The locally optimum rank detector achieves a simpler detector structure when reference observations, in addition to regular observations, are available. Without reference observations, we have to use the sign statistics of regular observations, and using the sign statistics results in a complex detector structure. Instead, more computations are necessary to deal with additional reference observations.

This paper presents a new adaptive blind separation of sources (BSS) method for linear and non-linear mixtures. The sources are assumed to be statistically independent with non-uniform and symmetrical PDF. The algorithm is based on both simulated annealing and density estimation methods using a neural network. Considering the properties of the vectorial spaces of sources and mixtures, and using some linearization in the mixture space, the new method is derived. Finally, the main characteristics of the method are simplicity and the fast convergence experimentally validated by the separation of many kinds of signals, such as speech or biomedical data.

In this paper, a novel cumulant-based adaptive notch filtering technique for the enhancement and tracking of a single sinusoid in additive noise is presented. In this technique, the enhanced signal is obtained as the output of a narrow bandpass filter implemented using a second-order pole-zero constraint IIR adaptive notch filter, which needs only one coefficient to be updated. The filter coefficient, which leads to identifying and tracking the sinusoidal frequency, is updated using a suggested adaptive algorithm employing a recursive estimate of the kurtosis and only one-sample-lag point of a selected one-dimensional fourth-order cumulant slice of the input signal. Therefore, the proposed technique provides automatically resistance to additive Gaussian noise. It is also shown that the presented technique outperforms the correlation-based counterpart in handling additive non-Gaussian noise. Simulation results are provided to show the effectiveness of the proposed algorithm in comparison with the correlation-based lattice algorithm.

The blind separation of sources is a recent and important problem in signal processing. Since 1984, it has been studied by many authors whilst many algorithms have been proposed. In this paper, the description of the problem, its assumptions, its currently applications and some algorithms and ideas are discussed.

To improve the resolution capability of the directions-of-arrival (DOA) estimation, some subspace-based methods have recently been developed by exploiting the specific signal properties (e.g. non-Gaussian property and cyclostationarity) of communication signals. However, these methods perform poorly as the ordinary subspace-based methods in multipath propagation situations, which are often encountered in mobile communication systems because of various reflections. In this paper, we investigate the direction estimation of coherent signals by jointly utilizing the merits of higher-order statistics and cyclostationarity to enhance the performance of DOA estimation and to effectively reject interference and noise. For estimating the DOA of narrow-band coherent signals impinging on a uniform linear array, a new higher-order cyclostationarity based approach is proposed by incorporating a subarray scheme into a linear prediction technique. This method can improve the resolution capability and alleviate the difficulty of choosing the optimal lag parameter. It is shown numerically that the proposed method is superior to the conventional ones.

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.

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 paper describes a new high resolution algorithm for the two-dimensional (2-D) frequency estimation problem, which, in particular, is noise insensitive in view of the fact that in many practical applications the contaminated noise may not be white noise. For this purpose, the approach is set in the context of higher-order statistics (HOS), which has demonstrated to be an effective approach under a colored noise environment. The algorithm begins with the consideration of the fourth-order moments of the available 2-D data. Two auxiliary matrices, constituted by a novel stacking of the diagonal slice of the computed fourth-order moments, are then introduced and through which the two frequency components can be precisely determined, respectively, via matrix factorizations along with the subspace rotational invariance (SRI) technique. Simulation results are also provided to verify the proposed algorithm.

This paper proposes a new method for recovering the original signals from their linear mixtures observed by the same number of sensors. It is performed by identifying the linear transform from the sources to the sensors, only using the sensor signals. The only assumption of the source signals is basically the fact that they are statistically mutually independent. In order to perform the 'blind' identification, some time-correlational information in the observed signals are utilized. The most important feature of the method is that the full information of available time-correlation data (second-order statistics) is evaluated, as opposed to the conventional methods. To this end, an information-theoretic cost function is introduced, and the unknown linear transform is found by minimizing it. The propsed method gives a more stable solution than the conventional methods.

Electronic systems are progressively replacing mechanical devices or human operation for identifying people or objects in everyday-life applications. Especially, the contactless identification systems available today have several advantages, but they cannot handle easily several simultaneously present items. This paper describes a solution to this problem, based on blind source separation techniques. The effectiveness of this approach is experimentally demonstrated, especially by using a real-time DSP-based implementation of the proposed system.

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.

An analog circuit is devised which selects and outputs the kth largest element among n input voltages. The circuit is composed of n basic transconductance amplifiers connected mutually with an O(n) length wire, thus the complexity of the circuit is O(n). The circuit becomes particularly simple for the case of the selection of the median of inputs.

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.