arXiv subjects

Marceau Coupechoux

Publications and source records attributed to Marceau Coupechoux.

At least 19 recordsLinked to original sources

arXiv2024

Bidding efficiently in Simultaneous Ascending Auctions with incomplete information using Monte Carlo Tree Search and determinization

For decades, Simultaneous Ascending Auction (SAA) has been the most widely used mechanism for spectrum auctions, and it has recently gained popularity for allocating 5G licenses in many countries. Despite its relatively simple rules, SAA introduces a complex strategic game with an unknown optimal bidding strategy. Given the high stakes involved, with billions of euros sometimes on the line, developing an efficient bidding strategy is of utmost importance. In this work, we extend our previous method, a Simultaneous Move Monte-Carlo Tree Search (SM-MCTS) based algorithm named $SMS^α$ to incomplete information framework. For this purpose, we compare three determinization approaches which allow us to rely on complete information SM-MCTS. This algorithm addresses, in incomplete framework, the four key strategic issues of SAA: the exposure problem, the own price effect, budget constraints, and the eligibility management problem. Through extensive numerical experiments on instances of realistic size with an uncertain framework, we show that $SMS^α$ largely outperforms state-of-the-art algorithms by achieving higher expected utility while taking less risks, no matter which determinization method is chosen.

cs.GT↗

arXiv2024

Bidding efficiently in Simultaneous Ascending Auctions with budget and eligibility constraints using Simultaneous Move Monte Carlo Tree Search

For decades, Simultaneous Ascending Auction (SAA) has been the most popular mechanism used for spectrum auctions. It has recently been employed by many countries for the allocation of 5G licences. Although SAA presents relatively simple rules, it induces a complex strategic game for which the optimal bidding strategy is unknown. Considering the fact that sometimes billions of euros are at stake in an SAA, establishing an efficient bidding strategy is crucial. In this work, we model the auction as a $n$-player simultaneous move game with complete information and propose the first efficient bidding algorithm that tackles simultaneously its four main strategic issues: the $\textit{exposure problem}$, the $\textit{own price effect}$, $\textit{budget constraints}$ and the $\textit{eligibility management problem}$. Our solution, called $SMS^α$, is based on Simultaneous Move Monte Carlo Tree Search (SM-MCTS) and relies on a new method for the prediction of closing prices. By introducing a new reward function in $SMS^α$, we give the possibility to bidders to define their own level of risk-aversion. Through extensive numerical experiments on instances of realistic size, we show that $SMS^α$ largely outperforms state-of-the-art algorithms, notably by achieving higher expected utility while taking less risks.

cs.GT↗

arXiv2023

Deep Reinforcement Learning for Uplink Scheduling in NOMA-URLLC Networks

This article addresses the problem of Ultra Reliable Low Latency Communications (URLLC) in wireless networks, a framework with particularly stringent constraints imposed by many Internet of Things (IoT) applications from diverse sectors. We propose a novel Deep Reinforcement Learning (DRL) scheduling algorithm, named NOMA-PPO, to solve the Non-Orthogonal Multiple Access (NOMA) uplink URLLC scheduling problem involving strict deadlines. The challenge of addressing uplink URLLC requirements in NOMA systems is related to the combinatorial complexity of the action space due to the possibility to schedule multiple devices, and to the partial observability constraint that we impose to our algorithm in order to meet the IoT communication constraints and be scalable. Our approach involves 1) formulating the NOMA-URLLC problem as a Partially Observable Markov Decision Process (POMDP) and the introduction of an agent state, serving as a sufficient statistic of past observations and actions, enabling a transformation of the POMDP into a Markov Decision Process (MDP); 2) adapting the Proximal Policy Optimization (PPO) algorithm to handle the combinatorial action space; 3) incorporating prior knowledge into the learning agent with the introduction of a Bayesian policy. Numerical results reveal that not only does our approach outperform traditional multiple access protocols and DRL benchmarks on 3GPP scenarios, but also proves to be robust under various channel and traffic configurations, efficiently exploiting inherent time correlations.

cs.NI↗

arXiv2022

Joint Power and Subcarrier Allocation in Multi-Cell Multi-Carrier NOMA

Non-orthogonal multiple access (NOMA) is a technology proposed for next generation cellular networks because of its high spectral efficiency and enhanced user connectivity. However, in the literature the optimal joint power and sub-carrier allocation for NOMA has been proposed for single cell only. Consequently, a global optimal algorithm for the joint power and sub-carrier allocation for NOMA system in multi-cell scenario is still an open problem. In this work, we propose a polyblock optimization based algorithm for obtaining a global optimal solution. It has reduced complexity due to a necessary and sufficient condition for feasible successive interference cancellation (SIC). Besides, we can adjust its optimization approximation parameter to serve as benchmark solution or to offer suitable practical solution for multi-cell multi-carrier NOMA systems. Numerical studies have shown its effectiveness.

cs.IT↗

arXiv2021

Optimal Trajectories of a UAV Base Station Using Hamilton-Jacobi Equations

We consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV). Assuming a traffic intensity map of users to be served, the UAV must travel from a given initial location to a final position within a given duration and serves the traffic on its way. The problem consists in finding the optimal trajectory that minimizes a certain cost depending on the velocity and on the amount of served traffic. We formulate the problem using the framework of Lagrangian mechanics. We derive closed-form formulas for the optimal trajectory when the traffic intensity is quadratic (single-phase) using Hamilton-Jacobi equations. When the traffic intensity is bi-phase, i.e. made of two quadratics, we provide necessary conditions of optimality that allow us to propose a gradient-based algorithm and a new algorithm based on the linear control properties of the quadratic model. These two solutions are of very low complexity because they rely on fast convergence numerical schemes and closed form formulas. These two approaches return a trajectory satisfying the necessary conditions of optimality. At last, we propose a data processing procedure based on a modified K-means algorithm to derive a bi-phase model and an optimal trajectory simulation from real traffic data.

math.OC↗

arXiv2021

DNN Based Beam Selection in mmW Heterogeneous Networks

We consider a heterogeneous cellular network wherein multiple small cell millimeter wave (mmW) base stations (BSs) coexist with legacy sub-6GHz macro BSs. In the mmW band, small cells use multiple narrow beams to ensure sufficient coverage and User Equipments (UEs) have to select the best small cell and the best beam in order to access the network. This process usually based on exhaustive search may introduce unacceptable latency. In order to address this issue, we rely on the sub-6GHz macro BS support and propose a deep neural network (DNN) architecture that utilizes basic components from the Channel State Information (CSI) of sub-6GHz network as input features. The output of the DNN is the mmW BS and beam selection that can provide the best communication performance. In the set of features, we avoid using the UE location, which may not be readily available for every device. We formulate a mmW BS selection and beam selection problem as a classification and regression problem respectively and propose a joint solution using a branched neural network. The numerical comparison with the conventional exhaustive search results shows that the proposed design demonstrate better performance than exhaustive search in terms of latency with at least 85\% accuracy.

cs.NI↗

arXiv2020

Secure and Robust MIMO Transceiver for Multicast Mission Critical Communications

Mission-critical communications (MCC) involve all communications between people in charge of the safety of the civil society. MCC have unique requirements that include improved reliability, security and group communication support. In this paper, we propose a secure and robust Multiple-Input-Multiple-Output (MIMO) transceiver, designed for multiple Base Stations supporting multicast MCC in presence of multiple eavesdroppers. We formulate minimization problems with the Sum-Mean-Square-Error (SMSE) at legitimate users as an objective function, and a lower bound for the MSE at eavesdroppers as a constraint. Security is achieved thanks to physical layer security mechanisms, namely MIMO beamforming and Artificial Noise (AN). Reliability is achieved by designing a system which is robust to Channel State Information errors. They can be of known distribution or norm-bounded. In the former case, a coordinate descent algorithm is proposed to solve the problem. In the latter case, we propose an worst-case based iterative algorithm. Numerical results at physical layer and system level reveal the crucial role of robust designs for reliable MCC. We show the interest of both robust design and AN to improve the security gap. We show that full BS cooperation in preferred for highly secured and reliable MCC but dynamic clustering allows to trade-off security and reliability against capacity.

cs.IT↗

arXiv2020

Beamwidth Optimization and Resource Partitioning Scheme for Localization Assisted mm-wave Communications

We study a mm-wave wireless network deployed along the roads of an urban area, to support localization and communication services simultaneously for outdoor mobile users. In this network, we propose a mm-wave initial beam-selection scheme based on localization-bounds, which greatly reduces the initial access delay as compared to traditional initial access schemes for standalone mm-wave base station (BS). Then, we introduce a downlink transmission protocol, in which the radio frames are partitioned into three phases, namely, initial access, data, and localization, respectively. We establish a trade-off between the localization and communication performance of mm-wave systems, and show how enhanced localization can actually improve the data-communication performance. Our results suggest that dense BS deployments enable to allocate more resources to the data phase while still maintaining appreciable localization performance. Furthermore, for the case of sparse deployments and large beam dictionary size (i.e., with thinner beams), more resources must be allotted to the localization phase for optimizing the rate coverage. Based on our results, we provide several system design insights and dimensioning rules for the network operators that will deploy the first generation of mm-wave BSs.

eess.SP↗

arXiv2020

Joint Subcarrier and Power Allocation in NOMA: Optimal and Approximate Algorithms

Non-orthogonal multiple access (NOMA) is a promising technology to increase the spectral efficiency and enable massive connectivity in 5G and future wireless networks. In contrast to orthogonal schemes, such as OFDMA, NOMA multiplexes several users on the same frequency and time resource. Joint subcarrier and power allocation problems (JSPA) in NOMA are NP-hard to solve in general. In this family of problems, we consider the weighted sum-rate (WSR) objective function as it can achieve various tradeoffs between sum-rate performance and user fairness. Because of JSPA's intractability, a common approach in the literature is to solve separately the power control and subcarrier allocation (also known as user selection) problems, therefore achieving sub-optimal result. In this work, we first improve the computational complexity of existing single-carrier power control and user selection schemes. These improved procedures are then used as basic building blocks to design new algorithms, namely Opt-JSPA, $\varepsilon$-JSPA and Grad-JSPA. Opt-JSPA computes an optimal solution with lower complexity than current optimal schemes in the literature. It can be used as a benchmark for optimal WSR performance in simulations. However, its pseudo-polynomial time complexity remains impractical for real-world systems with low latency requirements. To further reduce the complexity, we propose a fully polynomial-time approximation scheme called $\varepsilon$-JSPA. Since, no approximation has been studied in the literature, $\varepsilon$-JSPA stands out by allowing to control a tight trade-off between performance guarantee and complexity. Finally, Grad-JSPA is a heuristic based on gradient descent. Numerical results show that it achieves near-optimal WSR with much lower complexity than existing optimal methods.

math.OC↗

arXiv2020

Online Trajectory Optimization Using Inexact Gradient Feedback for Time-Varying Environments

This paper considers the problem of online trajectory design under time-varying environments. We formulate the general trajectory optimization problem within the framework of time-varying constrained convex optimization and proposed a novel version of the online gradient ascent algorithm for such problems. Moreover, the gradient feedback is noisy and allows us to use the proposed algorithm for a range of practical applications where it is difficult to acquire the true gradient. In contrast to the most available literature, we present the offline sublinear regret of the proposed algorithm up to the path length variations of the optimal offline solution, the cumulative gradient, and the error in the gradient variations. Furthermore, we establish a lower bound on the offline dynamic regret, which defines the optimality of any trajectory. To show the efficacy of the proposed algorithm, we consider two practical problems of interest. First, we consider a device to device (D2D) communications setting, and the goal is to design a user trajectory while maximizing its connectivity to the internet. The second problem is associated with the online planning of energy-efficient trajectories for unmanned surface vehicles (USV) under strong disturbances in ocean environments with both static and dynamic goal locations. The detailed simulation results demonstrate the significance of the proposed algorithm on synthetic and real data sets. Video on the real-world datasets can be found at {https://www.youtube.com/watch?v=FcRqqWtpf\_0}

math.OC↗

arXiv2019

Optimal Joint Subcarrier and Power Allocation in NOMA is Strongly NP-Hard

Non-orthogonal multiple access (NOMA) is a promising radio access technology for 5G. It allows several users to transmit on the same frequency and time resource by performing power-domain multiplexing. At the receiver side, successive interference cancellation (SIC) is applied to mitigate interference among the multiplexed signals. In this way, NOMA can outperform orthogonal multiple access schemes used in conventional cellular networks in terms of spectral efficiency and allows more simultaneous users. This paper investigates the computational complexity of joint subcarrier and power allocation problems in multi-carrier NOMA systems. We prove that these problems are strongly NP-hard for a large class of objective functions, namely the weighted generalized means of the individual data rates. This class covers the popular weighted sum-rate, proportional fairness, harmonic mean and max-min fairness utilities. Our results show that the optimal power and subcarrier allocation cannot be computed in polynomial time in the general case, unless P = NP. Nevertheless, we present some tractable special cases and we show that they can be solved efficiently.

cs.CC↗

arXiv2019

Weighted Sum-Rate Maximization in Multi-Carrier NOMA with Cellular Power Constraint

Non-orthogonal multiple access (NOMA) has received significant attention for future wireless networks. NOMA outperforms orthogonal schemes, such as OFDMA, in terms of spectral efficiency and massive connectivity. The joint subcarrier and power allocation problem in NOMA is NP-hard to solve in general, due to complex impacts of signal superposition on each user's achievable data rates, as well as combinatorial constraints on the number of multiplexed users per sub-carrier to mitigate error propagation. In this family of problems, weighted sum-rate (WSR) is an important objective function as it can achieve different tradeoffs between sum-rate performance and user fairness. We propose a novel approach to solve the WSR maximization problem in multi-carrier NOMA with cellular power constraint. The problem is divided into two polynomial time solvable sub-problems. First, the multi-carrier power control (given a fixed subcarrier allocation) is non-convex. By taking advantage of its separability property, we design an optimal and low complexity algorithm (MCPC) based on projected gradient descent. Secondly, the single-carrier user selection is a non-convex mixed-integer problem that we solve using dynamic programming (SCUS). This work also aims to give an understanding on how each sub-problem's particular structure can facilitate the algorithm design. In that respect, the above MCPC and SCUS are basic building blocks that can be applied in a wide range of resource allocation problems. Furthermore, we propose an efficient heuristic to solve the general WSR maximization problem by combining MCPC and SCUS. Numerical results show that it achieves near-optimal sum-rate with user fairness, as well as significant performance improvement over OMA.

cs.NI↗

arXiv2018

Optimal Trajectories of a UAV Base Station Using Lagrangian Mechanics

In this paper, we consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). We consider a map characterized by a traffic intensity of users to be served. The UAV BS must travel from a given initial location at an initial time to a final position within a given duration and serves the traffic on its way. The problem consists in finding the optimal trajectory that minimizes a certain cost depending on the velocity and on the amount of served traffic. We formulate the problem using the framework of Lagrangian mechanics. When the traffic intensity is quadratic (single-phase), we derive closed-form formulas for the optimal trajectory. When the traffic intensity is bi-phase, we provide necessary conditions of optimality and propose an Alternating Optimization Algorithm that returns a trajectory satisfying these conditions. The Algorithm is initialized with a Model Predictive Control (MPC) online algorithm. Numerical results show how we improve the trajectory with respect to the MPC solution.

math.OC↗

arXiv2018

Accurate Characterization of Dynamic Cell Load in Noise-Limited Random Cellular Networks

The analyses of cellular network performance based on stochastic geometry generally ignore the traffic dynamics in the network. This restricts the proper evaluation and dimensioning of the network from the perspective of a mobile operator. To address the effect of dynamic traffic, recently, the mean cell approach has been introduced, which approximates the average network load by the zero cell load. However, this is not a realistic characterization of the network load, since a zero cell is statistically larger than a random cell drawn from the population of cells, i.e., a typical cell. In this paper, we analyze the load of a noise-limited network characterized by high signal to noise ratio (SNR). The noise-limited assumption can be applied to a variety of scenarios, e.g., millimeter wave networks with efficient interference management mechanisms. First, we provide an analytical framework to obtain the cumulative density function of the load of the typical cell. Then, we obtain two approximations of the average load of the typical cell. We show that our study provides a more realistic characterization of the average load of the network as compared to the mean cell approach. Moreover, the prescribed closed-form approximation is more tractable than the mean cell approach.

cs.IT↗

arXiv2018

An Online Approach to D2D Trajectory Utility Maximization Problem

This paper considers the problem of designing the user trajectory in a device-to-device communications setting. We consider a pair of pedestrians connected through a D2D link. The pedestrians seek to reach their respective destinations while using the D2D link for data exchange applications such as file transfer, video calling, and online gaming. In order to enable better D2D connectivity, the pedestrians are willing to deviate from their respective shortest paths, at the cost of reaching their destinations slightly late. A generic trajectory optimization problem is formulated and solved for the case when full information about the problem in known in advance. Motivated by the D2D user's need to keep their destinations private, we also formulate a regularized variant of the problem that can be used to develop a fully online algorithm. The proposed online algorithm is quite efficient, and is shown to achieve a sublinear \emph{offline} regret while satisfying the required mobility constraints exactly. The theoretical results are backed by detailed numerical tests that establish the efficacy of the proposed algorithms under various settings.

math.OC↗

arXiv2017

Coverage Analysis and Load Balancing in HetNets with mmWave Multi-RAT Small Cells

We characterize a two tier heterogeneous network, consisting of classical sub-6GHz macro cells, and multi Radio Access Technology (RAT) small cells able to operate in sub-6GHz and millimeter-wave (mm-wave) bands. For optimizing coverage and to balance loads, we propose a two-step mechanism based on two biases for tuning the tier and RAT selection, where the sub-6GHz band is used to speed-up the initial access procedure in the mm-wave RAT. First, we investigate the effect of the biases in terms of signal to interference plus noise ratio (SINR) distribution, cell load, and user throughput. More specifically, we obtain the optimal biases that maximize either the SINR coverage or the user downlink throughput. Then, we characterize the cell load using the mean cell approach and derive upper bounds on the overloading probabilities. Finally, for a given traffic density, we provide the small cell density required to satisfy system constraints in terms of overloading and outage probabilities. Our analysis highlights the importance of deploying dual band small cells in particular when small cells are sparsely deployed or in case of heavy traffic.

cs.IT↗

arXiv2017

Sequential Decision Algorithms for Measurement-Based Impromptu Deployment of a Wireless Relay Network along a Line

We are motivated by the need, in some applications, for impromptu or as-you-go deployment of wireless sensor networks. A person walks along a line, starting from a sink node (e.g., a base-station), and proceeds towards a source node (e.g., a sensor) which is at an a priori unknown location. At equally spaced locations, he makes link quality measurements to the previous relay, and deploys relays at some of these locations, with the aim to connect the source to the sink by a multihop wireless path. In this paper, we consider two approaches for impromptu deployment: (i) the deployment agent can only move forward (which we call a pure as-you-go approach), and (ii) the deployment agent can make measurements over several consecutive steps before selecting a placement location among them (which we call an explore-forward approach). We consider a light traffic regime, and formulate the problem as a Markov decision process, where the trade-off is among the power used by the nodes, the outage probabilities in the links, and the number of relays placed per unit distance. We obtain the structures of the optimal policies for the pure as-you-go approach as well as for the explore-forward approach. We also consider natural heuristic algorithms, for comparison. Numerical examples show that the explore-forward approach significantly outperforms the pure as-you-go approach. Next, we propose two learning algorithms for the explore-forward approach, based on Stochastic Approximation, which asymptotically converge to the set of optimal policies, without using any knowledge of the radio propagation model. We demonstrate numerically that the learning algorithms can converge (as deployment progresses) to the set of optimal policies reasonably fast and, hence, can be practical, model-free algorithms for deployment over large regions.

cs.NI↗

arXiv2017

Deploy-As-You-Go Wireless Relay Placement: An Optimal Sequential Decision Approach using the Multi-Relay Channel Model

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of as-you-go deployment of relay nodes. The achievable rate formulas are for full-duplex radios at the relays and for decode-and-forward relaying. Deployment is done along the straight line joining a source node and a sink node at an unknown distance from the source. The problem is for a deployment agent to walk from the source to the sink, deploying relays as he walks, given that the distance to the sink is exponentially distributed with known mean. As a precursor, we apply the multi-relay channel achievable rate formula to obtain the optimal power allocation to relays placed along a line, at fixed locations. This permits us to obtain the optimal placement of a given number of nodes when the distance between the source and sink is given. Numerical work suggests that, at low attenuation, the relays are mostly clustered near the source in order to be able to cooperate, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that the effect of path-loss can be entirely mitigated if a large enough number of relays are placed uniformly between the source and the sink. The structure of the optimal power allocation for a given placement of the nodes, then motivates us to formulate the problem of as-you-go placement of relays along a line of exponentially distributed length, and with the exponential path-loss model, so as to minimize a cost function that is additive over hops. The hop cost trades off a capacity limiting term, motivated from the optimal power allocation solution, against the cost of adding a relay node. We formulate the problem as a total cost Markov decision process, establish results for the value function, and provide insights into the placement policy and the performance of the deployed network via numerical exploration.

cs.NI↗