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In this paper, we consider the consensus problem where a set of nodes cooperate to minimize a global cost. In particular, we consider an online setting and propose an online algorithm based on the alternating direction method of multipliers. Besides, we take into account the asynchronous operation of the nodes. In this context, we prove that the algorithm attains sublinear regret on the objective. Finally, we assess numerically the performance of the algorithm in a distributed sparse regression problem. ; Grant numbers : This work is partly supported by the Spanish and Catalan Governments by grants INTENSYV (TEC2013-44591-P) and 2014-SGR-1567.© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we propose a novel state estimation (SE) scheme for the distribution grid. It exclusively leverages on measurements from μPMUs (micro Phasor Measurement Units) making it possible to operate at a faster time scale than conventional SE approaches based on legacy measurements. To circumvent observability issues, we realize that the voltage drop in adjacent buses is limited and, on that basis, we formulate a SE regularized weighted total variation estimation (WTVSE) problem. The problem can be iteratively solved by resorting to the so-called Alternating Direction Method of Multipliers (ADMM). Further, we provide closed-form expressions for the updates of the primal and dual variables. The performance of the proposed scheme is numerically assessed on a 95-bus distribution system for a number of realistic conditions of noise, load and photovoltaic generation profiles. A number of benchmarks are provided, as well. ; Grant numbers : This work was partially supported by the Catalan government under grant SGR2014-1567; the Spanish government under grant TEC2013-44591- P (INTENSYV).© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we consider a scenario where a number of energy harvesting sensors cooperate to transmit a common message to a distant base station. The goal is to find the jointly optimal transmission (power allocation) policy that maximizes the total throughput for a given deadline. We solve the problem in a semi-analytical manner and rigorously prove its optimality. The computational complexity of the proposed scheme is analyzed in detail and compared with that of interior point methods. Performance is extensively assessed by means of computer simulations. As benchmarks, we consider the case where the transmission policies for each sensor are separately optimized, as well as other cluster-based suboptimal transmission strategies. ; Grant number : This work is partly supported by the project JUNTOS (TEC2010-17816) and by the Catalan Government under 2009 SGR 1046 (SGR-RC).© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we investigate the reconstruction of time-correlated sources in a point-to-point communications scenario comprising an energy-harvesting sensor and a Fusion Center (FC). Our goal is to minimize the average distortion in the reconstructed observations by using data from previously encoded sources as side information. First, we analyze a delay-constrained scenario, where the sources must be reconstructed before the next time slot. We formulate the problem in a convex optimization framework and derive the optimal transmission (i.e., power and rate allocation) policy. To solve this problem, we propose an iterative algorithm based on the subgradient method. Interestingly, the solution to the problem consists of a coupling between a 2-D directional water-filling algorithm (for power allocation) and a reverse water-filling algorithm (for rate allocation). Then, we find a more general solution to this problem in a delay-tolerant scenario where the time horizon for source reconstruction is extended to multiple time slots. Finally, we provide some numerical results that illustrate the impact of delay and correlation in the power and rate allocation policies, and in the resulting reconstruction distortion. We also discuss the performance gap exhibited by a heuristic online policy derived from the optimal (offline) one. ; Grant numbers : This work was partly sponsored by the Catalan Government under grant SGR2014-1567, the Spanish Government under projects PCIN-2013-027 (ECROPS) and TEC2013-44591-P (INTENSYV).© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we investigate the problem of jointly selecting a predefined number of energy-harvesting (EH) sensors and computing the optimal power allocation. The ultimate goal is to minimize the reconstruction distortion at the fusion center. This optimization problem is, unfortunately, non-convex. To circumvent that, we propose two suboptimal strategies: 1) a joint sensor selection and power allocation (JSS-EH) scheme that, we prove, is capable of iteratively finding a stationary solution of the original problem from a sequence of surrogate convex problems and 2) a separate sensor selection and power allocation (SS-EH) scheme, on which basis we can identify a sensible sensor selection and analytically find a power allocation policy by solving a convex problem. We also discuss the interplay between the two strategies. Performance in terms of reconstruction distortion, impact of initialization, actual subsets of selected sensors, and computed power allocation policies is assessed by means of computer simulations. To that aim, an EH-agnostic sensor selection strategy, a lower bound on distortion, and an online version of the SS-EH and JSS-EH schemes are derived and used for benchmarking. ; Grant numbers : This work was partially supported by the Catalan government under grant SGR2014-1567; the Spanish government under grant TEC2013-44591-P (INTENSYV), and grant PCIN-2013-027 (E-CROPS).© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we propose a multiarea state estimator based on successive convex approximation technique. Our scheme is hybrid since it exploits both non-linear and linear measurements coming from legacy meters and Phasor Measurement Units (PMUs), respectively. The resulting nonconvex optimization problem is solved in an iterative manner. In each iteration, the nonconvex terms in the cost function are approximated by a strongly-convex function. The resulting convex problem is distributedly solved by means of the so-called Alternating Direction Method of Multipliers (ADMM). We also prove convergence to a stationary solution of the original nonconvex state estimation problem. Performance is numerically assessed for the IEEE 14-bus and 30-bus test cases. Other optimization schemes from the literature are used as a benchmark. ; Grant numbers : This work is partly supported by the Spanish Government through INTENSYV (TEC2013-44591-P).© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

The fifth generation wireless networks must provide fast and reliable connectivity while coping with the ongoing traffic growth. It is of paramount importance that the required resources, such as energy and bandwidth, do not scale with traffic. While the aggregate network traffic is growing at an unprecedented rate, users tend to request the same popular contents at different time instants. Therefore, caching the most popular contents at the network edge is a promising solution to reduce the traffic and the energy consumption over the backhaul links. In this paper, two scenarios are considered, where caching is performed either at a small base station, or directly at the user terminals, which communicate using Device-to-Device (D2D) communications. In both scenarios, joint design of the transmission and caching policies is studied when the user demands are known in advance. This joint design offers two different caching gains, namely, the pre-downloading and local caching gains. It is shown that the finite cache capacity limits the attainable gains, and creates an inherent tradeoff between the two types of gains. In this context, a continuous time optimization problem is formulated to determine the optimal transmission and caching policies that minimize a generic cost function, such as energy, bandwidth, or throughput. The jointly optimal solution is obtained by demonstrating that caching files at a constant rate is optimal, which allows reformulation of the problem as a finite-dimensional convex program. The numerical results show that the proposed joint transmission and caching policy dramatically reduces the total cost, which is particularised to the total energy consumption at the Macro Base Station (MBS), as well as to the total economical cost for the service provider, when users demand economical incentives for delivering content to other users over the D2D links. ; Grant numbers : This work is partially supported by the Spanish Government through the projects INTENSYV (TEC2013-44591-P) and E-CROPs ...

In this paper, we propose two iterative synchronization schemes for distributed beamforming (DBF) with sidelobe control. The scenario that we address is that of a wireless sensor network surrounded by one intended base station (BS) and multiple unintended ones (serving otherWSNs). We consider two specific synchronization schemes with soft and hard constraints in terms of the received signal strength acceptable at the unintended base stations. The schemes merely require partial CSI at the BSs plus the broadcast of one-bit feedback messages from the intended BS messages to the sensor nodes. ; Grant njumbers : This work is partly supported by the project JUNTOS (TEC2010-17816), GRE3N (TEC2011-29006-C03-01) and by the Catalan Government under 2009 SGR 1046.© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we study the joint routing-scheduling problem in energy harvesting communication networks. Our policies, which are based on stochastic subgradient methods on the dual domain, act as an energy harvesting variant of the stochastic family of backpressure algorithms. Specifically, we propose two policies: first, the stochastic backpressure with energy harvesting, in which a node's routing-scheduling decisions are determined by the difference between the Lagrange multipliers associated to their queue stability constraints and their neighbors'; and second, the stochastic soft backpressure with energy harvesting, an improved algorithm where the routing-scheduling decision is of a probabilistic nature. For both policies, we show that given sustainable data and energy arrival rates, the stability of the data queues over all network nodes is guaranteed. Numerical results corroborate the stability guarantees and illustrate the minimal gap in performance that our policies offer with respect to classical ones that work with an unlimited energy supply. ; Grant numbers : This work was partially supported by the Catalan government under grant SGR2014-1567; the Spanish government under grant TEC2013-44591-P (INTENSYV), and grant PCIN-2013-027 (E-CROPS).© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we study wireless networked control systems with energy harvesting sensors. Multiple sensors share a wireless medium over which they transmit measurements to their respective controllers, and due to the shared medium, packet collisions occur if sensors transmit simultaneously. To alleviate this problem, we propose random access policies that satisfy a desired control performance on each control loop, while also satisfying the energy constraints imposed by the energy harvesting process. The optimal scheduling policy is shown to follow a simple thresholding operation. Moreover, we provide a stochastic dual method for their computation, which is shown to be decoupled across sensors. Finally, we verify numerically the properties of the proposed policy ; Grant numbers : This work was partially supported by the Catalan government under grant SGR2014-1567; the Spanish government under grant TEC2013-44591-P (INTENSYV) and grant PCIN-2013-027 (E-CROPS).© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we study the problem of jointly routing and scheduling traffic in an energy harvesting network. To this end, we leverage stochastic dual descent methods to propose a generalization of the well-known backpressure algorithm to energy harvesting networks. We name this policy energy harvesting backpressure (EH-BP) and show that it satisfies the fundamental property of backpressure-type algorithms. Namely, if given data arrival rates can be supported by given energy arrival rates and some routing-scheduling policy, they can be supported by the EH-BP policy. Numerical results attest to the properties of the proposed policy. ; Grant numbers : This work was partially supported by the Catalan government under grant SGR2014-1567; the Spanish government under grant TEC2013-44591-P (INTENSYV), and grant PCIN-2013-027 (E-CROPS).© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we study the problem of jointly routing and scheduling traffic in an energy harvesting network. To this end, we leverage stochastic dual descent methods to propose a generalization of the well-known backpressure algorithm to energy harvesting networks. We name this policy energy harvesting backpressure (EH-BP) and show that it satisfies the fundamental property of backpressure-type algorithms. Namely, if given data arrival rates can be supported by given energy arrival rates and some routing-scheduling policy, they can be supported by the EH-BP policy. Numerical results attest to the properties of the proposed policy. ; Grant numbers : This work was partially supported by the Catalan government under grant SGR2014-1567; the Spanish government under grant TEC2013-44591-P (INTENSYV), and grant PCIN-2013-027 (E-CROPS).

In this paper, we study wireless networked control systems with energy harvesting sensors. Multiple sensors share a wireless medium over which they transmit measurements to their respective controllers, and due to the shared medium, packet collisions occur if sensors transmit simultaneously. To alleviate this problem, we propose random access policies that satisfy a desired control performance on each control loop, while also satisfying the energy constraints imposed by the energy harvesting process. The optimal scheduling policy is shown to follow a simple thresholding operation. Moreover, we provide a stochastic dual method for their computation, which is shown to be decoupled across sensors. Finally, we verify numerically the properties of the proposed policy. ; Grant numbers : This work was partially supported by the Catalan government under grant SGR2014-1567; the Spanish government under grant TEC2013-44591-P (INTENSYV), and grant PCIN-2013-027 (E-CROPS).

The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed measurements, and exploiting network communication, each node aims at reconstructing the support and the non-zero values of its observed signal. In the literature, distributed greedy algorithms have been proposed to tackle this problem, among which the most reliable ones require a large amount of transmitted data, which barely adapts to realistic network communication constraints. In this paper, we address the problem through a reweighted ℓ1 soft thresholding technique, in which the threshold is iteratively tuned based on the current estimate of the support. The proposed method adapts to constrained networks, as it requires only local communication among neighbors, and the transmitted messages are indices from a finite set. We analytically prove the convergence of the proposed algorithm and we show that it outperforms the state-of-the-art greedy methods in terms of balance between recovery accuracy and communication load. ; Grant numbers : This work is supported by the Spanish Government through the project INTENSYV (TEC2013-44591-P), and by the Catalan Government (2014 SGR 1567).© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we tackle the in-network recovery of sparse signals with innovations. We assume that the nodes of the network measure a signal composed by a common component and an innovation, both sparse and unknown, according to the joint sparsity model 1 (JSM-1). Acquisition is performed as in compressed sensing, hence the number of measurements is reduced. Our goal is to show that distributed algorithms based on the alternating direction method of multipliers (ADMM) can be efficient in this framework to recover both the common and the individual components. Specifically, we define a suitable functional and we show that ADMM can be implemented to minimize it in a distributed way, leveraging local communication between nodes. Moreover, we develop a second version of the algorithm, which requires only binary messaging, significantly reducing the transmission load. ; Grant number : Catalan Government (2014SGR1567), Spanish project INTENSYV (TEC2013-44591-P).© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.