Nicolò Michelusi

Designing intelligent energy harvesting communication systems

From being a scientific curiosity only a few years ago, energy harvesting (EH) is well on its way to becoming a game-changing technology in the field of autonomous wireless networked systems. The promise of long-term, uninterrupted and self-sustainable operation in a diverse array of applications has captured the interest of academia and industry alike. Yet the road to the ultimate network of perpetual communicating devices is plagued with potholes: ambient energy is intermittent and scarce, energy storage capacity is limited, and devices are constrained in size and complexity. In dealing with these challenges, this article will cover recent developments in the design of intelligent energy management policies for EH wireless devices and discuss pressing research questions in this rapidly growing field.

On optimal transmission policies for energy harvesting devices

We consider an energy harvesting device whose state at a given time is determined by its energy level and an “importance” value, associated to the transmission of a data packet to the receiver at that particular time. We consider policies that, at each time, elect whether to transmit the data packet or not, based on the current energy level and data importance, so as to maximize the long-term average transmitted data importance. Under the assumption of i.i.d. Bernoulli energy arrivals, we show that the sensor should report only data with an importance value above a given threshold, which is a strictly decreasing function of the energy level, and we derive upper and lower bounds on the thresholds for any energy level. Leveraging on these findings, we construct a suboptimal policy that performs very close to the optimal one, at a fraction of the complexity. Finally, we demonstrate that a threshold policy, which on the average transmits with probability equal to the average energy arrival rate is asymptotically optimal as the energy storage capacity grows large.

Optimal Adaptive Random Multiaccess in Energy Harvesting Wireless Sensor Networks

Wireless sensors can integrate rechargeable batteries and energy-harvesting (EH) devices to enable long-term, autonomous operation, thus requiring intelligent energy management to limit the adverse impact of energy outages. This work considers a network of EH wireless sensors, which report packets with a random utility value to a fusion center (FC) over a shared wireless channel. Decentralized access schemes are designed, where each node performs a local decision to transmit/discard a packet, based on an estimate of the packets utility, its own energy level, and the scenario state of the EH process, with the objective to maximize the average long-term aggregate utility of the packets received at the FC. Due to the non-convex structure of the problem, an approximate optimization is developed by resorting to a mathematical artifice based on a game theoretic formulation of the multiaccess scheme, where the nodes do not behave strategically, but rather attempt to maximize a common network utility with respect to their own policy. The symmetric Nash equilibrium (SNE) is characterized, where all nodes employ the same policy; its uniqueness is proved, and it is shown to be a local maximum of the original problem. An algorithm to compute the SNE is presented, and a heuristic scheme is proposed, which is optimal for large battery capacity. It is shown numerically that the SNE typically achieves near-optimal performance, within 3% of the optimal policy, at a fraction of the complexity, and two operational regimes of EH-networks are identified and analyzed: an energy-limited scenario, where energy is scarce and the channel is under-utilized, and a network-limited scenario, where energy is abundant and the shared wireless channel represents the bottleneck of the system.

Optimal random multiaccess in energy harvesting Wireless Sensor Networks

We consider a Wireless Sensor Network where each sensor device is able to harvest energy from the environment, and randomly accesses the channel to transmit packets of random importance to a fusion center. If a collision occurs, the transmission fails and all packets involved are discarded. We design distributed transmission schemes where each sensor node, based on its own energy level and the importance of its own data packet, decides whether to transmit the packet or remain idle, so as to maximize the network utility, defined as the average long-term aggregate network importance of the data packets successfully reported to the fusion center. Due to the generally non-convex structure of the optimization problem, we resort to approximate solutions. In particular, we use a mathematical artifice based on a game theoretic formulation of the multiaccess problem, where each sensor node is a player that attempts to selfishly maximize the network utility. We characterize the Symmetric Nash Equilibrium (SNE) of this game, where all the sensor nodes employ the same policy. We prove the existence and uniqueness of the SNE, and we show that it is a local maximum of the original optimization problem. Moreover, we derive an algorithm to compute it.

Optimal transmission policies for Energy Harvesting Devices with Limited State-of-Charge Knowledge

Wireless sensors can be integrated with energy harvesting (EH) devices to enable long-term, autonomous operation, necessitating efficient energy management. Existing research assumes knowledge of the state-of-charge (SOC) of the rechargeable battery; however, accurate SOC estimation in real-world devices is typically costly or impractical. This paper investigates the impact of imperfect SOC knowledge and the design of policies to cope with such uncertainty. The optimization complexity is reduced by decoupling the different time scales of the system: first, the short-term average performance is optimized with respect to fast-varying exogenous state variables, under an average energy consumption constraint, but neglecting battery dynamics; then, the policy dictating the average energy consumption as a function of state variables evolving over longer time scales is optimized, based on the detailed battery dynamics. A local search algorithm is presented to determine a locally optimal policy. The performance degradation compared to the scenario with perfect SOC knowledge is shown to decrease with increasing storage capacity and decreasing uncertainty in the EH source, and is within 5% for most cases of practical interest. Moreover, near-optimal performance is achieved by only a loose SOC knowledge, which distinguishes between high/low SOC levels. Finally, the impact of time correlation in the EH source is investigated. EH state knowledge is shown to be more critical than SOC knowledge, hence precise knowledge of the former can obviate the need for accurate information about the latter.

UWB Sparse/Diffuse Channels, Part I: Channel Models and Bayesian Estimators

In this two-part paper, the problem of channel estimation in Ultra Wide-Band (UWB) systems is investigated. Due to the large transmission bandwidth, the channel has been traditionally modeled as sparse. However, some propagation phenomena, e.g., scattering from rough surfaces and frequency distortion, are better modeled by a diffuse channel. Herein, a novel Hybrid Sparse/Diffuse (HSD) channel model is proposed. Tailored to the HSD model, channel estimators are designed for different scenarios that vary in the amount of side information available at the receiver. An Expectation-Maximization algorithm to estimate the power delay profile of the diffuse component is also designed. The proposed methods are compared to unstructured and purely sparse estimators. The numerical results show that the HSD estimation schemes considerably improve the estimation accuracy and the bit error rate performance over conventional channel estimators. In Part II, the new channel estimators are evaluated with more realistic geometry-based channel emulators. The numerical results show that, even when the channel is generated in this manner, the new estimation strategies achieve high performance. Moreover, a Mean-Squared Error analysis of the proposed estimators is performed, in the high and low Signal to Noise Ratio regimes, thus quantifying, in closed form, the achievable performance gains.

Cognitive Access Policies under a Primary ARQ Process via Forward-Backward Interference Cancellation

This paper introduces a novel technique for access by a cognitive Secondary User (SU) using best-effort transmission to a spectrum with an incumbent Primary User (PU), which uses Type-I Hybrid ARQ. The technique leverages the primary ARQ protocol to perform Interference Cancellation (IC) at the SU receiver (SUrx). Two IC mechanisms that work in concert are introduced: Forward IC, where SUrx, after decoding the PU message, cancels its interference in the (possible) following PU retransmissions of the same message, to improve the SU throughput; Backward IC, where SUrx performs IC on previous SU transmissions, whose decoding failed due to severe PU interference. Secondary access policies are designed that determine the secondary access probability in each state of the network so as to maximize the average long-term SU throughput by opportunistically leveraging IC, while causing bounded average long-term PU throughput degradation and SU power expenditure. It is proved that the optimal policy prescribes that the SU prioritizes its access in the states where SUrx knows the PU message, thus enabling IC. An algorithm is provided to optimally allocate additional secondary access opportunities in the states where the PU message is unknown. Numerical results are shown to assess the throughput gain provided by the proposed techniques.

A Stochastic Model for Electron Transfer in Bacterial Cables

Biological systems are known to communicate by diffusing chemical signals in the surrounding medium. However, most of the recent literature has neglected the electron transfer mechanism occurring among living cells, and its role in cell-cell communication. Each cell relies on a continuous flow of electrons from its electron donor to its electron acceptor through the electron transport chain to produce energy in the form of the molecule adenosine triphosphate, and to sustain the cells vital operations and functions. While the importance of biological electron transfer is well-known for individual cells, the past decade has also brought about remarkable discoveries of multi-cellular microbial communities that transfer electrons between cells and across centimeter length scales, e.g., biofilms and multi-cellular bacterial cables. These experimental observations open up new frontiers in the design of electron-based communications networks in microbial communities, which may coexist with the more well-known communication strategies based on molecular diffusion, while benefiting from a much shorter communication delay. This paper develops a stochastic model that links the electron transfer mechanism to the energetic state of the cell. The model is also extensible to larger communities, by allowing for electron exchange between neighboring cells. Moreover, the parameters of the stochastic model are fit to experimental data available in the literature, and are shown to provide a good fit.

Correlated energy generation and imperfect State-of-Charge knowledge in energy harvesting devices

Nowadays, many devices in wireless sensor networks are provided with energy harvesting capability to allow for their continuous operation over long periods of time. In principle, the energy level within each sensor should be managed optimally to ensure the best performance. Network engineers, however, often consider optimality under the idealized assumption of perfect knowledge about the State-of-Charge (SOC) of the device. This information is not always realistic or accurate. In our previous work [1], we showed that optimal policies for sensing, transmission, and battery usage should rather consider uncertainty on the SOC of the device. In this paper, we extend that investigation, therein performed in the idealized scenario of i.i.d. energy arrivals, by considering a correlated energy generation process. We show that the knowledge of the SOC and that of the energy generation process are useful in a complementary manner, that is they can be traded for each other. Moreover, the knowledge on the state of the energy generation process can obviate the need for acquiring accurate SOC information. This investigation paves the road for a new line of research in wireless sensor networks, allowing a tighter interaction between the designers of energy harvesting and battery storage mechanisms on the one hand, and the engineers of network operation and control policies on the other.

UWB Sparse/Diffuse Channels, Part II: Estimator Analysis and Practical Channels

In this two-part paper, the problem of channel estimation in Ultra Wide-Band (UWB) systems is investigated. In Part I, a novel Hybrid Sparse/Diffuse (HSD) model is proposed for the UWB channel, and new channel estimation strategies are designed for this model. In this paper (Part II), a Mean-Squared Error (MSE) analysis of the Generalized MMSE and Generalized Thresholding Estimators developed in Part I is performed, for the asymptotic regimes of low and high SNR. The analysis quantifies the achievable MSE performance of these schemes over unstructured estimators. Specifically, we prove that it is beneficial to be conservative in the estimation of the sparse component, i.e., to assume that the sparse component is sparser than it actually is. Moreover, we analyze the scenario with a non-orthogonal pilot sequence, and establish a connection between the Generalized Thresholding estimator and conventional sparse approximation algorithms proposed in the literature. In addition to the theoretical analysis, these channel estimation schemes are evaluated in a more realistic geometry-based channel emulator, for which the HSD model developed in Part I is an approximation. The numerical results are shown to match the expected asymptotic MSE behavior. Moreover, the proposed estimation techniques are shown to outperform conventional unstructured and purely sparse estimators, from both an MSE and a bit error rate perspectives, even for the realistic geometry-based channel model.