Comparative Analytical Study of SCMA Detection Methods for PA Nonlinearity Mitigation

Non-orthogonal multiple access (NOMA) has emerged as a promising technology that allows for multiplexing several users over limited time-frequency resources. Among existing NOMA methods, sparse code multiple access (SCMA) is especially attractive; not only for its coding gain using suitable codebook design methodologies, but also for the guarantee of optimal detection using message passing algorithm (MPA). Despite SCMA’s benefits, the bit error rate (BER) performance of SCMA systems is known to degrade due to nonlinear power amplifiers at the transmitter. To mitigate this degradation, two types of detectors have recently emerged, namely, the Bussgang-based approaches and the reproducing kernel Hilbert space (RKHS)-based approaches. This paper presents analytical results on the error-floor of the Bussgang-based MPA, and compares it with a universally optimal RKHS-based MPA using random Fourier features (RFF). Although the Bussgang-based MPA is computationally simpler, it attains a higher BER floor compared to its RKHS-based counterpart. This error floor and the BER’s performance gap are quantified analytically and validated via computer simulations.

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Nonuniform Code Multiple Access

Wireless Communications and Mobile Computing ◽

10.1155/2018/7603797 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11

Author(s):

Cheng Yan ◽

Ningbo Zhang ◽

Guixia Kang

Keyword(s):

Message Passing ◽

Multiple Access ◽

Sparse Code ◽

Rate Performance ◽

Initial Information ◽

Codebook Design ◽

Constellation Design ◽

Message Passing Algorithm ◽

Sum Of Distances

For sparse code multiple access advanced (SCMAA), the quality of initial information on each resource node and the convergence reliability of the detected user in each decision process were unsatisfactory at the message passing algorithm (MPA) receiver. Driven by these problems, this paper proposes a nonuniform code multiple access (NCMA) scheme. In the codebook design of NCMA, different transmitted layers are generated from different complex multidimension constellations, respectively, and a novel basic complex multidimension constellation design is proposed to increase the minimum intrapartition distance. Then a novel criterion of permutation set is proposed to maximize the sum of distances between interfering dimensions of transmitted codewords multiplexed on any resource node, where the number of nonzero elements of transmitted codewords is more than 1. On the other side, an advanced MPA receiver is proposed to improve the reliability of detection on each transmitted layer of NCMA. Simulation results show that the block error rate performance of NCMA outperforms SCMAA and sparse code multiple access (SCMA) under the same spectral efficiency.

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SCMA Codebook Design Based on Decomposition of the Superposed Constellation for AWGN Channel

Electronics ◽

10.3390/electronics10172112 ◽

2021 ◽

Vol 10 (17) ◽

pp. 2112

Author(s):

Zhaoyang Hou ◽

Zheng Xiang ◽

Peng Ren ◽

Bohao Cao

Keyword(s):

Message Passing ◽

Multiple Access ◽

Euclidean Distance ◽

Additive White Gaussian Noise ◽

Factor Graph ◽

Codebook Design ◽

Awgn Channel ◽

Message Passing Algorithm ◽

Different Dimensions ◽

Better Than

In this study, we propose a method named decomposition of the superposed constellation (DCSC) to design sparse code multiple access (SCMA) codebooks for the additive white Gaussian noise (AWGN) channel. We prove that the power of the user symbols (USs) is accurately determined by the power of the superposed constellation (SC). Thus, we select quadrature amplitude modulation (QAM) constellations as the SC and decompose the SC into several groups of USs with power diversity. The minimum Euclidean distance (MED) between superposed symbols (SS-MED) in the receiver is determined by the selected QAM and MED between the multi-dimensional codewords (CW-MED) is optimized by matching the symbols on different dimensions. We propose a simplified DCSC (S-DCSC) by modifying the factor graph and avoiding the transmission of USs with low power, which greatly reduces the complexity of the message passing algorithm (MPA). The simulations show that the SS-MEDs of DCSC and S-DCSC are larger than those in previous papers and the BER performance of the proposed codebooks is better than others.

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Interpolation in wavelet spaces and the HRT-conjecture

Journal of Pseudo-Differential Operators and Applications ◽

10.1007/s11868-021-00386-y ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Eirik Berge

Keyword(s):

Compact Group ◽

Wavelet Transforms ◽

Reproducing Kernel ◽

Reproducing Kernel Hilbert Space ◽

Space Structure ◽

Locally Compact Group ◽

Locally Compact ◽

Positive Type ◽

Time Frequency ◽

Hrt Conjecture

AbstractWe investigate the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })\subset L^{2}(G)$$ W g ( H π ) ⊂ L 2 ( G ) arising from square integrable representations $$\pi :G \rightarrow \mathcal {U}(\mathcal {H}_{\pi })$$ π : G → U ( H π ) of a locally compact group G. We show that the wavelet spaces are rigid in the sense that non-trivial intersection between them imposes strong restrictions. Moreover, we use this to derive consequences for wavelet transforms related to convexity and functions of positive type. Motivated by the reproducing kernel Hilbert space structure of wavelet spaces we examine an interpolation problem. In the setting of time–frequency analysis, this problem turns out to be equivalent to the HRT-conjecture. Finally, we consider the problem of whether all the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })$$ W g ( H π ) of a locally compact group G collectively exhaust the ambient space $$L^{2}(G)$$ L 2 ( G ) . We show that the answer is affirmative for compact groups, while negative for the reduced Heisenberg group.

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Demonstration of Pattern Division Multiple Access with Message Passing Algorithm in MMW-RoF Systems

Optical Fiber Communication Conference (OFC) 2020 ◽

10.1364/ofc.2020.m2f.3 ◽

2020 ◽

Cited By ~ 1

Author(s):

Shuyi Shen ◽

You-Wei Chen ◽

Qi Zhou ◽

Gee-Kung Chang

Keyword(s):

Message Passing ◽

Multiple Access ◽

Message Passing Algorithm

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Overview of Sparse Graph for Multiple Access in Future Mobile Networks

Frequenz ◽

10.1515/freq-2016-0019 ◽

2017 ◽

Vol 71 (11-12) ◽

Author(s):

Jing Lei ◽

Baoguo Li ◽

Erbao Li ◽

Zhenghui Gong

Keyword(s):

Wireless Communications ◽

Mobile Networks ◽

Message Passing ◽

Multiple Access ◽

Low Density ◽

Sparse Graph ◽

Extrinsic Information ◽

Promising Technique ◽

Satisfactory Performance ◽

Message Passing Algorithm

AbstractMultiple access via sparse graph, such as low density signature (LDS) and sparse code multiple access (SCMA), is a promising technique for future wireless communications. This survey presents an overview of the developments in this burgeoning field, including transmitter structures, extrinsic information transform (EXIT) chart analysis and comparisons with existing multiple access techniques. Such technique enables multiple access under overloaded conditions to achieve a satisfactory performance. Message passing algorithm is utilized for multi-user detection in the receiver, and structures of the sparse graph are illustrated in detail. Outlooks and challenges of this technique are also presented.

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A Threshold-Based Max-log-MPA Low Complexity Multiuser Detection Algorithm

Sensors ◽

10.3390/s20041016 ◽

2020 ◽

Vol 20 (4) ◽

pp. 1016

Author(s):

Guanghua Zhang ◽

Zonglin Gu ◽

Qiannan Zhao ◽

Jingqiu Ren ◽

Weidang Lu

Keyword(s):

Computational Complexity ◽

Multiuser Detection ◽

Message Passing ◽

Multiple Access ◽

Low Complexity ◽

Detection Algorithm ◽

Necessary Condition ◽

Threshold Condition ◽

Message Passing Algorithm ◽

The Stability

Sparse Code Multiple Access (SCMA) technology is a new multiple access scheme based on non-orthogonal spread spectrum technology, which was proposed by Huawei in 2014. In the algorithm application of this technology, the original Message Passing Algorithm (MPA) has slow convergence speed and high algorithm complexity. The threshold-based MPA has a high Bit Error Ratio (BER) when the threshold is low. In the Maximum logarithm Message Passing Algorithm (Max-log-MPA), the approximation method is used, which will cause some messages to be lost and the detection performance to be poor. Therefore, in order to solve the above problems, a Threshold-Based Max-log-MPA (T-Max-log-MPA) low complexity multiuser detection algorithm is proposed in this paper. The Maximum logarithm (Max-log) algorithm is combined with threshold setting, and the stability of user nodes is considered as a necessary condition for decision in the algorithm. Before message updating, the user information nodes are judged whether the necessary conditions for the stability of the user node have been met, and then the threshold is determined. Only users who meet the threshold condition and pass the necessary condition of user node stability can be decoded in advance. In the whole process, the logarithm domain MPA algorithm is used to convert an exp operation and a multiplication operation into a maximum value and addition operation. The simulation results show that the proposed algorithm can effectively reduce the computational complexity while ensuring the BER, and with the increase of signal-to-noise ratio, the effect of the Computational Complexity Reduction Ratio (CCRR) is more obvious.

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A Comparative Study of Marginalized Graph Kernel and Message Passing Neural Network

10.26434/chemrxiv.14706117 ◽

2021 ◽

Author(s):

Yan Xiang ◽

Yu-Hang Tang ◽

Guang Lin ◽

Huai Sun

Keyword(s):

Neural Network ◽

Message Passing ◽

Reproducing Kernel ◽

Reproducing Kernel Hilbert Space ◽

Gaussian Process Regression ◽

Bayesian Optimization ◽

Graph Kernel ◽

Kernel Machine ◽

Molecular Features ◽

Hybrid Kernel

<p>This work presents a state-of-the-art hybrid kernel for molecular property predictions. The hybrid kernel consists of a marginalized graph kernel that operates on molecular graphs and radial basis function kernels that operate on global molecular features. Direct message passing neural network (D-MPNN) with global molecular features is used as strong baselines. After using Bayesian optimization to find the optimal hyperparameters, we benchmark the models on 11 publicly available data sets. Our results show that the prediction of the graph kernel is correlated to the prediction of D-MPNN, which indicates that the molecular representation learned from D-MPNN is very close to the reproducing kernel Hilbert space generated by the hybrid kernel. These results may provide clues for research on the interpretability of graph neural networks. In addition, ensembling the graph kernel models with D-MPNN is the best. The advantage of D-MPNN lies in computational efficiency, and the advantage of the graph kernel model lies in the inherent uncertainty qualification of Gaussian process regression. All codes for graph kernel machines used in this work can be found at <a href="https://github.com/Xiangyan93/Chem-Graph-Kernel-Machine">https://github.com/Xiangyan93/Chem-Graph-Kernel-Machine</a>.</p>

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Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation

International Journal of Neural Systems ◽

10.1142/s0129065716500118 ◽

2016 ◽

Vol 26 (03) ◽

pp. 1650011 ◽

Cited By ~ 15

Author(s):

Shasha Yuan ◽

Weidong Zhou ◽

Qi Wu ◽

Yanli Zhang

Keyword(s):

Riemannian Manifold ◽

Sparse Representation ◽

Epileptic Seizure ◽

Reproducing Kernel ◽

Reproducing Kernel Hilbert Space ◽

Seizure Detection ◽

Detection Methods ◽

Gaussian Kernel ◽

Epileptic Seizure Detection ◽

Eeg Recordings

Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.

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