Design and Analysis of Distributed Averaging with Quantized Communication

Consider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some value close to that average. Such an algorithm is called generically "distributed averaging," and our goal in this paper is to study the performance of a subclass of deterministic distributed averaging algorithms where the information exchange between neighboring nodes (agents) is subject to uniform quantization. With such quantization, convergence to the precise average cannot be achieved in general, but the convergence would be to some value close to it, called quantized consensus. Using Lyapunov stability analysis, we characterize the convergence properties of the resulting nonlinear quantized system. We show that in finite time and depending on initial conditions, the algorithm will either cause all agents to reach a quantized consensus where the consensus value is the largest quantized value not greater than the average of their initial values, or will lead all variables to cycle in a small neighborhood around the average. In the latter case, we identify tight bounds for the size of the neighborhood and we further show that the error can be made arbitrarily small by adjusting the algorithm's parameters in a distributed manner

Power-Optimal Feedback-Based Random Spectrum Access for an Energy Harvesting Cognitive User

In this paper, we study and analyze cognitive radio networks in which secondary users (SUs) are equipped with Energy Harvesting (EH) capability. We design a random spectrum sensing and access protocol for the SU that exploits the primary link's feedback and requires less average sensing time. Unlike previous works proposed earlier in literature, we do not assume perfect feedback. Instead, we take into account the more practical possibilities of overhearing unreliable feedback signals and accommodate spectrum sensing errors. Moreover, we assume an interference-based channel model where the receivers are equipped with multi-packet reception (MPR) capability. Furthermore, we perform power allocation at the SU with the objective of maximizing the secondary throughput under constraints that maintain certain quality-of-service (QoS) measures for the primary user (PU)

On Spectrum Sharing Between Energy Harvesting Cognitive Radio Users and Primary Users

This paper investigates the maximum secondary throughput for a rechargeable secondary user (SU) sharing the spectrum with a primary user (PU) plugged to a reliable power supply. The SU maintains a finite energy queue and harvests energy from natural resources and primary radio frequency (RF) transmissions. We propose a power allocation policy at the PU and analyze its effect on the throughput of both the PU and SU. Furthermore, we study the impact of the bursty arrivals at the PU on the energy harvested by the SU from RF transmissions. Moreover, we investigate the impact of the rate of energy harvesting from natural resources on the SU throughput. We assume fading channels and compute exact closed-form expressions for the energy harvested by the SU under fading. Results reveal that the proposed power allocation policy along with the implemented RF energy harvesting at the SU enhance the throughput of both primary and secondary links

Optimal Spectrum Access for a Rechargeable Cognitive Radio User Based on Energy Buffer State

This paper investigates the maximum throughput for a rechargeable secondary user (SU) sharing the spectrum with a primary user (PU) plugged to a reliable power supply. The SU maintains a finite energy queue and harvests energy from natural resources, e.g., solar, wind and acoustic noise. We propose a probabilistic access strategy by the SU based on the number of packets at its energy queue. We investigate the effect of the energy arrival rate, the amount of energy per energy packet, and the capacity of the energy queue on the SU throughput under fading channels. Results reveal that the proposed access strategy can enhance the performance of the SU.Comment: arXiv admin note: text overlap with arXiv:1407.726

Hierarchical fiber bundle strength statistics

Multi-scale modeling is currently one of the most active research topics in a wide range of disciplines. In this thesis we develop innovative hierarchical multi-scale models to analyze the probabilistic strength of fiber bundle structures. The Fiber Bundle Model (FBM) was developed initially by Daniels (1945), and then expanded, modified and generalized by many authors. Daniels considered a bundle of N fibers with identical elastic properties under uniform tensile stress. When a fiber breaks, the load from the broken fiber is distributed equally over all the remaining fibers (global load sharing). The strength of fibers is assigned randomly most often according to the Weibull probability distribution. In chapter 2, we develop for the first time an ad hoc hierarchical theory designed to tackle hierarchical architectures, thus allowing the determination of the strength of macroscopic hierarchical materials from the properties of their constituents at the nanoscale. The results show that the mean strength of the fiber bundle is reduced when scaling up from a fiber bundle to bundles of bundles. The hierarchical model developed in this study enables the prediction of strength values in good agreement with existing experimental results. This new ad hoc extension of the fiber bundle model is used for evaluating the role of hierarchy on structural strength. Different hierarchical architectures of fiber bundles have been investigated through analytical multiscale calculations based on a fiber bundle model at each hierarchical level. In general, we find that an increase in the number of hierarchical levels leads to a decrease in the strength of material. On a more abstract level, the hierarchical fiber bundle model (HFBM), an extension of the fiber bundle model (FBM) presented in this thesis, can be applied to any hierarchical system. FBMs are an established method helpful to understand hierarchical strength. Another extension of Daniels‘ theory for bimodal statistical strength has been implemented to model flaws in carbon nanotube fibers such as joints between carbon nanotubes, where careful analysis is necessary to assess the true mean strength. This model provides a more realistic description of the microscopic structure constituted by a nanotube-nanotube joint than a simple fiber bundle model. We demonstrate that the disorder distribution and the relative importance of the two failure modes have a substantial effect on mean strength of the structure. As mentioned, the fiber bundle model describes a collection of elastic fibers under load. The fibers fail successively and for each failure, the load is redistributed among the surviving fibers. In the fiber bundle model, the survival probability is defined as a ratio between number of surviving fibers and the total number of fibers in the bundle. We find that this classical relation is no longer suitable for a bundle with a small number of fibers, so that it is necessary to implement a modification into the probability function. It is possible to predict snap-back instabilities by inserting this modification in the theoretical expression of the load-strain (F-ε) relationship for the bundle, as discussed in chapter 4. Scrutiny into the composition of natural, or biological materials convincingly reveals that high material and structural efficiency can be attained, even with moderate-quality constituents, by hierarchical topologies, i.e., successively organized material levels. This is shown in chapter 5, where a composite bundle with two different types of fibers is considered, and an improvement in the mean strength is obtained for some specific hierarchical architectures, indicating that both hierarchy and material ―mixing‖ are necessary ingredients to obtain improved mechanical properties. In Chapter 6, we consider a novel modeling approach, namely we introduce self healing in a fiber bundle model. Here, we further assume that faile

Cooperative Access in Cognitive Radio Networks: Stable Throughput and Delay Tradeoffs

In this paper, we study and analyze fundamental throughput-delay tradeoffs in cooperative multiple access for cognitive radio systems. We focus on the class of randomized cooperative policies, whereby the secondary user (SU) serves either the queue of its own data or the queue of the primary user (PU) relayed data with certain service probabilities. The proposed policy opens room for trading the PU delay for enhanced SU delay. Towards this objective, stability conditions for the queues involved in the system are derived. Furthermore, a moment generating function approach is employed to derive closed-form expressions for the average delay encountered by the packets of both users. Results reveal that cooperation expands the stable throughput region of the system and significantly reduces the delay at both users. Moreover, we quantify the gain obtained in terms of the SU delay under the proposed policy, over conventional relaying that gives strict priority to the relay queue.Comment: accepted for publication in IEEE 12th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), 201

Energy-aware cooperative wireless networks with multiple cognitive users

In this paper, we study and analyze cooperative cognitive radio networks with arbitrary number of secondary users (SUs). Each SU is considered a prospective relay for the primary user (PU) besides having its own data transmission demand. We consider a multi-packet transmission framework that allows multiple SUs to transmit simultaneously because of dirty-paper coding. We propose power allocation and scheduling policies that optimize the throughput for both PU and SU with minimum energy expenditure. The performance of the system is evaluated in terms of throughput and delay under different opportunistic relay selection policies. Toward this objective, we present a mathematical framework for deriving stability conditions for all queues in the system. Consequently, the throughput of both primary and secondary links is quantified. Furthermore, a moment generating function approach is employed to derive a closed-form expression for the average delay encountered by the PU packets. Results reveal that we achieve better performance in terms of throughput and delay at lower energy cost as compared with equal power allocation schemes proposed earlier in the literature. Extensive simulations are conducted to validate our theoretical findings