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Approximate consensus is an important building block for distributed systems, used overtly or implicitly in applications as diverse as formation control, sensor fusion, and synchronization. Laplacian-based consensus, the current dominant approach, is extremely accurate and resilient, but converges slowly. Comparing Laplacian-based consensus to exact consensus algorithms, relaxing the requirements for accuracy and resilience should enable a spectrum of algorithms that incrementally tradeoff accuracy and/or resilience for speed. This manuscript demonstrates that may be so by beginning to populate this spectrum with a new approach to approximate consensus, Power-Law-Driven Consensus (PLD-consensus), which accelerates consensus by sending values across long distances using a self-organizing overlay network. Both a unidirectional and bidirectional algorithm based on this approach are studied. Although both have the same asymptotic O(diameter) convergence time (vs. O(diameter2) for Laplacian-based), unidirectional PLD-consensus is faster and more resilient than bidirectional PLD-consensus, but exhibits higher variance in the converged value.
To date, there have been a number of research proposals to explore the newly emerging wireless charging technologies based on radio-frequency (RF) signals, ambient or dedicated. In particular, research efforts towards achieving the goal of transmitting information and energy at the same time have been rapidly expanding, but the feasibility of this goal has not been fully addressed. Moreover, the respective coverage areas of transmitting information and energy are wildly different, the latter being considerably smaller than the former. This is because the receiver sensitivities are very different, namely -60 dBm for an information receiver and -10 dBm for an energy receiver [1, 2].
Owing to this limitation, recently a commercial implementation of RF energy transfer has been restricted to lower-power sensor nodes with dedicated RF energy transmitters, such as the Powercast wireless rechargeable sensor system [3] and the Cota system [4].
In this chapter, we discuss the implementation of long- and short-range RF energy harvesting systems, where the former is to provide far-field-based RF energy transfer over long distances with a 4 × 4 phased antenna array and the latter to provide biosensors with RF energy over short distances. An overall circuit design for these RF energy harvesting systems is described in detail, along with the measurement results to validate the feasibility of far-field-based RF energy transfer. We illustrate the designed test-beds which will be applied to develop sophisticated energy beamforming algorithms to increase the transmission range. Finally, a new research framework is developed through the cross-layer design of the RF energy harvesting system, which is intended to power a low-power sensor node, like the Internet-of-Things (IoT) sensor node. To this end, we present a circuit-layer stored energy evolution model based on the measurements which will be used in designing the upper-layer energy management algorithm for efficient control of the stored energy at the sensor node. The new framework will be useful because the existing works on RF energy harvesting do not explicitly take into account a realistic temporal evolution model of the stored energy in the energy storage device, like such as a supercapacitor.
Energy harvesting in wireless cellular networks is a cornerstone of emerging 5G and beyond 5G (B5G) cellular networks as it aims to “cut the last wires” of the existing wireless devices [1]. In particular, energy harvesting has a significant potential to attract subscribers since it promotes mobility and connectivity anywhere and anytime, which is one of the key visions of next-generation wireless networks. In general, wireless energy harvesting can be classified according to the following two categories.
• Ambient energy harvesting (EH). This refers to energy harvested from renewable energy sources (such as thermal, solar, wind, etc.) as well as energy harvested from radio signals of different frequencies in the environment that can be sensed by EH receivers (e.g., co-channel interference, TV or radio broadcasting, etc.).
• Dedicated EH. This enables the intentional transmission of energy from dedicated energy sources to energy harvesting devices.
To satisfy the power demands of delay-constrained wireless applications, it is of utmost importance to ensure the availability of sufficient energy at the user terminals whenever required. This fact has motivated researchers toward the development of dedicated wireless-powered cellular networks (WPCNs) where dedicated energy sources or hybrid access points (HAPs) take care of both energy transfer and information transmission to and from the subscribers.
In this chapter, we focus on dedicated EH techniques. We first highlight the associated challenges. Next, we theoretically characterize and comparatively analyze a number of different network architectures for centralized and distributed dedicated wireless EH. Numerical results are provided to validate the analytical results.
Major Challenges in Dedicated Wireless Energy Harvesting
In this section, we will discuss a number of major challenges related to dedicated wireless energy harvesting (WEH) from the perspective of network architecture and modeling and resource allocation.
Network Architectures for Wireless Energy Harvesting
Different network architectures have been studied for WEH. However, most of the studies have been limited to a two- or three-node network model, a central base station (BS) that takes care of both the wireless information transmission and energy transfer, and follows a specific configuration of energy harvesting; i.e., a user harvests energy from a centralized half-duplex BS or full-duplex BS or through randomly deployed power beacons (PBs), etc.
The concept of modulating backscatter for communication was first introduced by Stockman in 1948 [1] and promptly received a lot of attention from researchers and developers owing to its potential advantages. Basically, backscatter communication is a technique that allows wireless nodes to communicate without requiring any active radiofrequency (RF) components on the tag [2]. In a conventional backscatter communication system (CBCS), there are two main components, called the wireless tag reader device (WTRD) and the wireless tag device (WTD), as illustrated in Figure 6.1. The WTD in the CBCS is able not only to harvest energy from the received signals, but also to modulate and reflect the signals back to the WTRD. The signal reflection is caused by the intentional mismatch between the antenna and the load impedance at the WTD. Theoretically, when the load impedance is varied, it will generate the complex scatter coefficient which can be used to modulate the reflected signal with information bits. The WTRD then uses the receive antenna to receive reflected signals from the WTD and demodulate these signals to obtain the useful information.
In conventional backscattering communication systems, there are two special features that differ from traditional communication systems. First, in conventional backscattering communication systems, the receivers (i.e., WTRDs) have to be equipped with a power source to transmit RF signals to the transmitter (i.e., WTDs). Second, the transmitters do not need to be equipped with a power source to transmit data because they will reflect signals received by the receivers instead of generating their own signals. The second feature is the most important characteristic and also the main objective for the development of conventional backscattering communication systems. This special communication feature of CBCSs has received a great deal of attention, mainly because of the successful implementation of RFID systems and the potential use in sensor devices that are small in size and have a low power supply.
Typically, backscattering communication systems operate using RF signals and require the WTRD to be able to transmit RF signals to the WTD. However, a new solution, called ambient backscatter communication, which utilizes RF signals from ambient sources, e.g., TV signals [3] and Wi-Fi signals [4], to help the WTRD to obtain data from the WTD without generating RF signals has recently been introduced.
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Part II
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Architectures, Protocols, and Performance Analysis
By
Sudha Lohani, University of British Columbia, Vancouver, BC, Canada,
Roya Arab Loodaricheh, 314-2730 Acadia Road, Vancouver, BC, Canada,
Shankhanaad Mallick, 110-8738 French Street, Vancouver, BC, Canada,
Ekram Hossain, University of Manitoba, Winnipeg, MB, Canada,
Vijay Bhargava, University of British Columbia, Vancouver, BC, Canada
Energy harvesting has emerged as one of the enabling technologies for Green Communication. As the name suggests, energy harvesting is a technique by which energy of ambient sources, for example, solar, wind, and thermal, is converted into electrical energy and used to power network equipment or mobile devices [1, 2]. This technology makes use of perpetual renewable energy sources, which reduces the consumption of high-cost constant energy sources. Lately, wireless power transfer has gained much attention in the field of energy harvesting since wireless signal is also an ambient source of energy in itself [3, 4]. Owing to the lower range of harvested energy, RF energy harvesting has potential for powering smaller network nodes.
Wireless energy harvesting technology has been studied in two different paradigms of wireless communication networks. The first is simultaneous wireless information and power transfer (SWIPT) in downlink [5–7]. The SWIPT technique is used to transmit wireless energy to user equipments (UEs) whilst carrying out downlink information transmission to them as shown in Figure 4.1. The technological requirements necessary to enable this simultaneous information and energy transmission at the receiver circuit will be discussed later in this chapter. The SWIPT technique increases the energy efficiency of the network since the energy cost decreases for UEs capable of harvesting energy from the received information signal [8]. In other words, energy spent at the information transmitter is partially reused at the receiver. The reuse of energy is partial mainly because of the path-loss and non-ideal energy harvesting efficiency.
On the other hand, when the UEs are carrying out uplink transmission, it is not possible to transmit energy to them using the SWIPT technique. Hence, another important paradigm of wireless energy harvesting networks is wireless-powered communication (WPC) in the uplink [9, 10]. In this technique, some fraction of the uplink transmission duration is dedicated to downlink energy transmission (DET) from the access point (AP) to the UEs. The energy harvested during this time is utilized by the UEs for uplink information transmission (UIT) to the AP in the remaining fraction of time as shown in Figure 4.2.
Recently, there has been an upsurge of research interest in wireless-powered communication networks. These networks are based on energy harvesting and/or energy transfer technology, for mobile devices using wireless propagation media. This technology offers the capability of using different types of wireless medium, such as radio frequency and magnetic induction, to carry energy from dedicated sources to wireless nodes or to harvest energy from ambient sources. Therefore, this has become a promising solution to power energy-constrained wireless networks. Conventionally, energy-constrained wireless networks such as wireless sensor networks have a limited lifetime, which leads to significant deterioration in network performance and usability. By contrast, a network with wireless energy harvesting and transfer capability can be powered without using a fixed power supply. For example, it can harvest energy from environmental sources such as solar and wind energy or from other dedicated or non-dedicated sources which are tetherless. Hence, there is no need to charge or replace the batteries physically, which can improve the flexibility and availability of the network substantially. Wireless energy has many advantages over other energy sources, including indoor support and stable and more predictable supply.
There are three major types of wireless energy harvesting and transfer technique, namely, radio frequency (RF), inductive coupling, and magnetic resonance coupling techniques. In RF energy harvesting, radio signals with frequencies in the range from 3 kHz to 300 GHz are used as a medium to carry energy in the form of electromagnetic radiation. Inductive coupling is based on magnetic coupling that delivers electrical energy between two coils tuned to resonate at the same frequency. The electric power is carried through the magnetic field between two coils. Magnetic resonance coupling utilizes evanescent-wave coupling to generate and transfer electrical energy between two resonators. The resonator is formed by adding a capacitance on an induction coil. Inductive coupling and magnetic resonance coupling are near-field wireless transmission techniques featuring high power density and conversion efficiency. By contrast, RF energy transfer can be regarded as a far-field energy transfer technique. It is suitable for powering a larger number of devices distributed over a wide area. Wireless energy harvesting and transfer have found many applications and have recently been implemented in many devices, including mobile phones, healthcare devices, sensors, and RFID tags.
A cognitive radio network (CRN) is an intelligent radio network in which unlicensed users (i.e., secondary users) can opportunistically access idle channels when such channels are not occupied by licensed channels (i.e., primary users). The main purpose of CRNs is to utilize available spectrum efficiently, since spectrum is becoming more and more scarce due to the boom in wireless communication systems. Basically, we can define a cognitive radio as a radio that can change its transmitter parameters as a result of interaction with the environment in which it operates [1]. From this definition, there are two main characteristics of cognitive radio that are different from traditional communication systems, namely cognitive capability and reconifigurability [2].
• Cognitive capability. This characteristic enables cognitive users to obtain necessary information from their environment.
• Reconfigurability. After gathering information from the environment, the cognitive users can dynamically adjust their operating mode to environment variations in order to achieve optimal performance.
To support these characteristics of cognitive radio, there are four main functions that need to be implemented for cognitive users.
• Spectrum sensing. The goal of spectrum sensing is to determine the channel status and the activity of the licensed users by periodically sensing the target frequency band.
• Spectrum analysis. The information obtained from spectrum sensing is used to schedule and plan for spectrum access.
• Spectrum access. After a decision has been made on the basis of spectrum analysis, unlicensed users will be allocated access to the spectrum holes.
• Spectrum mobility. Spectrum mobility is a function related to the change of operating frequency band of cognitive users. The spectrum change must ensure that data transmission by cognitive users can continue in the new spectrum band.
Under these functions, cognitive users can utilize the limited spectrum resource in a more efficient and flexible way.
Recently, the development of wireless power transfer technologies has brought a new research direction, called wireless-powered cognitive radio networks (CRNs), which would seem to provide a promising solution for energy conservation for CRNs. In wireless-powered CRNs, secondary users are able to harvest energy wirelessly and then use the harvested energy to transmit data to the primary channels opportunistically.
This paper discusses the stochastic monotonicity property of the conditional order statistics from independent multiple-outlier scale variables in terms of the likelihood ratio order. Let X1, …, Xn be a set of non-negative independent random variables with Xi, i=1, …, p, having common distribution function F(λ1x), and Xj, j=p+1, …, n, having common distribution function F(λ2x), where F(·) denotes the baseline distribution. Let Xi:n(p, q) be the ith smallest order statistics from this sample. Denote by $X_{i,n}^{s}(p,q)\doteq [X_{i:n}(p,q)|X_{i-1:n}(p,q)=s]$. Under the assumptions that xf′(x)/f(x) is decreasing in x∈ℛ+, λ1≤λ2 and s1≤s2, it is shown that $X_{i:n}^{s_{1}}(p+k,q-k)$ is larger than $X_{i:n}^{s_{2}}(p,q)$ according to the likelihood ratio order for any 2≤i≤n and k=1, 2, …, q. Some parametric families of distributions are also provided to illustrate the theoretical results.
He would keep on trying to do this or that with a grim persistence that was painful to watch …
John Wyndham, ‘The Day of the Triffids’
Maple is a computer program capable of performing a wide variety of mathematical operations. It originated in the early 1980s as a computer algebra system, but today this description doesn't really do it justice. Maple has facilities for algebra, calculus, linear algebra, graphics (twoand three-dimensional plots, and animations), numerical calculations to arbitrary precision, and many other things besides. It is widely used in universities across the world, and is particularly useful for tasks that are tedious and error-prone when performed by humans, such as manipulating complicated series expansions and solving large sets of simultaneous equations. Used correctly, Maple can save time and quickly solve problems that would otherwise be intractable. Used incorrectly, it can lead to frustration, and the destruction of expensive IT equipment.
At the time of writing, the current version is Maple 2016. Versions before Maple 2015 were numbered starting from 1; the last of these was Maple 18. New features introduced in each version from Maple 4.0 onwards can be viewed using the help system (see Section 2.2). For the most part, recent changes have been relatively minor, at least as far as the material in this book is concerned. Consequently, all of the examples work with both Maple 2015 and Maple 2016. In fact, most will work in older versions as well, though naturally the number of exceptions increases the further back one goes. Two substantial new features are the dataplot command, discussed in Section 6.6, and the new rules concerning terminating characters, described in Appendix B (see also Section 2.3). Both of these were introduced in Maple 2015.
Why This Book?
This book is intended for students, teachers and researchers who will ultimately wish to use Maple for advanced applications. Here, ‘advanced’ means something more complex than evaluating a single integral, but not necessarily designing and running a simulation of the latest jet engine.