Blind separation of synchronous co-channel digital signals using anantenna array. II. Performance analysis

We have recently proposed a blind maximum likelihood approach for demodulating multiple co-channel digital signals received synchronously at an antenna array. This approach exploits the finite alphabet (FA) property of digital signals to simultaneously estimate the array response and symbol sequence for each signal. We have presented two computationally efficient block algorithms for computing the array response and signal estimates: iterative least-squares with projection (ILSP) and iterative least-squares with enumeration (ILSE). In this paper, we study the performance of these algorithms using both analysis and simulation. We derive the probability of error in detecting the signals under the assumption that the array responses are known. We use this probability to estimate the probability of error in the algorithms. Simulation results confirm that the detection error probability yields a good approximation to the performance of the blind algorithms     

A decoupled approach to adaptive signal separation using an antennaarray

This paper considers a new approach to the problem of adaptive separation of digitally modulated signals arriving at an antenna array. The basic idea is to decouple the estimation procedure, treating one signal at a time to be the signal of interest. The method uses an iterative scheme similar to the well-documented iterative least squares with projection (ILSP) algorithm, exploiting the finite alphabet (FA) property of the signals to obtain signal estimates. The proposed algorithm is analyzed in terms of consistency and uniqueness properties, and a statistical performance analysis is carried out. The analysis together with simulation results indicate that a significant saving in computational complexity is accomplished relative to ILSP, while essentially having similar performance     

Least squares acceleration filtering for the estimation of signalderivatives and sharpness at extrema [and application to biologicalsignals]

A family of finite impulse-response (FIR) filters is derived which estimate the second derivative or "acceleration" of a digitized signal. The acceleration is obtained from parabolas that are continuously fit to the signal using a least squares optimization criterion. A closed-form solution for the filter coefficients is obtained. The general approach is computationally simple, can be performed in real-time, and is robust in the presence of noise. An important application of the method, that of measuring sharpness in biologic signals, is presented using the electroencephalogram (EEG) and electrocardiogram (EKG) signals as examples. Furthermore, the design method is extended to derive FIR filters for estimating derivatives of arbitrary order in digital signals of biologic or other origins.     

A subspace approach to blind space-time signal processing forwireless communication systems

The two key limiting factors facing wireless systems today are multipath interference and multiuser interference. In this context, a challenging signal processing problem is the joint space-time equalization of multiple digital signals transmitted over multipath channels. We propose a blind approach that does not use training sets to estimate the transmitted signals and the space-time channel. Instead, this approach takes advantage of spatial and temporal oversampling techniques and the finite alphabet property of digital signals to determine the user symbol sequences. The problem of channels with largely differing and ill-defined delay spreads is discussed. The proposed approach is tested on actual channel data     

Blind equalization of IIR channels using hidden Markov models andextended least squares

In this paper, we present a blind equalization algorithm for noisy IIR channels when the channel input is a finite state Markov chain. The algorithm yields estimates of the IIR channel coefficients, channel noise variance, transition probabilities, and state of the Markov chain. Unlike the optimal maximum likelihood estimator which is computationally infeasible since the computing cost increases exponentially with data length, our algorithm is computationally inexpensive. Our algorithm is based on combining a recursive hidden Markov model (HMM) estimator with a relaxed SPR (strictly positive real) extended least squares (ELS) scheme. In simulation studies we show that the algorithm yields satisfactory estimates even in low SNR. We also compare the performance of our scheme with a truncated FIR scheme and the constant modulus algorithm (CMA) which is currently a popular algorithm in blind equalization     

Blind separation of synchronous co-channel digital signals using anantenna array. I. Algorithms

We propose a maximum-likelihood (ML) approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal. Uniqueness of the estimates is established for BPSK signals. We introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner. Computationally efficient algorithms for both block and recursive estimation of the signals are presented. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful In wireless communication systems. Simulation results demonstrate its promising performance     

Recursive blind symbol estimation of convolutionally codedcochannel signals

A recursive blind equalizer is presented that directly estimates the transmitted symbols of multiple cochannel signals in the presence of ISI. The algorithm exploits shift structure present in the data model and the finite alphabet property of the signals. The proposed method possesses a separation property that allows the symbol sequences for each user to be estimated independently of the others. Problematic issues surrounding unknown and mismatched channel lengths for the cochannel users can be handled effectively in the recursive equalizer. Additionally, if the cochannel signals are encoded prior to transmission, we show how the code structure can be incorporated into the recursive equalizer to improve its performance     

基于最大信噪比盲源分离的脑电信号伪迹滤波算法

心电和眼电伪迹是脑电信号中最常见的干扰,本文提出一种基于最大信噪比盲源分离的伪迹滤波算法.该算法以分离矩阵为变元建立源信号的信噪比目标函数,寻找能使目标函数达到极大(或极小)值的分离矩阵,进而通过分离矩阵求得估计信号.算法的实施过程是,首先利用小波变换去除在原始脑电信号中的部分噪声,然后用基于最大信噪比盲源分离的伪迹滤...     

一种充分利用变量结构的解卷积 混合盲源分离新方法

 针对卷积混合盲源分离问题,提出一种基于接收信号不同延时下自相关矩阵组的联合块内对角化方法.为了求解表征联合块内对角化近似程度的基于最小二乘的三二次代价函数,给出基于梯度下降法的三迭代算法.该算法在充分利用混迭矩阵的块Toeplitz结构和源信号相关矩阵的块内对角化结构的基础上,交替估计代价函数中的三组待定参数,搜索代价函数最小点,从而得到混迭矩阵的估计,实现信道的盲均衡和源信号的盲分离.分析了三迭代算法的收敛性能,证明即使存在估计误差时,该算法依然全局渐进收敛.仿真结果表明,与其他经典的两步算法相比,提出的一步算法能够更好地估计混迭矩阵并恢复出源信号,有效地解决了卷积混合盲源分离问题.     

On the use of kernel structure for blind equalization

The mathematical theory of kernel (null space) structure of Hankel and Hankel-like matrices is applied to the problem of blind equalization of cochannel signals. This approach provides a new perspective on the blind equalization problem and gives insights into the identifiability conditions already presented in the literature. An algorithm is presented that tracks the exact null space of the symbol matrix even in the presence of noise. This work exploits the shift structure in the oversampled channel output and the finite alphabet property of the signals. Previously, these two properties were used independently in a two-step (equalize then separate) process. A contribution of the new approach is that is allows simultaneous exploitation of both the shift structure and the finite alphabet property of the signals     

一类基于非线性PCA准则的复数信号盲分离算法

在阵列信号处理过程中，经常遇到复数信号盲分离问题。例如，卷积混合型的源信号的盲分离；声纳信号盲分离。本文提出了一类基于非线性准则的复数信号盲分离算法。将非线性函数引入学习过程，由算法自动调节学习速率。计算机仿真实验验证了算法的有效性，文中给出了验证结果。     

盲信号分离在数字无线通信中的一种应用

本文提出了基于神经网络的盲信号分离在数字无线通信中的一种应用。利用本文中的天线阵,接收到的信号可以看作是由Ｎ个独立的信号源所激励的线性混合系统的输出,应用基于神经网络的鲁棒性很好的盲分离算法＾〖７〗,实现多用户信号的分离。我们还就其在数字无线通讯中的应用进行了计算机模拟,模拟结果显示分离效果是令人满意的。     

Multichannel Convolution Blind Separation Algorithm for MIMO DSSS/CDMA System

Direct-sequence spread-spectrum (DSSS)/code division multiple access (CDMA) transmissions are now widely used for secure communications and multiple access. They can be transmitted at a low signal-to-noise ratio, and have a low probability of interception and capture. How to obtain the original users' signal in a noncooperative context or estimate the spreading sequence in blind conditions is a very difficult problem. Most of the signal sources are assumed to be instantaneous mixtures. In fact, the received CDMA signals are linearly convoluted. A more complicated blind source separation (BSS) algorithm is required to achieve better source separation. In this paper, a new BSS algorithm is proposed for separating linearly convolved signals in CDMA systems when the mixture coefficients of the signal and channel response are totally unknown, but some knowledge about the temporal model does exist. This algorithm is based on minimizing the squared cross-output-channel-correlation criterion. The simulation results show the effectiveness of the algorithm in the blind detection of DS-CDMA signals.     

Geometric method for blind signal separation of multichannel MPSK signals

In this letter, the problem of blind source separation of Multiple-Phase-Shift-Keying (MPSK) digital signal is considered. The geometry of received MPSK signals constellation is exploited. The column vectors of received signals can be regarded as the points of hyper-cube. All the possible distinct vectors of received signals are found by clustering, and mixing matrix and sources are estimated by searching out the pairing vectors and eliminating redundant information in all possible distinct vectors. Simulation results give the polar diagram of estimated original signals. They show that the proposed algorithm is effective when the original signals is Quadrature-Phase-Shift-Keying (QPSK) or 8-Phase-Shift-Keying (8PSK).     

OFDM系统中基于恒模的盲信道估计算法

该文提出了一种适用于采用PSK调制方式的正交频分复用(OFDM)系统的准盲信道估计算法。该算法首先利用系统信号的恒模特性得到有限个可能的信道,然后利用信号的有限字符特性从可能信道中寻找出最佳信道,因而具有较低的计算复杂度。与现有的盲信道估计算法不同,该算法利用二阶统计量而不是高阶统计量估计信道,获得了较好的估计性能。仿真结果表明,该算法的性能优于基于有限字符特性的盲信道估计算法。     

基于时间可预测性的差分搜索盲信号分离算法

针对基于仿生智能优化的盲信号分离算法计算量偏大的问题,提出了一种新的基于差分搜索的盲信号分离算法。采用信号在时间上的可预测性度量作为目标函数,使用差分搜索算法对目标函数进行优化求解。利用去相关消源方法从混合信号中去除每次分离出的源信号成分,通过逐次分离最终实现对所有源信号的成功恢复。仿真实验表明,所提算法可以有效实现对混合信号的盲分离。与其他算法相比,该算法在保证了更高分离精度的同时,具有更低的运算量。     

A hyperplane-based algorithm for the digital co-channelcommunications problem

The relationship between the blind digital co-channel communications problem and the problem of finding a separating hyperplane in IR^d is explored. A simple model for the blind digital co-channel communications problem is X=AS, where X is a known IR ^d×N matrix. A is an unknown full-rank IR^d×d matrix, and S is an unknown full-rank d×N matrix with elements drawn from a multiple-amplitude-shift-keying (M-ASK) alphabet S. An algorithm with proof is given that solves for A and S up to a simple matrix factor. The algorithm is extended to the complex quadrature-amplitude modulation (QAM) alphabet. The key step in this algorithm involves finding a separating hyperplane parallel to one of the hyperplanes defining the received signal vectors. The geometric interpretation of this relationship is discussed. Examples with noisy data are presented and refinements to the algorithm are discussed     

源信号数目大于观察信号数目情况下的盲源分离

独立分量分析(ICA)作为一种有效的盲源分离技术(BSS）是信号处理领域的热点。传统的独立分量分析都要求观察信号数目大于或者等于源信号数目，然而对于脑电图(EEG)等的一些信号处理中存在的源信号数目大于观察信号数目的情况，传统的独立分量分析算法不能有效分离。该文针对源信号数目大于观察信号数目的情况，在传统的独立分量分析技术的基础上，给出了一个新的学习算法，并将新算法与传统的独立分量算法进行了比较。实验仿真结果证明该算法在给定2个混合信号的情况下能够较好地分离3个未知语音信号源，成功实现了源信号数目大于观察信号数目情况下的盲源分离。     

On the existence of universal nonlinearities for blind sourceseparation

Many density-based methods for blind signal separation employ one or more models for the unknown source distribution(s). This paper considers the issue of density model mismatch in maximum likelihood (ML)-type blind signal separation algorithms. We show that the score function nonlinearity, which was previously derived from the standpoint of statistical efficiency, is also the most robust in maintaining a separation solution for the ML algorithm class. We also consider the existence of a universally applicable nonlinearity for separating all signal types, deriving two results. First, among nonlinearities with a convergent Taylor series, a single fixed nonlinearity for universal separation using the natural gradient algorithm cannot exist. Second, among nonlinearities with a single adjustable parameter, a previously proposed threshold nonlinearity can separate all signals with symmetric amplitude distributions as long as the threshold parameter is properly chosen. The design of "difficult-to-separate" signal distributions is also discussed     

基于增殖系数的混沌信号提取算法

本文提出一种基于混沌信号特性的信号盲提取算法,由于不同的混沌信号在相空间里面对应着不同的吸引子二阶增长率,利用这个特点定义了增殖系数（Proliferation Exponent,PE）并将其作为混沌信号提取的目标函数.首先分析基于增殖系数的梯度搜索方法在解决盲提取问题时存在不足,并将混沌信号的盲提取问题转化为带约束的优化问题,提出利用改进的粒子群优化算法解决信号盲提取的优化问题,通过惯性系数动态调整和最优位置的扰动,提高算法的寻优性能.实验结果表明基于增殖系数的信号提取算法能有效地提取混沌信号,提取的信号在时域和相空间与源信号接近,同时算法也表现出对噪声污染的鲁棒性.