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Decorrelation of multichannel signals has played a crucial preprocessing role (in prewhitening and orthogonalization) for many signal processing applications. Classical decorrelation techniques can only be applied for signal vectors. Nonetheless, many emerging big-data and sensor-network applications involve signal tensors (signal samples required to be arranged in a tensor form of arbitrary orders). Meanwhile, the existing tensor-decorrelation methods have serious limitations. First, the correlation-tensors have to be of certain particular orders. Second, the unrealistic assumption of the specific signal-tensor form, namely the canonical polyadic (CP) form, is made. Third, the correlation-tensor has to be full-rank or an extra preprocessor based on principal component analysis is required for any non-full-rank correlation tensor. To remove the aforementioned impractical limitations, we propose a novel robust approach for high-dimensional multichannel decorrelation, which can accommodate signal tensors of arbitrary orders, forms, and ranks without any need of extra preprocessor. In this work, we introduce two new tensor-decorrelation algorithms. Our first new algorithm is designed to tackle full-rank correlation-tensors and our second new algorithm is designed to tackle non-full-rank correlation-tensors. Meanwhile, we also propose a new parallel-computing paradigm to accelerate our proposed new tensor-decorrelation algorithms. To demonstrate the applicability of our proposed new scheme, we also apply our proposed new tensor-decorrelation approach to pre-whiten the tensor signals and analyze the corresponding convergence-speed and misadjustment performances of the tensor least-mean-squares (TLMS) filter. Finally, we assess the computational- and memory-complexities of our proposed new algorithms by simulations over both artificial and real data. Simulation results show that our proposed new multichannel-decorrelation algorithms outperform the existing tensor-decorrelation methods in terms of convergence speed, eigenspread, normalized mean square error (NRMSE), and estimation accuracy.

A novel dynamic human-posture recognition approach using tensor regression is proposed in this work. In our proposed approach, a new dynamic segmentation scheme based on hidden logistic regression (HLR) is first undertaken to segment multidimensional skeletal graph data. Within each segment of multidimensional data, a new feature tensor consists of high-dimensional skeletal-graph time-series (SGTS) involving multijoint 3-D coordinates and their temporal differences. Regression models can thus be trained from these collected feature tensors with respect to each type of human posture of interest. Experiments using real-world Kinect data are conducted to evaluate the effectiveness of our proposed novel tensor-based human-posture recognition scheme. In comparison with two prevalent deep learning models, namely the graph convolutional network (GCN) and the Transformer, our proposed novel tensor-based human-posture recognition approach can achieve the highest recognition accuracy of ${97}\%$ . Furthermore, we have evaluated the performance of our proposed new method using the open-source Kinect dataset, namely the UTKinect dataset, for one-shot learning. Our proposed novel tensor-based human-posture recognition approach still significantly outperforms the aforementioned prevalent deep learning models for one-shot learning.

Linear discriminant analysis (LDA) is a well-known feature-extraction technique for data analytic and pattern classification. As the dimensionality of multimedia data has increased in this big era, it is often to characterize data by tensors. Over the past two decades, researchers have thus explored to extend LDA to the general tensor space, especially in two common ways: LDA of tensors using tensor decomposition methods (by conversion of tensors to matrices) and LDA of tensors built upon the T-product. However, both of the aforementioned approaches have restrictions thereby. A critical problem about how to carry out LDA of arbitrary scatter tensors based on the Einstein product still remains unsolved by the existing methods. Therefore, we propose a novel tensor LDA (a.k.a. TLDA) approach, which can carry out the LDA of arbitrary-dimensional scatter-tensors without any need of tensor decomposition. Besides, for reducing the computation time, we also design a parallel paradigm to execute our proposed TLDA in this work. Numerical experiments conducted over real multimedia data demonstrate the efficacy of our proposed new TLDA in terms of classification accuracy. Moreover, the comparison of the classification accuracies, computational-complexities, and memory-complexities of our proposed novel TLDA scheme and other existing tensor-based LDA methods is made. By leveraging TLDA for high-dimensional feature extraction, segmentation, and user-item interaction data processing, future multimedia recommendation systems can facilitate more accurate, engaging, and satisfactory user experience over the Internet.

Composite modulation (CM) has been considered the essential component in the next generation intelligent telemetry, tracking, and command (TT&C) systems. For the cognitive TT&C scenario, the CM parameters must be blindly estimated without any a priori knowledge in practice. In this article, a blind modulation-index estimation method for the CM TT&C signals is proposed. In our proposed approach, the power-level ratio between the primary carrier and the dominant secondary carrier is first measured from the frequency spectrum of the CM signal. The relationship between such a power-level ratio and the modulation-index $K_{p}$ is formulated analytically. Then, a hybrid interpolation mechanism of Hermite and cubic-spline schemes is proposed to estimate the unknown modulation index $K_{p}$ within a prespecified range. According to our empirical study, the CM receiver incorporated with our proposed blind modulation-index estimator can greatly reduce the bit-error rate (BER). Finally, Monte Carlo simulations are carried out to evaluate the effectiveness and superiority of our proposed blind modulation-index estimation method in terms of the normalized mean square error and the BER for a cognitive TT&C transponder using the $K_{p}$ estimates generated by our proposed method.

Nowadays, wireless local-area networks (WLANs) are widely deployed in residential and commercial areas. The coverage quality is essential to users. The full coverage appears to be one of the most crucial problems to be considered during the network and access-point/router deployment (placement). We formulate the light-of-sight (LoS) coverage problem using the visibility-graph framework. In this work, for arbitrary multiply-connected or simply-connected polygonal/prismatic fields-of-interest subject to an arbitrary link-range restriction, we investigate how the full LoS coverage can be achieved by a minimum number of access-points/routers. Based on the new mathematical lemmas we derive, we design a novel graph-theoretical approach accordingly. Our proposed new scheme can be deemed the first-ever systematic approach to the best of our knowledge. Our proposed new approach is also evaluated in terms of the coverage efficiency, the number of access-points/routers, and the peak link-distance ratio for full LoS coverage in comparison with the existing solution to the art gallery problem.

Automatic composite-modulation classification (ACMC) is deemed to be an essential and important cognitive mechanism adopted for the next generation intelligent telemetry, tracking, and command (TT&C), cognitive aerospace communications, and space surveillance as it can automatically recognize the unknown composite-modulation (CM) scheme of the received signal. In this work, we introduce a novel ACMC method using the hybrid feature-vectors based on our proposed new cyclic-paw-print images extracted from the CM signals. In our proposed novel approach, according to the polyspectral analysis of the received CM signals, a received CM signal can be converted to a gray-scale image matrix, named cyclic-paw-print (CPP), which can be very robust against noise. Then, the discrete cosine transform (DCT) and discrete wavelet transform (DWT) are simultaneously applied to the obtained CPP matrix and the hybrid DCT/DWT feature-vector is further constructed thereby. Finally, the sequential minimal optimized support vector machine (SMO-SVM) is adopted as the classifier using such feature vectors. Our proposed new ACMC technique requires a lower computational complexity and leads to a higher recognition-accuracy than other existing ACMC methods according to Monte Carlo simulations and experiments using real CM signal data.