MIMO Instantaneous Blind Identification Based on Second-Order Temporal Structure

This paper presents a new MIMO instantaneous blind identification algorithm based on second-order temporal property and steepest-descent method. Second-order temporal structure is reformulated in a particular way, such that each column of the unknown mixing matrix satisfies a system of nonlinear multivariate homogeneous polynomial equations. The nonlinear system is solved by an improved steepest-descent method. We convert the nonlinear system into an optimal problem by constructing an optimal objective function which includes a “valley-filled” item to obtain a valid solution. Our algorithm allows estimating the mixing matrix for scenarios with 4 sources and 3 sensors, etc. Finally, simulations show its effectiveness with more accurate solutions than the algorithm with homotopy method.

Greater robustness of second order statistics than higher order statistics algorithms to distortions of the mixing matrix in blind source separation of human EEG: Implications for single-subject and group analyses

We prove that rational data of bounded input length are uniformly distributed (in the classical sense of H. Weyl, in [42]) with respect to the probability distribution of condition numbers of numerical analysis. We deal both with condition numbers of linear algebra and with condition numbers for systems of multivariate polynomial equations. For instance, we prove that for a randomly chosen n\times n rational matrix M of bit length O(n 4 log n) + log w , the condition number k(M) satisfies k(M) ≤ w n 5/2 with probability at least 1-2w -1 . Similar estimates are established for the condition number μ_ norm of M. Shub and S. Smale when applied to systems of multivariate homogeneous polynomial equations of bounded input length. Finally, we apply these techniques to estimate the probability distribution of the precision (number of bits of the denominator) required to write approximate zeros of systems of multivariate polynomial equations of bounded input length.

Blind single-channel source separation is a long-standing machine learning and signal processing problem. Traditional blind source separation (BSS) algorithms were proposed to solve this task utilizing multiple signal constraints. Generative adversarial network (GAN) are free from statistical constraints and samples, but the role of adversarial training in the task of BSS has not been fully demonstrated. Therefore, a new separation network model that enables to learn the known separated signal distribution from the stepwise fine estimation of the unknown mixture distribution was presented in this paper, and a self-attention mechanism was introduced to solve the problem of the blurring details of the generated image by the generator which preserves image details in the process of image separation. Compared with the existing single-channel blind source separation algorithm based on generative adversarial network-neural egg separation (NES), the detailed information of this new separation algorithm is more prominent, and the source signal in the mixed image has been separated more effectively, and has better separation performance than the classic blind source separation algorithms.

Blind separation of non-stationary sources using continuous density hidden Markov models

This paper studies the blind identification problem for multiple-input multiple-output (MIMO) FIR channels, in which the source signals are modulated by high order periodic precoders. A set of new design criteria of the periodic precoders is proposed from the channel blind identification viewpoint for multiuser channels. It is shown that, due to the fact that high order periodic precoders are used in the modelling problem, certain simple orthogonality among user’s signals can be introduced by a set of proper designed periodic precoders. This results in a simple blind identification algorithm and the impulse response of every subchannel can also be determined uniquely up to a unitary scalar based on the received signals’ second order statistics (SOS) and a priori information of the periodic precoders. Simulation results illustrate that the developed blind identification algorithm is efficient.

Various methods are proposed to estimate the DOA (direction of arrival) of source signal. MUSIC method uses the peak point of MUSIC spectrum to estimate DOA. The method that uses the image of video camera to estimate DOA is also proposed. Mixing matrix can be calculated by arranging the frequency transfer function calculated from DOA and separation matrix of source signal is equal to the inverse of mixing matrix. However, if the frequency range of source signal is wide, calculation accuracy of the separation matrix is worse since mixing matrix becomes adverse condition in low frequency. ILRMA can estimate wideband source signals precisely by updating signal power and separation matrix alternatively. ILRMA is characterized by learning the signal power in time-frequency domain using low rank approximation. However, if source signals are high rank, the learning error of signal power occurs in using ILRMA. To resolve these problems, this paper proposes a new method, which can improve separation accuracy by using the prior information of DOA. In this method, regularization term calculated from DOA is added to NMF's objective function. By adding this regularization term, signal power can be calculated correctly even if source signals are high rank. In order to verify the estimation accuracy of source signals in using proposed method, numerical experiment was conducted and the estimation accuracy in using proposed method was compared with that in using ILRMA under the condition that DOA was already-known. In this experiment, three source signals and six noises were mixed and three sensors received the mixed signals. The estimation accuracy of source signals by proposed method was better than ILRMA. This experimental result proves that proposed method can improve the estimation accuracy of source signals by using DOA even if source signals are high rank and exist in wideband frequency range.

In this paper, we propose a novel algorithm for underdetermined blind identification problem in blind source separation. The proposed algorithm is based on the charrelation matrix of observed signals. The charrelation matrix not only can be considered as a generalized second-order covariance matrix, but also incorporates higher-order information. It is significant for blind separation problem based on statistic characteristics to extract statistical information. The problem of underdetermined blind identification is converted as a tensor decomposition model. The mixing matrix can be estimated from the rank-1 terms of the tensor decomposition. Theoretical analysis and simulation results illustrate the proposed algorithm performs competitive estimation performance compared to the underdetermined blind identification algorithm based on second-order covariance and fourth-order cumulant.

Blind source separation has found applications in various areas including biomedical signal processing and genomic signal processing. Often, blind source separation is solved via independent component analysis (ICA) by assuming and utilizing mutual independence among source signals. However, in bio-signal and genomic signal processing, the assumption of independence is often untrue, and the performance of the ICA approach is not as good. Much effort has been devoted to searching alternative approaches to blind source separation without the independence assumption. One idea known as network component analysis (NCA) is developed to identify the underlying regulatory signals of transcription factors in the gene regulatory network. In this paper we show that NCA is a general method for blind source separation using a priori information on the mixing matrix. An alternative proof of identifiability using NCA is proposed and a novel method to solve the problem is developed. Validation is made through computer simulations.

A frequently encountered problem in signal processing is harmonic retrieval in additive colored Gaussian or non-Gaussian noise, especially when the frequencies of the harmonic signals are very close in space. The purpose of this paper is to develop an efficient Blind Source Separation (BSS) algorithm from linear mixtures of source signals, which enables to separate harmonic source signals using only one observed channel signal even if the frequencies of the harmonic signals are closely spaced. First, we establish the BSS based harmonic retrieval model in additive noise by using the only one observed channel, and analyze the fundamental principle by utilizing BSS method to retrieve harmonics. Then, we propose a BSS-based approach to the harmonic retrieval by resorting the concept of W-disjoint orthogonality in the over-complete BSS situation, and as a result, we get the separation algorithm using only one channel mixed signals. Simulation results show that the proposed separation algorithm-BSS-HR is able to separate the harmonic source signals.

To address the significant performance degradation of conventional underdetermined blind source separation algorithms for frequency-hopping (FH) signals under time-frequency (TF) overlapping conditions, this brief presents a novel three-stage scheme based on the TF distribution of FH signals. In the first stage, key parameters of the FH signal are estimated using a TF binary graph. In the second step, the initial mixing matrix is estimated for non-overlapping and overlapping carrier frequencies employing density peaks clustering and tensor decomposition methods, respectively. In the third step, the final mixing matrix, directions of arrival (DOA), and source signals are estimated using the expectation-maximization algorithm within the nonnegative matrix factorization model. Finally, different segments of the FH signals are spliced together based on the DOAs of different source signals. Comprehensive experimental results demonstrate the superior performance of the proposed algorithm compared to state-of-the-art algorithms. Even at a signal-to-noise ratio of 5 dB, the correlation coefficient of the estimated source signals can still reach 0.91.

There is a large family of contrast (or cost) functions in blind source separation that can yield learning algorithms for extracting single source signals from linear mixtures. One of these families is based on higher order statistics (HOSs), which assumes the statistical independence of source signals and their non-Gaussianity (all except one) in order to successfully extract them one by one. In cases in which source signals exhibit unit variance and the mixing matrix is orthonormal, many HOS contrast functions are equivalent (e.g., kurtosis, fourth cumulant, and fourth moment). However, these contrast functions are estimated in practice from a finite data set, which introduces stochastic errors, so their equivalence has remained uncertain. Our letter introduces error bounds for several sample-based HOS contrast functions, which demonstrate their dependence upon different source signal statistics and, thus, more importantly, provide a foundation for comparing them in terms of accuracy.

The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NP-hard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaustive search for small fields, and a Gröbner base algorithm for large fields. Gröbner base algorithms have large exponential complexity and cannot solve in practice systems with n ≥ 15. Kipnis and Shamir [9] have recently introduced a new algorithm called “relinearization”. The exact complexity of this algorithm is not known, but for sufficiently overdefined systems it was expected to run in polynomial time.In this paper we analyze the theoretical and practical aspects of relinearization. We ran a large number of experiments for various values of n and m, and analysed which systems of equations were actually solvable. We show that many of the equations generated by relinearization are linearly dependent, and thus relinearization is less efficient that one could expect. We then develop an improved algorithm called XL which is both simpler and more powerful than relinearization. For all 0 < ε ≤ 1/2, and m ≥ εn 2, XL and relinearization are expected to run in polynomial time of approximately \( n^{\mathcal{O}(1/\sqrt \varepsilon )} \). Moreover, we provide strong evidence that relinearization and XL can solve randomly generated systems of polynomial equations in subexponential time when m exceeds n by a number that increases slowly with n.KeywordsQuadratic EquationExhaustive SearchAsymptotic ComplexityExact ComplexityMultivariate EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A new blind channel identification and equalization method is proposed that exploits the cyclostationarity of oversampled communication signals to achieve identification and equalization of possibly nonminimum phase (multipath) channels without using training signals. Unlike most adaptive blind equalization methods for which the convergence properties are often problematic, the channel estimation algorithm proposed here is asymptotically ex-set. Moreover, since it is based on second-order statistics, the new approach may achieve equalization with fewer symbols than most techniques based only on higher-order statistics. Simulations have demonstrated promising performance of the proposed algorithm for the blind equalization of a three-ray multipath channel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The solution of a system of nonlinear algebraic or transcendental equations is probably one of the most difficult problems in numerical analysis. In general, it is almost impossible to find the solution, unless an approximate value is already known. Linear equations occur more frequently in numerical calculations, simply because it is difficult and sometimes impossible to solve the corresponding nonlinear problem. Most of the equations governing the physical world are nonlinear, but very often for simplicity and tractability linear models are considered. Solution of boundary value problems for differential equations also lead to a nonlinear equation or a system of nonlinear equations. Solution of a system of nonlinear equations also arises in numerical analysis, while deriving certain formulae. As we have seen in Chapter 6, the Gaussian quadrature formulae can be obtained by solving a system of nonlinear equations.