The growth of e-commerce has led to a significant increase in parcel deliveries. In 2021, e-commerce accounted for 13.4% of retail trade, and it is projected to grow by 3% each year. To meet the demand for more efficient parcel delivery practices, it is essential to improve the organization of parcel collection (first mile), large-scale parcel transportation between different regions (middle mile), and final delivery to the customer (last mile). This is crucial not only for reducing the environmental impact but also for mitigating the disturbances caused by such activities.In this study, we focus on the middle mile part. The studied problem deals with the parcel delivery between different regional distribution centers with possibility to use the cross-dock. The deliveries are performed directly or through a route. In the context of this research, the objective is to minimize the total distance travelled per parcel for all deliveries. The primary challenge is naturally presented as a vehicle routing problem. To address the complexity of accounting for all the unique specifities of the studied problem, a MIP model is developed. The problem being NP-hard, we show that solving instances with commercial solver (CPLEX) reaches its limits very quickly even for small-size problems.

In this paper, the energy efficiency of a two-user downlink NOMA system aided by several ambient backscatter devices is investigated. We analyze both the tradeoff and the ratio between achievable rates versus power consumption, assuming that the backscatter devices are in fully cooperative mode. In the case of two backscatter devices, we derive a closed-form solution in terms of the optimal reflection coefficients and power allocation policy by exploiting the properties of the energy-efficiency objective and the Pareto boundary of the feasible set. For more than two backscatter devices, the problem becomes difficult and our methodology cannot be extended easily. Nevertheless, we evaluate the performance of NOMA aided by several (up to four) backscatter devices via numerical simulations. Our numerical results show that the energy efficiency of the two-user NOMA system increases with the number of cooperative backscatter devices. Moreover, in the high noise regime, the relative efficiency gain increases with the number of backscatter devices reaching up to 370 % compared to conventional NOMA.

The high degree of variability present in current and emerging mobile wireless networks calls for mathematical tools and techniques that transcend classical (convex) optimization paradigms. The aim of this short survey paper is to provide a gentle introduction to online learning and optimization algorithms that are able to provably cope with this variability and provide policies that are asymptotically optimal in hindsight-a property known as no regret. The focal point of this survey will be to delineate the trade-off between the information available as feedback to the learner, and the achievable regret guarantees starting with the case of gradient-based (first-order) feedback, then moving on to value-based (zeroth-order) feedback, and, ultimately, pushing the envelope to the extreme case of a single bit of feedback. We illustrate our theoretical analysis with a series of practical wireless network examples that highlight the potential of this elegant toolbox.

mmWave communication requires accurate and continuous beam steering to overcome the severe propagation loss and user mobility. In this paper, we leverage a self-supervised deep learning approach to exploit sub-6 GHz channels and propose a novel method to predict beamforming vectors in the mmWave band for a single access point– user link. This complex channel-beam mapping is learned via data issued from the DeepMIMO dataset. We then compare our proposed method with existing supervised deep learning and classic reinforcement learning methods. Our simulations show that choosing an appropriate beam steering method depends on the target application and is a tradeoff between data rate and computational complexity. We also investigate tuning the size of our neural network depending on the number of transmit and receive antennas at the access point. Finally, we extend our method to the case of multiple links and introduce a federated learning (FL) approach to efficiently predict their mmWave beams by sharing only the weights of the locally trained neural networks (and not the local data). We investigate both synchronous and asynchronous FL methods. Our numerical simulations show the high potential of our approach, especially when the local available data is scarce or imperfect.

In this paper, the energy efficiency of multi-user non orthogonal multiple access (NOMA) systems in the presence of a backscatter device is investigated. The energy efficiency maximization problem is formulated as a tradeoff between the sum rate and the total power consumption and shown to be non-convex. We then derive a closed-form expression of the optimal reflection coefficient. Remarkably, the obtained expression allows the reformulation of the optimization in terms of the power allocation policy into a convex optimization problem that has recently been solved in closed form. This overall solution can then be exploited to reduce the computational complexity of Dinkelbach's algorithm for maximizing the ratio sum rate vs. total power. Simulation results show that the presence of backscatter devices significantly improve the energy efficiency of NOMA systems and reach up to 450% relative gains compared to OMA.

This paper investigates the energy efficiency of a multi-user downlink non-orthogonal multiple access (NOMA) system. The energy-efficiency maximization representing the tradeoff between the sum rate versus the overall power consumption is formulated as a bi-criterion optimization problem; being convex, scalarization is suitable for its solution. Assuming that each individual user has a minimum quality of service constraint, we prove that the solution of the scalarized objective can be obtained in closed form. Hence, our solution characterizes the entire Pareto-optimal boundary of the rate vs. power tradeoffs. In the special case of maximizing the ratio sum rate vs. overall power, our solution reduces the complexity of the Dinkelbach procedure to a univariate bisection method. At last, our simulation results highlight the benefit of NOMA over OMA in terms of the rate vs. power optimal tradeoff.

This paper investigates a power allocation problem in an optimal and closed-form manner for a relay-aided cognitive network composed of one primary and secondary user/destination pair (e.g., a cellular link coexisting with a device-to-device link in a device-to-device enabled cellular communication setup) and one secondary full-duplex relay. By exploiting the monotonic properties of the objective function and the geometry of the feasible set, we provide the optimal and closed-form power allocation policy assuming the relay performs either Decode-and-Forward (DF) or Compress-and-Forward (CF). We then conjecture that if the secondary direct link is missing, then DF always outperforms CF, irrespective from the system parameters. This conjecture is sustained by numerous numerical simulations.

Wireless secret key generation (W-SKG) from shared randomness (e.g., from the wireless channel fading realizations), is a well established scheme that can be used for session key agreement. W-SKG approaches can be of particular interest in delay constrained wireless networks and notably in the context of ultra reliable low latency communications (URLLC) in beyond fifth generation (B5G) systems. However W- SKG schemes are known to be malleable over the so called "advantage distillation" phase, during which observations of the shared randomness are obtained at the legitimate parties. As an example, an active attacker can act as a man-in- the-middle (MiM) by injecting pilot signals and/or can mount denial of service attacks (DoS) in the form of jamming. This paper investigates the impact of injection and reactive jamming attacks in W-SKG. First, it is demonstrated that injection attacks can be reduced to - potentially less harmful - jamming attacks by pilot randomization; a novel system design with randomized QPSK pilots is presented. Subsequently, the optimal jamming strategy is identified in a block fading additive white Gaussian noise (BF-AWGN) channel in the presence of a reactive jammer, using a game theoretic formulation. It is shown that the impact of a reactive jammer is far more severe than that of a simple proactive jammer.

Lipschitz continuity is a central requirement for achieving the optimal O(1/T) rate of convergence in monotone, deterministic variational inequalities (a setting that includes convex minimization, convex-concave optimization, nonatomic games, and many other problems). However, in many cases of practical interest, the operator defining the variational inequality may become singular at the boundary of the feasible region, precluding in this way the use of fast gradient methods that attain this rate (such as Nemirovski's mirror-prox algorithm and its variants). To address this issue, we propose a novel smoothness condition which we call Bregman smoothness, and which relates the variation of the operator to that of a suitably chosen Bregman function. Leveraging this condition, we derive an adaptive mirror prox algorithm which attains an O(1/T) rate of convergence in problems with possibly singular operators, without any prior knowledge of the problem's Bregman constant (the Bregman analogue of the Lipschitz constant). We also present an extension of our algorithm to stochastic variational inequalities where the algorithm achieves a $O(1/\sqrt{T})$ convergence rate.

Secret key generation (SKG) from shared randomness at two remote locations has been shown to be vulnerable to denial of service attacks in the form of jamming. Typically, such attacks are alleviated with frequency hopping/spreading techniques that rely on expansion of the system bandwidth. In the present study, energy harvesting (EH) is exploited as a novel counter-jamming approach that alleviates the need for extra bandwidth resources. Assuming the legitimate users have EH capabilities, the idea is that part of the jamming signal can potentially be harvested and converted into useful communication power. In this framework, the competitive interaction between a pair of legitimate users and a jammer is formulated as a zero-sum game. A critical transmission power for the legitimate users is identified which allows to completely characterize the unique NE of the game in closed form. Remarkably, this threshold also provides the option to effectively neutralize the jammer, i.e., prevent the jammer from carrying out the attack altogether. Through numerical evaluations, EH is shown to be a counter-jamming approach that can offer substantial gains in terms of relative SKG rates.

Jamming attacks have been shown to disrupt secret key generation (SKG) in systems that exploit the reciprocity of the wireless medium to generate symmetric keys at two remote locations through public discussion. In this study, the use of frequency hopping/spreading in Rayleigh block fading additive white Gaussian noise (BF-AWGN) channels is investigated as a means to counteract such attacks. The competitive interaction between a pair of legitimate users and a jammer is formulated as a zero-sum game and the corresponding Nash equilibria (NE) are characterized analytically and in closed form. It is found that the jammer's optimal strategy is to spread its power across the entire spectrum. On the contrary, the pair of legitimate users should use frequency spreading only in favorable transmission conditions, and frequency hopping otherwise (e.g., low signal to jamming power ratio). Numerical results show that frequency hopping/spreading in BF-AWGN channels is an effective technique for combating jamming attacks in SKG systems; a modest increase of the system bandwidth can substantially increase the SKG rates.

Channel state information (CSI) is essential for efficient power and spectrum allocation policies. In cognitive radio (CR) channels, although perfect CSI of the direct link (between the secondary transmitter and the secondary receiver) is a reasonable assumption at the secondary transmitter (ST), however, perfect knowledge of its interfering links to the primary receivers (PRs) is not. Power allocation and scheduling algorithms are often based on perfect global CSI at the secondary transmitter (ST). In this paper, we analyze the impact of channel estimation errors on both the secondary and primary users. On the one hand, the robustness of water-filling type of algorithms allowing the secondary user (SU) to minimize its power consumption under QoS and CR interference power constraints to channel estimation errors in the SU interfering links is analyzed. On the other hand, the impact of these estimation errors on the PU interference constraints is also analyzed. To this aim, we consider the worst case with respect to these estimation errors. Our analysis shows that the water-filling algorithm provides robustness in terms of power consumption and scheduling of the SU given the realistic estimation error models especially when the SU is overestimating the interfering power gains. We also provide possible solutions to ensure that the created interference is below the tolerated thresholds.

Jamming attacks represent a critical vulnerability for wireless secret key generation (SKG) systems. In this paper, two counter-jamming approaches are investigated for SKG systems: first, the employment of energy harvesting (EH) at the legitimate nodes to turn part of the jamming power into useful communication power, and, second, the use of channel hopping or power spreading in block fading channels to reduce the impact of jamming. In both cases, the adversarial interaction between the pair of legitimate nodes and the jammer is formulated as a two-player zero-sum game and the Nash and Stackelberg equilibria are characterized analytically and in closed form. In particular, in the case of EH receivers, the existence of a critical transmission power for the legitimate nodes allows the full characterization of the game's equilibria and also enables the complete neutralization of the jammer. In the case of channel hopping versus power spreading techniques, it is shown that the jammer's optimal strategy is always power spreading while the legitimate nodes should only use power spreading in the high signal-to-interference ratio (SIR) regime. In the low SIR regime, when avoiding the jammer's interference becomes critical, channel hopping is optimal for the legitimate nodes. Numerical results demonstrate the efficiency of both counter-jamming measures.

User mobility has become a key attribute in the design of optimal resource allocation policies for future wireless networks. This has become increasingly apparent in cognitive radio (CR) systems where the licensed, primary users (PUs) of the network must be protected from harmful interference by the network's opportunistic, secondary users (SUs): here, unpredictability due to mobility requires the implementation of safety net mechanisms that are provably capable of adapting to changes in the users' wireless environment. In this context, we propose a distributed learning algorithm that allows SUs to adjust their power allocation profile (over the available frequency carriers) “on the fly”, relying only on strictly causal channel state information. To account for the interference caused to the network's PUs, we incorporate a penalty function in the rate-driven objectives of the SUs, and we show that the proposed scheme matches asymptotically the performance of the best fixed power allocation policy in hindsight. Specifically, in a system with S orthogonal subcarriers and transmission horizon T, this performance gap (known as the algorithm's average regret) is bounded from above as O(T-1logS). We also validate our theoretical analysis with numerical simulations which confirm that the network's SUs rapidly achieve a “no-regret” state under realistic wireless cellular conditions. Moreover, by finetuning the choice of penalty function, the interference induced by the SUs can be kept at a sufficiently low level, thus guaranteeing the PUs' requirements.

In this paper, we examine the maximization of energy efficiency (EE) in next-generation multiuser MIMO-OFDM networks that vary dynamically over time-e.g., due to user mobility, fluctuations in the wireless medium, modulations in the users' load, etc. Contrary to the static/stationary regime, the system may evolve in an arbitrary manner, so users must adjust “on the fly,” without being able to predict the state of the system in advance. To tackle these issues, we propose a simple and distributed online optimization policy that leads to no regret, i.e., it allows users to match (and typically outperform) even the best fixed transmit policy in hindsight, irrespective of how the system varies with time. Moreover, to account for the scarcity of perfect channel state information (CSI) in massive MIMO systems, we also study the algorithm's robustness in the presence of measurement errors and observation noise. Importantly, the proposed policy retains its no-regret properties under very mild assumptions on the error statistics: on average, it enjoys the same performance guarantees as in the noiseless deterministic case. Our analysis is supplemented by extensive numerical simulations, which show that, in realistic network environments, users track their individually optimum transmit profile even under rapidly changing channel conditions, achieving gains of up to 600% in energy efficiency over uniform power allocation policies.

We propose an online power allocation algorithm for optimizing energy efficiency (throughput per unit of transmit power) in multi-user, multi-carrier systems that evolve dynamically over time (e.g. due to changes in the wireless environment or the users' load). Contrary to the static/ergodic regime, a fixed optimal power allocation profile (either static or in the mean) does not exist, so we draw on exponential learning techniques to design an algorithm that is able to adapt to system changes "on the fly". Specifically, the proposed transmit policy leads to no regret, i.e., it is asymptotically optimal in hindsight, irrespective of the system's evolution over time. Importantly, despite the algorithm's simplicity and distributed nature, users are able to track their individually optimum transmit profiles as they vary with time, even under rapidly changing network conditions.

This work proposes a distributed power allocation scheme for maximizing energy efficiency in the uplink of OFDMA-based HetNets where a macro-tier is augmented with small cell access points. Each user equipment (UE) in the network is modeled as a rational agent that engages in a non-cooperative game and allocates its available transmit power over the set of assigned subcarriers to maximize its individual utility (defined as the user's throughput per Watt of transmit power) subject to a target rate requirement. In this framework, the relevant solution concept is that of Debreu equilibrium, a generalization of the concept of Nash equilibrium. Using techniques from fractional programming, we provide a characterization of equilibrial power allocation profiles. In particular, Debreu equilibria are found to be the fixed points of a water-filling best response operator whose water level is a function of rate constraints and circuit power. Moreover, we also describe a set of sufficient conditions for the existence and uniqueness of Debreu equilibria exploiting the contraction properties of the best response operator. This analysis provides the necessary tools to derive a power allocation scheme that steers the network to equilibrium in an iterative and distributed manner without the need for any centralized processing. Numerical simulations are used to validate the analysis and assess the performance of the proposed algorithm as a function of the system parameters.

In this work, we derive a distributed power control algorithm for energy-efficientuplink transmissions in interference-limited cellular networks, equipped with either multiple or shared relays. The proposed solution is derived by modeling the mobile terminals as utility-driven rational agents that engage in a noncooperative game, under minimum-rate constraints. The theoretical analysis of the game equilibrium is used to compare the performance of the two different cellular architectures. Extensive simulations show that the shared relay concept outperforms the distributed one in terms of energy efficiency in most network configurations.

This work proposes a distributed power allocation scheme for maximizing the energy efficiency in the uplink of non-cooperative small-cell networks based on orthogonal frequency-division multiple-access technology. This is achieved by modeling user terminals as rational agents that engage in a non-cooperative game in which every terminal selects the power loading so as to maximize its own utility (the user's throughput per Watt of transmit power) while satisfying minimum rate constraints. In this framework, we prove the existence of a Debreu equilibrium (also known as generalized Nash equilibrium) and we characterize the structure of the corresponding power allocation profile using techniques drawn from fractional programming. To attain the equilibrium in a distributed fashion, we also propose a method based on an iterative water-filling best response process. Numerical simulations are then used to assess the convergence of the proposed algorithm and the performance of its end-state as a function of the system parameters.

In this paper, we examine cognitive radio systems that evolve dynamically over time due to changing user and environmental conditions. To combine the advantages of orthogonal frequency division multiplexing (OFDM) and multiple-input, multiple-output (MIMO) technologies, we consider a MIMO-OFDM cognitive radio network where wireless users with multiple antennas communicate over several non-interfering frequency bands. As the network's primary users (PUs) come and go in the system, the communication environment changes constantly (and, in many cases, randomly). Accordingly, the network's unlicensed, secondary users (SUs) must adapt their transmit profiles "on the fly" in order to maximize their data rate in a rapidly evolving environment over which they have no control. In this dynamic setting, static solution concepts (such as Nash equilibrium) are no longer relevant, so we focus on dynamic transmit policies that lead to no regret: specifically, we consider policies that perform at least as well as (and typically outperform) even the best fixed transmit profile in hindsight. Drawing on the method of matrix exponential learning and online mirror descent techniques, we derive a no-regret transmit policy for the system's SUs which relies only on local channel state information (CSI). Using this method, the system's SUs are able to track their individually evolving optimum transmit profiles remarkably well, even under rapidly (and randomly) changing conditions. Importantly, the proposed augmented exponential learning (AXL) policy leads to no regret even if the SUs' channel measurements are subject to arbitrarily large observation errors (the imperfect CSI case), thus ensuring the method's robustness in the presence of uncertainties.

In this paper, a novel game-theoretic model of the complex interactions between network service providers (NSPs) and users in heterogeneous small-cell networks is investigated. In this game, the NSPs selfishly aim at maximizing their profit while, simultaneously, the users seek to optimize their chosen service's quality-price tradeoff. A Stackelberg formulation in which the NSPs act as leaders and the users as followers is proposed. The users' interactions are modeled as a general nonatomic game. The existence of a Wardrop equilibrium (WE) in the users' game is proven, and its expression as a solution of a fixed-point equation is provided (irrespective of the number of NSPs, services offered, pricing policies, and QoS functions). Moreover, a set of sufficient conditions that ensure the uniqueness of the WE is provided. Notably, the uniqueness of the equilibrium for the particular case of congestion games is shown. An algorithm approximating these equilibria is provided and its convergence to an ε-WE is proven. The existence of Nash equilibria for the leaders' game is shown and illustrated via numerical simulations.

In this paper, we analyze the optimal blockwise subcarrier allocation scheme in coded Orthogonal Frequency Division Multiple Access (OFDMA) uplink systems without channel state information at the transmitter side. Due to the Discrete Fourier Transform, the subcarrier gains in OFDMA systems are correlated and this correlation plays a determinant role since it causes a degradation of the transmission performance. As a consequence, there exist some subcarrier allocation schemes which are preferable to achieve higher diversity gains. We propose the minimization of an inter-carrier sum-correlation function defined as the sum of correlations of each subcarrier with respect to the others in the same allocation scheme. We show the robustness of the proposed blockwise allocation policy to the effect of carrier frequency offsets (CFO). Moreover, we propose the block-size which provides the best trade-off between diversity and CFO for practical values of CFO. Finally, numerical simulations validating our results are presented.

We analyze the problem of finding the optimal signal covariance matrix for multiple-input multiple-output (MIMO) multiple access channels by using an approach based on ”ex-ponential learning”, a novel optimization method which applies more generally to (quasi-)convex problems defined over sets of positive-definite matrices (with or without trace constraints). If the channels are static, the system users converge to a power allocation profile which attains the sum capacity of the channel exponentially fast (in practice, within a few iterations); otherwise, if the channels fluctuate stochastically over time (following e.g. a stationary ergodic process), users converge to a power profile which attains their ergodic sum capacity instead. An important feature of the algorithm is that its speed can be controlled by tuning the users' learning rate; correspondingly, the algorithm converges within a few iterations even when the number of users and/or antennas per user in the system is large.

We analyze the power allocation problem for orthogonal multiple access channels by means of a non-cooperative potential game in which each user distributes his power over the channels available to him. When the channels are static, we show that this game possesses a unique equilibrium; moreover, if the network's users follow a distributed learning scheme based on the replicator dynamics of evolutionary game theory, then they converge to equilibrium exponentially fast. On the other hand, if the channels fluctuate stochastically over time, the associated game still admits a unique equilibrium, but the learning process is not deterministic; just the same, by employing the theory of stochastic approximation, we find that users still converge to equilibrium. Our theoretical analysis hinges on a novel result which is of independent interest: in finite-player games which admit a (possibly nonlinear) convex potential, the replicator dynamics converge to an ε-neighborhood of an equilibrium in time O(\log(1/ε)).

We introduce a new channel, which consists of an interference channel (IC) in parallel with an interference relay channel (IRC), to analyze the interaction between two selfish and cognitive transmitters who compete for a relay implementing the amplify-and-forward protocol. It is shown that whatever the relay location there is always an equilibrium in the resource allocation game where the users selfishly share their power between the IC and IRC. The uniqueness and determination of this equilibrium is analyzed for two cases: the relay amplification gain is fixed; the IRC direct links are negligible. We show how to exploit this analysis to optimally locate the relay either in terms of individual rate or system sum-rate. Simulations are provided and show, in particular, how the users' selfish behavior leads to sharing the space in regions where the relay is used by only one user or not used at all.

In this paper, we consider the multiple input multiple output (MIMO) quasi static channel. Our objective is to study the power allocation (over the transmit antennas) problem where not only the performance with respect to (w.r.t.) the transmission reliability but also the cost in terms of the consumed power is accounted for. We first review the existing results w.r.t energy efficiency functions (benefit per cost) which focus mainly on the single input single output (SISO) case and then propose several extensions to the MIMO case. Then, we introduce a new energy efficiency metric based on the outage probability. We conjecture that there is a non-trivial solution to the proposed optimization problem. Several special cases are thoroughly analyzed and simulation results will be provided to sustain the conducted analysis.

A game theoretic approach is used to derive the optimal decentralized power allocation (PA) in fast fading multiple access channels where the transmitters and receiver are equipped with multiple antennas. The players (the mobile terminals) are free to choose their PA in order to maximize their individual transmission rates (in particular they can ignore some specified centralized policies). A simple coordination mechanism between users is introduced. The nature and influence of this mechanism is studied in detail. The coordination signal indicates to the users the order in which the receiver applies successive interference cancellation and the frequency at which this order is used. Two different games are investigated: the users can either adapt their temporal PA to their decoding rank at the receiver or optimize their spatial PA between their transmit antennas. For both games a thorough analysis of the existence, uniqueness and sum-rate efficiency of the network Nash equilibrium is conducted. Analytical and simulation results are provided to assess the gap between the decentralized network performance and its equivalent virtual multiple input multiple output system, which is shown to be zero in some cases and relatively small in general.