Symbol Vector Research Articles

Efficient symbol level precoding design for full-duplex integrated sensing and communication systems

Full-duplex (FD) integrated sensing and communication (ISAC) system attracts much attention because adopting the FD mode can enhance the transmission efficiency and reduce the transmission time of the ISAC system. However, the inevitable self-interference (SI) in FD mode would result in severe performance degradation. This paper considers the FD ISAC system and investigates a symbol-level precoding (SLP) design, which minimizes the Cramér-Rao Bound of target angle estimation while considering the constant-envelope power restraint, SI suppression and the quality of service requirement. Due to the non-convex fractional problem and the unit-modulus constraint, the optimization problem is reformulated by implementing the Schur complement, where the optimal waveform is obtained via the semidefinite programming algorithm. The SLP design that optimizes each symbol vector for all users may suffer high computational complexity of matrix multiplication with high numbers of users. A grouped SLP strategy in which the communication users are divided into several groups on the basis of channel correlation is proposed to reduce the complexity. The proposed grouped SLP design only suppresses group-to-group interference and converts the intra-group interference into a constructive interference, which can reduce the dimension of each precoded signal significantly, resulting in a low computational complexity. Simulation results illustrate that the proposed SLP design can effectively mitigate SI, which can improve the accuracy of target detection. Moreover, the proposed grouped-SLP design can further reduce computational complexity without dramatic performance degradation.

A Novel Symbol Detection Strategy based on Discrete Elephant Herding Optimization Algorithm for MIMO-FBMC/OQAM System

The rapidly growing technological enhancements in wireless communication have pushed the researchers to develop various transmission schemes in recent decades. Multiple-input multiple-output - filter bank multicarrier/offset quadrate amplitude modulation (MIMO-FBMC/OQAM) is one of these schemes with exclusive features. However, unless an efficient symbol detector is employed, we cannot fully benefit from the superior features of MIMO-FBMC/OQAM system as the symbol vectors cannot be detected accurately at the receiver side. An ideal symbol detector is expected to have the capability of recovering the symbol vectors in the most accurate way without causing too much enhancement in the computational complexity. To meet this expectation, we have modified the conventional maximum likelihood (ML) strategy. Instead of using an exhaustive search procedure, which guarantees the highest detection performance but causes an excessive computational load in the ML scheme, an efficient metaheuristic algorithm called discrete elephant herding optimization (DEHO) was employed for optimizing the symbol vectors. With the integration of DEHO to the conventional ML in the aforementioned way, we have not only obtained a considerable reduction in the complexity of ML, but also reached the near-optimal symbol detection performance by outperforming the other symbol detectors considered in this paper.

Vector Symbolic Finite State Machines in Attractor Neural Networks.

Hopfield attractor networks are robust distributed models of human memory, but they lack a general mechanism for effecting state-dependent attractor transitions in response to input. We propose construction rules such that an attractor network may implement an arbitrary finite state machine (FSM), where states and stimuli are represented by high-dimensional random vectors and all state transitions are enacted by the attractor network's dynamics. Numerical simulations show the capacity of the model, in terms of the maximum size of implementable FSM, to be linear in the size of the attractor network for dense bipolar state vectors and approximately quadratic for sparse binary state vectors. We show that the model is robust to imprecise and noisy weights, and so a prime candidate for implementation with high-density but unreliable devices. By endowing attractor networks with the ability to emulate arbitrary FSMs, we propose a plausible path by which FSMs could exist as a distributed computational primitive in biological neural networks.

Symbol detection based on a novel discrete harmony search algorithm in MIMO-FBMC/OQAM system

Due to its high spectral efficiency and various other advantages, filter bank multicarrier/offset quadrate amplitude modulation (FBMC/OQAM) has long been considered as a candidate waveform for the fifth generation (5G) and beyond telecommunication technologies. On the other hand, it is possible to both increase the data rate and alleviate the channel fading effects by using the multiple-input multiple-output (MIMO) antenna structure in the FBMC/OQAM transceiver. However, since the symbol detection is an indispensable task to be fulfilled in wireless communication, it is crucial to employ an efficient symbol detector at the MIMO-FBMC/OQAM receiver. Maximum likelihood (ML) detector, which always finds the optimal symbols by trying all of the possible symbol combinations likely to be transmitted, is known for its extremely high computational complexity making it impractical to be used in any system. On the other hand, it is possible to both considerably reduce the ML complexity and achieve the near-ML performance by optimizing the symbol vectors instead of implementing an exhaustive search. Since searching for the optimal symbol combination in discrete space is a combinatorial optimization problem, we developed a novel discrete harmony search (disHS) algorithm to perform this operation. According to the simulation results, the newly developed disHS algorithm not only achieves near-ML performance with lower computational complexity, but also clearly leaves behind the other symbol detectors considered in this paper.

Conjunctive block coding for hyperdimensional graph representation

Knowledge Graphs (KGs) have become a pivotal knowledge representation tool in machine learning, not only providing access to existing knowledge but also enabling the discovery of new knowledge through advanced applications. Among the scalable reasoning methods used for such applications, distributed graph embedding approaches, particularly GNNs, have become popular for large-scale graph-related tasks. However, many of these methods have limitations in their interpretability and fail to take into account structural similarity in their representation. Hyperdimensional Computing (HDC), also known as Vector Symbolic Architecture (VSA), addresses this issue by using well-defined cognitive operations on distributed representations of symbolic concepts. This work proposes and evaluates a new vector symbolic graph representation, CLOG, that preserves approximate structural similarity beyond edge correspondence and fundamentally differs from previous methods. The model's effectiveness in graph representation is evaluated through theoretical analysis, graph reconstruction experiments, and link prediction task, highlighting its efficiency and accuracy. This approach significantly advances the field by enhancing the capabilities of HDC in graph representation, representing a notable improvement over existing methods.

Testing and Enhancing Adversarial Robustness of Hyperdimensional Computing

Brain-inspired hyperdimensional computing (HDC), also known as Vector Symbolic Architecture (VSA), is an emerging “non-von Neumann” computing scheme that imitates human brain functions to process information or perform learning tasks using abstract and high-dimensional patterns. Compared with deep neural networks (DNNs), HDC shows advantages such as compact model size, energy efficiency, and few-shot learning. Despite of those advantages, one under-investigated area of HDC is the adversarial robustness; existing works have shown that HDC is vulnerable to adversarial attacks where attackers can add minor perturbations onto the original inputs to “fool” HDC models, producing wrong predictions. In this paper, we systematically study the adversarial robustness of HDC by developing a systematic approach to test and enhance the robustness of HDC against adversarial attacks with two main components: (1), which is a highly-automated testing tool that can generate high-quality adversarial data for a given HDC model; and (2), which utilizes the adversarial data generated by to enhance the adversarial robustness of HDC models. The core idea of is built on top of fuzz testing method. We customize the fuzzing approach by proposing a similarity-based coverage metric to guide to continuously mutate original inputs to generate new inputs that can trigger incorrect behaviors of HDC model. Thanks to the use of differential testing, does not require knowing the labels of the samples beforehand. For enhancing the adversarial robustness, we design, implement, and evaluate to defend HDC models against adversarial data. The core idea of is an adversarial detector which can be trained by -generated adversarial samples. During inference, once an adversarial sample is detected, will override the prediction result with an “invalid” signal. We evaluate the proposed methods on 4 datasets and 5 adversarial attack scenarios with 6 adversarial generation strategies and 2 defense mechanisms, and compare the performance correspondingly. is able to differentiate between benign and adversarial inputs with over 90% accuracy, which is up to 55% higher than adversarial training-based baselines. To the best of our knowledge, this paper presents the first comprehensive effort in systematically testing and enhancing the robustness against adversarial data of this emerging brain-inspired computational model.

Towards Artificial General Intelligence - A Survey of Hyperdimensional Computing and Vector Symbolic Architectures with Quantum Computing for Multivariate Predictions

To achieve true artificial intelligence would be to mimic the human brain. Some have espoused that current systems that we call AI today are nothing more than if-else statements. There are other arguments that state that indeed, the act of decision making itself is a bunch of nested if-else statements. However, we note that the human brain and through processes that are far more complicated than that has levels of cognition that far outweigh those of any machines that have been made today. While computing systems perform better at certain tasks than human beings do, they remain inherently specific. Human minds are generally creative and knowledge making entities. In this paper, we explore the current progress made towards achieving Artificial General Intelligence and look at it from the angle of Hyperdimensional Computing and Vector Symbolic Architectures both running with the power of quantum computing. We explain how the achievement of AGI will lead to a much more sustainable form of industrial development as has been touted through advancements towards the Fourth Industrial Revolution.

Low Complexity Detection of Spatial Modulation Aided OTFS in Doubly-Selective Channels

A spatial modulation-aided orthogonal time frequency space (SM-OTFS) scheme is proposed for high-Doppler scenarios, which relies on a low-complexity distance-based detection algorithm. We first derive the delay-Doppler (DD) domain input-output relationship of our SM-OTFS system by exploiting an SM mapper, followed by characterizing the doubly-selective channels considered. Then we propose a distance-based ordering subspace check detector (DOSCD) exploiting the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information of the transmit symbol vector. Moreover, we derive the discrete-input continuous-output memoryless channel (DCMC) capacity of the system. Finally, our simulation results demonstrate that the proposed SM-OTFS system outperforms the conventional single-input-multiple-output (SIMO)-OTFS system, and that the DOSCD conceived is capable of striking an attractive bit error ratio (BER) vs. complexity trade-off.

Single-RF MIMO-OFDM Using ESPAR

A novel beamspace multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) transmission system using a single-radio-frequency (RF) electronically steerable parasitic array radiator (ESPAR) is described. It makes use of recent results for decomposing the patterns of any arbitrary ESPAR onto an orthogonal basis set using the Theory of Characteristic Modes (TCM). Leveraging this decomposition, OFDM symbols can be mapped into the beamspace domain so that the ESPAR can be used to transmit multiple streams of OFDM symbols using a single RF chain. In the proposed approach, we use the Linde-Buzo-Gray (LBG) algorithm to quantize the OFDM symbol vectors and form a codebook. A binary search tree is then utilized to efficiently find the reactive loads of ESPAR to excite the radiation patterns corresponding to the quantized symbols. It is shown by simulation that quantized codewords and the corresponding radiation patterns can be excited using ESPAR. In addition, the simulated bit error rate (BER) results of the proposed approach are shown to be close to that of conventional MIMO-OFDM systems, demonstrating the effectiveness of implementing a single-RF MIMO-OFDM transmitter.

A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges

This is Part II of the two-part comprehensive survey devoted to a computing framework most commonly known under the names Hyperdimensional Computing and Vector Symbolic Architectures (HDC/VSA). Both names refer to a family of computational models that use high-dimensional distributed representations and rely on the algebraic properties of their key operations to incorporate the advantages of structured symbolic representations and vector distributed representations. Holographic Reduced Representations [ 321 , 326 ] is an influential HDC/VSA model that is well known in the machine learning domain and often used to refer to the whole family. However, for the sake of consistency, we use HDC/VSA to refer to the field. Part I of this survey [ 222 ] covered foundational aspects of the field, such as the historical context leading to the development of HDC/VSA, key elements of any HDC/VSA model, known HDC/VSA models, and the transformation of input data of various types into high-dimensional vectors suitable for HDC/VSA. This second part surveys existing applications, the role of HDC/VSA in cognitive computing and architectures, as well as directions for future work. Most of the applications lie within the Machine Learning/Artificial Intelligence domain; however, we also cover other applications to provide a complete picture. The survey is written to be useful for both newcomers and practitioners.

Signal Vector Design for Quadrature Index Modulation

In this paper, we propose a new technique of quadrature index modulation with signal vector design (QIM-SSD), which can directly transmit a three-dimensional (3D) constellation symbol and expand an antenna index (AI) bit. The basic principle of QIM-SSD is as follows: two components of a mapped 3D signal symbol are first modulated on the upper and lower parts of transmit antennas (TAs) by two specific AI vectors with two blocks of AI bits, respectively, resulting in a space vector symbol. The remaining one component is modulated on one TA activated by the specific AI vector with one block of AI bits, then forming another space vector symbol. Furthermore, based on the resulted two space vector symbols, an additional bit is used to determine the real and imaginary parts of a complex transmit vector. The research of this paper is summarized as follows: firstly, the system model of QIM-SSD is introduced in detail. Then, the minimum Euclidean distance and the average bit error probability (BEP) are analyzed. With assumption of perfect channel estimation and maximum likelihood (ML) detection, simulation results demonstrate that the average BEP performance of QIM-SSD is better than that of the conventional QIM with three dimensional constellation and QSM at the same spectral efficiency by MATLAB simulator.

Vector Symbolic Architectures as a Computing Framework for Emerging Hardware

This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for implementation in stochastic, emerging hardware, and it naturally expresses the types of cognitive operations required for artificial intelligence (AI). We demonstrate in this article that the field-like algebraic structure of VSA offers simple but powerful operations on high-dimensional vectors that can support all data structures and manipulations relevant to modern computing. In addition, we illustrate the distinguishing feature of VSA, “computing in superposition,” which sets it apart from conventional computing. It also opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. We sketch ways of demonstrating that VSA are computationally universal. We see them acting as a framework for computing with distributed representations that can play a role of an abstraction layer for emerging computing hardware. This article serves as a reference for computer architects by illustrating the philosophy behind VSA, techniques of distributed computing with them, and their relevance to emerging computing hardware, such as neuromorphic computing.

Sensing matrix design for wideband channel estimation in millimeter‐wave hybrid multiple‐input multiple‐output system

AbstractHybrid analog/digital multiple‐input multiple‐output (MIMO) system is proposed to support low complexity multi‐stream communication in millimeter‐wave (mmWave) frequencies. The main idea of channel estimation methods for mmWave hybrid MIMO systems is based on leveraging the sparsity nature of the channel in the angle and delay domain. Sparse signal recovery algorithms have been used to reconstruct the channel coefficients. Due to the lack of information about the angle of arrival and angle of departure before channel estimation, random values are common choices for precoders and combiners. Moreover, the training pilot symbols are considered to be random variables. In this article, we propose sequential time domain sensing matrix design and sequential frequency domain sensing matrix design algorithms to design these variables in order to enhance sparse signal recovery performance and consequently the channel estimation accuracy. Our methods are based on reducing the correlation between the sensing matrix columns, which is defined in the sparse formulation of the channel estimation problem. We design the training radio frequency precoders/combiners phase angle values and pilot symbol vectors with the aid of a sequential procedure that has a reasonable complexity. Simulation results show that utilizing the designed values instead of random variables increased the performance of the channel estimation, especially when we deal with a higher number of variables.

Capacity and outage performance of multiple AF relays based cooperative OFDM-QIM system

In this paper, we propose a multiple amplify-and-forward (AF) relays based cooperative orthogonal frequency division multiplexing (OFDM) with quadrature index modulation (C-OFDM-QIM) system to enhance the spectral efficiency and the transmission reliability, where two independent subcarrier subsets are activated to convey the real and imaginary symbol vectors, respectively, and the per-subcarrier relay selection (RS) scheme is adopted to select the relay with the maximum end-to-end signal-to-noise ratio (SNR) for each active subcarrier. Both fixed-gain AF and variable-gain AF protocols are investigated at the selected relays. Based on the order statistics and the max-flow min-cut theory, the closed-form average outage probability (AOP) and the average capacity are derived, respectively. Numerical results demonstrate that the theoretical AOP is correct and accurate and the proposed C-OFDM-QIM system outperforms the traditional cooperative OFDM with index modulation (C-OFDM-IM) system in the spectral efficiency, the outage performance, and the average capacity.

Performance Bound for MIMO Systems Using One-Bit ADCs Over Rayleigh Fading Channels

This study explores the performance of multiple-input multiple-output (MIMO) systems with one-bit analog-to-digital converters (ADCs) over Rayleigh fading channels. We particularly aim to characterize the pairwise error probability (PEP) achieved by maximum likelihood detection (MLD), which provides the optimal detection performance of the considered systems. First, the upper bound of the PEP is derived by leveraging Jensen’s inequality and the Chernoff bound. The asymptotic bounds of the PEP are then characterized to clarify the impact of the one-bit ADCs on the diversity order of the MIMO systems. Notably, the diversity order of the MIMO systems with one-bit ADCs is the same as the number of receive antennas only when transmitting two symbol vectors with the opposite sign. Except for this special case, the asymptotic bound of the PEP is saturated at a high signal-to-noise ratio due to the use of the one-bit ADCs. Using simulations, we verify that the analytical results coincide with the asymptotic behavior of the PEP of the MLD for MIMO systems with one-bit ADCs over Rayleigh fading channels.

Deep Unfolded Sparse Refinement Network Based Detection in Uplink Massive MIMO

Massive multiple-input multiple-output (mMIMO) is a promising technique to realize the ever-increasing demand for high-speed data, quality of service (QoS), and energy efficiency for 5G and beyond wireless systems. However, the increased number of users in mMIMO systems significantly affects performance of the existing approximate matrix inversion based and matrix inversion less iterative symbol detection techniques. Conventional detection algorithms cannot learn the inter-relations of input-output parameters based on available data without having specific mathematical models of communication scenarios. Moreover, existing deep learning (DL) based symbol detection models lack in-network compression, resulting in large training time and high computational load while expected to be deployed in a low latency communication system. In this article, a sparse refinement architecture is proposed for symbol detection in uplink mMIMO. The proposed DL architecture requires less trainable parameters as compared to a conventional fully connected detection network and refines the estimated symbol vector in each layer. Convergence of the proposed symbol detection technique is analytically justified. An expression for the approximate upper bound on the BER is derived which is supported by simulations. The obtained results prove viability of the proposed symbol detection model as compared to the several existing state-of-art uplink mMIMO detection techniques, in terms of superior the error performance and low computational complexity.

Spatial Index Modulation With the Combination of Both Antenna Indexes and Two Constellations

In this paper, in order to further exploit the antenna index (AI) domain for increasing the spectral efficiency, we propose a new schematic of enhanced generalized spatial modulation with both three dimension constellation and QAM constellation (EGSM-3DQ) to enhance the active AI combinations with the construction of three dimension (3D) signal constellation. In the EGSM-3DQ, a transmit vector symbol (TVS) consists of two spatial vector symbols (SVS) with the aid of one vector index bit, one SVS of which is obtained by modulating three components of a 3D signal symbol on two or three active transmit antennas (TAs) through the 3D Signal Mapper and AI Vector Modulator, another SVS of which is obtained by modulating one or multiple mapped QAM symbols on one or multiple active TAs through the AI Vector Selector. In addition, by jointing the AIes and multiple constellations such as the 3D and QAM, PAM constellations, grouping EGSM (gEGSM) is proposed to develop the group index combinations to increase extra index information. Finally, the comparisons of squared minimum Euclidean distances (MED) and the average bit error probability are provided. Simulation results show that the proposed schemes improve the bit error rate performance as compared with conventional systems.

Asymptotic Analysis of RLS-Based Digital Precoder With Limited PAPR in Massive MIMO

This paper focuses on the performance analysis of a class of limited peak-to-average power ratio (PAPR) precoders for downlink multi-user massive multiple-input multiple-output (MIMO) systems. Contrary to conventional precoding approaches based on simple linear precoders such as maximum ratio transmission (MRT) and regularized zero-forcing (RZF), the precoders in this paper are obtained by solving a convex optimization problem. To be specific, these precoders are designed so that the power of each precoded symbol entry is restricted, and the PAPR at each antenna is tunable. By using the Convex Gaussian Min-max Theorem (CGMT), we analytically characterize the empirical distribution of the precoded vector and the joint empirical distribution between the distortion and the intended symbol vector. This allows us to study the performance of these precoders in terms of per-antenna power, per-user distortion power, signal-to-noise and distortion ratio (SINAD), and bit error probability. We show that for this class of precoders, there is an optimal transmit per-antenna power that maximizes the system performance in terms of SINAD and bit error probability.

Anomaly Detection and Pattern Differentiation in Monitoring Data from Power Transformers

Aiming at the problem of abnormal data generated by a power transformer on-line monitoring system due to the influences of transformer operation state change, external environmental interference, communication interruption, and other factors, a method of anomaly recognition and differentiation for monitoring data was proposed. Firstly, the empirical wavelet transform (EWT) and the autoregressive integrated moving average (ARIMA) model were used for time series modelling of monitoring data to obtain the residual sequence reflecting the anomaly monitoring data value, and then the isolation forest algorithm was used to identify the abnormal information, and the monitoring sequence was segmented according to the recognition results. Secondly, the segmented sequence was symbolised by the improved multi-dimensional SAX vector representation method, and the assessment of the anomaly pattern was made by calculating the similarity score of the adjacent symbol vectors, and the monitoring sequence correlation was further used to verify the assessment. Finally, the case study result shows that the proposed method can reliably recognise abnormal data and accurately distinguish between invalid and valid anomaly patterns.

Design and Feasibility Verification of 6G Wireless Communication Systems with State of the Art Technologies

Frequencies above 100 GHz are the promising frequency bands for 6G wireless communication systems because of the abundant unexplored and unused spectrum. The increasing global demand for ultra-high spectral efficiencies, data rates, speeds and bandwidths in next-generation wireless networks motivates the exploration of peak capabilities of massive MIMO (Multi–Input–Multi–Output) wireless access technology at THz bands (0.1–10 THz). The smaller wavelengths (order of microns) of these frequencies give an advantage of making high gain antennas with smaller physical dimensions and allows massive spatial multiplexing. This paper presents the design of ultra-massive MIMO (ultra-mMIMO) hybrid beamforming system for multi users and its feasibility to function at THz frequency bands. The functionality of the proposed system is verified at higher order modulation schemes to achieve higher spectral efficiencies using performance metrics that includes error vector magnitude, symbol constellations, and antenna array radiation beams. The performance results suggest to use a particular mMIMO antenna configuration based on number of independent data streams per user and strongly recommended to use higher number of data streams per user in order to achieve higher throughputs that satisfy the needs of 6G wireless systems. Also the performance of the proposed system at 0.14 THz is compared with mmWave systems that operate at 28 GHz and 73 GHz bands to justify the feasibility of the proposed work.