Moore Curve Research Articles

Multi-Input Multi-Output Antenna Array Design for 5G N78 Applications in Smartphones

This article presents a compact, high isolation Multi Input Multi Output (MIMO) Antenna system operating on (3408-3760) MHz for the fifth generation N78 Applications in mobile phone terminals. The suggested MIMO antenna system is built from four antenna elements. These antennas are placed over two slim side borders of a mobile device's frame to adhere to the current trend of slim and full-screen smartphone devices. The antenna element is composed of two parts: the front part and the back part. The front part consists of the second iteration of Moore curve fractal geometry and an I-shaped feeding line. The back part is of an L-shaped shorted to the system’s ground plane. The desirable antenna diminishment is accomplished based on Moore curve fractal geometry. Low mutual coupling among antennas is attained based on self-isolated and spatial diversity methods, which are less than -16.6 dB. The scattering parameters, antenna gains, antenna efficiencies, and radiation pattern characteristics have all been examined to gauge the performance of the suggested antenna element. In addition, the MEGs and ECCs are examined to understand the MIMO performance of the suggested system. The proposed four-element MIMO antenna system achieves the desired antenna and MIMO characteristics, making it a strong contender for the upcoming 5G mobile devices.

Efficient Multi-UAV Path Planning for Collaborative Area Search Operations

Efficient UAV path-planning algorithms significantly improve inspection efficiency and reduce costs. However, due to the limitation of battery capacity, the endurance of existing UAVs is limited, making it difficult for them to directly undertake information collection, cruising, and inspection tasks over large work areas. This paper considers the problem of path allocation for multiple UAVs to minimize work time and reports research on multi-UAV (unmanned aerial vehicle) multi-task long-duration operation path planning. We propose a multi-UAV collaborative search algorithm based on the greedy algorithm (MUCS-GD) and a multi-UAV collaborative search algorithm based on the binary search algorithm (MUCS-BSAE), and later apply two UAV collaborative search algorithms to five UAV flight paths: (1) a snake curve path, (2) a “square wave signal” curve path, (3) a Peano curve path, (4) a Hilbert curve path, and (5) a Moore curve path, and compare the simulation results. We found that the performance of MUCS-BSAE was better than that of MUCS-GD in all of the above flight paths. In addition, the path with the “square wave signal” curve was the near-optimal path among all the flight paths. Finally, we improved the MUCS-BSAE applied on the “square wave signal” curve path and obtained an improved collaborative search algorithm for multiple UAVs based on the binary search algorithm (IMUCS-BSAE), which further reduced the working time of the UAV.

Design and Analysis of Fractal-Shaped High-Impedance Surface Unit Cell Characteristics

Fractal geometries consistently provide solutions to several electromagnetic design problems. In this paper, fractal geometries such as Hilbert and Moore curves are used to design efficient High-Impedance Surfaces. Modern communication devices have many sensors that are needed to communicate wirelessly. The critical component of wireless communications is antennas. Planar microstrip patch antennas are popular due to their low profile, compactness, and good radiation characteristics. The structural disadvantages of microstrip antennas are that they have surface waves that propagate over the ground plane. High-Impedance Surface (HIS) planes are a prominent solution to minimize and eliminate surface waves. The HIS structures behave as active LC filters that suppress surface waves at their resonance frequency. The resonance frequency of the structure is obtained by its LC equivalent or by analyzing the reflection phase characteristics. This work presents conventional HIS structures similar to mushroom HIS and fractal HIS such as Hilbert curve and Moore curve HIS. The HIS reflection phase characteristics are obtained by applying periodic boundary conditions with plane wave illumination. The results were obtained in terms of the reflection phase angle. The conventional mushroom structures show narrow band characteristics at given dimensions of 10 mm × 10 mm and 20 mm × 20 mm. These structures are helpful in the replacement of PEC ground planes for patch antennas under sub-6 GHz. The Hilbert and Moore fractals are also designed and have a multiband response that can be useful for L, S, and C band applications. Another design challenge of HIS is protrusions, which make design difficult. The work also presents the effect of having vias and the absence of vias on reflection phase characteristics. The response shows the least and no significant effect of vias under the x-band operation.

Location Privacy-Preserving Query Scheme Based on the Moore Curve and Multi-User Cache

With the rapid development of the Internet of Things, location-based services have emerged in many social and business fields. In obtaining the service, the user needs to transmit the query data to an untrusted location service provider for query and then obtain the required content. Most existing schemes tend to protect the user’s location privacy information while ignoring the user’s query privacy. This paper proposes a secure and effective query privacy protection scheme. The multi-user cache is used to store historical query results, reduce the number of communications between users and untrusted servers, and introduce trust computing for malicious users in neighbor caches, thereby reducing the possibility of privacy leakage. When the cache cannot meet the demand, the user’s location coordinates are converted using the Moore curve, processed using encryption technology, and sent to the location service provider to prevent malicious entities from accessing the transformed data. Finally, we simulate and evaluate the scheme on real datasets, and the experimental results demonstrate the safety and effectiveness of the scheme.

Parikh Fuzzy Vector for Finite Words of Rectangular Hilbert Space Filling Curve

Parikh Fuzzy vector for finite words of Rectangular Hilbert Space Filling Curve is introduced. Recurrence relations for this vector and its complement vector are produced. It is shown that the components of the Parikh Fuzzy vector are equally distributed at the limiting level. Hence, it is observed that the Parikh Fuzzy vector tends to a constant vector as n tends to infinity. Moreover, it is also valid to any other kinds of Space Filling Curves like Lebesgue Space Filling Curve, Peano Curve and Moore Curve

A STUDY OF FRACTAL GEOMETRY IN WIRELESS SENSOR NETWORKS

Fractal geometry is a subject that studies non-integer dimensional figures. Most of the fractal geometry figures have a nested or recursive structure. This paper attempts to apply the nested or recursive structure characteristics of fractal geometry to wireless sensor networks. We selected two filling curves, Node-Gosper and Moore, as our research subjects. Node-Gosper Curve is a curve based on node-replacement with a fractal dimension of two. Its first-order graph consists of seven basic line segments. When the hierarchy becomes larger, it can be filled with a hexagonal-like shape. To allow the mobile anchor node of wireless sensor networks to walk along this curve, the number of levels of the Node-Gosper Curve can be adjusted according to parameters such as the sensing area and transmission range. Many space-filling curves have the common shortcoming that they cannot loop on their own, that is, the starting point and the end point are not close, which will cause the mobile anchor node to use extra paths from the end point back to the starting point. The Moore curve has a self-loop, i.e., the starting point and the ending point are almost at the same position. This paper applies Moore curve to the path planning of the mobile anchor node. We can use this path to traverse the entire sensing area and stay in the central point of each square cluster to collect the information of the nodes where the events occurred. The self-loop characteristic of the Moore curve is expected to reach each sensor to collect data faster than other space filling curves, that is, the transmission latency of the sensor traversal will be reduced

PLVA: Privacy-Preserving and Lightweight V2I Authentication Protocol

Vehicular ad hoc networks (VANETs) significantly improves the efficiency and safety of driving since it reduces traffic jams and avoiding accidents, in which the necessary security goals are guaranteed using cryptographic method. In reality, the computation efficiency is very important in implementing the protocol in VANETs. When a vehicle with high speed enters in the coverage of a roadside unit (RSU), the computation overhead of authentication not only affects the communication experience, but also downgrades the driving safety. The feasible solution is to share a message in advance between vehicle and RSU with the help of certification authority (CA), however, CA can deduce the vehicle’s route that should be privacy. In this paper, a privacy-preserving and lightweight V2I authentication (PLVA) protocol is proposed. Specifically, in the beginning phase, all roadside units in a region are converted to a vector using the Moore curve technique, then, a vehicle deduces the RSUs’ information on its planning route using BGN homomorphic encryption before the vehicle begins its trip, meanwhile, CA knows nothing about the route plan although it assists the above process. With the deduced RSUs’ information, fast authentication is achieved between vehicle and each RSU on its route. Moreover, performance evaluation illustrates that our PLVA is efficient in practical VANETs environment.

Implementation of hybrid fractal metamaterial inspired frequency band reconfigurable multiband antenna for wireless applications

In the present paper authors propose the design and analysis of a hepta band metamaterial inspired octagonal shape antenna using hybrid fractals for wireless applications. Multiband characteristics in the designed antenna is accomplished by introducing of slotted octagonal shape radiating part with hybrid fractal form of Moore curve and Koch curve and two SRR cells. The frequency band reconfigurability is obtained with aid of PIN diodes placed inside the strips connected between Moore curve (fused with centered Koch curve) and feedline. During ON mode of PIN diode antenna operates at seven microwave frequency S-band WiMAX (3.4~3.69 GHz—IEEE 802.16e)/Lower C-band terrestrial fixed and mobile broadband application (4.25~4.76 GHz)/C-band WLAN (5.15~5.35/5.75~5.825 GHz—IEEE 802.11a] (5.4~5.9 GHz)/Lower X-band Earth exploration-satellite service ITU region 2 (7.9~8.4 GHz)/Upper X-band Amateur satellite operating band (10.45~10.50 GHz)/Lower Ku-band Radar communication application (13.25~13.75 GHz)/Middle Ku-band Geostationary satellite service (14.2~14.5 GHz) covering various wireless applications. Proposed design exhibit hexa/hepta band features during OFF/ON mode of PIN diode. An acceptable gain, stable radiation characteristics, and good impedance matching are observed at all the resonant frequencies of the proposed structure.

Infinite Numerical Computing Applied to Hilbert’s, Peano’s, and Moore’s Curves

The Peano and the Hilbert curves, denoted by P and H respectively, are historically the first and some of the best known space-filling curves. They have a fractal structure, many variants (as the well-known Moore curve M or a probably new “looped” version $${\overline{H}}$$ of H), and a huge number of applications in the most diverse fields of mathematics and experimental sciences. In this paper, we employ a recently proposed computational system, allowing numerical calculations with infinite and infinitesimal numbers, to investigate the behavior of such curves and to highlight the differences with the classical treatment. In particular, we perform several types of computations and give many examples based not only on the curves H and P, but also on their d-dimensional versions $$H^d$$ and $$P^d$$, respectively. Following our approach, it is easy to apply this new computational methodology to many other geometrical contexts, with interesting advantages such as summarizing in a single (infinite) number, representing the final result of a sequence of computations, much information both on the geometrical meaning of such a sequence and on the base geometrical structure itself.

Privacy-preserving spatial query protocol based on the Moore curve for location-based service

The cloud computing has attracted a multitude of data owners to outsource computing and acquire location-based services from cloud service providers. The privacy-preserving spatial query on outsourced data has become a research hotspot in the location-based service. The existing schemes may damage the confidentiality of data, or be trapped by the large computation and communication overhead. The majority of them focus on the protection of original data and location information, while ignoring the significance of query records. In order to find a balance between security, efficiency and accuracy, this paper proposes a spatial transformation scheme for location-based services in outsourced environment, and designs a privacy-preserving k-nearest neighbor (k-NN) protocol. We utilize the Moore curve to perform a one-way transformation of the original data, and adopt the encryption to prevent malicious access to the transformed data by untrusted entities. The proposed protocol accomplishes efficient and accurate k-NN query in the transformed space while guaranteeing the confidentiality of outsourced data and the user's location. In addition, we propose a secure optimization method based on the oblivious transfer to protect the privacy of query records. Performance analysis shows that the proposed protocol has considerable efficiency advantage over existing schemes without sacrificing security and accuracy.

Design of Heating Coils Based on Space-Filling Fractal Curves for Highly Uniform Temperature Distribution

Heating coils utilize the concept of resistive heating to convert electrical energy into thermal energy. Uniform heating of the target area is the key performance indicator for heating coil design. Highly uniform distribution of temperature can be achieved by using a dense metal distribution in the area under consideration, however, this increases the cost of production significantly. A low-cost and efficient heating coil should have excellent temperature uniformity while having minimum metal consumption. In this work, space-filling fractal curves, such as Peano curve, Hilbert curve and Moore curve of various orders, have been studied as geometries for heating coils. In order to compare them in an effective way, the area of the geometries has been held constant at 30 mm × 30 mm and a constant power of 2 W has been maintained across all the geometries. Further, the thickness of the metal coils and their widths have been kept constant for all geometries. Finite Element Analysis (FEA) results show Hilbert and Moore curves of order-4, and Peano curve of order-3 outperform the typical double-spiral heater in terms of temperature uniformity and metal coil length.

Moore, Minkowski and Koch Curves Based Hybrid Fractal Antenna for Multiband Applications

Today’s world, multiband antenna has immensely beneficial for fulfill the requirements of wireless communication. In this paper, Hybrid Fractal Antenna (HFA) is designed using three popular fractal curves koch, minkowski and moore. The generator curve is created by adding minkowski curve and invert of koch curve. This hybrid generator curve is then superimposed on moore curve to get proposed HFA. FR4 material is used for the design of proposed HFA. The effect of defected ground and dielectric constant of different materials on the performance of antenna is studied. Proposed antenna is fabricated and S11 in dB is measured using Vector Network Analyzer. A comparison between simulated and measured return loss is done. It is found that simulated and measured results are agreement with each other. The antenna parameters such as return loss, VSWR, radiation pattern, gain are described in this article. A gain of 20.1 dB is obtained at frequency 1.70 GHz. The maximum bandwidth of proposed HFA is 2870 MHz and VSWR range varies between 1.887MAX and 1.008MIN. The dimensions of proposed HFA is 41.5 × 37 mm2 which is small as compared to existing hybrid geometries in literature. This proposed HFA can be used for Bluetooth (2.4 GHz), Wi-Fi (IEEE 802.11b and 802.11g) Wireless LAN (5.5 GHz), Wireless computer networking (2.4 GHz and 5.5 GHz), Wi-MAX (5.20 GHz–5.8 GHz), Satellite communication uplink (5.90 GHz), Military satellite downlink (7.25–7.30 GHz) applications.

One machine, one minute, three billion tetrahedra

SummaryThis paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points, and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multithreaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space‐filling curve. The performances of our implementation have been measured on three different processors: an Intel core‐i7, an Intel Xeon Phi, and an AMD EPYC, on which we have been able to compute three billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator, which takes as input the triangulated surface boundary of the volume to mesh.

Split ring resonator based multiband hybrid fractal antennas for wireless applications

In this paper, initially two Moore Antennas are designed which are different from each other in terms of 50 Ω microstrip transmission line only. Same size Feed line is applied at right and left side of the substrate and termed as Left Side Feed Line (LFL) and Right Side Feed Line (RFL). To improve the multiband behavior of Moore Antenna, it is being fused with Koch curve and resultant antenna is named as Moore – Koch Hybrid Fractal Antenna (MKHFA) where Koch curves are superimposed on Moore curve. Two distinct MKHFA’s are designed as MKHFA with LFL and MKHFA with RFL. In order to attain the more number of frequency bands, improved gain, better impedance matching and improved bandwidth, both the MKHFA’s are loaded with Split Ring Resonator (SRR). Proposed antennas are designed on FR4 glass epoxy substrate with thickness 1.6 mm, relative permittivity 4.4. Results of Moore Antenna has been compared with MKHFA and found that MKHFA exhibits multiband behavior. A comparison between unloaded MKHFA using LFL/RFL and loaded MKHFA using LFL/RFL has been made and found that later case exhibits better results in terms of increase in number of frequency bands, bandwidth enhancement and improvement in gain. Prototypes of proposed MKHFA using LFL loaded with SRR and MKHFA using RFL loaded with SRR have been fabricated and tested for their results. The comparison between the simulated and measured results have been done and found in good agreement with each other. The overall dimensions of proposed MKHFA using LFL/RFL loaded with SRR is 25 mm × 25 mm and can be useful for different wireless applications such as Bluetooth (2.41–2.49 GHz) for ISM band, IEEE 802.11 g/b (2.40–2.48 GHz), WiMAX (2.5–2.69 GHz), WLAN (5.15–5.35 GHz), X-band satellite communication (7.1–7.76 GHz). Proposed MKHFA using LFL loaded with SRR also reports peak gain 5.76 dB and bandwidth 770 MHz, whereas, MKHFA using RFL loaded with SRR confirms peak gain 8.56 dB and bandwidth 750 MHz.

Moore's curve structuring of ferromagnetic composite PE-NiFe absorbers

A ferromagnetic material involving nickel-iron particles embedded in a polyethylene matrix is synthesized and electrically characterized between 1 and 12 GHz. These measurements show the combination of electric and magnetic activity along with significant loss terms. We take benefit of these properties for the design of broadband electromagnetic absorbers. To this aim, we use a fractal structuring based on Moore curves. The advantage of etching patterns over metallic ones is clearly evidenced, and several pattern absorbers identified by their Moore's order iteration are designed and analyzed under oblique incidence.

An efficient trajectory based routing scheme for delay-sensitive data in wireless sensor network

Exploiting sink mobility for balancing the energy dissipation of sensor nodes and preventing energy holes is a growing trend in the field of wireless sensor network (WSN). The mobile sink moves throughout the network and collects data in a single-hop fashion resulting in less energy consumption of the sensor nodes. Despite the advantage of this scheme, data forwarding to the mobile sink during an emergency situation is a major issue that should be dealt with. For efficient data delivery within the stipulated deadline, the sensor node which has sensed a delay-intolerant data needs to forward the data towards the mobile sink. In this paper, a Moore curve based trajectory of the mobile sink has been considered for efficient sink based data collection. This work is also motivated by anycast forwarding of delay sensitive data to the mobile sink before the sensed data lose its relevance, where the node follows a strict sleep-wake pattern. We have evaluated the effectiveness of the proposed trajectory based data collection scheme by simulation using MATLAB. The delay-intolerant data routing scheme (DRS) shows that the data reaches the mobile sink within the given deadline while restricting the energy dissipation of the sensor nodes to a minimum. This have been verified by extensive simulations which show that when compared to static sink, the usage of a mobile sink improves the network lifetime by almost 12%. This work has also been compared with an existing work (PMDD) to show its validity. The simulation results depict that DRS shows an improvement of about 25%–29% in terms of network lifetime.

Cross‐layer technique for boosting base‐station anonymity in wireless sensor networks

SummaryA wireless sensor network (WSN) principally is composed of many sensor nodes and a single in situ base station (BS), which are randomly distributed in a given area of interest. These sensor nodes transmit their measurements to the BS over multihop wireless paths. In addition to collecting and processing the sensed data, the BS performs network management operations. Because of the importance of the BS to the WSN, it is the most attractive target of attacks for an adversary. Basically, the adversary opts to locate the BS and target it with denial‐of‐service attack to temporarily or indefinitely disrupt the WSN operation. The adversary can intercept the data packet transmissions and use traffic analysis techniques such as evidence theory to uncover the routing topology. To counter such an attack, this paper presents a novel technique for boosting the BS anonymity by grouping nodes into clusters and creating multiple mesh‐based routing topologies among the cluster heads (CHs). By applying the closed space‐filling curves such as the Moore curve, for forming a mesh, the CHs are offered a number of choices for disseminating aggregated data to the BS through inter‐CH paths. Then, the BS forwards the aggregated data as well so that it appears as one of the CHs. The simulation results confirm the effectiveness of the proposed technique in boosting the anonymity of the BS.

Efficient Privacy-Preserving Protocol for k-NN Search over Encrypted Data in Location-Based Service

With the development of mobile communication technology, location-based services (LBS) are booming prosperously. Meanwhile privacy protection has become the main obstacle for the further development of LBS. The k-nearest neighbor (k-NN) search is one of the most common types of LBS. In this paper, we propose an efficient private circular query protocol (EPCQP) with high accuracy rate and low computation and communication cost. We adopt the Moore curve to convert two-dimensional spatial data into one-dimensional sequence and encrypt the points of interest (POIs) information with the Brakerski-Gentry-Vaikuntanathan homomorphic encryption scheme for privacy-preserving. The proposed scheme performs the secret circular shift of the encrypted POIs information to hide the location of the user without a trusted third party. To reduce the computation and communication cost, we dynamically divide the table of the POIs information according to the value of k. Experiments show that the proposed scheme provides high accuracy query results while maintaining low computation and communication cost.

HAWK: An Unmanned Mini-Helicopter-Based Aerial Wireless Kit for Localization

This paper presents a fully functional and highly portable mini Unmanned Aerial Vehicle (UAV) system, HAWK, for conducting aerial localization. HAWK is a programmable mini helicopter Draganflyer X6 armed with a wireless sniffer Nokia N900. We developed custom PI-Control laws to implement a robust waypoint algorithm for the mini helicopter to fly a planned route. A Moore space filling curve is designed as a flight route for HAWK to survey a specific area. A set of theorems were derived to calculate the minimum Moore curve level for sensing all targets in the area with minimum flight distance. With such a flight strategy, we can confine the location of a target of interest to a small hot area. We can recursively apply the Moore curve-based flight route to the hot area for a fine-grained localization of a target of interest. We have conducted extensive experiments to validate the feasibility of HAWK and our theory. A demo of HAWK in autonomous fly is available at http://www.youtube.com/watch?v=ju86xnHbEq0.

A Novel Privacy Preserving Location-Based Service Protocol With Secret Circular Shift for $k$-NN Search

Location-based service (LBS) is booming up in recent years with the rapid growth of mobile devices and the emerging of cloud computing paradigm. Among the challenges to establish LBS, the user privacy issue becomes the most important concern. A successful privacy-preserving LBS must be secure and provide accurate query [e.g., -nearest neighbor (NN)] results. In this work, we propose a private circular query protocol (PCQP) to deal with the privacy and the accuracy issues of privacy-preserving LBS. The protocol consists of a space filling curve and a public-key homomorphic cryptosystem. First, we connect the points of interest (POIs) on a map to form a circular structure with the aid of a Moore curve. And then the homomorphism of Paillier cryptosystem is used to perform secret circular shifts of POI-related information (POI-info), stored on the server side. Since the POI-info after shifting and the amount of shifts are encrypted, LBS providers (e.g., servers) have no knowledge about the user's location during the query process. The protocol can resist correlation attack and support a multiuser scenario as long as the predescribed secret circular shift is performed before each query; in other words, the robustness of the proposed protocol is the same as that of a one-time pad encryption scheme. As a result, the security level of the proposed protocol is close to perfect secrecy without the aid of a trusted third party and simulation results show that the k-NN query accuracy rate of the proposed protocol is higher than 90% even when is large.