Impact of Device Caching and Handovers on the Performance of 3D UAV Networks with Blockages

We investigate an urban network characterized by blockages, where unmanned aerial vehicles (UAVs) offer ad-hoc coverage to mobile users with distinct service rate requirements. The UAV-BSs are modeled using a two-dimensional (2-D) marked-poisson point process (MPPP), where the marks represent the altitude of each UAV-base station (UAV-BS). Initially, we model the network blockages and analyze the association probabilities of line-of-sight (LoS) and non-line-of-sight (NLoS) UAV-BSs using stochastic geometry. Subsequently, we derive the bth moment of the conditional success probability (CSP) and employ a meta distribution (MD)-based analytical framework of signal-to-interference noise ratio (SINR) taking into account the blockage distribution in the network. Furthermore, we proposea cache-based handover management strategy that dynamically selects the cell search time and delays the received signal strength (RSS)-based base station (BS) associations. This strategy aims to minimize unnecessary handovers (HOs) experienced by users by leveraging caching capabilities at user equipment (UE). We evaluate the HO rate and average throughput experienced by users ensuring their service rate requirements are met. We demonstrate that LoS associations decrease as the network density increases due to the substantial increase of NLoS UAV-BSs in the network. Additionally, we show that the presence of blockages does not necessarily have a negative impact on network reliability

Optimizing Sharpe Ratio: Risk-Adjusted Decision-Making in Multi-Armed Bandits

Sharpe Ratio (SR) is a critical parameter in characterizing financial time series as it jointly considers the reward and the volatility of any stock/portfolio through its variance. Deriving online algorithms for optimizing the SR is particularly challenging since even offline policies experience constant regret with respect to the best expert Even-Dar et al (2006). Thus, instead of optimizing the usual definition of SR, we optimize regularized square SR (RSSR). We consider two settings for the RSSR, Regret Minimization (RM) and Best Arm Identification (BAI). In this regard, we propose a novel multi-armed bandit (MAB) algorithm for RM called UCB-RSSR for RSSR maximization. We derive a path-dependent concentration bound for the estimate of the RSSR. Based on that, we derive the regret guarantees of UCB-RSSR and show that it evolves as O(log n) for the two-armed bandit case played for a horizon n. We also consider a fixed budget setting for well-known BAI algorithms, i.e., sequential halving and successive rejects, and propose SHVV, SHSR, and SuRSR algorithms. We derive the upper bound for the error probability of all proposed BAI algorithms. We demonstrate that UCB-RSSR outperforms the only other known SR optimizing bandit algorithm, U-UCB Cassel et al (2023). We also establish its efficacy with respect to other benchmarks derived from the GRA-UCB and MVTS algorithms. We further demonstrate the performance of proposed BAI algorithms for multiple different setups. Our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems. Consequently, our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems.

Impact of Urban Street Geometry on the Detection Probability of Automotive Radars

Prior works have analyzed the performance of millimeter wave automotive radars in the presence of diverse clutter and interference scenarios using stochastic geometry tools instead of more time-consuming measurement studies or system-level simulations. In these works, the distributions of radars or discrete clutter scatterers were modeled as Poisson point processes in the Euclidean space. However, since most automotive radars are likely to be mounted on vehicles and road infrastructure, road geometries are an important factor that must be considered. Instead of considering each road geometry as an individual case for study, in this work, we model each case as a specific instance of an underlying Poisson line process and further model the distribution of vehicles on the road as a Poisson point process - forming a Poisson line Cox process. Then, through the use of stochastic geometry tools, we estimate the average number of interfering radars for specific road and vehicular densities and the effect of radar parameters such as noise and beamwidth on the radar detection metrics. The numerical results are validated with Monte Carlo simulations.

Best Arm Identification Based Beam Acquisition in Stationary and Abruptly Changing Environments

We study the initial beam acquisition problem in millimeter wave (mm-wave) networks from the perspective of best arm identification in multi-armed bandits (MABs). For the stationary environment, we propose a novel algorithm called concurrent beam exploration, CBE, in which multiple beams are grouped based on the beam indices and are simultaneously activated to detect the presence of the user. The best beam is then identified using a Hamming decoding strategy. For the case of orthogonal and highly directional thin beams, we characterize the performance of CBE in terms of the probability of missed detection and false alarm in a beam group (BG). Leveraging this, we derive the probability of beam selection error and prove that CBE outperforms the state-of-the-art strategies in this metric. Then, for the abruptly changing environments, e.g., in the case of moving blockages, we characterize the performance of the classical sequential halving (SH) algorithm. In particular, we derive the conditions on the distribution of the change for which the beam selection error is exponentially bounded. In case the change is restricted to a subset of the beams, we devise a strategy called K-sequential halving and exhaustive search, K-SHES, that leads to an improved bound for the beam selection error as compared to SH. This policy is particularly useful when a near-optimal beam becomes optimal during the beam-selection procedure due to abruptly changing channel conditions. Finally, we demonstrate the efficacy of the proposed scheme by employing it in a tandem beam refinement and data transmission scheme.

Cache Enabled UAV HetNets Access xHaul Coverage Analysis and Optimal Resource Partitioning

We study an urban wireless network in which cache-enabled UAV-Access points (UAV-APs) and UAV-Base stations (UAV-BSs) are deployed to provide higher throughput and ad-hoc coverage to users on the ground. The cache-enabled UAV-APs route the user data to the core network via either terrestrial base stations (TBSs) or backhaul-enabled UAV-BSs through an xHaul link. First, we derive the association probabilities in the access and xHaul links. Interestingly, we show that to maximize the line-of-sight (LoS) unmanned aerial vehicle (UAV) association, densifying the UAV deployment may not be beneficial after a threshold. Then, we obtain the signal to interference noise ratio (SINR) coverage probability of the typical user in the access link and the tagged UAV-AP in the xHaul link, respectively. The SINR coverage analysis is employed to characterize the successful content delivery probability by jointly considering the probability of successful access and xHaul transmissions and successful cache-hit probability. We numerically optimize the distribution of frequency resources between the access and the xHaul links to maximize the successful content delivery to the users. For a given storage capacity at the UAVs, our study prescribes the network operator optimal bandwidth partitioning factors and dimensioning rules concerning the deployment of the UAV-APs.

Actively Tracking the Optimal Arm in Non-Stationary Environments with Mandatory Probing

We study a novel multi-armed bandit (MAB) setting which mandates the agent to probe all the arms periodically in a non-stationary environment. In particular, we develop \texttt{TS-GE} that balances the regret guarantees of classical Thompson sampling (TS) with the broadcast probing (BP) of all the arms simultaneously in order to actively detect a change in the reward distributions. Once a system-level change is detected, the changed arm is identified by an optional subroutine called group exploration (GE) which scales as $\log_2(K)$ for a $K-$armed bandit setting. We characterize the probability of missed detection and the probability of false-alarm in terms of the environment parameters. The latency of change-detection is upper bounded by $\sqrt{T}$ while within a period of $\sqrt{T}$, all the arms are probed at least once. We highlight the conditions in which the regret guarantee of \texttt{TS-GE} outperforms that of the state-of-the-art algorithms, in particular, \texttt{ADSWITCH} and \texttt{M-UCB}. Furthermore, unlike the existing bandit algorithms, \texttt{TS-GE} can be deployed for applications such as timely status updates, critical control, and wireless energy transfer, which are essential features of next-generation wireless communication networks. We demonstrate the efficacy of \texttt{TS-GE} by employing it in a n industrial internet-of-things (IIoT) network designed for simultaneous wireless information and power transfer (SWIPT).

Estimation of Bistatic Radar Detection Performance Under Discrete Clutter Conditions Using Stochastic Geometry

We propose a metric called the bistatic radar detection coverage probability to evaluate the detection performance of a bistatic radar under discrete clutter conditions. Such conditions are commonly encountered in indoor and outdoor environments where passive radars receivers are deployed with opportunistic illuminators. Backscatter and multipath from the radar environment give rise to ghost targets and point clutter responses in the radar signatures resulting in deterioration in the detection performance. In our work, we model the clutter points as a Poisson point process to account for the diversity in their number and spatial distribution. Using stochastic geometry formulations we provide an analytical framework to estimate the probability that the signal to clutter and noise ratio from a target at any particular position in the bistatic radar plane is above a predefined threshold. Using the metric, we derive key radar system perspectives regarding the radar performance under noise and clutter limited conditions; the range at which the bistatic radar framework can be approximated to a monostatic framework; and the optimal radar transmitted power and bandwidth. Our theoretical results are experimentally validated with Monte Carlo simulations.

Optimization of Network Throughput of Joint Radar Communication System Using Stochastic Geometry

Recently joint radar communication (JRC) systems have gained considerable interest for several applications such as vehicular communications, indoor localization and activity recognition, covert military communications, and satellite-based remote sensing. In these frameworks, bistatic/passive radar deployments with directional beams explore the angular search space and identify mobile users/radar targets. Subsequently, directional communication links are established with these mobile users. Consequently, JRC parameters such as the time trade-off between the radar exploration and communication service tasks have direct implications on the network throughput. Using tools from stochastic geometry (SG), we derive several system design and planning insights for deploying such networks and demonstrate how efficient radar detection can augment the communication throughput in a JRC system. Specifically, we provide a generalized analytical framework to maximize the network throughput by optimizing JRC parameters such as the exploration/exploitation duty cycle, the radar bandwidth, the transmit power, and the pulse repetition interval. The analysis is further extended to monostatic radar conditions, which is a special case in our framework. The theoretical results are experimentally validated through Monte Carlo simulations. Our analysis highlights that for a larger bistatic range, lower operating bandwidth and a higher duty cycle must be employed to maximize the network throughput. Furthermore, we demonstrate how a reduced success in radar detection due to higher clutter density deteriorates the overall network throughput. Finally, we show peak reliability of 70% of the JRC link metrics for a single bistatic transceiver configuration.

Kolmogorov-Smirnov Test-Based Actively-Adaptive Thompson Sampling for Non-Stationary Bandits

We consider the non-stationary multi-armed bandit (MAB) framework and propose a Kolmogorov-Smirnov (KS) test based Thompson Sampling (TS) algorithm named TS-KS, that actively detects change points and resets the TS parameters once a change is detected. In particular, for the two-armed bandit case, we derive bounds on the number of samples of the reward distribution to detect the change once it occurs. Consequently, we show that the proposed algorithm has sub-linear regret. Contrary to existing works, our algorithm is able to detect a change when the underlying reward distribution changes even though the mean reward remains the same. Finally, to test the efficacy of the proposed algorithm, we employ it in two case-studies: i) task-offloading scenario in wireless edge-computing, and ii) portfolio optimization. Our results show that the proposed TS-KS algorithm outperforms not only the static TS algorithm but also it performs better than other bandit algorithms designed for non-stationary environments. Moreover, the performance of TS-KS is at par with the state-of-the-art forecasting algorithms such as Facebook-PROPHET and ARIMA.

Optimization of Radar Parameters for Maximum Detection Probability Under Generalized Discrete Clutter Conditions Using Stochastic Geometry

We propose an analytical framework based on stochastic geometry (SG) formulations to estimate a radar's detection performance under generalized discrete clutter conditions. We model the spatial distribution of discrete clutter scatterers as a homogeneous Poisson point process and the radar cross-section of each extended scatterer as a random variable of the Weibull distribution. Using this framework, we derive a metric called the radar detection coverage probability as a function of radar parameters such as transmitted power, system noise temperature and radar bandwidth; and clutter parameters such as clutter density and mean clutter cross-section. We derive the optimum radar bandwidth for maximizing this metric under noisy and cluttered conditions. We also derive the peak transmitted power beyond which there will be no discernible improvement in radar detection performance due to clutter limited conditions. When both transmitted power and bandwidth are fixed, we show how the detection threshold can be optimized for best performance. We experimentally validate the SG results with a hybrid of Monte Carlo and full wave electromagnetic solver based simulations using finite difference time domain (FDTD) techniques.