THE NONEMPTINESS AND COMPACTNESS OF MILD SOLUTION SETS FOR RIEMANN-LIOUVILLE FRACTIONAL DELAY DIFFERENTIAL VARIATIONAL INEQUALITIES

This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities,which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality.Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

Small-Space Microphone Array Fractional Delay Algorithm Based on FIR Filter for Cochlear Implant

Directional speech enhancement of signals from microphone arrays is an effective way to improve speech recognition for cochlear implant users. The strict implant size limitation results in a short distance between microphones. The fractional delay problem due to the short distance between microphones is solved by a maximal flat （Maxflat） finite impulse response （FIR） filter, using the Maxflat error criteria at a low frequency containing most of the speech information and energy. The fractional Maxfiat FIR filter approximates the ideal digital fractional filter at the magnitude response, phase response, and phase delay characteristics, and is also very low order. The results demonstrate that the Maxflat FIR filter accurately and effectively solves the fractional digital delay and is very suitable for real-time speech processing in practical cochlear implant products.

ALMOST AUTOMORPHIC MILD SOLUTIONS TO SOME FRACTIONAL DELAY DIFFERENTIAL EQUATIONS

In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction principle.

Dependence Analysis of the Solutions on the Parameters of Fractional Delay Differential Equations

In this paper,we investigate the dependence of the solutions on the parameters(order,initial function,right-hand function)of fractional delay differential equations(FDDEs)with the Caputo fractional derivative.Some results including an estimate of the solutions of FDDEs are given respectively.Theoretical results are verified by some numerical examples.

A True-Time-Delay Array Architecture for Wideband Multi-Beam Tracking

The true-time delay(TTD)units are critical for solving beam squint and frequency selective fading inWideband Large-Scale Antenna Systems(LSASs).In this work,we propose a TTD array architecture for wideband multi-beam tracking that eliminates the beam squint phenomenon and filters out interference signals by applying a spatial filter and time delay estimations(TDEs).The paper presents a novel approach to spatial filter design by introducing a transformation matrix that can optimize the beam response in a specific direction and at a specific frequency.Using the variable fractional delay(VFD)filters,we propose a TDE algorithm with a Newton-Raphson iteration update process that corrects the arrival time delay difference between sensors.Simulations and examples have demonstrated that the proposed architecture can achieve beam tracking within 10 ms at the low signalto-noise ratio(SNR)and demodulation loss is less than 0.5 dB in wideband multi-beam scenarios.

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.

High-resolution digital beamforming of UWB signals based on Carathéodory representation for delay compensation and array extrapolation

To realize high-resolution digital beamforming(DBF)of ultra-wideband(UWB) signals, we propose a DBF method based on Carath ′eodory representation for delay compensation and array extrapolation. Delay compensation by Carath ′eodory representation could achieve high interpolation accuracy while using the single channel sampling technique. Array extrapolation by Carath ′eodory representation reformulates and extends each snapshot, consequently extends the aperture of the original uniform linear array(ULA) by several times and provides a better realtime performance than the existing aperture extrapolation utilizing vector extrapolation based on the two dimensional autoregressive(2-D AR) model. The UWB linear frequency modulated(LFM) signal is used for simulation analysis. Simulation results demonstrate that the proposed method is featured by a much higher spatial resolution than traditional DBF methods and lower sidelobes than using Lagrange fractional filters.

ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,we construct a kind of oneparameter finite difference(OPFD)method.It is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and space.In implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method.For 2D problems,we develop another kind of OPFD method.For such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG scheme.In particular,we prove that ADI scheme can arrive at second-order accuracy in time and space.With some numerical experiments,the computational effectiveness and accuracy of the methods are further verified.Moreover,for the suggested methods,a numerical comparison in computational efficiency is presented.

Radar Sensing via OTFS Signaling

By multiplexing information symbols in the delay-Doppler(DD)domain,orthogonal time frequency space(OTFS)is a promising candidate for future wireless communication in high-mobility scenarios.In addition to the superior communication performance,OTFS is also a natural choice for radar sensing since the primary parameters(range and velocity of targets)in radar signal processing can be inferred directly from the delay and Doppler shifts.Though there are several works on OTFS radar sensing,most of them consider the integer parameter estimation only,while the delay and Doppler shifts are usually fractional in the real world.In this paper,we propose a two-step method to estimate the fractional delay and Doppler shifts.We first perform the two-dimensional(2D)correlation between the received and transmitted DD domain symbols to obtain the integer parts of the parameters.Then a difference-based method is implemented to estimate the fractional parts of delay and Doppler indices.Meanwhile,we implement a target detection method based on a generalized likelihood ratio test since the number of potential targets in the sensing scenario is usually unknown.The simulation results show that the proposed method can obtain the delay and Doppler shifts accurately and get the number of sensing targets with a high detection probability.

Study on moving target detection to passive radar based on FM broadcast transmitter

Target detection by a noncooperative illuminator is a topic of general interest in the electronic warfare field. First of all, direct-path interference （DPI） suppression which is the technique of bottleneck of moving target detection by a noncooperative frequency modulation（FM） broadcast transmitter is analyzed in this article; Secondly, a space-time-frequency domain synthetic solution to this problem is introduced： Adaptive nulling array processing is considered in the space domain, DPI cancellation based on adaptive fractional delay interpolation （AFDI） technique is used in planned time domain, and long-time coherent integration is utilized in the frequency domain; Finaily, an experimental system is planned by considering FM broadcast transmitter as a noncooperative illuminator, Simulation results by real collected data show that the proposed method has a better performance of moving target detection.

Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

In this paper,we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations(RSFDEs)with time delay,which constitute an important class of differential equations of practical significance.We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions.The numerical method is proved to be uniquely solvable,stable and convergent with second order accuracy in both space and time.Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.

Approximate Controllability of Neutral Functional Differential Systems with State-Dependent Delay

This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.

Measurements of effective delayed neutron fraction in a fast neutron reactor using the perturbation method

A perturbation method is proposed to obtain the effective delayed neutron fraction βeff of a cylindrical highly enriched uranium reactor. Based on reactivity measurements with and without a sample at a specified position using the positive period technique, the reactor reactivity perturbation Ap of the sample in βeff units is measured. Simulations of the perturbation experiments are performed using the MCNP program. The PERT card is used to provide the difference dk of effective neutron multiplication factors with and without the sample inside the reactor. Based on the relationship between the effective multiplication factor and the reactivity, the equation βeff=dk/△ρ is derived. In this paper, the reactivity perturbations of 13 metal samples at the designable position of the reactor are measured and calculated. The average βeff value of the reactor is given as 0.00645, and the standard uncertainty is 3.0%. Additionally, the perturbation experiments for fleer can be used to evaluate the reliabilities of the delayed neutron parameters. This work shows that the delayed neutron data of 235U and 23SU froin G.R. Keepin＇s publication are more reliable than those from ENDF-B6.0, ENDF-B7.0, JENDL3.3 and CENDL2.2.

Effect of chip rate on the ranging accuracy in a regenerative pseudo-noise ranging system

The ranging accuracy of a pseudo-noise ranging system is mainly decided by range jitter and time delay discrimination. Many factors can affect the ranging accuracy, one of which is the chip rate. In digital signal processing, the time delay discrimination and autocorrelation function of sampled ranging sequences of different chip rates are very different. An approximation simulation model is established according to an in-phase quadrature (I/Q) correlator which is used to evaluate the time delay. Simulation results of the range jitter and time delay discrimination show that the chip rate which provides a non-integer sample-to-chip rate ratio can achieve a higher ranging accuracy, and some test results validate the simulation model. In some design missions, the simulation results may help to select an optimum sample-to-chip rate ratio to satisfy the design requirement on the ranging accuracy.