Toshihiro Furukawa

Fast communication: Iterative partial matrix shrinkage algorithm for matrix rank minimization

This paper proposes a new matrix shrinkage algorithm for matrix rank minimization problems. The proposed algorithm provides a low rank solution by estimating a matrix rank and shrinking non-dominant singular values iteratively. We study the convergence properties of the algorithm, which indicate that the algorithm gives approximate low-rank solutions. Numerical results show that the proposed algorithm works efficiently for hard problems with low computing time.

The orthogonal projection algorithm for block adaptive signal processing

The authors propose a block adaptive algorithm for estimating the impulse response of discrete-time systems and discuss some of its properties. This algorithm, in which the performance measure is the block mean square error (BMSE), consists of block processing and orthogonal projection arithmetic and updates the adaptive filters coefficients once for each block of data. That is, the algorithm is based on orthogonal projection to the subspace spanned by input vectors corresponding to the block index. Some fundamental theorems are derived with respect to this algorithm, and they are substantiated by computer simulations.<<ETX>>

A consideration of blind source separation using wavelet transform

We propose a new method of blind source separation for convolutive mixtures. We use a wavelet transform which can get information from the two sides of time and frequency when we change the observed signals into the time-frequency domain. Our idea is to use a new estimation equation of the separating matrix for time delay. We aim to improve the separation performance. We show the result of desktop simulation of artificially controlled data.

A recurrent RBF network for non-linear channel

In this paper, we will propose a recurrent RBF equalizer for non-linear channel with time-varying characteristics. In the conventional equalization method for that, its channel characteristic is estimated with FIR model, and the noise-free received signals are estimated with this estimate. Then the recurrent RBF equalizers parameters are updated with this result. However, this method is not available lo nonlinear channel. In this paper, we firstly introduce MSB of the difference between the received signal and the estimate of noise-free received signal as the cost function to estimate all noise-free received signals, because this cost function is minimized when the noise-free received signal is equal to this estimate. Then, we estimate all estimates of noise-free received signal by minimizing this cost function using LMS algorithm, and the recurrent RBF equalizer is updated with these values.

A consideration on the computational requirements of blind equalization using the orthogonal projection

The equalization using the traditional blind estimation is based on the channel outputs and knowledge of the probabilistic property of input signal. But it is difficult for conventional implementation with on-line processing because the traditional algorithms need high-order momentum. We present a new method using the orthogonal projection, in order to enable the on-line processing of blind equalization. First, we estimate the characteristics of the channel using both the skewness and the kurtosis of the output of the channel. Secondly, we will design an equalizer using the orthogonal projection onto the received signal space. The proposed method is based on designing an equalizer parameter so that the matrix P/sub N,N/=W/sub N,N/H/sub N,N/ may be the orthogonal projection matrix onto the received signal space, where W/sub N,N/ and H/sub N,N/ demote the impulse response matrix of an equalizer to be designed and that of the channel respectively. The impulse response matrix of an equalizer is basically expressed with Moore-Penrose inverse matrix. The proposed blind equalization algorithm can be implemented with on-line processing, it is expected that the convergence characteristics of the proposed equaliser are better than that of the traditional device.

A robust adaptive algorithm, for block signal processing

An analysis is made of the behavior of a block orthogonal projection algorithm (BOPA) applied to a practical system in which the input signal is smooth-colored and additive noise is observed at the output of an unknown filter. Using this result, a block adaptive algorithm is presented. This algorithm is based on singular-value decomposition and obtained by truncating several smaller singular values.<<ETX>>

A consideration on the blind estimation of single-input double-output system using orthogonal direct sum decomposition of received signal space

Subspace methods with second-order statistics based on principal component analysis (PCA) basically need to calculate the eigenvalues and the eigenvectors of the autocorrelation matrix of the received signal. However, the calculation of the eigenvalues and the eigenvectors of the matrix requires much computational complexity. We propose a new algorithm based on PCA without solving the eigenvalues and the eigenvectors of the matrix. Moreover, we perform the proposed method under the condition that noise-variance is known, but we confirm that the proposed method is effective to a certain degree when noise-variance is unknown. We show the effectiveness of the proposed method by numerical examples.

Blind identification of second-order statistics using periodic Toeplitz system

Blind identification (BI) is a method to estimate a system of a channel with a priori knowledge of the transmitted signals and the received signals. This paper presents the method to estimate the impulse response of a channel using second-order statistics (SOS) of the cyclostationary (CS) received signals. In the paper, we consider the case in which the received signals are oversampled at the rate 1/mT (m=2,3, /spl middot//spl middot//spl middot/, n) when the received signals are sampled at the baud rate. We estimate the impulse response of a channel using the method in the double-sampling. Next, we estimate the impulse response of a channel using a result that extended the method in the sampling rate 1/mT(m=3, /spl middot//spl middot//spl middot/, n). Here, we need to calculate an inverse matrix of the matrix constructed using both the auto-correlation and the cross-correlation function in estimating the impulse response of a channel. In this paper, we take notice of the cyclic property of the matrix and apply periodic Toeplitz system (PTS) to get the inverse of the matrix.

A new solution method for linear equation using the gradient method

The authors present a new block adaptive algorithm. This algorithm is based on the gradient method, orthogonal projection arithmetic onto one-dimension subspace and the Gram-Schmidt orthogonalization procedure. The adjustment vectors are generated as the linear combination of some orthogonal bases derived from the input vectors in the adaptive filter. Therefore, when a complete orthogonal vector set is generated, the proposed algorithm can estimate an optimum coefficient vector within a block. The characteristics of the proposed algorithm are described. Computer simulation results show that the proposed algorithm has a stable performance and fast convergence speed.<<ETX>>

A proposal of a new blind equalizer using output signals of decision device

Some of authors proposed the blind equalization algorithm for communication systems. In the algorithm, we realize higher reliability of the recovered signals and faster convergence rate of the algorithm, because the parameter included in Sato cost function is adjusted by using both outputs of the equalizer and the decision device. However, we cannot apply this method to communication systems except binary code systems. Then, in this paper, we extend the previously proposed method to the method applied for multilevel code systems. And we confirm the performance evaluation of the extended method by the computer simulation.