Orthogonal Sequences Research Articles

Estimation of bit error rate in 2×2 and 4×4 multi-input multi-output-orthogonal frequency division multiplexing systems

<span lang="EN-US">Multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems with multiple input antennas and multiple output antennas in dynamic environments face the challenge of channel estimation. To overcome this challenge and to improve the performance and signal-to-noise ratio, in this paper we used the Kalman filter for the correct estimation of the signal in dynamic environments. To obtain the original signal at the receiver end bit error rate factor plays a major role. If the signal to noise ratio is high and the bit error rate is low then signal strength is high, the signal received at the receiver end is almost similar to the </span><em><span lang="EN-US">i<sup>th</sup></span></em><span lang="EN-US"> transmitted signal. The dynamic tracking characteristic of Kalman filter is used to establish a dynamic space-time codeword and a collection of orthogonal pilot sequences to prevent interference among transmissions in this paper. Using the simulation, the Kalman filter method can be compared to the other channel estimation method presented in this paper that can track time-varying channels rapidly.</span>

Location-aided user selection and sum-rate analysis for mmWave NOMA

In this paper, we propose a user selection scheme based on location-aided interference prediction to reduce the training overhead in a non-orthogonal multiple access (NOMA) system. First, we cluster the users based on their location information, enabling the use of non-orthogonal pilot sequence within a cluster and orthogonal pilot sequence between different clusters to reduce the uplink pilot training length. Secondly, we exploit the location information in the computation of the covariance matrices, enabling the prediction of the interference between users. The predicted interference is employed to select the set of users with minimum interference for uplink channel estimation and downlink NOMA data transmission. Finally, the achievable sum-rate of the massive multiple-input multiple-output millimeter wave NOMA system is analyzed. The analytical and numerical results reveal that the location information can be exploited for user selection to reduce the effect of pilot contamination, enhancing the uplink channel estimation and downlink achievable sum-rate.

Symmetry-Breaking Dendrimer Synthons in Colloidal Crystal Engineering with DNA

Breaking symmetry in colloidal crystals is challenging due to the inherent chemical and structural isotropy of many nanoscale building blocks. If a non-particle component could be used to anisotropically encode such building blocks with orthogonal recognition properties, one could expand the scope of structural and compositional possibilities of colloidal crystals beyond what is thus far possible with purely particle-based systems. Herein, we report the synthesis and characterization of novel DNA dendrimers that function as symmetry-breaking synthons, capable of programming anisotropic and orthogonal interactions within colloidal crystals. When the DNA dendrimers have identical sticky ends, they hybridize with DNA-functionalized nanoparticles to yield three distinct colloidal crystals, dictated by dendrimer size, including a structure not previously reported in the field of colloidal crystal engineering, Si2Sr. When used as symmetry-breaking synthons (when the sticky ends deliberately consist of orthogonal sequences), the synthesis of binary and ternary colloidal alloys with structures that can only be realized through directional interactions is possible. Furthermore, by modulating the extent of shape anisotropy within the DNA dendrimers, the local distribution of the nanoparticles within the crystals can be directed.

Covariance-Based Activity Detection With Orthogonal Pilot Sequences for Cell-Free Distributed Massive MIMO Systems

The grant-free random access (GFRA) has been the mainstream access scheme in the massive ultra-reliable low-latency communications (mURLLC). Device activity detection is the foremost issue in GFRA. Most of previous works assume unique non-orthogonal pilot sequence assignment in device activity detection which brings about severe inter-device interference and requires high-complexity access point (AP) coordination to eliminate interference. Taking advantage of the good cross-correlation characteristic of orthogonal pilot sequences and the sparsity in power domain of cell-free (CF) distributed massive multiple-input multiple-output (mMIMO) systems, this paper proposes a novel orthogonal pilot sequences based activity detection (OPSAD) algorithm to alleviate inter-device interference and thus improve device activity detection performance. In the proposed OPSAD algorithm, the min-max covariance interference (MMCI) pilot assignment algorithm considering AP selection and power control is introduced and a new interference metric is defined to efficiently capture the inter-device interference in this algorithm. Simulation results show that the proposed algorithm reduces computational complexity and achieves better performance than the benchmark algorithm utilizing non-orthogonal pilot sequences in practical mURLLC scenario.

OPTIMIZATION OF THE DESIGN PARAMETERS USING THE TAGUCHI METHOD IN INCLINED IMPINGEMENT MULTIJET HEAT TRANSFER WITH RECTANGULAR FINNED HEAT SINK

Thanks to the rapid advancement in technology, especially for the systems having high temperatures and high heat fluxes, the interest in studies on impingement jets to improve the cooling efficiency increased in recent years. The current study focuses on determining the optimization of the inclined multijet array to reduce the temperature of electronic devices. In this study, the cooling was performed on the inclined surfaces by making use of impingement multijets via heat sinks consisting of rectangular fins modeled in different geometries and optimum cooling conditions were achieved. In achieving the optimum cooling conditions, the Taguchi method was used since it was thought to offer a reduction in time and costs in industrial applications. In this study, 11 different parameters were examined at three different levels in order to determine the optimum conditions for impingement multijet applications. The Nusselt number was set as the performance characteristic and the L<sub>27</sub>(3<sup>11</sup>) orthogonal sequence was used as the experiment plan for 11 parameters that were determined. When calculating the Nusselt number by using nozzle diameter, the optimum results were achieved using the following parameters: 40 mm of nozzle diameter, 9 m/s of air velocity, 20 mm of vertical distance between slices, 4444 W/m<sup>2</sup> of heat flux, 20 mm of vertical distance between fins, 15 mm of fin width, 30° of fin angle, 15 mm of horizontal distance between slices, 10° of heat sink angle, 20 mm of horizontal distance between fins, and 8 of nozzle diameter/heat sink dimensionless distance ratio. The flat plate and optimum heat sink established using the data obtained were compared under the optimum conditions obtained from the analysis and to the optimum conditions obtained using the finned optimum heat sink and it was determined that, under the optimum conditions, the finned heat sink improved the heat transfer by 28.61% when compared to the flat plate.

A Comprehensive Survey of Candidate Waveforms for 5G, beyond 5G and 6G Wireless Communication Systems

The evolution of global mobile data over the past decades in broadcasting, Internet of Things (IoT), education, healthcare, commerce, and energy has put strong pressure on 3G/4G mobile networks to improve their service offerings. These generations of mobile networks were initially invented to meet the requirements of the above-mentioned applications. However, as the requirements in these applications continue to increase, new mobile technologies such as 5G (fifth generation), 5G and beyond (B5G, beyond fifth generation), and 6G (sixth generation) are still progressing and being experimented. These networks are very heterogeneous generations of mobile networks that will have to offer very high throughput per user, good energy efficiency, better traffic capacity per area, improved spectral efficiency, very low latency, and high mobility. To meet these requirements, the radio interface of future mobile networks will have to be flexible and rationalized the available frequency resources. Therefore, new modulation methods, access techniques and waveforms capable of supporting these technological changes are proposed. This review presents brief descriptions of the types of 5G, B5G, and 6G waveforms. The 5G consists of OFDM including its transmission techniques: generalized frequency division multiplexing (GFDM), filter bank based multi-carrier (FBMC), universal filtered multi-carrier (UFMC), and index modulation (IM). Meanwhile, the 6G covers orthogonal time frequency space (OTFS), orthogonal chirp division multiplexing (OCDM) and orthogonal time sequence multiplexing (OTSM). The networks’ potentialities, advantages, disadvantages, and future directions are outlined.

MIMO Coded Generalized Reduced Dimension Fourier Algorithm for 3-D Microwave Imaging

In this paper, to accelerate data acquisition and image reconstruction procedures in a multistatic short-range microwave imaging scenario, an orthogonal coding approach with Fourier domain processing is presented. First, a special two-dimensional (2D) multiple-input multiple-output (MIMO) structure is introduced to fully electronically synthesize the 2D aperture. Then, the model of the transmitted and received signals by a MIMO stepped-frequency-modulated radar is presented, with special considerations about orthogonal, balanced and optimal sequences. On the receiver side, the backscatter frequency response extraction process is formulated with the aim of obtaining individual information of all channels. Finally, based on the introduced model, a fast Fourier-based algorithm with reduced dimensions, named MIMO coded generalized reduced dimension Fourier (CGRDF), is mathematically derived. It includes extracting phase and amplitude compensators with the aim of mapping 4D to 2D spatial data, transferring the backscatter transfer function from the spatial domain to the wavenumber domain, extracting the smoothing filter, compensating the curvature of the wavefront of all scatterers, extracting the reflectivity function and an additional range compensator. The results of numerical simulations show the satisfactory and reliable performance of the proposed approach in terms of the information retrieval process and processing speed.

Characterization of the D-Laguerre–Hahn orthogonal polynomials of class one via the cubic decomposition

In the present work, we deal with a monic orthogonal polynomial sequence (MOPS) deduced by its cubic decomposition (CD) . Our goal is to determine all D-Laguerre–Hahn strict of class one of these sequences. From the CD structure, only one family of MOPS appears in connection with the D-Laguerre–Hahn of class zero of Jacobi type in the singular case and the nonsingular one. Their recurrence coefficients are highlighted.

The Assembled Genome of the Stroke-Prone Spontaneously Hypertensive Rat.

We report the creation and evaluation of a de novo assembly of the genome of the spontaneously hypertensive rat, the most widely used model of human cardiovascular disease. The genome is assembled from long read sequencing (PacBio HiFi and continuous long read data [CLR]) and scaffolded with long-range structural information obtained from Bionano optical maps and proximity ligation sequencing proximity analysis of the genome. The genome assembly was polished with Illumina short reads. Completeness of the assembly was investigated using Benchmarking Universal Single Copy Orthologs analysis. The genome assembly was also evaluated with the rat reference gene set, using NCBI automated protocols. We also generated orthogonal single molecule transcript sequence reads (Iso-Seq) from 8 tissues and used them to validate the coding assembly, to annotate the assembly with RNA transcripts representing unique full length transcript isoforms for each gene and to determine whether divergences between RefSeq sequences and the assembly were attributable to assembly errors or polymorphisms. The assembly analysis indicates that this assembly is comparable in contiguity and completeness to the current rat reference assembly, while the use of HiFi sequencing yields an assembly that is more correct at the single base level. Synteny analysis was performed to uncover the extent of synteny and the presence and distribution of chromosomal rearrangements between the reference and this assembly. The resulting genome assembly is reference quality and captures significant structural variation.

Downlink Resource Allocation With Pilot Length Optimization for User-Centric Cell-Free MIMO Networks

Pilot length is a crucial parameter in cell-free multiple-input multiple-output (MIMO) networks, which could significantly affect the downlink throughput. In this letter, we jointly optimize the user scheduling, power allocation and pilot length for user-centric (UC) cell-free MIMO networks. We consider the frequency band is uniformly split into several sub-channels. As the number of users scheduled on one sub-channel is commonly small, orthogonal pilot sequences are adopted among users on each sub-channel to avoid pilot contamination. To achieve user fairness, we aim to maximize the minimum ergodic user rate in the downlink transmission, yielding a challenging mix-integer non-convex optimization. Inspired by the weighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -norm approximation in compressive sensing together with successive convex approximation (SCA), an iterative scheme is then proposed to solve the problem. Simulation results demonstrate that the proposed scheme outperforms its state-of-the-art counterpart, which is a three-step algorithm including user grouping, sub-channel allocation, and power optimization.

Multi-response optimization of AISI H11 using Taguchi and Grey relational analysis

Tool & Die is one of the important department in the manufacturing industries that takes care of proper designing and fabrication of tools and dies required for the production. In this sector, tool steels are used as the primary source of materials. These tool steels belongs to the family of carbon and alloy steels. Mostly used alloying elements are chromium, tungsten, molybdenum and vanadium and are heat-treated. The objective of the work involves machinability study of AISI H11 chromium hot-worked steel extensively used for tool & die making. It deals with the analysis of machining parameters and its influences on the responses considered. Here the controlling parameters considered are cutting speed (Cs), feed rate (Fr) and depth of cut (Dc) and responses as surface roughness (Ra) and material removal rate (Mrr). Each controlling parameters are assigned with 3 levels and experimental runs were executed as per taguchi robust design. To determine multi-objective optimal solution, grey relational analysis (GRA) is employed. GRA is used as it provides a feasible platform for converting a multi-objective function into single-objective function. The experimental runs were performed as per L27 orthogonal array sequence in CNC end-milling. The responses recorded are then analyzed using analysis of variance (ANOVA) and optimal solutions are validated through confirmatory runs. The entire machinability study of AISI H11 is performed in two conditions involving rough machining and finish machining. This has been addressed based on the machining scenario followed in industries taking up job orders. The confirmatory results for rough machining recorded was found to be 0.7871 microns against predicted value of 0.7654 microns resulting with a deviation error of 2.88%. Similarly, for finish machining, confirmatory runs recorded 0.8579 microns against predicted value of 0.8357 microns resulting with a deviation error of 2.66%. The deviation level indicated above between predicted and observed values are minimum, which shows the reliability of the optimal solutions arrived in.

Dynamic Spectrum Control-Assisted Secure and Efficient Transmission Scheme in Heterogeneous Cellular Networks

Abstract Heterogeneous cellular networks (HCNs) are envisioned as a promising architecture to provide seamless wireless coverage and increase network capacity. However, the densified multi-tier network architecture introduces excessive intra- and cross-tier interference and makes HCNs vulnerable to eavesdropping attacks. In this article, a dynamic spectrum control (DSC)-assisted transmission scheme is proposed for HCNs to strengthen network security and increase the network capacity. Specifically, the proposed DSC-assisted transmission scheme leverages the idea of block cryptography to generate sequence families, which represent the transmission decisions, by performing iterative and orthogonal sequence transformations. Based on the sequence families, multiple users can dynamically occupy different frequency slots for data transmission simultaneously. In addition, the collision probability of the data transmission is analyzed, which results in closed-form expressions of the reliable transmission probability and the secrecy probability. Then, the upper and lower bounds of network capacity are further derived with given requirements on the reliable and secure transmission probabilities. Simulation results demonstrate that the proposed DSC-assisted scheme can outperform the benchmark scheme in terms of security performance. Finally, the impacts of key factors in the proposed DSC-assisted scheme on the network capacity and security are evaluated and discussed.

Division problem of a regular symmetric form the case x 3 u = λxv

ABSTRACT We study the following problem: given a regular symmetric form (linear functional) v, find all the regular symmetric forms u which satisfy the equation . We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to u. Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted.

A design and flexible assignment of orthogonal binary sequence sets for (QS)-CDMA systems

A design and flexible assignment of orthogonal binary sequence sets for (QS)-CDMA systems

New constructions of Z-complementary code sets and mutually orthogonal complementary sequence sets

New constructions of Z-complementary code sets and mutually orthogonal complementary sequence sets

Curved Planar Reformation: A Useful Method for Screening Dental Pathologies in Chronic Rhinosinusitis via Paranasal Sinus Computed Tomography.

(1) Background: Curved planar reformation (CPR) is a multiplanar reformatting technique of computed tomography (CT) commonly used during dental cone-beam CT (CBCT) to generate panorex-like images for dental evaluation. Here, we evaluated the utility of an additional CPR sequence in detecting dental pathologies in patients with chronic rhinosinusitis (CRS). (2) Methods: CRS patients who underwent paranasal sinus CT were enrolled retrospectively. The CT images featured three orthogonal sequences and a reconstructed CPR sequence. Additional dental CBCT was performed in patients with pathologies with a strongly suspected odontogenic origin. Dental pathologies detected by CT, CPR, and CBCT were analyzed. (3) Results: A total of 82 CRS patients (37 females and 45 males; mean age 47.3 ± 13.7 years) were included, of whom 23 underwent dental CBCT. In total, 1058 maxillary teeth were evaluated. Compared with paranasal sinus CT, CPR identified greater frequencies of dental pathologies, particularly caries (p < 0.001), periapical lesions (p < 0.001), and fistulae (p = 0.014). CBCT identified greater frequencies of periodontal dental pathologies (p = 0.046) and premolar caries (p = 0.002) compared with CPR. CBCT and CPR detected molar dental pathologies at similar frequencies. (4) Conclusions: CPR could increase the diagnostic rate of odontogenic pathologies compared with standard CT orthogonal views, especially when the sinusitis is caused by caries, periapical lesions, or fistulae. The addition of a CPR sequence allows for simple screening of dental pathologies in CRS patients without a need for additional radiation.

High-Efficiency PCSK-CFFH System Design for IoT Networks

Industrial Internet of Things (IIoT) brings opportunities for innovation and upgrading to industrial production, but meanwhile, it poses unprecedented challenges on the physical layer of wireless communications. In this article, we propose a novel frequency hopping transmission scheme for IIoT, which owns much high efficiency and strong anti-jamming ability. This new scheme is built based on the combination of coherent fast frequency hopping (CFFH) and cyclic code shift key (CCSK), named phase cyclic shift-keying-based CFFH (PCSK-CFFH). For the proposed PCSK-CFFH system, the shift of orthogonal base sequence is adopted to modulate the phases among interhop, instead of transmitting each hop with the same phase as conventional CFFH. This scheme is able to further exploit the extra dimensions of CFFH signals and enables the CFFH system to transmit additional information at no extra cost on either bandwidth or power. Moreover, the bit error rate performance of the proposed PCSK-CFFH system is analyzed theoretically. To improve its ability against severe narrow-band jamming, the selection combining is introduced in our scheme. Furthermore, the anti-jamming performance of the proposed PCSK-CFFH system is also demonstrated. Finally, the simulation results are shown to demonstrate that: by introducing the interhop dimension to CFFH, PCSK-CFFH improves the power efficiency and spectrum efficiency by multiple times and simultaneously inherits the excellent anti-jamming performance of the conventional CFFH system. It can be concluded that the proposed PCSK-CFFH scheme has a great potential to be applied to low-power and highly reliable IIoT communications.

Basic theory of finite-type relations between orthogonal polynomial sequences

A theory of finite-type relations between two orthogonal polynomial sequences is developed. In fact, we find necessary and sufficient conditions for the extended connection coefficients which should be fulfilled for a finite-type relation. Next, a simplification criterion is given and some applications in the domain of continuous, discrete and quantum semiclassical orthogonal polynomials are treated into detail.

Three-phase DNA-origami stepper mechanism based on multi-leg interactions

Nanoscale stepper motors such as kinesin and dynein play a key role in numerous natural processes such as mitotic spindle formation during cell division or intracellular organelle transport. Their high efficacy in terms of operational speed and processivity has inspired the investigation of biomimetic technologies based on the use of programmable molecules. In particular, several designs of molecular walkers have been explored using DNA nanotechnology. Here, we study the actuation of a DNA-origami walker on a DNA-origami track based on three principles: 1) octapedal instead of bipedal walking for greater redundancy; 2) three pairs of orthogonal sequences, each of which fuels one repeatable stepping phase for cyclically driven motion with controlled directionality based on strain-based step selection; 3) designed size of only 3.5 nm per step on an origami track. All three principles are innovative in the sense that earlier demonstrations of steppers relied on a maximum of four legs on at least four orthogonal sequences to drive cyclic stepping, and took steps much larger than 3.4 nm in size. Using gel electrophoresis and negative-stain electron microscopy, we demonstrate cyclic actuation of DNA-origami structures through states defined by three sets of specific sequences of anchor points. However, this mechanism was not able to provide the intended control over directionality of movement. DNA-origami-based stepper motors will offer a future platform for investigating how increasing numbers of legs can be exploited to achieve robust stepping with relatively small step sizes.

A note on norm retrievable real Hilbert space frames

In this manuscript, we present several new results in finite and countable dimensional real Hilbert space norm retrieval by vectors and projections. We make a detailed study of when hyperplanes do norm retrieval. Also, we show that the families of norm retrievable frames {fi}i=1m in Rn are not dense in the family of m≤(2n−2)-element sets of vectors in Rn for every finite n and the families of vectors which do norm retrieval in ℓ2 are not dense in the infinite families of vectors in ℓ2. We also show that if a Riesz basis does norm retrieval in ℓ2, then it is an orthogonal sequence. We provide numerous examples to show that our results are best possible.