (BS) may cause poor performance especially for edge users. Device-to-device (D2D) communication enables nearby user as a relay to help BS forward information, thereby improving the network coverage and quality of service (QoS) of edge users. This paper proposes a distance-based D2D matching mechanism for general cellular networks, where a relay user who successfully connects to its targeted BS can transmit data to its closest user for D2D communication. A link of BS to D2D pair contains two sublinks, which occur at different time phases in each cell. Assuming a nonsynchronous system, we consider that there exists cross-layer interference for D2D links. Based on the techniques of stochastic geometry, we develop the performance of coverage probability and ergodic rate of the D2D network. A key intermediate step in this analysis is the derivation of the interference expressions for D2D links caused by BSs and cochannel D2D users. Then, we derive the meta distribution of the signal-to-interference ratio (SIR) to capture the performance changes of individual links. Simulation results demonstrate that our matching mechanism based on the appropriate time resource allocation favors the edge users with a higher probability of successful communication and transmission rate.

On the SIR Meta Distribution for Cache-Enabled Wireless Networks With Random Discontinuous Transmission: Analysis and Optimization

A fine-grained analysis of the cache-enabled networks is crucial for system design. In this paper, we focus on the meta distribution of the signal-to-interference ratio for the cache-enabled networks where the locations of the base stations are modeled as a Poisson point process. With the application of the random caching and the random discontinuous transmission schemes, we derive the moments of the conditional successful transmission probability, the exact meta distribution and its beta approximation by utilizing stochastic geometry. The closed-form expressions of the mean and variance of the local delay (i.e., the jitter) are also derived. We then consider the maximization of the mean successful transmission probability and the minimization of the average system transmission delay by jointly optimizing the caching probability and the BS active probability. Finally, the numerical results demonstrate the superiority of the proposed optimization schemes over the existing caching strategies and reveal the impacts of the key network parameters on the cache-enabled networks in terms of successful transmission probability, successful transmission probability variance, meta distribution, mean local delay and jitter.

Unified Analysis of Coordinated Multipoint Transmissions in mmWave Cellular Networks

This article performs a unified analysis of three coordinated multipoint (CoMP) transmission strategies in the downlink of mmWave cellular networks, including the fixed-number base station (BS) cooperation (FNC), the fixed-region BS cooperation (FRC), and the interference-aware BS cooperation (IAC). We first develop a comprehensive framework for CoMP operation in cellular networks, and investigate the network performance under a Poisson point process (PPP) model together with mmWave spectrum. To show what fraction of users in the network achieve target reliability for a given signal to interference-plus-noise ratio (SINR)/signal-to-interference ratio (SIR), we derive the SINR/SIR meta distributions, and further obtain the coverage probability as well as mean local delay for the three cooperation strategies. A pivotal intermediate step to compute the performance metrics is the derivation of joint distributions of distances between a typical user and cooperative BSs. Our analysis demonstrates that parameters of blockage have a significant influence on the network performance for the three CoMP schemes. We find that the FRC scheme makes more users achieve the given link reliability for the scenario with a low density of BSs, while the IAC scheme provides better performance for the network with a high density of BSs. Moreover, the optimal CoMP scheme can be approximately selected by considering the nearest distance from the serving BS to user and the radius of the approximate line-of-sight (LoS) region in the cellular networks.