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Harpreet S. Dhillon

Publications and source records attributed to Harpreet S. Dhillon.

At least 109 records · Page 6Linked to original sources

Deep Reinforcement Learning for Minimizing Age-of-Information in UAV-assisted Networks

Unmanned aerial vehicles (UAVs) are expected to be a key component of the next-generation wireless systems. Due to their deployment flexibility, UAVs are being considered as an efficient solution for collecting information data from ground nodes and transmitting it wirelessly to the network. In this paper, a UAV-assisted wireless network is studied, in which energy-constrained ground nodes are deployed to observe different physical processes. In this network, a UAV that has a time constraint for its operation due to its limited battery, moves towards the ground nodes to receive status update packets about their observed processes. The flight trajectory of the UAV and scheduling of status update packets are jointly optimized with the objective of achieving the minimum weighted sum for the age-of-information (AoI) values of different processes at the UAV, referred to as weighted sum-AoI. The problem is modeled as a finite-horizon Markov decision process (MDP) with finite state and action spaces. Since the state space is extremely large, a deep reinforcement learning (RL) algorithm is proposed to obtain the optimal policy that minimizes the weighted sum-AoI, referred to as the age-optimal policy. Several simulation scenarios are considered to showcase the convergence of the proposed deep RL algorithm. Moreover, the results also demonstrate that the proposed deep RL approach can significantly improve the achievable sum-AoI per process compared to the baseline policies, such as the distance-based and random walk policies. The impact of various system design parameters on the optimal achievable sum-AoI per process is also shown through extensive simulations.

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A Reinforcement Learning Framework for Optimizing Age-of-Information in RF-powered Communication Systems

In this paper, we study a real-time monitoring system in which multiple source nodes are responsible for sending update packets to a common destination node in order to maintain the freshness of information at the destination. Since it may not always be feasible to replace or recharge batteries in all source nodes, we consider that the nodes are powered through wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy (referred to as the age-optimal policy) that jointly optimizes WET and scheduling of update packet transmissions with the objective of minimizing the long-term average weighted sum of Age-of-Information (AoI) values for different physical processes (observed by the source nodes) at the destination node, referred to as the sum-AoI. To solve this optimization problem, we first model this setup as an average cost Markov decision process (MDP). Due to the extreme curse of dimensionality in the state space of the formulated MDP, classical reinforcement learning algorithms are no longer applicable to our problem. Motivated by this, we propose a deep reinforcement learning (DRL) algorithm that can learn the age-optimal policy in a computationally-efficient manner. We further characterize the structural properties of the age-optimal policy analytically, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the age-optimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average weighted sum-AoI.

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Performance Characterization of Canonical Mobility Models in Drone Cellular Networks

In this paper, we characterize the performance of several canonical mobility models in a drone cellular network in which drone base stations (DBSs) serve user equipments (UEs) on the ground. In particular, we consider the following four mobility models: (i) straight line (SL), (ii) random stop (RS), (iii) random walk (RW), and (iv) random waypoint (RWP), among which the SL mobility model is inspired by the simulation models used by the third generation partnership project (3GPP) for the placement and trajectory of drones, while the other three are well-known canonical models (or their variants) that offer a useful balance between realism and tractability. Assuming the nearest-neighbor association policy, we consider two service models for the UEs: (i) UE independent model (UIM), and (ii) UE dependent model (UDM). While the serving DBS follows the same mobility model as the other DBSs in the UIM, it is assumed to fly towards the UE of interest in the UDM and hover above its location after reaching there. The main contribution of this paper is a unified approach to characterize the point process of DBSs for all the mobility and service models. Using this, we provide exact mathematical expressions for the average received rate and the session rate as seen by the typical UE. Further, using tools from calculus of variations, we concretely demonstrate that the simple SL mobility model provides a lower bound on the performance of other general mobility models (including the ones in which drones follow curved trajectories) as long as the movement of each drone in these models is independent and identically distributed (i.i.d.). To the best of our knowledge, this is the first work that provides a rigorous analysis of key canonical mobility models for an infinite drone cellular network and establishes useful connections between them.

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Meta Distribution for Downlink NOMA in Cellular Networks with 3GPP-inspired User Ranking

This paper presents the meta distribution analysis of the downlink two-user non-orthogonal multiple access (NOMA) in cellular networks. We propose a novel user ranking technique wherein the users from the cell center (CC) and cell edge (CE) regions are paired for the non-orthogonal transmission. Inspired by how users are partitioned in 3GPP cellular models, the CC and CE users are characterized based on the mean powers received from the serving and the dominant interfering BSs. We demonstrate that the proposed technique ranks users in an accurate order with distinct link qualities, which is imperative for the performance of NOMA system. The exact moments of the meta distributions for the CC and CE users under NOMA and orthogonal multiple access (OMA) are derived. In addition, we provide tight beta distribution approximations for the meta distributions and exact expressions of the mean local delays and the cell throughputs for the NOMA and OMA cases. To the best of our knowledge, this is the first comprehensive analysis of NOMA using stochastic geometry with 3GPP-inspired user ranking scheme that depends upon both of the link qualities from the serving and dominant interfering BSs.

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Millimeter Wave Integrated Access and Backhaul in 5G: Performance Analysis and Design Insights

With the emergence of integrated access and backhaul (IAB) in the fifth generation (5G) of cellular networks, backhaul is no longer just a passive capacity constraint in cellular network design. In fact, this tight integration of access and backhaul is one of the key ways in which 5G millimeter wave (mm-wave) heterogeneous cellular networks (HetNets) differ from traditional settings where the backhaul network was designed independently from the radio access network (RAN). With the goal of elucidating key design trends for this new paradigm, we develop an analytical framework for a two-tier HetNet with IAB where the macro base stations (MBSs) provide mm-wave backhaul to the small cell base stations (SBSs). For this network, we derive the downlink rate coverage probability for two types of resource allocations at the MBS: 1) integrated resource allocation (IRA): where the total bandwidth (BW) is dynamically split between access and backhaul, and 2) orthogonal resource allocation (ORA): where a static partition is defined for the access and backhaul communications. Our analysis concretely demonstrates that offloading users from the MBSs to SBSs may not provide similar rate improvements in an IAB setting as it would in a HetNet with fiber-backhauled SBS. Our analysis also shows that it is not possible to improve the user rate in an IAB setting by simply densifying the SBSs due to the bottleneck on the rate of wireless backhaul links between MBS and SBS.

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A Mathematical Justification for Exponentially Distributed NLOS Bias

In the past few decades, the localization literature has seen many models attempting to characterize the non-line-of-sight (NLOS) bias error commonly experienced in range measurements. These models have either been based on specific measurement data or chosen due to attractive features of a particular distribution, yet to date, none have been backed by rigorous analysis. Leveraging tools from stochastic geometry, this paper attempts to fill this void by providing the first analytical backing for an NLOS bias error model. Using a Boolean model to statistically characterize the random locations, orientations, and sizes of reflectors, and assuming first-order (i.e., single-bounce) reflections, the distance traversed by the first-arriving NLOS path is characterized. Under these assumptions, this analysis reveals that NLOS bias exhibits an exponential form and can in fact be well approximated by an exponential distribution -- a result consistent with previous NLOS bias error models in the literature. This analytically derived distribution is then compared to a common exponential model from the literature, revealing this distribution to be a close match in some cases and a lower bound in others. Lastly, the assumptions under which these results were derived suggest this model is aptly suited to characterize NLOS bias in 5G millimeter wave systems as well.

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3GPP-inspired Stochastic Geometry-based Mobility Model for a Drone Cellular Network

This paper deals with the stochastic geometry-based characterization of the time-varying performance of a drone cellular network in which the initial locations of drone base stations (DBSs) are modeled as a Poisson point process (PPP) and each DBS is assumed to move on a straight line in a random direction. This drone placement and trajectory model closely emulates the one used by the third generation partnership project (3GPP) for drone-related studies. Assuming the nearest neighbor association policy for a typical user equipment (UE) on the ground, we consider two models for the mobility of the serving DBS: (i) UE independent model, and (ii) UE dependent model. Using displacement theorem from stochastic geometry, we characterize the time-varying interference field as seen by the typical UE, using which we derive the time-varying coverage probability and data rate at the typical UE. We also compare our model with more sophisticated mobility models where the DBSs may move in nonlinear trajectories and demonstrate that the coverage probability and rate estimated by our model act as lower bounds to these more general models. To the best of our knowledge, this is the first work to perform a rigorous analysis of the 3GPP-inspired drone mobility model and establish connection between this model and the more general non-linear mobility models.

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Machine Learning meets Stochastic Geometry: Determinantal Subset Selection for Wireless Networks

In wireless networks, many problems can be formulated as subset selection problems where the goal is to select a subset from the ground set with the objective of maximizing some objective function. These problems are typically NP-hard and hence solved through carefully constructed heuristics, which are themselves mostly NP-complete and thus not easily applicable to large networks. On the other hand, subset selection problems occur in slightly different context in machine learning (ML) where the goal is to select a subset of high quality yet diverse items from a ground set. In this paper, we introduce a novel DPP-based learning (DPPL) framework for efficiently solving subset selection problems in wireless networks. The DPPL is intended to replace the traditional optimization algorithms for subset selection by learning the quality-diversity trade-off in the optimal subsets selected by an optimization routine. As a case study, we apply DPPL to the wireless link scheduling problem, where the goal is to determine the subset of simultaneously active links which maximizes the network-wide sum-rate. We demonstrate that the proposed DPPL approaches the optimal solution with significantly lower computational complexity than the popular optimization algorithms used for this problem in the literature.

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Analysis of Transmission Rate of Wireless Networks under the Broadcast Approach with Continuum of Transmission Layers

In this letter, we characterize the performance of broadcast approach with continuum of transmission layers in random wireless networks where the channel state information (CSI) is assumed to be known only at the receiver. By modeling the transmitter-receiver pairs using bipolar Poisson point process, we derive analytical expressions for the mean and variance of achievable transmission rate and the network transmission capacity under broadcast approach. Our analysis shows that the broadcast approach provides better mean transmission rate with lower variance compared to outage strategy.

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Coverage and Rate Analysis of Downlink Cellular Vehicle-to-Everything (C-V2X) Communication

In this paper, we present the downlink coverage and rate analysis of a cellular vehicle-to-everything (C-V2X) communication network where the locations of vehicular nodes and road side units (RSUs) are modeled as Cox processes driven by a Poisson line process (PLP) and the locations of cellular macro base stations (MBSs) are modeled as a 2D Poisson point process (PPP). Assuming a fixed selection bias and maximum average received power based association, we compute the probability with which a {\em typical receiver}, an arbitrarily chosen receiving node, connects to a vehicular node or an RSU and a cellular MBS. For this setup, we derive the signal-to-interference ratio (SIR)-based coverage probability of the typical receiver. One of the key challenges in the computation of coverage probability stems from the inclusion of shadowing effects. As the standard procedure of interpreting the shadowing effects as random displacement of the location of nodes is not directly applicable to the Cox process, we propose an approximation of the spatial model inspired by the asymptotic behavior of the Cox process. Using this asymptotic characterization, we derive the coverage probability in terms of the Laplace transform of interference power distribution. Further, we compute the downlink rate coverage of the typical receiver by characterizing the load on the serving vehicular nodes or RSUs and serving MBSs. We also provide several key design insights by studying the trends in the coverage probability and rate coverage as a function of network parameters. We observe that the improvement in rate coverage obtained by increasing the density of MBSs can be equivalently achieved by tuning the selection bias appropriately without the need to deploy additional MBSs.

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Joint Energy and SINR Coverage in Spatially Clustered RF-powered IoT Network

Owing to the ubiquitous availability of radio-frequency (RF) signals, RF energy harvesting is emerging as an appealing solution for powering IoT devices. In this paper, we model and analyze an IoT network which harvests RF energy and receives information from the same wireless network. In order to enable this operation, each time slot is partitioned into charging and information reception phases. For this setup, we characterize two performance metrics: (i) energy coverage and (ii) joint signal-to-interference-plus-noise (SINR) and energy coverage. The analysis is performed using a realistic spatial model that captures the spatial coupling between the locations of the IoT devices and the nodes of the wireless network (referred henceforth as the IoT gateways), which is often ignored in the literature. In particular, we model the locations of the IoT devices using a Poisson cluster process (PCP) and assume that some of the clusters have IoT gateways (GWs) deployed at their centers while the other GWs are deployed independently of the IoT devices. The level of coupling can be controlled by tuning the fraction of total GWs that are deployed at the cluster centers. Due to the inherent intractability of computing the distribution of shot noise process for this setup, we propose two accurate approximations, using which the aforementioned metrics are characterized. Multiple system design insights are drawn from our results. For instance, we demonstrate the existence of optimal slot partitioning that maximizes the system throughput. In addition, we explore the effect of the level of coupling between the locations of the IoT devices and the GWs on this optimal slot partitioning. Particularly, our results reveal that the optimal value of time duration for the charging phase increases as the level of coupling decreases.

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Average Peak Age-of-Information Minimization in UAV-assisted IoT Networks

Motivated by the need to ensure timely delivery of information (e.g., status updates) in the Internet-of-things (IoT) paradigm, this paper investigates the role of an Unmanned aerial vehicle (UAV) as a mobile relay to minimize the average Peak Age-of-information (PAoI) for a source-destination pair. For this setup, we formulate an optimization problem to jointly optimize the UAV's flight trajectory as well as energy and service time allocations for packet transmissions. In order to solve this non-convex problem, we propose an efficient iterative algorithm and establish its convergence analytically. Closed-form solutions for some sub-problems are also provided. One of the sub-problems we solve in this procedure is to jointly optimize the energy and service time allocations for a given trajectory of the UAV. This problem is of interest on its own right because in some cases we may not be able to alter the UAV's trajectory based on the locations of the IoT devices (especially when its primary mission is something else). Our numerical results quantify the gains that can be achieved by additionally optimizing the UAV's trajectory.

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Unified Analysis of HetNets using Poisson Cluster Process under Max-Power Association

Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). Despite its undisputed relevance to HetNets -- corroborated by the models used in industry -- the PCP's use in performance analysis has been limited. This is primarily because of the lack of analytical tools to characterize performance metrics such as the coverage probability of a user connected to the strongest BS. In this paper, we develop an analytical framework for the evaluation of the coverage probability, or equivalently the complementary cumulative density function (CCDF) of signal-to-interference-and-noise-ratio (SINR), of a typical user in a K-tier HetNet under a max power-based association strategy, where the BS locations of each tier follow either a Poisson point process (PPP) or a PCP. The key enabling step involves conditioning on the parent PPPs of all the PCPs which allows us to express the coverage probability as a product of sum-product and probability generating functionals (PGFLs) of the parent PPPs. In addition to several useful insights, our analysis provides a rigorous way to study the impact of the cluster size on the SINR distribution, which was not possible using existing PPP-based models.

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Bandwidth Partitioning and Downlink Analysis in Millimeter Wave Integrated Access and Backhaul for 5G

With the increasing network densification, it has become exceedingly difficult to provide traditional fiber backhaul access to each cell site, which is especially true for small cell base stations (SBSs). The increasing maturity of millimeter wave (mm-wave) communication has opened up the possibility of providing high-speed wireless backhaul to such cell sites. Since mm-wave is also suitable for access links, the third generation partnership project (3GPP) is envisioning an integrated access and backhaul (IAB) architecture for the fifth generation (5G) cellular networks in which the same infrastructure and spectral resources will be used for both access and backhaul. In this paper, we develop an analytical framework for IAB-enabled cellular network using which its downlink rate coverage probability is accurately characterized. Using this framework, we study the performance of three backhaul bandwidth (BW) partition strategies: 1) equal partition: when all SBSs obtain equal share of the backhaul BW; 2) instantaneous load-based partition: when the backhaul BW share of an SBS is proportional to its instantaneous load; and 3) average load-based partition: when the backhaul BW share of an SBS is proportional to its average load. Our analysis shows that depending on the choice of the partition strategy, there exists an optimal split of access and backhaul BW for which the rate coverage is maximized. Further, there exists a critical volume of cell-load (total number of users) beyond which the gains provided by the IAB-enabled network disappear and its performance converges to that of the traditional macro-only network with no SBSs.

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Performance Analysis of MRC under Spatially Correlated Interference using Mixture-based Method

Effect of interference correlation on wireless systems is often studied by modeling the locations of interferers as a Poisson Point Process (PPP). However, in many cases, the complicated nature of this correlation limits the analytical tractability of the PPP-based approach. For example, for an interference-aware $N$-antenna Maximum-Ratio Combining (MRC) receiver, the analytical expression for outage probability is available only for $N=2$. For $N>2$, the exact analysis using standard PPP-based approach becomes intractable because of which one has to either resort to bounds or to simulations. In this letter, we overcome this issue and derive the MRC outage probability for an arbitrary $N$ by employing the mixture-based method of modeling the correlation in the interference powers. This method offers a much simpler analytical structure to the correlated interference, thereby lending analytical tractability to such analyses. The mixture parameter ($q$) is tuned based on the matching of joint Signal-to-Interference Ratio (SIR) statistics, which results in a very accurate mixture-based result. The tightness of these approximations is verified using Monte Carlo simulations.

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A Tractable Analysis of the Blind-spot Probability in Localization Networks under Correlated Blocking

In localization applications, the line-of-sight between anchors and targets may be blocked by obstacles in the environment. A target that is invisible (i.e., without line-of-sight) to a sufficient number of anchors cannot be unambiguously localized and is, therefore, said to be in a blind spot. In this paper, we analyze the blind spot probability of a typical target by using stochastic geometry to model the randomness in the obstacle and anchor locations. In doing so, we handle correlated anchor blocking induced by the obstacles, unlike previous works that assume independent anchor blocking. We first characterize the regime over which the independent blocking assumption underestimates the blind spot probability of the typical target, which in turn, is characterized as a function of the distribution of the visible area, surrounding the target location. Since this distribution is difficult to characterize exactly, we formulate the nearest two-obstacle approximation, which is equivalent to considering correlated blocking for only the nearest two obstacles from the target and assuming independent blocking for the remaining obstacles. Based on this, we derive an approximate expression for the blind spot probability, which helps determine the anchor deployment intensity needed for the blind spot probability of a typical target to be at most a threshold, $μ$.

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Johnson-Mehl Cell-based Analysis of UL Cellular Network with Coupled User and BS Locations

In this work, we analyze the performance of the uplink (UL) of a cellular network where the base station (BS) locations follow a homogeneous Poisson point process (PPP), and the locations of users and BSs are spatially coupled. In order to capture this coupling, we consider that users attached to a BS are located uniformly at random independently of each other in the Johnson-Mehl (JM) cell of that BS. For this system model, we derive analytical expressions for the UL signal to interference ratio (SIR) coverage probability and average spectral efficiency (SE) of a typical user in the network. One of the key intermediate steps in our analysis is the approximate, but accurate, characterization of the area distribution of a typical JM cell. Another key intermediate step is the accurate statistical characterization of the point process formed by the interfering users that subsequently enables the coverage probability analysis. We present coverage probability and SE results for a typical user and study the interplay between different system parameters.

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Stochastic Geometry-based Uplink Analysis of Massive MIMO Systems with Fractional Pilot Reuse

In this work, we analyze the performance of the uplink (UL) of a massive MIMO network considering an asymptotically large number of antennas at base stations (BSs). We model the locations of BSs as a homogeneous Poisson point process (PPP) and assume that their service regions are limited to their respective Poisson-Voronoi cells (PVCs). Further, for each PVC, based on a threshold radius, we model the cell center (CC) region as the Johnson-Mehl (JM) cell of its BS while rest of the PVC is deemed as the cell edge (CE) region. The CC and CE users are located uniformly at random independently of each other in the JM cell and CE region, respectively. In addition, we consider a fractional pilot reuse (FPR) scheme where two different sets of pilot sequences are used for CC and CE users with the objective of reducing the interference due to pilot contamination for CE users. Based on the above system model, we derive analytical expressions for the UL signal-to-interference-and-noise ratio (SINR) coverage probability and average spectral efficiency (SE) for randomly selected CC and CE users. In addition, we present an approximate expression for the average cell SE. One of the key intermediate results in our analysis is the approximate but accurate characterization of the distributions of the CC and CE areas of a typical cell. Another key intermediate step is the accurate characterization of the pair correlation functions of the point processes formed by the interfering CC and CE users that subsequently enables the coverage probability analysis. From our system analysis, we present a partitioning rule for the number of pilot sequences to be used for CC and CE users as a function of threshold radius that improves the average CE user SE while achieving similar CC user SE with respect to unity pilot reuse.

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