Quadrature error and offset error suppression circuitry for silicon micro-gyroscope

The reasons for inducing quadrature error and offset error are analyzed and the expressions of quadrature error and offset error are induced. The open-loop system analysis indicates that, in order to avoid the appearance of harmonic peaks, the frequency difference δf between drive mode and sense mode must be less than 1/（2Qy）. In order to eliminate the effects of the quadrature error and the offset error, as well as the inherent non- linearity in the capacitance-type sensors, a closed-loop feedback control circuit with quadrature correction is designed. The experimental results indicate that the quadrature error and offset error are corrected. By comparing with open-loop detection, the closed-loop feedback control circuit with quadrature correction decreases the non-linearity of the scale factor from 16. 02% to 0. 35 %, widens the maximum rate capability from ± 270 （°）/s to ± 370 （°）/s and increases the stability of zero bias from 155. 2 （°）/h to 60. 6 （°）/h.

ERROR ANALYSIS IN DIFFERENTIAL QUADRATURE METHOD

Error estimation for the differential quadrature (DQ)with various sets of grid spacing is presented. A general formula is given to compute the weighting coefficients directly. It is found that the maximum error of the Do method with roots of Chebyshev polynomials including two end POints (-1 and + 1 ) is the smallest among the several sets of grid spacing investigated herein.

Deep Learning Based Signal Detection for Quadrature Spatial Modulation System

With the development of communication systems, modulation methods are becoming more and more diverse. Among them, quadrature spatial modulation(QSM) is considered as one method with less capacity and high efficiency. In QSM, the traditional signal detection methods sometimes are unable to meet the actual requirement of low complexity of the system. Therefore, this paper proposes a signal detection scheme for QSM systems using deep learning to solve the complexity problem. Results from the simulations show that the bit error rate performance of the proposed deep learning-based detector is better than that of the zero-forcing(ZF) and minimum mean square error(MMSE) detectors, and similar to the maximum likelihood(ML) detector. Moreover, the proposed method requires less processing time than ZF, MMSE,and ML.

STAP method based on atomic norm minimization with array amplitude-phase error calibration

In this paper,a space-time adaptive processing(STAP)method is proposed for the airborne radar with the array amplitude-phase error considered,which is based on atomic norm minimization(ANM).In the conventional ANM-based STAP method,the influence of the array amplitude-phase error is not considered and restrained,which inevitably causes performance deterioration.To solve this problem,the array amplitude-phase error is firstly estimated.Then,by pre-estimating the array amplitude-phase error information,a modified ANM model is built,in which the array amplitude-phase error factor is separated from the clutter response and the clutter covariance matrix(CCM)to improve the estimation accuracy of the CCM.To prove that the atomic norm theory is applicable in the presence of the array amplitude-phase error,the clutter sparsity is analyzed in this paper.Meanwhile,simulation results demonstrate that the proposed method is superior to the state-of-the-art STAP method.Moreover,the measured data is used to verify the effectiveness of the proposed method.

Alternative Error Bounds for Some Numerical Quadrature Rules

Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.

ON THE ERROR OF QUADRATURE FORMULAE FOR CAUCHY PRINCIPAL VALUE INTEGRALS BASED ON PIECEWISE INTERPOLATION

We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the estimates where quadrature error) is determined for fixed i and which means that not only the. order, but also the coefficient of the main term of is determined. The behaviour of these error constants is compared -with the corresponding ones obtained for the. method of subtraction of the singularity. As it turns out, these error constants have, in general, the same asymptotic behaviour.

Differential quadrature time element method for structural dynamics

An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.

Semi-blind Adaptive Beamforming for High-throughput Quadrature Amplitude Modulation Systems

A semi-blind adaptive beamforming scheme is proposed for wireless systems that employ high-throughput quadrature amplitude modulation signalling. A minimum number of training symbols, equal to the number of receiver antenna arrayts elements, are first utilised to provide a rough initial least squares estimate of the beamformer＇s weight vector. A concurrent constant modulus algorithm and soft decision-directed scheme is then applied to adapt the beamformer. This semi-blind adaptive beamforming scheme is capable of converging fast to the minimum mean-square-error beamforming solution, as demonstrated in our simulation study.

A 3-D Polarization Quadrature Amplitude Modulation Method and Constellation Mapping

As a new three-dimensional(3-D)modulation,Polarization Quadrature Amplitude Modulation(PQAM) can be regarded as the combination of Pulse amplitude modulation(PAM) and Quadrature Amplitude Modulation(QAM) Modulation.It can better improve the digital communication efficiency and reduce the Symbol error rate(SER) of the system than one-dimensional or two-dimensional modulation scheme.How to design a feasible constellation is the most concerned problem of PQAM currently.This paper first studies the relationship between the SER theoretical value of PQAM and the distribution of M and N,proposes a new M,N allocation scheme.Secondly,a new and straightforward design method of constructing higher-level 3-D signal constellations,which can be matched with the PQAM,and the constellation can divided into three different structures according to the ary for PQAM.Finally,the simulation results show that:in PQAM system,the modulation scheme and the constellation mapping scheme are proposed in this paper which can effectively reduce the system SER and improve the anti-noise performance of the system.

OPTIMAL QUADRATURE OF THE SOBOLEV CLASS W_1~r(R) DEFINED ON WHOLE REAL AXIS

In this paper,we study the optimal quadrature problem with Hermite-Birkhoff type,on the Sobolev class(R)defined on whole red axis,and we give an optimal algorithm and determite its optimal error.

Enhanced quadrature signaling-based cooperative transmission with full rate and full diversity

Quadrature signaling-based cooperative transmission is an efficient and simple scheme to obtain spatial diversity.However,this scheme causes date rate loss compared with direct transmission.In this work,our focus is on recovering from the data rate loss while simultaneously achieving spatial diversity.Particularly,an enhanced quadrature signaling-based cooperative scheme was designed,which can realize full-rate transmission by using the signal space diversity(SSD)technique.Then,accurate bit error rate(BER)expression for the full-rate scheme was derived over independent and non-identically distributed(INID)Rayleigh fading channels.Specifically,a closed-form BER expression is obtained,which is quite tight over the whole SNR range,and thus allows for rapid and efficient evaluation of system performance under various channel conditions.Moreover,an asymptotic approximation of the BER was derived to show that the full-rate scheme can achieve full diversity.Simulation results verify the tightness of the analysis and show that the full-rate scheme significantly outperforms the traditional quadrature signaling-based scheme by about 2 dB with the same complexity order.

Error Control Strategies for Numerical Integrations in Fast Collocation Methods

We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.

Turbo-Coded Modulation of EVRC Speech Encoder with Unequal Error Protection for Fading Channels

The Enhanced Variable Rate Codec (EVRC) is a standard for the Speech Service Option 3 for Wideband Spread Spectrum Digital System, which has been employed in both IS-95 cellular systems and ANSI J-STC-008 PCS (Personal Communications Systems). This paper investigated the combination of turbo codes with Unequal Error Protection (UEP) and 16-QAM modulation for EVRC codec of Rate 1 to get power and bandwidth efficient coding scheme. The results show that the UEP system outperforms the Equal Error Protection (EEP) one by 1.45 dB at BER of 10 -5.

Metrology of Optical Communication Systems Using Error Vector Magnitude

Error vector magnitude (EVM) as a performance metric for M-ary quadrature amplitude modulation (QAM) formats in optical coherent systems is presented. It is shown that the calibrated BER, which would otherwise be under-estimated without the correction factor, can reliably monitor the performance of optical coherent systems near the target BER of 10-3 for quadrature phase shift keying (QPSK), 16-QAM, and 64-QAM employing carrier phase recovery with differential decoding to compensate for laser phase noise. The impact on the number of symbols used to estimate the BER from EVM analysis is also presented and compared to the BER obtained by error counting.

Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions

Three kinds of effective error bounds of the quadrature formulas with multiple nodes that are generalizations of the well-known Micchelli-Rivlin quadrature formula, when the integrand is a function analytic in the regions bounded by confocal ellipses, are given. A numerical example which illustrates the calculation of these error bounds is included.

硅微陀螺仪的机械耦合误差分析

研究了硅微陀螺仪机械耦合误差的产生机理。以z轴硅微陀螺仪为研究对象,以动力学方程和矩阵理论为基础,分析了由于加工非理想性产生的不等弹性、阻尼不对称和质量不平衡产生误差的信号,建立了机械耦合误差信号的数学模型,并定量分析了z轴硅微陀螺仪样品的机械耦合误差信号。结果表明,机械耦合误差信号包含了正交耦合误差和与有用信号同相位的误差信号,其中正交耦合误差为主要误差信号,且主要由不等弹性产生。最后,测试了z轴硅微陀螺仪的正交耦合误差信号为342.59°/s,且与理论结果相吻合。因此,抑制和补偿正交耦合误差是减小机械耦合误差的关键技术之一。

硅微陀螺仪的误差分析

以z轴硅微陀螺仪为研究对象,对加工误差产生的误差信号进行了分析.由于加工误差,使得陀螺仪结构不对称,主要表现为支承梁不对称、梳齿间距不等,产生了不等弹性、阻尼不对称以及力不平衡这三种现象.以动力学方程为基础,分析了不等弹性和阻尼不对称产生的误差信号;以静电理论为基础,分析了驱动梳齿和敏感梳齿间距不等时产生的误差信号.分析结果表明,这些误差信号包含了正交耦合误差和与有用信号同相位的误差信号.最后,介绍了一种减小正交误差的方法,并进行了仿真.

硅微陀螺正交误差直流校正设计与分析

为硅微陀螺设计了一种正交误差直流校正方法,通过设计校正结构和加载直流电压实现正交校正。建立了存在正交误差时敏感质量的运动微分方程,分析明确了正交响应的成因和对驱动运动轨迹的影响。为硅微陀螺设计了正交校正结构,实现构建静电耦合弹性系数并利用驱动运动产生校正静电力。校正力的频率和相位无需电路控制,使该方法相较于传统校正方法具备特殊优势。设计并分析了校正电压的两种加载方式,通过实验测试验证了正交响应幅值随校正电压的变化规律。实测校正电压接近理论值,证明了校正结构设计的正确性。该方法在双线振动式硅微陀螺中具有重要应用价值。

微机械振动陀螺仪正交误差分析

本文在简要介绍微机械振动陀螺仪工作原理的基础上,分析影响陀螺仪性能的正交误差所产生的原因,推导其内在的数学机理,并探讨抑制或消除正交误差影响的方法和措施。

正交双通道幅相误差的两种校正方法

讨论了正交双通道幅相不一致的数字校正原理 ,提出了两种获得幅相误差函数的方法 ,包括最小二乘法和改进的Gram Schmidt正交化方法 .计算机仿真结果说明该方法是有效的 .