Coverage and Rate Analysis for Co-Existing RF/VLC Downlink Cellular Networks

This paper provides a stochastic geometry framework to perform the coverage and rate analysis of a typical user in co-existing VLC and RF networks covering a large indoor area. The developed framework can be customized to capture the performance of a typical user in various network configurations such as (i) RF-only, in which only small base-stations (SBSs) are available to provide the coverage to a user, (ii) VLC-only, in which only optical BSs (OBSs) are available to provide the coverage to a user, (iii) opportunistic RF/VLC, where a user selects the network with maximum received signal power, and (iv) hybrid RF/VLC, where a user can simultaneously utilize the available resources from both RF and VLC networks. The developed model for VLC network precisely captures the impact of the field-of-view (FOV) of the photo-detector (PD) receiver on the number of interferers, distribution of the aggregate interference, association probability, and the coverage of a typical user. Closed-form approximations are presented for special cases of practical interest and for asymptotic scenarios such as when the intensity of SBSs becomes very low. The derived expressions enable us to obtain closed-form solutions for various network design parameters (such as intensity of OBSs and SBSs, transmit power, and/or FOV) such that the number of active users can be distributed optimally among RF and VLC networks. Also, we optimize the network parameters in order to prioritize the association of users to VLC network. Finally, simulations are carried out to verify the derived analytical solutions. Important trade-offs between height and intensity of OBSs are highlighted to optimize the performance of a user in VLC networks

Ambient RF Energy Harvesting in Ultra-Dense Small Cell Networks: Performance and Trade-offs

In order to minimize electric grid power consumption, energy harvesting from ambient RF sources is considered as a promising technique for wireless charging of low-power devices. To illustrate the design considerations of RF-based ambient energy harvesting networks, this article first points out the primary challenges of implementing and operating such networks, including non-deterministic energy arrival patterns, energy harvesting mode selection, energy-aware cooperation among base stations (BSs), etc. A brief overview of the recent advancements and a summary of their shortcomings are then provided to highlight existing research gaps and possible future research directions. To this end, we investigate the feasibility of implementing RF-based ambient energy harvesting in ultra-dense small cell networks (SCNs) and examine the related trade-offs in terms of the energy efficiency and signal-to-interference-plus-noise ratio (SINR) outage probability of a typical user in the downlink. Numerical results demonstrate the significance of deploying a mixture of on-grid small base stations (SBSs)~(powered by electric grid) and off-grid SBSs~(powered by energy harvesting) and optimizing their corresponding proportions as a function of the intensity of active SBSs in the network.Comment: IEEE Wireless Communications, to appea

Multi-tier Drone Architecture for 5G/B5G Cellular Networks: Challenges, Trends, and Prospects

Drones (or unmanned aerial vehicles [UAVs]) are expected to be an important component of fifth generation (5G)/beyond 5G (B5G) cellular architectures that can potentially facilitate wireless broadcast or point-to-multipoint transmissions. The distinct features of various drones such as the maximum operational altitude, communication, coverage, computation, and endurance impel the use of a multi-tier architecture for future drone-cell networks. In this context, this article focuses on investigating the feasibility of multi-tier drone network architecture over traditional single-tier drone networks and identifying the scenarios in which drone networks can potentially complement the traditional RF-based terrestrial networks. We first identify the challenges associated with multi-tier drone networks as well as drone-assisted cellular networks. We then review the existing state-of-the-art innovations in drone networks and drone-assisted cellular networks. We then investigate the performance of a multi-tier drone network in terms of spectral efficiency of downlink transmission while illustrating the optimal intensity and altitude of drones in different tiers numerically. Our results demonstrate the specific network load conditions (i.e., ratio of user intensity and base station intensity) where deployment of drones can be beneficial (in terms of spectral efficiency of downlink transmission) for conventional terrestrial cellular networks

Integral Approximations for Coverage Probability

This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B x^{\alpha/2}) \} x$. Four different approximations are studied. For systems that are interference-limited or noise-limited, conditions are identified when the approximations are valid. For intermediate cases, we recommend the use of Laplace approximation. Numerical results validate the accuracy of the approximations

Accuracy of Distance-Based Ranking of Users in the Analysis of NOMA Systems

We characterize the accuracy of analyzing the performance of a NOMA system where users are ranked according to their distances instead of instantaneous channel gains, i.e., product of distance-based path-loss and fading channel gains. Distance-based ranking is analytically tractable and can lead to important insights. However, it may not be appropriate in a multipath fading environment where a near user suffers from severe fading while a far user experiences weak fading. Since the ranking of users in a NOMA system has a direct impact on coverage probability analysis, impact of the traditional distance-based ranking, as opposed to instantaneous signal power-based ranking, needs to be understood. This will enable us to identify scenarios where distance-based ranking, which is easier to implement compared to instantaneous signal power-based ranking, is acceptable for system performance analysis. To this end, in this paper, we derive the probability of the event when distance-based ranking yields the same results as instantaneous signal power-based ranking, which is referred to as the accuracy probability. We characterize the probability of accuracy considering Nakagami-m fading channels and three different spatial distribution models of user locations in NOMA. We illustrate the impact of accuracy probability on uplink and downlink coverage probability

Analysis of SINR Outage in Large-Scale Cellular Networks Using Campbell's Theorem and Cumulant Generating Functions

The signal-to-noise-plus-interference ratio (SINR) outage probability is one of the key performance parameters of a wireless cellular network, and its analytical as well as numerical evaluation has occupied many researchers. Recently, the introduction of stochastic geometric modeling of cellular networks has brought the outage problem to the forefront again. A popular and powerful approach is to exploit the available moment generating function (or Laplace transform) of received signal and interference, whenever it exists, by applying the Gil-Pelaez inversion formula. However, with the stochastic geometric modeling, the moment generating function may either be too complicated to exist in closed-form or at worst may not exist. Toward this end, in this paper, we study two alternate ways of evaluating the SINR outage. In the first case, we emphasize the significance of calculating cumulants over moments and exploit the fact that the cumulants of point processes are easily calculable using Campbell's theorem. The SINR outage is then analytically characterized by Charlier expansion based on Gaussian and Student's $t$-distributions and their associated Hermite and Krishnamoorthy polynomials. In the second case, we exploit the saddle point method, which gives a semi-analytical method of calculating the SINR outage, whenever the cumulant generating function of received signal and interference exists. For the purpose of demonstration, we apply these techniques on a downlink cellular network model where a typical user experiences a coordinated multi-point transmission, and the base stations are modeled by homogeneous Poisson point process. For the convenience of readers, we also provide a brief overview of moments, cumulants, their generating functions, and Campbell's theorem, without invoking measure theory. Numerical results illustrate the accuracy of the proposed mathematical approaches

Meta Distribution of the 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 $-1$-st moment in a static network setting), and the meta distribution (which is the complementary cumulative distribution function of the conditional success probability and can be approximated by using the $1$-st and $2$-nd moments). For uplink NOMA, to make the framework tractable, we propose two point process models for the spatial locations of the 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, average 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 favour orthogonal multiple access (OMA)

Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions

This letter proposes the use of saddle point approximation (SPA) to evaluate the outage probability of wireless cellular networks. Unlike traditional numerical integration-based approaches, the SPA approach relies on cumulant generating functions (CGFs) and eliminates the need for explicit numerical integration. The approach is generic and can be applied to a wide variety of distributions, given that their CGFs exist. We illustrate the usefulness of SPA on channel fading distributions such as Nakagami-$m$, Nakagami-$q$ (Hoyt), and Rician distributions. Numerical results validate the accuracy of the proposed SPA approach.Comment: 4 pages, 4 figures, submitted to IEEE Wireless Communications Letter

Meta Distribution of SIR in Dual-Hop Internet-of-Things (IoT) Networks

This paper characterizes the meta distribution of the downlink signal-to-interference ratio (SIR) attained at a typical Internet-of-Things (IoT) device in a dual-hop IoT network. The IoT device associates with either a serving macro base station (MBS) for direct transmissions or associates with a decode and forward (DF) relay for dual-hop transmissions, depending on the biased received signal power criterion. In contrast to the conventional success probability, the meta distribution is the distribution of the conditional success probability (CSP), which is conditioned on the locations of the wireless transmitters. The meta distribution is a fine-grained performance metric that captures important network performance metrics such as the coverage probability and the mean local delay as its special cases. Specifically, we derive the moments of the CSP in order to calculate analytic expressions for the meta distribution. Further, we derive mathematical expressions for special cases such as the mean local delay, variance of the CSP, and success probability of a typical IoT device and typical relay with different offloading biases. We take in consideration in our analysis the association probabilities of IoT devices. Finally, we investigate the impact of increasing the relay density on the mean local delay using numerical results

Downlink Power Control in Two-Tier Cellular Networks with Energy-Harvesting Small Cells as Stochastic Games

Energy harvesting in cellular networks is an emerging technique to enhance the sustainability of power-constrained wireless devices. This paper considers the co-channel deployment of a macrocell overlaid with small cells. The small cell base stations (SBSs) harvest energy from environmental sources whereas the macrocell base station (MBS) uses conventional power supply. Given a stochastic energy arrival process for the SBSs, we derive a power control policy for the downlink transmission of both MBS and SBSs such that they can achieve their objectives (e.g., maintain the signal-to-interference-plus-noise ratio (SINR) at an acceptable level) on a given transmission channel. We consider a centralized energy harvesting mechanism for SBSs, i.e., there is a central energy storage (CES) where energy is harvested and then distributed to the SBSs. When the number of SBSs is small, the game between the CES and the MBS is modeled as a single-controller stochastic game and the equilibrium policies are obtained as a solution of a quadratic programming problem. However, when the number of SBSs tends to infinity (i.e., a highly dense network), the centralized scheme becomes infeasible, and therefore, we use a mean field stochastic game to obtain a distributed power control policy for each SBS. By solving a system of partial differential equations, we derive the power control policy of SBSs given the knowledge of mean field distribution and the available harvested energy levels in the batteries of the SBSs.Comment: IEEE Transactions on Communications, 201