Analytical blind channel identification

A novel analytical blind single-input single-output (SISO) identification algorithm is presented, based on the noncircular second-order statistics of the output. It is shown that statistics of order higher than two are not mandatory to restore identifiability. Our approach is valid, for instance, when the channel is excited by phase shift keying (PSK) inputs. It is shown that the channel taps need to satisfy a polynomial system of degree 2 and that identification amounts to solving the system. We describe the algorithm that is able to solve this particular system entirely analytically, thus avoiding local minima. Computer results eventually show the robustness with respect to noise and to channel length overdetermination. Identifiability issues are also addressed.     

Cross-spectrum based blind channel identification

A novel cross-correlation based framework is proposed for the problem of blind equalization in communications. We assume that we have access to two observations obtained either by sampling, at the symbol rate, the outputs of two sensors or by oversampling, by a factor of two, the output of a single sensor. In either case, the two observations correspond to the outputs of two channels excited by the same input. The channels are estimated using the theory of signal reconstruction from phase only. The phase used is the phase of the cross spectrum of the observations filtered through their minimum phase equivalent filters. We provide an analytical study of the propagation of noise effects in the phase estimate. Comparisons with existing methods indicate that the proposed approach is robust to noise and, at low signal-to-noise ratio (SNR), leads to significantly smaller channel estimation errors. Besides robustness to noise, the proposed method does not require knowledge of channel lengths, which are determined via an iterative procedure     

A least-squares approach to blind channel identification

Conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input. In some practical applications, however, the input statistical model may not be known, or there may not be sufficient data to obtain accurate enough estimates of certain statistics. In this paper, we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel FIR systems without requiring the knowledge of the input statistical model. A new blind identification algorithm based solely on the system outputs is proposed. Necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented     

Unbiased blind adaptive channel identification and equalization

The blind adaptive equalization and identification of communication channels is a problem of important current theoretical and practical concerns. Previously proposed solutions for this problem exploit the diversity induced by sensor arrays or time oversampling, leading to the so-called second-order algebraic/statistical techniques. The prediction error method is one of them, perhaps the most appealing in practice, due to its inherent robustness to ill-defined channel lengths as well as for its simple adaptive implementation. Unfortunately, the performance of prediction error methods is known to be severely limited in noisy environments, which calls for the development of noise (bias) removal techniques. We present a low-cost algorithm that solves this problem and allows the adaptive estimation of unbiased linear predictors in additive noise with arbitrary autocorrelation. This algorithm does not require the knowledge of the noise variance and relies on a new constrained prediction cost function. The technique can be applied in other noisy prediction problems. Global convergence is established analytically. The performance of the denoising technique is evaluated over GSM test channels     

QR factorization based blind channel identification withsecond-order statistics

Most eigenstructure-based blind channel identification and equalization algorithms with second-order statistics need SVD or EVD of the correlation matrix of the received signal. In this paper, we address new algorithms based on QR factorization of the received signal directly without calculating the correlation matrix. This renders the QR factorization-based algorithms more robust against ill-conditioned channels, i.e., those channels with almost common zeros among the subchannels. First, we present a block algorithm that performs the QR factorization of the received data matrix as a whole. Then, a recursive algorithm is developed based on the QR factorization by updating a rank-revealing ULV decomposition. Compared with existing algorithms in the same category, our algorithms are computationally more efficient. The computation in each recursion of the recursive algorithm is on the order of O(m²) if only equalization is required, where m is the dimension of the received signal vector. Our recursive algorithm preserves the fast convergence property of the subspace algorithms, thus converging faster than other adaptive algorithms such as the super-exponential algorithm with comparable computational complexities. Moreover, our proposed algorithms do not require noise variance estimation. Numerical simulations demonstrate the good performance of the proposed algorithms     

Improved blind channel identification using a parametric approach

In wireless communications, the channel has a known manifold structure due to the sensor array response, pulse-shaping function, and sampling phase. By exploiting this information, the method presented in this article achieves improved performance over unstructured blind channel estimation schemes. The approach is subspace-based, and can take advantage of multiple channel estimates if available, e.g., from different time slots in TDMA systems. Its performance is numerically simulated and compared against the original unstructured channel subspace method     

Asymptotic analysis of blind multiuser detection with blind channel estimation

The analytical performance of the subspace-based blind linear minimum mean-square error (MMSE) multiuser detection algorithm in general multipath multi-antenna code-division multiple-access (CDMA) systems is investigated. In blind multiuser detection, the linear MMSE detector of a given user is estimated from the received signals, based on the knowledge of only the spreading sequence of that user. Typically, the channel of that user must be estimated first, based on the orthogonality between the signal and noise subspaces. An asymptotic limit theorem for the estimate of the blind linear detector (when the received signal sample size is large) is obtained, based on which approximate expressions of the average output signal-to-inference plus noise ratios (SINRs) and bit error rates (BERs) for both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulations are given. Corresponding results for group-blind multiuser detectors are also obtained. Examples are provided to demonstrate the excellent match between the theory developed in this paper and the simulation results.     

Data-recursive algorithms for blind channel identification inoversampled communication systems

Data-recursive algorithms are presented for performing blind channel identification in oversampled communication systems. Novel on-line solutions with complexities that are only linear in the oversampling rate are considered, and mean convergence conditions are provided. Numerical results are presented for a binary phase-shift keyed (BPSK) system     

Parameter estimation and blind channel identification in impulsivesignal environments

New methods for parameter estimation and blind channel identification in impulsive signal environments are presented, where the signals/noise are modeled as symmetric α-stable (SαS) processes. First, we present methods for estimating the parameters (characteristic exponent α and dispersion γ) of a SαS distribution from a time series. The fractional lower order moments, with both positive and negative orders, and their applications to signal processing are introduced. Then we present a new algorithm for blind channel identification using the output fractional lower order moments, and the α-Spectrum, a new spectral representation for impulsive signals, is introduced. From the α-Spectrum, we establish the blind identifiability conditions of any FIR channel (mixed-phase, unknown order) with i.i.d. SαS (α>1) input. As a byproduct, a simple algorithm for recovering the phase of any type of a signal from the magnitude of its z-transform is presented. The novelty of our paper is in parameter estimation and blind identification of the FIR channel based on fractional lower order moments of its output data. Monte Carlo simulations clearly demonstrate the performance of the new methods     

The application of blind channel identification techniques toprestack seismic deconvolution

One objective of seismic signal processing is to identify the layered subsurface structure by sending seismic wavelets into the ground. This is a blind deconvolution process since the seismic wavelets are usually not measurable and therefore, the subsurface face layers are identified only by the reflected seismic signals. Conventional methods often approach this problem by making assumptions about the subsurface structures and/or the seismic wavelets. In this paper an alternative technique is presented. It applies blind channel identification methods to prestack seismic deconvolution. A unique feature of this proposed method is that no such assumptions are needed. In addition, it fits into the structure of current seismic data acquisition techniques, thus no extra cost is involved. Simulations on both synthetic and field seismic data demonstrate that it is a promising new method for seismic signal processing     

MIMO channel blind identification in the presence of spatiallycorrelated noise

We address the problem of the second-order blind identification of a multiple-input multiple-output (MIMO) transfer function in the presence of additive noise. The additive noise is assumed to be (temporally) white, i.e., uncorrelated in time, but we do not make any assumption on its spatial correlation. This problem is thus equivalent to the second-order blind identification of a MIMO transfer function in the noiseless case but from a partial auto-covariance function {R_n }_n≠0. Our approach consists of computing the missing central covariance coefficient R₀ from this partial auto-covariance sequence. It can be described simply within the algebraic framework of rational subspaces. We propose an identifiability result that requires very mild assumptions on the transfer function to be estimated. Practical subspace-based identification algorithms are deduced and tested via simulations     

Recursive blind identification of non-Gaussian time-varying ARmodel and application to blind equalisation of time-varying channel

A novel method for the blind identification of a non-Gaussian time-varying autoregressive model is presented. By approximating the non-Gaussian probability density function of the model driving noise sequence with a Gaussian-mixture density, a pseudo maximum-likelihood estimation algorithm is proposed for model parameter estimation. The real model identification is then converted to a recursive least squares estimation of the model time-varying parameters and an inference of the Gaussian-mixture parameters, so that the entire identification algorithm can be recursively performed. As an important application, the proposed algorithm is applied to the problem of blind equalisation of a time-varying AR communication channel online. Simulation results show that the new blind equalisation algorithm can achieve accurate channel estimation and input symbol recovery     

Energy constrained frequency-domain normalized LMS algorithm for blind channel identification

This paper deals with the blind adaptive identification of single-input multi-output (SIMO) finite impulse response acoustic channels from noise-corrupted observations. The normalized multichannel frequency-domain least-mean-squares (NMCFLMS) algorithm [1] is known to be a very effective and efficient technique for identification of such channels when noise effects can be ignored. It, however, misconverges in presence of noise [2]. In this paper, we present an analysis of noise effects on the NMCFLMS algorithm and propose a novel technique for ameliorating such misconvergence characteristics of the NMCFLMS algorithm for blind channel identification (BCI) with noise by attaching a spectral constraint in the adaptation rule. Experimental results demonstrate that the robustness of the NMCFLMS algorithm for BCI can be significantly improved using such a constraint.     

线性盲信道辨识算法中存在的问题及解决方法

传统的盲信道辨识与均衡技术大多采用高阶统计的方法，这种方法有一些弊端。后来开始研究基于二阶统计的方法，这是一个较大的突破。基于二阶统计的盲信道辨识算法大致有以下五种：线性预测算法LPA^[1][2]，外积分解算法OPDA^[3][4]，多步线性预测算法MSLP^[5],最小均方平滑算法LSS^[6]和约束最小输出能量算法CMOE^[7]。但是这些算法的仿真结果显示信道是不能被辨识的，该文将通过分析这些算法，指出导致辨识失败的原因；并在数字通信系统的背景下，给出解决方法。     

Closed-form blind channel identification and source separation inSDMA systems through correlative coding

We address the problem of blind identification of multiuser multiple-input multiple-output (MIMO) finite-impulse response (FIR) digital systems. This problem arises in spatial division multiple access (SDMA) architectures for wireless communications. We present a closed-form, i.e., noniterative, consistent estimator for the MIMO channel based only on second-order statistics. To obtain this closed form we introduce spectral/correlation asymmetry between the sources by filtering each source output with adequate correlative filters. Our algorithm uses the closed form MIMO channel estimate to cancel the intersymbol interference (ISI) due to multipath propagation and to discriminate between the sources at the wireless base station receiver. Simulation results show that, for single-user channels, this technique yields better channel estimates in terms of mean-square error (MSE) and better probability of error than a well-known alternative method. Finally, we illustrate its performance for MIMO channels in the context of the global system for mobile communications (GSM) system     

Adaptive blind channel identification algorithm based on linearprediction for SIMO FIR systems

An adaptive algorithm for blind identification of single-input multiple-output (SIMO) FIR systems is proposed. It is based on the one-step forward linear prediction (LP) technique and can be implemented by an RLS adaptation. Unlike most second-order statistics (SOS)-based approaches, the proposed solution does not require the computation of the correlation matrix or its inverse explicitly. The obtained results demonstrate that the proposed approach is able to deliver better performance compared with the typical batch algorithm. It is also observed that the proposed algorithm can tolerate the appearance of near common zeros among the subchannels     

Asymptotically optimal blind fractionally spaced channel estimationand performance analysis

When the received data are fractionally sampled, the magnitude and phase of most linear time-invariant FIR communications channels can be estimated from second-order output only statistics. We present a general cyclic correlation matching algorithm for known order FIR blind channel identification that has closed-form expressions for calculating the asymptotic variance of the channel estimates. We show that for a particular choice of weights, the weighted matching estimator yields (at least for large samples) the minimum variance channel estimator among all unbiased estimators based on second-order statistics. Furthermore, the matching approach, unlike existing methods, provides a useful estimate even when the channel is not uniquely identifiable from second-order statistics     

基于误差-参数分析的超分辨率盲辨识和复原算法

提出了一种实现规整化超分辨率复原算法的新方案,用来去除欠采样过程中的空间积分模糊和补零插值导致的边缘波纹.并将这种新方案运用到误差-参数分析法来准确地估计表征模糊函数的参数.当运动估计存在误差时,将误差-参数分析法和搜索算法相结合,降低参数辨识的计算量.仿真实验证明了提出的超分辨率算法实现方案和盲辨识方案的有效性.     

Performance analysis for subband identification

The so-called subband identification method has been introduced recently as an alternative method for identification of finite-impulse response systems with large tap sizes. It is known that this method can be more numerically efficient than the classical system identification method. However, no results are available to quantify its advantages. This paper offers a rigorous study of the performance of the subband method. More precisely, we aim to compare the performance of the subband identification method with the classical (fullband) identification method. The comparison is done in terms of the asymptotic residual error, asymptotic convergence rate, and computational cost when the identification is carried out using the prediction error method, and the optimization is done using the least-squares method. It is shown that by properly choosing the filterbanks, the number of parameters in each subband, the number of subbands, and the downsampling factor, the two identification methods can have compatible asymptotic residual errors and convergence rate. However, for applications where a high order model is required, the subband method is more numerically efficient. We study two types of subband identification schemes: one using critical sampling and another one using oversampling. The former is simpler to use and easier to understand, whereas the latter involves more design problems but offers further computational savings.     

Performance analysis of the matrix pair method for blind channelidentification

We study the estimation variance performance of the matrix pair (MP) method for estimating the impulse responses of multiple FIR channels driven by an unknown input sequence. A first-order perturbation analysis of the large-data-size performance of the MP method is presented and an explicit expression for the estimation variance is derived. Both the theoretical and simulation results are used to investigate the statistical performance of the MP method and a number of new insights are revealed