This paper presents a deep neural network (DNN) based symbol detection and modulation classification detector (SDMCD) for mixed blind signals detection. Unlike conventional methods that employ symbol detection after modulation classification, the proposed SDMCD can perform symbol recovery and modulation identification simultaneously. A cumulant and moment feature vector is presented in conjunction with a low complexity sparse autoencoder architecture to complete mixed signals detection. Numerical results show that SDMCD scheme has remarkable symbol error rate performance and modulation classification accuracy for various modulation formats in AWGN and Rayleigh fading channels. Furthermore, the proposed detector has robust performance under the impact of frequency and phase offsets.

This letter proposes a novel modulation classification method for overlapped sources named LRGP involving multinomial logistic regression (MLR) and multi-gene genetic programming (MGGP). MGGP based feature engineering is conducted to transform the cumulants of the received signals into highly discriminative features and a MLR based classifier is trained to identify the combination of the modulation formats of the overlapped sources instead of signal separation. Extensive simulations demonstrate that LRGP yields superior performance compared with existing methods.

In a speech enhancement system for impact noise, it is important for any impact noise activity to be detected. However, because impact noise occurs suddenly, it is not always easy to detect. We propose a method for impact noise activity detection based on the kurtosis of an instantaneous power spectrum. The continuous duration of a generalized impact noise is shorter than that of speech, and the power of such impact noise varies dramatically. Consequently, the distribution of the instantaneous power spectrum of impact noise is different from that of speech. The proposed detection takes advantage of kurtosis, which depends on the sharpness and skirt of the distribution. Simulation results show that the proposed noise activity detection improves the performance of the speech enhancement system.

A new near-field source localization algorithm based on a uniform linear array was proposed. The proposed algorithm estimates each parameter separately but does not need pairing parameters. It can be divided into two important steps. The first step is bearing-related electric angle estimation based on the ESPRIT algorithm by constructing a special cumulant matrix. The second step is the other electric angle estimation based on the 1-D MUSIC spectrum. It offers much lower computational complexity than the traditional near-field 2-D MUSIC algorithm and has better performance than the high-order ESPRIT algorithm. Simulation results demonstrate that the performance of the proposed algorithm is close to the Cramer-Rao Bound (CRB).

In this paper, we introduce a generalized minimum mean-square error short-time spectral amplitude estimator with a new prior estimation of the speech probability density function based on moment-cumulant transformation. From the objective and subjective evaluation experiments, we show the improved noise reduction performance of the proposed method.

ICA (Independent Component Analysis) has a remarkable capability of separating mixtures of stochastic random signals. However, we often face problems of separating mixtures of deterministic signals, especially sinusoidal signals, in some applications such as radar systems and communication systems. One may ask if ICA is effective for deterministic signals. In this paper, we analyze the basic performance of ICA in separating mixtures of complex sinusoidal signals, which utilizes the fourth order cumulant as a criterion of independency of signals. We theoretically show that ICA can separate mixtures of deterministic sinusoidal signals. Then, we conduct computer simulations and radio experiments with a linear array antenna to confirm the theoretical result. We will show that ICA is successful in separating mixtures of sinusoidal signals with frequency difference less than FFT resolution and with DOA (Direction of Arrival) difference less than Rayleigh criterion.

A new method of segmentation for Synthetic Aperture Radar (SAR) images using the skewness wavelet energy has been presented. The skewness is the third order cumulant which measures the local texture along the region-based active contour. Nonlinearity in intensity inhomogeneities often occur in SAR images due to the speckle noise. In this paper we propose a region-based active contour model that is able to use the intensity information in local regions and to cope with the speckle noise and nonlinear intensity inhomogeneity of SAR images. We use a wavelet coefficients energy distribution to analyze the SAR image texture in each sub-band. A fitting energy called skewness wavelet energy is defined in terms of a contour and a functional so that, the regions and their interfaces will be modeled by level set functions. A functional relationship has been calculated on these level sets in terms of the third order cumulant, from which an energy minimization is derived. Minimizing the calculated functions derives the optimal segmentation based on the texture definitions. The results of the implemented algorithm on the test images from the Radarsat SAR images of agricultural and urban regions show a desirable performance of the proposed method.

In this paper we show some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large deviation rate function in general, which is expressed as a pair of the lower and upper IS rate functions. In particular, we are interested in establishing the general large deviation rate functions that are derivable as the Fenchel-Legendre transform of the cumulant generating function. The final goal is to show, under some mild condition, a necessary and sufficient condition for the IS rate function to be derivable as the Fenchel-Legendre transform of the cumulant generating function, i.e., to be a rate function of Gartner-Ellis type.

The present letter deals with the blind equalization problem of a single-input single-output infinite impulse response (SISO-IIR) channel with additive Gaussian noise. To solve the problem, we propose a new criterion for maximizing constrainedly a fourth-order cumulant. The algorithms derived from the criterion have such a novel property that even if Gaussian noise is added to the output of the channel, an effective zero-forcing (ZF) equalizer can be obtained with as little influence of Gaussian noise as possible. To show the validity of the proposed criterion, some simulation results are presented.

In this study, we propose a robust approach for blind source separation (BSS) by using radial basis function networks (RBFNs) and higher-order statistics (HOS). The RBFN is employed to estimate the inverse of a hypothetical complicated mixing procedure. It transforms the observed signals into high-dimensional space, in which one can simply separate the transformed signals by using a cost function. Recently, Tan et al. proposed a nonlinear BSS method, in which higher-order moments between source signals and observations are matched in the cost function. However, it has a strict restriction that it requires the higher-order statistics of sources to be known. We propose a cost function that consists of higher-order cumulants and the second-order moment of signals to remove the constraint. The proposed approach has the capacity of not only recovering the complicated mixed signals, but also reducing noise from observed signals. Simulation results demonstrate the validity of the proposed approach. Moreover, a result of application to X-ray image separation also shows its practical applicability.

In this study, a fourth-order cumulants based iterative algorithm for blind channel equalization is introduced, which is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum phase characteristic of the channel. The transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel inputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple reordering and scaling. In simulation studies, both a closed-form and a stochastic version of the proposed algorithm are tested with three-ray multi-path channels, and their performances are compared with the methods based on conventional second-order statistics and higher-order statistics (HOS) as well. Relatively good results with fast convergence speed are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

This paper considers a link of two problems; multichannel blind deconvolution and multichannel blind identification of linear time-invariant dynamic systems. To solve these problems, cumulant maximization has been proposed for blind deconvolution, while cumulant matching has been utilized for blind identification. They have been independently developed. In this paper, a cumulant maximization criterion for multichannel blind deconvolution is shown to be equivalent to a least-squares cumulant matching criterion after multichannel prewhitening of channel outputs. This equivalence provides us with a new link between a cumulant maximization criterion for blind deconvolution and a cumulant matching criterion for blind identification.

In this paper we consider blind source separation (BSS) problem of signals which are spatially uncorrelated of order four, but temporally correlated of order four (for instance speech or biomedical signals). For such type of signals we propose a new sufficient condition for separation using fourth order statistics, stating that the separation is possible, if the source signals have distinct normalized cumulant functions (depending on time delay). Using this condition we show that the BSS problem can be converted to a symmetric eigenvalue problem of a generalized cumulant matrix Z(4)(b) depending on L-dimensional parameter b, if this matrix has distinct eigenvalues. We prove that the set of parameters b which produce Z(4)(b) with distinct eigenvalues form an open subset of RL, whose complement has a measure zero. We propose a new separating algorithm which uses Jacobi's method for joint diagonalization of cumulant matrices depending on time delay. We empasize the following two features of this algorithm: 1) The optimal number of matrices for joint diago- nalization is 100-150 (established experimentally), which for large dimensional problems is much smaller than those of JADE; 2) It works well even if the signals from the above class are, additionally, white (of order two) with zero kurtosis (as shown by an example).

This study is aimed to explore a fast convergence method of blind equalization using higher order statistics (cumulants). The efforts are focused on deriving new theoretical solutions for blind equalizers rather than investigating practical algorithms. Under the common assumptions for this framework, it is found that the condition for blind equalization is directly associated with an eigenproblem, i. e. the lag coefficients of the equalizer can be obtained from the eigenvectors of a higher order statistics matrix. A method of blind phase recovery is also proposed for QAM systems. Computer simulations show that very fast convergence can be achieved based on the approach.

A novel cumulant based MUSIC like DOA estimation algorithm for multicarrier modulation has been proposed in this paper. While the conventional MUSIC algorithm is not applicable to a correlation matrix calculated from received signals transmitted over the different carriers, the proposed algorithm can estimate the DOA of the signals with multicarrier modulation. The proposed algorithm does not require the sensor array responses for the frequency range of the interest and the initial phases of the carriers. With the proposed algorithm the number of signals whose DOA are estimated can be increased and the accuracy of the DOA estimation can be improved by employing larger number of carriers.

This letter presents a new algorithm for improving the Signal to Noise Ratio (SNR) of complex sinusoidal signals contaminated by additive Gaussian noises using sum of Higher-Order Statistics (HOS). We conduct some computer simulations to show that the proposed algorithm can improve the SNR more than 7 dB compared with the conventional coherent integration when the SNR of the input signal is -10 dB.

This study is aimed to derive a new theoretical solution for blind equalizers. Undr the common assumptions for this framework, it is found that the condition for blind equalization is directly associated with an eigenproblem, i.e. the tap coefficients of the equalizer appear as an eigenvector of a higher order statistics matrix. Computer simulations show that very fast convergence can be achieved based on the approach.

A cumulant-based lattice algorithm for multichannel adaptive filtering is proposed in this paper. Proposed algorithm takes into account the advantages of higer-order statistics, that is, improvement of estimation accuracy, blindness to colored Gaussian noise and the possibility to estimate the nonminimum-phase system etc. Without invoking the Instrumental Variable () method as used in other papers [1], [2], the algorithm is derived directly from the recursive pseudo-inverse matrix. The behavior of the algorithm is illustrated by numerical examples.

This paper addresses the problem of estimating the parameters of multivariate ARMA processes by using higher-order statistics called cumulants. The main objective in this paper is to extend the idea of the q-slice algorithm in univariate ARMA processes to multivariate ARMA processes. It is shown for a multivariate ARMA process that the MA coefficient matrices can be estimated up to postmultiplication of a permutation matrix by using the third-order cumulants and of an extended permutation matrix by using the fourth-order cumulants. Simulation examples are included to demonstrate the effectiveness of the proposed method.