Nonlinearity-Compensation-Free Optical Frequency Domain Reflectometry Based on Electrically-Controlled Optical Frequency Sweep

A nonlinearity-compensation-free optical frequency domain reflectometry (OFDR) scheme is proposed and experimentally demonstrated based on the electrically-controlled optical frequency sweep. In the proposed scheme, the linear frequency sweep light is generated by propagating an ultra-narrow-linewidth continuous-wave (CW) light through an electro-optic frequency shifter which consists of a dual-parallel Mach-Zehnder modulator (DPMZM) and an electronic 90° hybrid, where the electro-optic frequency shifter is driven by a linear frequency modulated signal generated by a direct digital synthesizer (DDS). Experimental results show that the spatial resolution and signal-to-noise ratio (SNR) of the proposed OFDR scheme without the nonlinear phase compensation are comparable to those of OFDR employing a commercial tunable laser source (TLS), an auxiliary interferometer, and a software-based nonlinear phase compensation method. The proposed OFDR scheme is helpful to reduce the complexity of the optical structure and eliminate the difficulty of developing the nonlinear phase compensation algorithm.     

近距离超宽带调频连续波雷达非线性校正研究

调频连续波雷达凭借其结构简单、造价低廉等优势在目标探测与识别等方面体现出重要的应用价值,然而系统的非线性调制问题成为制约其性能的重要因素。传统的非线性校正方法能够在一定程度上估计非线性,但估计过程中的误差传递问题导致校正效果并不理想。基于该问题,本文提出一种基于多项式回归的方法实现非线性的准确估计。所提算法首先将非线性相位建模为多项式函数,然后通过多项式回归实现参数的联合估计,以消除误差传递问题。基于估计出的参数,通过时域重采样操作实现非线性的校正。仿真结果表明,所提算法不仅能够准确估计出多项式参数,而且在一定信噪比下比传统算法更接近克拉美—罗界。X波段FMCW雷达实测数据处理结果显示,本文所提算法可以有效消除非线性误差。      

非线性系统分谐波振荡的两种分析方法

本文提出了分析高阶非线性系统分谐波振荡的一种符号算法和一种图解法．这两种分析方法均适用于非线性函数为f(x)=ax-bx^3的情况，而图解法也适于，(x)为五次多项式的情况，且可用来确定多解系统的全部周期解．文末给出一个具有6个解的例子．     

Analyzing of multicomponent undersampled signals by HAF

The phenomenon of frequency ambiguity may appear in radar or communication systems. S. Barbarossa(1991) had unwrapped the frequency ambiguity of single component uri-dersampled signals by Wigner-Ville distribution(WVD). But there has no any effective algorithm to analyze multicomponent undersampled signals by now. A new algorithm to analyze multicomponent undersampled signals by high-order ambiguity function (HAF) is proposed here. HAF analyzes polynomial phase signals by the method of phase rank reduction, its advantage is that it does not have boundary effect and is not sensitive to the cross-items of multicomponent signals. The simulation results prove the effectiveness of HAF algorithm.     

一种新的机载SAR回波高阶多项式相位误差提取方法

当载机在SAR回波方位子孔径时间内运动较复杂时,二次相位误差模型不能准确描述载机运动造成的相位误差。针对此情况,该文借鉴PACE算法的思想,提出了一种提取SAR回波中时域高阶多项式相位误差的TPACE算法。TPACE算法将图像对比度函数作为目标函数,以时域高阶多项式相位误差模型系数作为自变量,通过最优化方法提取时域误差系数。文中详细推导了对比度函数关于误差模型系数的梯度表达式,分析了TPACE与以往提取时域高阶多项式相位误差的算法计算量之差别。实际超宽带SAR回波数据处理结果表明,TPACE能有效提取时域高阶多项式误差,是一种计算量相对较小的SAR自聚焦算法。     

基于HAF估计的超宽带LFM信号距离像频域校正

为更准确且简洁地表达超宽带的线性调频(LFM)信号的非线性相位,文中采用一种高阶模糊函数,而不是经典的泰勒展开来表达非线性相位多项式,并用高阶模糊函数(HAF)法估计非线性相位多项式系数。针对因目标延时不同导致的非线性程度不同的问题,采用了一种频域校正法补偿回波的非线性相位,一次性完成不同距离目标的一维距离像聚焦,无需对不同距离目标分别进行校正处理,算法效率大大提高。     

Analysis of Multicomponent Polynomial Phase Signals

While the theory of estimation of monocomponent polynomial phase signals is well established, the theoretical and methodical treatment of multicomponent polynomial phase signals (mc-PPSs) is limited. In this paper, we investigate several aspects of parameter estimation for mc-PPSs and derive the Crameacuter-Rao bound. We show the limits of existing techniques and then propose a nonlinear least squares (NLS) approach. We also motivate the use the Nelder-Mead simplex algorithm for minimizing the nonlinear cost function. The slight increase in computational complexity is a tradeoff for improved mean square error performance, which is evidenced by simulation results     

基于四次相位模型的改进NCS机载大斜视SAR成像

在斜视成像模式下,合成孔径雷达回波信号的距离向和方位向之间存在严重的相位耦合效应,影响高分辨聚焦.非线性调频变标(NCS)算法在二维频域进行三次相位滤波,并补偿二次距离压缩(SRC)随距离的线性变化,在一定程度上改善了斜视成像的聚焦性能.但随着斜视角的进一步增大,三次以上的高阶相位以及SRC随距离的非线性变化对高分辨聚焦的影响也逐渐加大,从而降低成像性能.文中提出基于回波四次相位多项式模型的改进NCS算法,该算法通过两维频域中的三次及四次相位滤波以补偿参考距离处的相位耦合项,并且考虑了SRC随距离的非线性变化对聚焦的影响.通过仿真及实测数据的成像效果验证了该方法的可行性及有效性.     

多项式建模解电离层相位污染阶数选择新方法

电离层相位污染使天波超视距雷达杂波频谱展宽,影响舰船等低速目标检测.针对这一问题,近年来发展了基于分段多项式相位建模和高阶模糊函数的(HAF)解电离层污染算法,如何合理地选取模型阶数是该算法的核心.给出了两种改进的自适应多项式建模阶数选择方法.并利用仿真方法进行了验证,结果表明:基于高阶模糊函数变换性质的频域和时域阶数选择方法的计算量较现有算法有较大提高,且频域法可在较低信噪比下准确判断多项式阶数.     

基于最大似然法的天波超视距雷达相位解污染算法

电离层解相位污染是天波超视距雷达信号处理的关键技术之一。由于模型的不准确性和电离层的复杂性,已有算法在污染较大时大多精度不高。该文提出一种基于最大似然法的相位解污染算法。该算法将信号建模为相位多项式,通过最大化似然函数来实现污染相位的估计。为了避免最大似然法中的矩阵求逆运算,该文进一步将最大似然问题转化为最小二乘问题,利用遗传算法求解相位系数。仿真结果表明,与传统算法比较,该文算法具有以下优点:相比HRR算法和CED算法,该文算法精度更高,校正后的信号频谱更加尖锐;在相位污染较大的情况下,该文算法仍具有较高的精度,有利于目标信息的提取;该文算法采用高阶多项式,避免分段处理和矩阵求逆,简化了运算。     

A parametric method for non-stationary interference suppression in direct sequence spread-spectrum systems

The problem of non-stationary interference suppression in direct sequence spread-spectrum (DS-SS) systems is considered. The phase of interference is approximated by a polynomial within the considered interval. According to the local polynomial Fourier transform (LPFT) principle, the received signal is dechirped by using the obtained phase approximation and the interference is, in turn, suppressed by excising the corrupted low-pass frequency band. For the estimation of polynomial coefficients, we use the product high-order ambiguity function (PHAF), known for its capability to successfully resolve components of a multicomponent polynomial-phase signal (PPS). The proposed method can suppress interferences with both polynomial and non-polynomial phase. In addition, it can suppress both monocomponent and multicomponent interferences. The simulations show that the proposed method outperforms time-frequency (TF) methods, that successfully deal with multicomponent interferences, in terms of the error probability and computational complexity.     

多项式非线性系统多频输入稳态响应的计算

针对工程实际中广泛存在并且有着十分重要应用的一大类非线性电路和系统,即非线性项为幂级数形式的非线性系统,本文称之为多项式非线性系统,提出了一种多频稳态响应的递归化计算方法,将这种非线性系统在多频输入下的稳态响应计算问题化为不断求解同一个线性系统在不同多频输入下的稳态响应,并且基于所构建的算法原理,采用目前广泛使用的Matlab语言编制了通用程序.大量算例表明,本文所提出的方法可以十分有效的用于计算这类系统的多频稳态响应.     

Nonlinear phase correction with an extended statistical algorithm

This paper presents a new magnetic resonance imaging (MRI) phase correction method. The linear phase correction method using autocorrelation proposed by Ahn and Cho (AC method) is extended to handle nonlinear terms, which are often important for polynomial expansion of phase variation in MRI. The polynomial coefficients are statistically determined from a cascade series of n-pixel-shift rotational differential fields (RDFs). The n-pixel-shift RDF represents local vector rotations of a complex field relative to itself after being shifted by n pixels. We have found that increasing the shift enhances the signal significantly and extends the AC method to handle higher order nonlinear phase error terms. The n-pixel-shift RDF can also be applied to improve other methods such as the weighted least squares phase unwrapping method proposed by Liang. The feasibility of the method has been demonstrated with two-dimensional (2-D) in vivo inversion-recovery MRI data.     

稀疏重构下的非线性调频信号参数估计算法

非线性调频信号广泛应用于雷达声纳领域，其具有多阶多项式相位、未知参数多的特点，给参数估计带来困难。针对此问题，本文提出一种稀疏重构下的非线性调频信号参数估计算法。该方法利用Gabor原子良好时频特性，以 范数稀疏正则最小二乘模型为目标函数，并推导了问题的二阶锥规划（SOCP）形式，最终通过求解的Gabor原子进行参数估计。算法分析信号的时频特征，完成信号的分解重构，适应于各类调频信号。仿真实验证明，本文算法对调频信号二阶与一阶相位参数估计精度都贴近CRB，而对二阶参数的估计较二次相位差分算法更适应较低信噪比。      

A stable adaptive Hammerstein filter employing partial orthogonalization of the input signals

This paper presents an algorithm that adapts the parameters of a Hammerstein system model. Hammerstein systems are nonlinear systems that contain a static nonlinearity cascaded with a linear system. In this paper, the static nonlinearity is modeled using a polynomial system, and the linear filter that follows the nonlinearity is an infinite-impulse response (IIR) system. The adaptation of the nonlinear components is improved by orthogonalizing the inputs to the coefficients of the polynomial system. The step sizes associated with the recursive components are constrained in such a way as to guarantee bounded-input bounded-output (BIBO) stability of the overall system. This paper also presents experimental results that show that the algorithm performs well in a variety of operating environments, exhibiting stability and global convergence of the algorithm.     

Passive localization of near-field sources by path following

A new algorithm for passively estimating the ranges and bearings of multiple narrow-band sources using a uniform linear sensor array is presented. The algorithm is computationally efficient and converges globally. It minimizes the MUSIC cost function subject to geometrical constraints imposed by the curvature of the received wavefronts. The estimation problem is reduced to one of solving a set of two coupled 2D polynomial equations. The proposed algorithm solves this nonlinear problem using a modification of the path-following (or homotopy) method. For an array having m sensors, the algorithm reduces the global 2D search over range and bearing to 2(m-1) independent 1D searches. This imparts a high degree of parallelism that can be exploited to obtain source location estimates very efficiently     

Polynomial-Approximation-Based Control for Nonlinear Systems

This paper is concerned with the stabilization problem for nonlinear systems. A new polynomial-approximation-based approach for modeling nonlinear systems is first proposed. The nonlinearity is approximated by polynomials, and the approximation errors are treated as modeling uncertainties. The original nonlinear systems are converted into polynomial systems with modeling uncertainties. In order to highlight the approximation accuracy, the piecewise polynomial approximation functions are utilized. A novel polynomial state-feedback controller is designed to solve the stabilization problem. Furthermore, switched polynomial state-feedback controllers are designed to improve the performance. The stabilization conditions are presented in terms of sum of squares, which can be numerically solved via SOSTOOLS. Finally, simulation examples are provided to demonstrate the feasibility of the proposed method and show its advantage over the polynomial-fuzzy-model-based approach.     

An Accurate Digital Predistortion for Wideband Power Amplifiers Based on Directly Solving the Inverse Model Function

Digital predistortion (DPD) is one of the most effective techniques that can compensate for the distortions caused by the nonlinearities and memory effects of power amplifiers (PAs). In this paper, a new DPD solution which directly solves the inverse function of a PA model is presented for wideband transmitter applications. The major components of the general memory polynomial (GMP) model are selected to effectively characterize the PA’s nonlinearity and memory effects through model identification. In the direct learning algorithm that followed, the DPD function is obtained by constructing and then solving the reverse function of the identified PA model. Due to the high accuracy of the proposed modeling process and the direct learning algorithm, the DPD function is accurately derived, which could significantly compensate for the nonlinear distortions. Simulations and experiments are performed on wideband long-term evolution (LTE) signals to evaluate the effectiveness of the proposed DPD method. It is demonstrated that a 22-dB adjacent channel leakage ratio improvement is achieved for a 100-MHz LTE-advanced signal, which even outperforms the conventional GMP-based DPD method by about 3 dB.     

A Nonlinear Acoustic Echo Canceller Using Sigmoid Transform in Conjunction With RLS Algorithm

Nonlinearity of amplifiers and/or loudspeakers gives rise to nonlinear echo in acoustic systems, which seriously degrades the performance of speech and audio communications. Many nonlinear acoustic echo cancellation (AEC) methods have been proposed. In this paper, a simple yet efficient nonlinear echo cancellation scheme is presented by using an adaptable sigmoid function in conjunction with a conventional transversal adaptive filter. The new scheme uses the least mean square (LMS) algorithm to update the parameters of sigmoid function and the recursive least square (RLS) algorithm to determine the coefficient vector of the transversal filter. The proposed AEC is proved to be convergent under some mild assumptions. Computer simulations show that the proposed scheme gives a superior echo cancellation performance over the well known Volterra filter approach when the echo path suffers from the saturation-type nonlinear distortion. More importantly, the new AEC has a much lower computational complexity than the Volterra-filter-based method.      

Model based phase unwrapping of 2-D signals

A parametric model and a corresponding parameter estimation algorithm for unwrapping 2-D phase functions are presented. The proposed algorithm performs global analysis of the observed signal. Since this analysis is based on parametric model fitting, the proposed phase unwrapping algorithm has low sensitivity to phase aliasing due to low sampling rates and noise, as well as to local errors. In its first step, the algorithm fits a 2-D polynomial model to the observed phase. The estimated phase is then. Used as a reference information that directs the actual phase unwrapping process. The phase of each sample of the observed field is unwrapped by increasing (decreasing) it by the multiple of 2π, which is the nearest to the difference between the principle value of the phase and the estimated phase value at this coordinate. In practical applications, the entire phase function cannot be approximated by a single 2-D polynomial model. Hence, the observed field is segmented, and each segment is fit with its own model. Once the phase model of the observed field has been estimated, we can repeat the model-based unwrapping procedure described earlier for the case of a single segment and a single model field