We introduce a novel mathematical framework for optimizing cellular network deployments, providing robust coverage and capacity for heterogeneous 3D user distributions. We establish necessary conditions and propose an iterative algorithm to fine-tune critical base station (BS) parameters, including location, horizontal bearing, vertical antenna tilt, and transmit power. In our case study, we optimize both existing and newly deployed BSs to support ground users and uncrewed aerial vehicles (UAVs) along designated corridors. Results indicate that the framework significantly enhances UAV connectivity while preserving near-optimal performance for ground users.

We study a heterogeneous Rayleigh fading wireless sensor network (WSN) in which sensor nodes surveil a field of interest and communicate their sensory data with base stations with the aid of access points as relays. With the goal of improving the energy efficiency of the network, we consider both large-scale and small-scale signal propagation effects in our system model and aim to optimize the node deployment as an effective measure to reduce the wireless communication power consumption of the WSN. We propose a new framework, in which hard deterministic connectivity constraints on communication links are replaced with realistic limitations on outage due to severe stochastic fading. We also consider a radio energy model that reflects the exponential dependence of the transmission power on the rate. We derive the necessary conditions for the optimal deployment that not only minimize the power consumption, but also guarantee all wireless links to have an outage probability below the given threshold. Our theoretical findings are accompanied by simulations that indicate significant performance gains compared to existing node deployment algorithms in the literature.

We present a new framework based on quantization theory to design cellular networks optimized for both legacy ground users and uncrewed aerial vehicle (UAV) corridors, dedicated aerial highways for safe UAV flights. Our framework leverages antenna tilts and transmit power at each base station to enhance coverage and quality of service among users. We develop a comprehensive mathematical analysis and optimization algorithms for multiple system-level performance metrics, including received signal strength and signal-to-interference-plus-noise ratio. Realistic antenna radiation patterns and propagation channel models are considered, alongside a generic 3D user distribution that allows for performance prioritization on the ground, along UAV corridors, or a desired tradeoff between the two. We demonstrate the efficacy of the proposed framework through case studies, showcasing the non-trivial combinations of antenna tilts and power levels that improve coverage and signal quality along UAV corridors while incurring only a marginal impact on the ground user performance compared to scenarios without UAVs.

In this article, we introduce a new mathematical framework for the analysis and design of UAV corridors in cellular networks, while considering a realistic network deployment, antenna radiation pattern, and propagation channel model. By leveraging quantization theory, we optimize the electrical tilts of existing ground cellular base stations to maximize the coverage of both legacy ground users and UAVs flying along specified aerial routes. Our practical case study shows that the optimized network results in a cell partitioning that significantly differs from the usual hexagonal pattern, and that it can successfully guarantee coverage all over the UAV corridors without degrading the perceived signal strength on the ground.

We study a heterogeneous wireless sensor network (WSN) where$N$heterogeneous access points (APs) gather data from densely deployed sensors and transmit their sensed information to$M$heterogeneous fusion centers (FCs) via multi-hop wireless communication. The heterogeneous optimal deployment of APs and FCs is modeled as an optimization problem with total wireless communication power consumption of the network as its objective function. We consider both static WSNs, where APs and FCs retain their deployed position, and mobile WSNs where APs and FCs can move from their initial deployment to their optimal locations. Based on the derived necessary conditions for the optimal deployment in static WSNs, we propose an iterative algorithm to deploy APs and FCs. In addition, we study the necessary conditions of the optimal movement-efficient deployment in mobile WSNs with constrained movement energy and present iterative algorithms to find such deployments, accordingly. Simulation results show that our proposed deployment algorithms outperform the existing methods in the literature, and achieve a lower total wireless communication power in both static and mobile WSNs.

We study a heterogeneous two-tier wireless sensor network in which N heterogeneous access points (APs) collect sensing data from densely distributed sensors and then forward the data to M heterogeneous fusion centers (FCs). This heterogeneous node deployment problem is modeled as an optimization problem with the total power consumption of the network as its cost function. The necessary conditions of the optimal AP and FC node deployment are explored in this paper. We provide a variation of Voronoi Diagram as the optimal cell partition for this network and show that each AP should be placed between its connected FC and the geometric center of its cell partition. In addition, we propose a heterogeneous two-tier Lloyd algorithm to optimize the node deployment. Furthermore, we study the sensor deployment when the communication range is limited for sensors and APs. Simulation results show that our proposed algorithms outperform the existing clustering methods like Minimum Energy Routing, Agglomerative Clustering, Divisive Clustering, Particle Swarm Optimization, Relay Node placement in Double-tiered Wireless Sensor Networks, and Improved Relay Node Placement, on average.

We study a wireless ad-hoc sensor network (WASN) where N sensors gather data from the surrounding environment and transmit their sensed information to M fusion centers (FCs) via multi-hop wireless communications. This node deployment problem is formulated as an optimization problem to make a trade-off between the sensing uncertainty and energy consumption of the network. Our primary goal is to find an optimal deployment of sensors and FCs that minimizes a Lagrangian combination of sensing uncertainty and energy consumption. To support arbitrary routing protocols in WASNs, the routing-dependent necessary conditions for the optimal deployment are explored. Based on these necessary conditions, we propose a routing-aware Lloyd-like algorithm to optimize node deployment. Simulation results show that our proposed algorithm outperforms the existing deployment algorithms, on average.

We study a heterogeneous two-tier wireless sensor network in which N heterogeneous access points (APs) collect sensing data from densely distributed sensors and then forward the data to M heterogeneous fusion centers (FCs). This heterogeneous node deployment problem is modeled as a quantization problem with distortion defined as the total power consumption of the network. The necessary conditions of the optimal AP and FC node deployment are explored in this paper. We provide a variation of Voronoi diagrams as the optimal cell partition for this network, and show that each AP should be placed between its connected FC and the geometric center of its cell partition. In addition, we propose a heterogeneous two-tier Lloyd-like algorithm to optimize the node deployment. Simulation results show that our proposed algorithm outperforms the existing methods like Minimum Energy Routing, Agglomerative Clustering, and Divisive Clustering, on average.

Time Series Classification (TSC) is important in many applications including IoT, medical, stock market analysis, economic forecasting, process and quality control and Big Data systems. The problem of time series classification has been studied separately for univariate (UTS) and multivariate (MTS) time series using different datasets and techniques. In this paper, we propose a unique, off-the-shelf approach to classifying time series that improves the current state-of-the-art accuracy for UTS and its generalization to MTS. Our technique maps each time series to a Gramian Angular Difference Field (GADF), interprets that as an image and uses Google's pre-trained Convolutional Neural Network (trained on Inception v3) to map the GADF images into a 2048-dimensional vector space. Then, a multilayer perceptron (MLP) with three hidden layers, and a softmax activation function at the output is used to achieve the final classification. Our method yields competitive results for training and prediction in the UTS case while delivering superior results for MTS datasets. Unlike many published results, our technique is robust in the presence of variable length time series with missing data points, and scales well with the size of dataset.

Lattice codes are known to outperform random codes for certain networks, especially in the Gaussian two-way relay channels (GTWRCs) where lattice codes are able to exploit their linearity. As an extension of the GTWRC, in this paper, we consider the asymmetric Gaussian two-way line network where two nodes exchange their messages through multiple relays. We first investigate the capacity region of the full-duplex two-way two-relay line network. The results can be extended to an arbitrary number of relays and to half-duplex scenarios. This channel consists of four nodes: 1 ↔ 2 ↔ 3 ↔ 4, where nodes 1 and 4 with the help of two full-duplex relays, i.e., nodes 2 and 3, exchange their messages with each other. Using lattice codes, we design a novel scheme that allows the relay nodes to send the data in both directions simultaneously under an asymmetric rate region. In the proposed scheme, each relay decodes the sum of lattice points and then re-encodes it into another lattice codeword (which satisfies the transmit power constraint at the relay). It is shown that the proposed scheme achieves the capacity region of asymmetric two-way line network within 0.5 bit independent of the number of relays.