Multidimensional Signal Space Research Articles

Multidimensional Signal Space Non-Orthogonal Multiple Access With Imperfect SIC: A Novel SIC Reduction Technique

Multidimensional Signal Space Non-Orthogonal Multiple Access With Imperfect SIC: A Novel SIC Reduction Technique

Visual exploratory analysis of DCE-MRI data in breast cancer by dimensional data reduction: A comparative study

One trend in modern medical imaging is the growing signal dimension in new multi-modal or multivariate imaging approaches. To analyze such high dimensional data, new approaches need to be proposed and evaluated. The scope of this study is to investigate the potential of three different algorithms for dimensional data reduction for the visual exploration of biomedical signals arising from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) applied to breast cancer detection. The algorithms employed are the established Principal Component Analysis (PCA) and Self-Organizing Maps (SOM), and the recently proposed Locally Linear Embedding (LLE). The experimental dataset comprises the time-series associated with the voxels of six benign and six malignant breast tumors. In order to visually explore the dataset, the multi-dimensional signal space of all the time-series is projected into a two-dimensional space by PCA, SOM and LLE, respectively. We show how the visualization of the respective projected spaces with customized colors can allow the user to discover hidden regularities in the data, in particular with regard to the differentiation between benign and malignant lesions. The performances of the three algorithms are quantitatively compared, while discussing their advantages and drawbacks.

Multi-Dimensional Generalization in Space and Time Domains for Middleton's Study in Stochastic Evaluation of Correlative Many Em Noise Processes - Abstract

in this paper, a statistical study on correlative many electromagnetic (abbr., EM) interferences is given mainly from a theoretical viewpoint on the basis of random walk problem in multi-dimensional signal space, along to the same study line as in our previous paper. First, a joint multi-variate characteristic function of Hankel transform type matched to many kinds of EM environmental fluctuation waves is introduced especially in an extended form (in space and time domains) of D. Middleton's basic result. Then, a joint multivariate probability density function (abbr., pdf) is explicitly derived for correlative many kinds of EM random fluctuations with a power scaled variable (or an effective value) observed by many receivers of mean square operation type, especially by laying emphasis upon a derivation of explicit pdf expression for correlative two kinds of EM fluctuation waves. The effectiveness of the proposed method is experimentally confirmed through an acoustic type simulation experiment with joint space-time non-Poisson interference as one of the same wave motion type environment as EM environment and an application to the actual EM environment.

Sequence detection for binary ISI channels using signal-space partitioning

Binary symbol detection based on a sequence of finite observation signals is formulated in the multidimensional signal space. A systematic space partitioning method is proposed to divide the entire space into two decision regions using a set of hyperplanes. The resulting detector structure consists of K parallel linear classifiers followed by a K-to-1 Boolean mapper, and is well suited to high-speed implementation. Compared to direct implementation of the fixed-delay tree search (FDTS) detection rule, the proposed signal-space formulation results in a considerable saving in digital hardware. Examples taken from binary-input intersymbol interference (ISI) channels are used to demonstrate the proposed technique. Block processing strategies suitable for high-speed applications are also discussed.

A Fundamental Study On the Statistical Evaluation of Receiver Response for an Electromagnetic Wave Environment in Multi-Dimensional Signal Space- Theory and Basic Experiment

In this paper, a statistical electromagnetic (abbr., EM) interference study is constructed mainly from a theoretical viewpoint on the basis of N-dimensional random walk problem in multi-dimensional signal space. First, a characteristic function of the Hankel transform type matched to this EM environmental study is introduced especially in an extended form of D. Middleton's basic result. Then, the probability density function (abbr., pdf) is explicitly derived for the EM random fluctuation with a power scaled variable (or an effective value) measured by a receiver with a mean square operation. The proposed theory is verified by showing the agreement with one of D. Middleton's great researches as a special case of the proposed expressions. Moreover, the effectiveness of the proposed method is experimentally confirmed through an acoustic type simulation of EM environment and the application to a simplified actual EM environment with joint space-time non-Poisson interference as one of the same wave motion type environment as EM environment.

A Stochastic Evaluation Theory in Multi-Dimensional Signal Space for EM Interference Noise and Its Experimental Relationship to Acoustic Environment

A Stochastic Evaluation Theory in Multi-Dimensional Signal Space for EM Interference Noise and Its Experimental Relationship to Acoustic Environment

A systematic approach to signal space detection

A general procedure is developed to implement the fixed delay tree search (FDTS) detector in the multi-dimensional signal space. The procedure systematically finds a required set of hyperplanes that divide the entire space into different decision regions. A Boolean mapping function is also analytically determined which generates a final binary decision from several intermediate binary variables that indicate the position of the observation vector relative to given hyperplanes. The proposed technique is demonstrated on a (1+D)/sup 2/ partial response channel driven by the (1,k)-coded input.

Hybrid block-convolutional rate-1/2 coding strategy for constant envelope (CE)Q2PSK

The authors address the problem of trellis coding on multidimensional signal space for incorporation into a 4D quadrature-quadrature phase-shift keying (Q/sup 2/PSK) communication system. A low-complexity rate- 1/2 hybrid block-convolutional coding scheme is proposed, to be utilised in a constant envelope (CE)Q/sup 2/PSK system configuration. The encoder and decoder designs have been structured to facilitate simple implementation with standard components. The bit error rate performance of the proposed coding scheme is studied by means of simulation on a non-frequency selective Rician fading channel assuming coherent detection. The benefits of the use of channel state information (CSI) in conjunction with maximum-likelihood Viterbi decoding are also considered.

A multidimensional isomorphic operator and its properties-a proposal of finite-extent multidimensional cepstrum

We propose a new multidimensional homomorphic operator that replaces the conventional complex cepstrum transformation. We treat multidimensional signals of finite support since any signal we can actually observe and deal with is of finite support. We first show that for any sequence of finite support there exists a coordinate transformation that transforms the support of a given sequence into the first quadrant in the multidimensional signal space. We then propose a new multidimensional homomorphic operator /spl Psi/ which transforms a sequence of finite support into another sequence of finite support in the first quadrant. It is proved that the operator /spl Psi/ is an isomorphism between two multidimensional signal spaces of finite support where finite convolution and usual addition, respectively, are defined as binomial operations. It is also shown that unlike the conventional complex cepstrum, the proposed operator /spl Psi/ is quite simple to compute and requires no complicated procedure like phase unwrapping, while it maintains the special features of the conventional complex cepstrum transformation that are useful in homomorphic signal processing. Moreover we clarify some algebraic structure of the multidimensional signal space with the finite convolution as a binomial operation. Finally it is shown by a numerical example that the deconvolution system using the proposed operator /spl Psi/ gives a much better result than the conventional complex cepstrum method. >

Trellis coded modulation for additive impulsive noise

AbstractThis paper discusses the situation where the trellis coded modulation (TCM) is applied to the digital subscriber loop (DSL) using a balanced pair cable, and examines the effectiveness. The usual error‐correcting code cannot be applied successfully to the balanced pair since the loss increases with the increase of the transmission bandwidth. When TCM is applied, on the other hand, the transmission performance for the Gaussian noise can be improved without increasing the transmission bandwidth. The major factor deteriorating the performance in DSL, however, is the impulsive noise. From such a viewpoint, this paper examined the effectiveness of TCM for the impulsive noise.First, the probability density of the impulsive noise is derived from the measurement of the exiting DSL, and the channel capacity is calculated. It is shown that it is necessary and sufficient to double the transmitting symbols and to assign the produced redundancy to the error‐correction. This is the same as the known result for the Gaussian noise, but the coding gain by the ideal coding is 18 dB, which is larger than in the case of the Gaussian noise. The coding gain of 9 dB is obtained by the simulation using the 8‐state convolutional code, which is larger than 4 dB in the case of the Gaussian noise. The reason for this improvement is discussed from the viewpoint of the probability distribution of the noise and the signal mapping in the multidimensional signal space.

Space distortion and decomposition theory

It is shown that the mathematical methods hitherto used for solving pattern recognition problems are usually not well adapted with respect to the natural class-forming processes of patterns generated from objects of the real world. Especially the well known method using a multidimensional signal space is not suited for typical pattern recognition problems, although its value is unobjected for signal detection problems. The paper proposes to regard the class-forming process of patterns with the aid of spatial transformations, where here the three-dimensional space of the real world is considered. Accordingly, a space distortion theory for both two-dimensional and three-dimensional objects, respectively, has been developed. It leads to recognition schemes using a generalized correlation technique. The generalization consists of an adaptive spatial transformation process prior to correlation. By this way, pattern recognition is supposed to be an adaptive control process using optimization methods. The decomposition theory proposes the application of this method on separate parts of the decomposed picture.

The Effect of Certain Linear Correlation on Many Correlated Random Walk Processes in Multidimensional Signal Space

The Effect of Certain Linear Correlation on Many Correlated Random Walk Processes in Multidimensional Signal Space

Two Nonlinearly Correlated Random Walk Processes in Multidimensional Signal Space

Two Nonlinearly Correlated Random Walk Processes in Multidimensional Signal Space