Optimal signal reconstruction in noisy filter bank systems:multirate Kalman synthesis filtering approach

A multirate Kalman synthesis filter is proposed in this paper to replace the conventional synthesis filters in a noisy filter bank system to achieve optimal reconstruction of the input signal. Based on an equivalent block representation of subband signals, a state-space model is introduced for an M-band filter bank system with subband noises. The composite effect of the input signal, analysis filter bank, decimators, and interpolators is represented by a multirate state-space model. The input signal is embedded in the state vector, and the corrupting noises in subband paths are generally considered as additive noises. Hence, the signal reconstruction problem in the M-band filter bank systems with subband noises becomes a state estimation procedure in the resultant multirate state-space model. The multirate Kalman filtering algorithm is then derived according to the multirate state-space model to achieve optimal signal reconstruction in noisy filter bank systems. Based on the optimal state estimation theory, the proposed multirate Kalman synthesis filter provides the minimum-variance reconstruction of the input signal. Two numerical examples are also included. The simulation results indicate that the performance improvement of signal reconstruction in noisy filter bank systems is remarkable     

Reconstruction of nonuniformly sampled time-limited signals using prolate spheroidal wave functions

Shannon's sampling theory is based on the reconstruction of bandlimited signals which requires infinite number of uniform time samples. Indeed, one can only have finite number of samples for numerical implementation. In this paper, as a dual of the bandlimited reconstruction, a solution for time-limited signal reconstruction from nonuniform samples is proposed. The system model we present is based on the idea that time-limited signals which are also nearly bandlimited can be well approximated by a low-dimensional subspace. This can be done by using prolate spheroidal wave functions as the basis. The order of the projection on this basis is obtained by means of the time–frequency dimension of the signal, especially in the case of non-stationary signals. The reconstruction requires the estimation of the nonuniform sampling times by means of an annihilating filter. We obtain the reconstruction parameters by solving a linear system of equations and show that our finite-dimensional model is not ill-conditioned. The practical aspects of our method including the dimensionality reduction are demonstrated by processing synthetic as well as real signals.     

Image reconstruction and multidimensional field estimation from randomly scattered sensors.

Many important problems in statistical signal processing can be formulated as function estimation from randomly scattered sensors in a multidimensional space, e.g., image reconstruction from photon-limited images and field estimation from scattered sensors. We present a novel approach to the study of signal reconstruction from random samples in a multidimensional space. In particular, we study a classical iterative reconstruction method and demonstrate that it forms a sequence of unbiased estimates for band-limited signals, which converge to the true function in the mean-square sense. We subsequently rely on the iterative estimation method for multidimensional image reconstruction and field estimation from sensors scattered according to a multidimensional Poisson and uniform distribution. Computer simulation experiments are used to demonstrate the efficiency of the iterative estimation method in image reconstruction and field estimation from randomly scattered sensors.     

An Efficient Scheme to Achieve Differential Unitary Space‐Time Modulation on MIMO‐OFDM Systems

Differential unitary space‐time modulation (DUSTM) has emerged as a promising technique to obtain spatial diversity without intractable channel estimation. This paper presents a study of the application of DUSTM on multiple‐input multiple‐output orthogonal frequency division multiplexing (MIMO‐OFDM) systems with frequency‐selective fading channels. From the view of a correlation analysis between subcarriers of OFDM, we obtain the maximum achievable diversity of DUSTM on MIMO‐OFDM systems. Moreover, an efficient implementation strategy based on subcarrier reconstruction is proposed, which transmits all the signals of one signal matrix in one OFDM transmission and performs differential processing between two adjacent OFDM blocks. The proposed method is capable of obtaining both spatial and multipath diversity while reducing the effect of time variation of channels to a minimum. The performance improvement is confirmed by simulation results.     

分布式MIMO系统多分量调制信号频率估计

针对分布式多输入多输出系统中的多频偏估计问题进行了研究,提出一种多分量调制信号的高分辨率频率盲估计方法。该方法避免了直接对多分量调制信号进行稀疏表示,无需导频等先验信息,避免传统频率估计方法中的内插、去相位混叠等处理,可一次性精确估计出所有信号频率。通过正定盲源分离方法从接收信号中分离出多个源信号,经过盲去调制处理,将其转换成多单频信号,根据多单频信号的稀疏表示,利用一个随机的压缩矩阵对信号进行压缩,再在压缩域中通过 模优化重构该稀疏信号,获得频率估计。仿真结果表明,与现有算法相比,所提方法可在少数据量、低信噪比下获得高精度估计性能,可在5dB时达到1e-6的平均均方误差。      

MIMO-OFDM系统中信道盲估计与检测

针对MIMO-OFDM系统,提出了一种基于子空间的盲信道估计与检测方案,该算法将阵列信号处理的思想应用到MIMO-OFDM系统中,通过发送端信号的冗余编码,利用一种类ESPRIT算法进行盲信号检测和信道估计。仿真结果表明该算法的有效性及其信道盲估计方法的性能。     

基于线性化的混沌压缩感知重构算法

随着信号的数据量和带宽不断增长,压缩感知作为一种新的信号低速率获取理论迅速成为信号处理界的热点。目前,压缩感知一般采用线性测量方式。混沌压缩感知是一种利用混沌系统实现非线性测量,非线性等式约束L1范数最小化实现信号重构的压缩感知理论;具有实现结构简单,测量数据保密性强等特点。但是,现有算法不能有效地求解非线性等式约束L1范数最小化,求解结果受到额外参数影响。该文通过对非线性约束线性化处理,将非线性等式约束L1范数最小化问题转化为一系列二次锥规划问题,利用线性化迭代二次锥规划算法进行求解,保证了算法的收敛性和提高了信号的重构性能。本文以Henon混沌为例,研究了频域稀疏信号的重构性能,数值模拟证明了该算法的有效性。      

多径环境下的直扩信号伪码周期估计

针对低信噪比条件下多径直接序列扩频(直扩)信号伪码周期估计的难题,拓展了先前提出的单径环境下基于信号功率谱二次处理的方法,提出了在低信噪比条件下多径环境中直扩信号的伪码周期估计的二次谱算法.该算法首先对多径直扩信号求取功率谱,然后将所得到的功率谱作为一输入信号求其第二次功率谱,所得二次功率谱将在伪码周期整数倍处出现代表信号存在的尖峰脉冲,通过对这些尖峰脉冲闻的距离进行检测就可以获得多径直扩信号伪码周期参数的检测估计.理论分析和计算机仿真结果表明:该算法可以有效地估计出多径环境下直扩信号的伪码周期,且估计性能和多径环境密切相关.     

The design of 2-D nonseparable directional perfect reconstruction filter banks

In this paper, we develop a directional 2-D nonseparable filter bank that can perfectly reconstruct the downsampled subband signals. The filter bank represents two powerful image and video processing tools: directional subband decomposition and perfect reconstruction. The directional filter banks consist of (1) the input signal and the subband signals modulation, (2) diamond shape prefilter, and (3) four different parallelogram shape prefilters. This paper addresses the design and implementation of a two-band filter bank that is proved to be able to provide perfect reconstruction of the downsampled subband signals. Finally, we use a conventional 1-D half-band filter as a prototype and then apply the McClellan transform for the specific 2-D diamond shape and parallelogram shape subfilters. This method is extremely simple in designing the analysis/synthesis subfilters for the filter bank.     

Discrete cosine harmonic wavelet transform and its application to signal compression and subband spectral estimation using modified group delay

This paper proposes a new harmonic wavelet transform (HWT) based on discrete cosine transform (DCTHWT) and its application for signal or image compression and subband spectral estimation using modified group delay (MGD). Further, the existing DFTHWT has also been explored for image compression. The DCTHWT provides better quality decomposed decimated signals, which enable improved compression and MGD processing. For signal/image compression, compared to the HWT based on DFT (DFTHWT), the DCTHWT reduces the reconstruction error. Compared to DFTHWT for the speech signal considered for a compression factor of 0.62, the DCTWHT provides a 30% reduction in reconstruction error. For an image, the DCTHWT algorithm due to its real nature, is computationally simple and more accurate than the DFTHWT. Further compared to Cohen–Daubechies–Feauveau 9/7 biorthogonal symmetric wavelet, the DCTHWT, with its computational advantage, gives a better or comparable performance. For an image with 6.25% coefficients, the reconstructed image by DFTHWT is significantly inferior in appearance to that by DCTHWT which is reflected in the error index as its values are 3.0 and 2.65%, respectively. For spectral estimation, DCTHWT reduces the bias both in frequency (frequency resolution) and spectral magnitude. The reduction in magnitude bias in turn improves the signal detectability. In DCTHWT, the improvement in frequency resolution and the signal detectability is not only due to good quality DCT subband signals but also due to their stretching (decimation) in the wavelet transform. The MGD reduces the variance while preserving the frequency resolution achieved by DCT and decimation. In view of these, the new spectral estimator facilitates a significant improvement both in magnitude and frequency bias, variance and signal detection ability; compared to those of MGD processing of both DFT and DCT fullband and DFT subband signals.     

直扩信号伪码的盲估计方法的研究

对直接序列扩频通信的信号检测方法进行了综述,重点讨论了自相关域检测方法、四阶累积量方法、谱分析与信号子空间分解法,其中四阶统积量方法和谱分析与信号子空间分解法的最低检测门限远低于相关算法,谱分析与信号子空间分解法在直接序列扩频(DS/SS)信号的伪码周期估计以及伪码序列盲估计中,利用功率谱二次处理结合信号子空间分解的方法可以实现对低信噪比DS/SS信号的估计。     

Optimal reconstruction of ARMA signals with decimated samples under corrupting noise by use of multirate Kalman filter

A multirate modeling theory of the ARMA stochastic signals is derived from a state-space viewpoint in this work. Its application to the signal reconstruction problem for the recovery of the complete ARMA signal from its noise-corrupted, missing-sample sequence is then developed in detail. The proposed estimation-interpolation problem can be resolved by using the multirate optimal state estimation scheme of this work. Theoretically, the multirate Kalman reconstruction filters derived in this paper produce the minimum variance estimation and interpolation of the original complete, clean ARMA signal. Practically, the numerical examples show that the multirate Kalman reconstruction filters illustrate good estimation/interpolation performances, not only for synthetic ARMA sequences but also for human speech signals.     

基于压缩感知的DOA估计稀疏化模型与性能分析

利用压缩感知理论解决阵列信号到达角(DOA)估计问题,具有对快拍数据量要求低、可处理相关源等优点。将压缩感知理论应用于信源DOA估计的一个关键问题是建立信源信号的稀疏化模型。该文在均匀线阵模型下系统分析了角度划分对DOA估计稀疏重构性能的影响,从对相关性的分析出发给出了信号的最优稀疏化模型。分析结果表明在实际应用中基于信源信号等正弦空间稀疏化的重构模型是最优的。实验对比了新的稀疏化模型与传统的等角度划分方式得到的流形矩阵的可重构性能,并进行了关于信号重构和信源DOA估计的详细实验分析,验证了所提模型的优越性。     

Efficient algorithms for Volterra system identification

In this paper, nonlinear filtering and identification based on finite-support Volterra models are considered. The Volterra kernels are estimated via input-output statistics or directly in terms of input-output data. It is shown that the normal equations for a finite-support Volterra system excited by zero mean Gaussian input have a unique solution if, and only if, the power spectral process of the input signal is nonzero at least at m distinct frequencies, where m is the memory of the system. A multichannel embedding approach is introduced. A set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format. Efficient algorithms for the estimation of the Volterra parameters are derived for batch, as well as for adaptive processing. An efficient order-recursive method is presented for the determination of the Volterra model structure. The proposed methods are illustrated by simulations     

An Analog Squaring Technique Based on Asynchronous Sigma–Delta Modulation

Accurate analog squarers are required for different signal processing functions, such as amplitude modulation, frequency shifting, signal power estimation, and neural and image processing. Transistor-level analog squarers suffer from limited accuracy, particularly in modern deep-submicrometer technology, where the squared law of the MOS transistor in the saturation region is no longer valid. Based on the asynchronous sigma–delta modulator (ASDM), a new circuit that provides the squared value of the input signal is proposed. For slowly varying input signals, the filtered output is a replica of the squared input signal. In this brief, the proposed analog squarer is studied, and the analytical results are validated by simulation in the time domain. The effect of analog imperfections on the accuracy of the squarer is also analyzed by showing that a high signal-to-noise-plus-distortion ratio can be obtained for typical values of the mismatch and up to frequencies near half the maximum frequency of the ASDM limit cycle.      

Sparsity aware consistent and high precision variable selection

Variable selection is fundamental while dealing with sparse signals that contain only a few number of nonzero elements. This is the case in many signal processing areas extending from high-dimensional statistical modeling to sparse signal estimation. This paper explores a new and efficient approach to model a system with underlying sparse parameters. The idea is to get the noisy observations and estimate the minimum number of underlying parameters with acceptable estimation accuracy. The main challenge is due to the non-convex optimization problem to be solved. The reconstruction stage deals with some suitable objective function in order to estimate the original sparse signal by performing variable selection procedure. This paper introduces a suitable objective function in order to simultaneously recover the true support of the underlying sparse signal while still achieving an acceptable estimation error. It is shown that the proposed method performs the best variable selection compared to the other algorithms, while approaching the lowest least mean squared error in almost all the cases.     

新型多路数控增益放大器

介绍了一种新型多路数控增益放大器。该放大器具有8路模拟信号输入通道,采用3位数字信号控制通道位;每个通道均具有256级增益控制,采用8位数字信号控制放大倍数;输入信号采用绝对值处理电路,具备极性判别信号输出。采用多芯片微组装技术实现,体积小、重量轻,可用做小型微机处理电路的模拟接口芯片。简要介绍了基于该放大器的某设备控制与保护系统的应用示例。     

基于时延估计算法的透明转发器的实现方法

讨论了转发器实现收发不间断的方法,提出了在自适应噪声相消的系统上,将简化的分数阶傅里叶变换理论应用于时延估计,进而将干扰信号重构抵消。推导了该算法,并提出基于该算法实现收发同时进行的转发器系统,即透明转发器。给出本系统模型框图,该透明转发器采用最小均方(LMS)算法建立自适应系统控制结构,能够通过自适应滤波器将自发干扰信号减除,并将不相关的背景噪声抵消。最后利用 MATLAB 软件仿真了基于该算法的透明转发器在具体信号上的运用,实验结果表明该方法实现了不间断转发功能,并且系统结构简单、易实现。     

单信道混合数字通信信号的时延估计方法

单通道混合通信信号的参数估计是无线通信信号处理的热门方向。本文针对单信道两路数字通信信号混合的时延估计问题,根据混合信号的循环自相关函数与信号调制参数的关系,提出了两种基于循环自相关的时延估计方法。两种方法分别针对信道参数未知的情况和信道参数已知的情况,利用循环自相关函数构建关于两路时延参数的方程组,通过解方程组获得了两路信号时延的闭式估计。另外本文也对单通道混合数字通信信号时延估计的克拉美罗界进行了分析。最后利用计算机仿真实验,考察了不同条件下两种方法的性能,表明了它们的性能特点和适用的条件。      

四阶累积量稀疏表示的DOA估计方法

针对现有稀疏重构DOA估计算法不能抑制噪声项以及在高斯色噪声背景下不再适用的问题,本文提出了基于四阶累积量稀疏重构的DOA估计方法。首先,利用接收数据的四阶累积量构建了稀疏表示模型,该模型抑制了噪声项;其次对四阶累计量矩阵进行奇异值分解,化简了稀疏表示模型,通过奇异值分解,不仅减小了数据规模,而且进一步抑制了噪声。对于稀疏表示模型的求解,先利用信号子空间与噪声子空间的正交特性选取权值矢量,然后利用加权l1范数法对模型求解实现DOA估计。理论分析和仿真实验表明本文算法在高斯白噪声和色噪声背景下均适用;能够处理非相干和相干信号,且在低信噪比条件下,对相干信号有更高的估计精度;较之同类的稀疏重构算法,本文算法具有较低的算法复杂度和更高的角度分辨力。