Mean Local Delay Research Articles

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.

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.

Radar Detection in Vehicular Networks: Fine-Grained Analysis and Optimal Channel Access

Automotive radar is a critical feature in advanced driver-assistance systems. It is important in enhancing vehicle safety by detecting the presence of other vehicles in the vicinity. The performance of radar detection is, however, affected by the interference from radars of other vehicles as well as the variation in the target radar cross-section (RCS) due to varying physical features of the target vehicle. Considering such interference and random RCS, this work provides a fine-grained performance analysis of radar detection. Specifically, using stochastic geometry, we calculate the meta distribution of the signal-to-interference-and-noise ratio that permits the reliability analysis of radar detection at individual vehicles. We also evaluate the delay aspect of radar detection, namely, the mean local delay which is the average number of transmission attempts needed until the first successful target detection. For a given target distance, we obtain the optimal transmit probability that maximizes the density of successful detection while keeping the mean local delay below a threshold. We also provide several system design insights in terms of the fraction of reliable radar links, transmission delay, the density of vehicles, and congestion control. Finally, leveraging the derived framework, we present an online algorithm to select the transmit probability in a distributed manner, particularly when system parameters such as vehicular density and interferer locations are unknown to individual vehicles. We demonstrate the efficacy of the proposed online framework for selecting the optimal transmit probability within a deadline of 0.1 ms, which is critical for sustaining automotive safety applications and services.

Adaptive Rate NOMA for Cellular IoT Networks

Internet-of-Things (IoT) technology is envisioned to enable a variety of real-time applications by interconnecting billions of sensors/devices. These IoT devices rely on low-power wide-area wireless connectivity for transmitting, mostly fixed- but small-size, status updates of the random processes observed by them. Owing to their ubiquity, cellular networks are seen as a natural candidate for providing reliable wireless connectivity to IoT devices. Given the massive number of IoT devices, enabling non-orthogonal multiple access (NOMA) for the mobile users and IoT devices is appealing in terms of the efficient utilization of spectrum compared to the orthogonal multiple access (OMA). For instance, the uplink NOMA can also be configured such that the mobile users adapt their transmission rates depending upon the channel conditions while the IoT devices transmit at a fixed rate. For this setting, we analyze the ergodic capacity of the mobile users and the mean local delay of IoT devices using stochastic geometry. Our analysis demonstrates that the aforementioned NOMA configuration provides better ergodic capacity for mobile users compared to OMA when delay constraint of IoT devices is strict. We also show that NOMA supports a larger packet size at IoT devices than OMA under the same delay constraint.

Spatio-Temporal Analysis of Meta Distribution for Cell-Center/Cell-Edge Users

Emergence of various types of wireless applications has brought about fast growing and diversified traffic in cellular networks. To gain a comprehensive understanding of the influences caused by the differentiated and dynamic traffic is vital for the design of the next-generation wireless networks. In this paper, we develop a mathematical framework for meta-distribution analysis by utilizing queueing theory and stochastic geometry to capture the spatial (geographical location) and temporal randomness (queue status) of traffic. We derive the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula> -th moment of the conditional successful transmission probability (STP) and the closed-form expressions of the meta distribution for the cell-center users (CCUs) and the cell-edge users (CEUs), respectively. The results are further extended to obtain the analytical expression of the meta distribution by taking the temporal random arrival of traffic into consideration. Moreover, the mean local delays for the CCUs and CEUs are derived. Finally, the impact of key network parameters on the meta distribution and the corresponding mean local delay is investigated.

Abstract 12017: Correlates of Regional Diastolic Dysfunction in Patients With Heart Failure With Preserved Ejection Fraction

Introduction: The underlying mechanisms of regional myocardial dysfunction in patients with heart failure with preserved ejection fraction (HFpEF) remain poorly defined. Hypothesis: We investigated physiological correlates of regional diastolic dysfunction in HFpEF using a novel technique based on point-by-point measurement of local diastolic delay. Methods: We enrolled 30 patients with HFpEF (LVEF &gt;50%, E/e' &gt;15, NT-proBNP &gt;300 pg/ml). In all patients we performed electroanatomical mapping of the left ventricle and assessed regional diastolic function by a novel algorithm based on the measurement of local diastolic delay. Local diastolic delay was considered significant if the time delay between global left ventricular end diastolic time and local diastolic time was &gt;50 msec. At the time of mapping, we performed clinical evaluation, echocardiography and measured plasma levels of 27 biomarkers of angiogenesis and endothelial dysfunction. Results: Our cohort included 23 male and 7 female patients, aged 46-70 years. Using electroanatomical mapping we measured regional diastolic function in 4820 mapping points. The mean local diastolic delay was &gt;50 msec in 12 patients (Group A), and &lt;50 msec in 18 patients (Group B). The groups did not differ in age (64±11 years in Group A vs. 51±8 years in Group B, P=0.22), gender, (male: 83% vs. 73%, P=0.48), creatinine (1.08±0.31 mg/dL vs. 1.10±0.30 mg/dL, P=0.52), LVEF (56±4% vs. 58±7%, P=0.42), or NT-proBNP levels (1570±1310 pg/mL vs. 1230±1240 pg/mL, P=0.22). However, in Group A, we found higher values of E/e’ (18.2±3.4 vs. 17.0±2.8 in Group B, P=0.04), and lower myocardial viability (unipolar voltage: 7.73±1.8 mV vs. 9.03±2.1 mV, P=0.02). When compared to Group B, patients in Group A displayed lower levels of pro-angiogenic biomarkers (vascular endothelial growth factor: 33±22 pg/mL vs. 47±24 pg/mL, P=0.01; platelet-derived growth factor: 47±23 pg/mL vs. 78±34 pg/mL, P=0.02), and higher levels of anti-angiogenic biomarkers (agiopoietin-2: 7.0±3.8 ng/mL vs. 2.7±1.0 ng/mL, P=0.01; endostatin: 87±33 ng/mL vs. 65±21 ng/mL, P=0.02). Conclusion: In patients with HFpEF, regional diastolic dysfunction appears to be associated with increased E/e’, decreased myocardial viability, and impaired angiogenesis.

Low Power Wide Area IoT Networks: Reliability Analysis in Coexisting Scenarios

Low-power wide-area networks (LPWANs) are emerging technologies aiming at serving sporadic IoT traffic. While reliability of LPWANs in single-technology deployment has been well investigated, there is lack of research on performance evaluation in coexisting scenarios. To tackle this problem, we start by modeling statistics of aggregated interference from asynchronous sources over shared radio resources. Then, using stochastic geometry, we derive the closed-form statistics of reliability, mean success probability, and the mean local delay, defined as the mean time (in numbers of attempts) until a packet is successfully received by the nearest access point. We further investigate the interplay between traffic-load, access points density, and quality of communications in coexistence scenarios. Then, we derive the communications parameters regions, in terms of transmission power, access point density, and time activity factor, for which, the mean local delay is finite. The numerical and simulation results also corroborate the analysis.

Performance Analysis of Cellular-Relay Vehicle-to-Vehicle Communications

Vehicle-to-vehicle (V2V) communication-based cooperative vehicular networks are a key technology for future smarter transportation systems as they provide various applications for addressing road safety and traffic congestion. To alleviate the performance limitations of existing dedicated short-range communication (DSRC) protocols, cellular-assisted V2V communications have been proposed recently, wherein cellular base stations (BSs) relay the transmission from one vehicle to another. Such cellular-assisted communications have shown promise for more reliable V2V communications with a wider capacity and longer transmission distances. In this study, we theoretically analyze the performance of cellular-relay (CR) V2V communications, in which a vehicle first transmits a message to its nearest BS via uplink, and then, the BS forwards the message to a destination vehicle via downlink. We model the road segments through a Poisson line process and the positions of vehicles through a Poisson point process on the roads; subsequently, we derive a theoretical expression for the probability of a successful CR transmission and the mean local delay in the CR transmission. Furthermore, we propose a performance metric to evaluate the difference between the performances of CR and direct V2V communications, and it can be applied to automatic transmission mode selection (i.e., CR or direct) for V2V communications. We evaluate the analytical results using numerical examples and demonstrate the impacts of various system parameters on the performances of CR and direct V2V communications.

Stochastic geometry based analysis for heterogeneous networks: a perspective on meta distribution

The meta distribution as a new performance metric can provide much more fine-grained information about the individual link reliability, and is of great value for the analysis and design of the future cellular networks. In this paper, we investigate the stochastic geometry based analysis for heterogeneous networks from the perspective on the meta distribution. The comprehensive overview for the fundamental framework of the meta distribution is provided, which involves the concepts of the meta distribution and its related performance metric (e.g., mean local delay and spatial outage capacity) and the efficient calculation methods of the meta distribution. The insights of the meta distribution are also stated by the comparison with standard success probability. The various applications of the meta distribution to heterogeneous networks are summarized and categorized by different types of technologies. Furthermore, some open issues and future work are discussed to promote the development and application of the meta distribution.

Meta Distribution of the SIR in Moving Networks

Moving networks (MNs) with moving base stations (BSs) provide ubiquitous and constant services to cellular devices/user equipment (UEs) in 5-th generation systems. Moving BSs are mounted on top of vehicles. To describe the randomness of the BSs, a tractable stochastic geometry model for MNs is proposed. A definition of the conditional success probability and meta distribution (MD) of the signal-to-interference ratio (SIR) for MNs is proposed. The MD is used to assess the benefits of MNs. In single-tier MNs with high mobility, we determine the moments of the conditional success probability given the point process for the calculation of the MD and the mean local delay. The results show that the mean local delay is finite and the variance is reduced to 0. A closed-form approximation of the variance is proposed for general mobility levels. Using the approximated variance, we propose a beta approximation of the MD. The single-tier model is then extended to a two-tier heterogeneous MN model. Tractable expressions of the mean success probability and the variance for both the overall network and the typical UE in each tier are obtained. They reveal that moving BSs can reduce the variance among UEs while keeping the mean success probability constant.

Drone-Initiated D2D-Aided Multihop Multicast Networks for Emergency Information Dissemination

Due to their fast and flexible deployment, drones can support terrestrial networks for rapid information dissemination by broadcasting emergency messages to ground devices in public safety scenarios (e.g., bushfire and flood). In this paper, we consider a drone-initiated device-to-device-aided (D2D-aided) multihop multicast network where a drone is deployed to broadcast an emergency alert message to all terrestrial D2D users at the first time slot. After that, the D2D users that have successfully received the message become the active transmitters and multicast the message through multihop for the next time slots. Using stochastic geometry, we propose a general analytical framework to compute the link coverage probability, the mean local delay for a D2D user and the network coverage probability. The Monte Carlo simulation results confirm the accuracy of the proposed framework. Our results reveal the impacts of the different system parameters (i.e., height and transmit power of the drone and density and sensitivity radius of the D2D users) on the link performance and the network performance. It is found that a higher drone altitude provides better link and network coverage probabilities and lower mean local delay. The results show that under practical setups, the cell edge user located 2 km from the ground projection of the drone has a link coverage probability around 90% after 5 time slots and a mean local delay of 2.32 time slots with a drone height as low as 200 m.

Meta Distribution of SIR in Large-Scale Uplink and Downlink NOMA Networks

We develop an analytical framework to derive the meta distribution and moments of the conditional success probability (CSP), which is defined as success probability for a given realization of the transmitters, in large-scale co-channel uplink and downlink non-orthogonal multiple access (NOMA) networks with one NOMA cluster per cell. The moments of CSP translate to various network performance metrics such as the standard success or signal-to-interference ratio (SIR) coverage probability (which is the 1-st moment), the mean local delay (which is the −1st moment in a static network setting), and the meta distribution (which is the complementary cumulative distribution function of the success or SIR coverage probability and can be approximated by using the 1st and 2nd moments). For the uplink NOMA network, to make the framework tractable, we propose two point process models for the spatial locations of the inter-cell interferers by utilizing the base station (BS)/user pair correlation function. We validate the proposed models by comparing the second moment measure of each model with that of the actual point process for the inter-cluster (or inter-cell) interferers obtained via simulations. For downlink NOMA, we derive closed-form solutions for the moments of the CSP, success (or coverage) probability, mean local delay, and meta distribution for the users. As an application of the developed analytical framework, we use the closed-form expressions to optimize the power allocations for downlink NOMA users in order to maximize the success probability of a given NOMA user with and without latency constraints. Closed-form optimal solutions for the transmit powers are obtained for two-user NOMA scenario. We note that maximizing the success probability with latency constraints can significantly impact the optimal power solutions for low SIR thresholds and favor orthogonal multiple access.

SIR Meta Distribution of $K$ -Tier Downlink Heterogeneous Cellular Networks With Cell Range Expansion

Heterogeneous cellular networks (HCNs) constitute a necessary step in the evolution of cellular networks. In this paper, we apply the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on K-tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (HIP) model, with range expansion bias (offloading bias) in each tier. Expressions for the b-th moment of the conditional success probability for both the entire network and each tier are derived, based on which the exact meta distributions and the beta approximations are evaluated and compared. Key performance metrics including the mean success probability, the variance of the conditional success probability, the mean local delay and the asymptotic SIR gains of each tier are obtained. The results show that the biases are detrimental to the overall mean success probability of the whole network and that the b-th moment curve (versus the SIR threshold) of the conditional success probability of each tier can be excellently approximated by the horizontal shifted versions of the first moment curve of the single-tier PPP network. We also provide lower bounds for the region of the active probabilities of the base stations to keep the mean local delay of each tier finite.

The Meta Distribution of the SIR for Cellular Networks With Power Control

The meta distribution of the signal-to-interference ratio (SIR) provides fine-grained information about the performance of individual links in a wireless network. This paper focuses on the analysis of the meta distribution of the SIR for both the cellular network uplink and downlink with fractional power control. For the uplink scenario, an approximation of the interfering user point process with a non-homogeneous Poisson point process is used. The moments of the meta distribution for both scenarios are calculated. Some bounds, the analytical expression, the mean local delay, and the beta approximation of the meta distribution are provided. The results give interesting insights into the effect of the power control in both the uplink and downlink. Detailed simulations show that the approximations made in the analysis are well justified.

The SIR Meta Distribution in Poisson Cellular Networks With Base Station Cooperation

The meta distribution provides fine-grained information on the signal-to-interference ratio (SIR) compared with the SIR distribution at the typical user. This paper first derives the meta distribution of the SIR in heterogeneous cellular networks with downlink coordinated multipoint transmission/reception, including joint transmission (JT), dynamic point blanking (DPB), and dynamic point selection/dynamic point blanking (DPS/DPB), for the general typical user and the worst-case user (the typical user located at the Voronoi vertex in a single-tier network). A more general scheme called JT-DPB, which is the combination of JT and DPB, is studied. The moments of the conditional success probability are derived for the calculation of the meta distribution and the mean local delay. An exact analytical expression, the beta approximation, and simulation results of the meta distribution are provided. From the theoretical results, we gain insights on the benefits of different cooperation schemes and the impact of the number of cooperating base stations and other network parameters.

On the SIR Meta Distribution for Poisson Networks With Interference Cancellation

This letter presents a theoretical framework for the analysis of the meta distribution of the SIR for Poisson networks with interference cancellation (IC) enabled at the receivers, which gives deep insight into the network performance on a link-wise basis. A simple but insightful IC model named C-IC is studied for which the exact $b$ th moment of the meta distribution and its beta distribution approximation and some useful bounds are validated. The conditions for the mean local delay to be finite are also stated. The results show that IC improves the performance not only in terms of the mean but also in terms of the variance of the meta distribution.

A Fine-Grained Analysis of Millimeter-Wave Device-to-Device Networks

Enabling device-to-device (D2D) communications in millimeter-wave (mm-wave) networks is of critical importance for the next-generation mobile networks to support very high data rates (multi-gigabits-per-second) for mobile devices. In this paper, we provide a fine-grained performance analysis of the mm-wave D2D communication networks. Specifically, we first establish a general and tractable framework to investigate the performance of mm-wave D2D networks using the Poisson bipolar model integrated with several features of the mm-wave band. To show what fraction of users in the network achieve target reliability if the required signal-to-interference-plus-noise ratio (SINR) (or QoS requirement) is given, we derive the meta distributions of the SINR and the data rate. Interestingly, in mm-wave D2D networks, the standard beta approximation for the meta distribution does not work very well when highly directional antenna arrays are used or the node density is small. To resolve this issue, we provide a modified approximation by using higher moments of the conditional SINR distribution, which is shown to be closer to the exact result. On this basis, we also derive the mean local delay and spatial outage capacity to provide a comprehensive investigation on the impact of mm-wave features on the performance of D2D communication.

Analysis of D2D Underlaid Cellular Networks: SIR Meta Distribution and Mean Local Delay

We study the performance of device-to-device (D2D) communication underlaying cellular wireless network in terms of the meta distribution of the signal-to-interference ratio (SIR), which is the distribution of the conditional SIR distribution given the locations of the wireless nodes. Modeling D2D transmitters and base stations as Poisson point processes (PPPs), moments of the conditional SIR distribution are derived in order to calculate analytical expressions for the meta distribution and the mean local delay of the typical D2D receiver and cellular downlink user. It turns out that for D2D users, the total interference from the D2D interferers and base stations is equal in distribution to that of a single PPP, while for downlink users, the effect of the interference from the D2D network is more complicated. We also derive the region of transmit probabilities for the D2D users and base stations that result in a finite mean local delay and give a simple inner bound on that region. Finally, the impact of increasing the base station density on the mean local delay, the meta distribution, and the density of users reliably served is investigated with numerical results.

On the Impact of Coordination on Local Delay and Energy Efficiency in Poisson Networks

The local delay characterizes the number of time slots required for a node to successfully transmit a packet to its target receiver. In this letter, we explore the impact of coordinated transmission on the mean local delay and the energy efficiency, in a Poisson network model. Leveraging tools from point process theory, we derive analytical expressions of the mean local delay and the long-term energy efficiency, without and with coordinated transmission. We find that coordinated transmission greatly decreases the mean local delay and also improves the long-term energy efficiency under certain network configurations.