Low Implementation Complexity Research Articles

FPGA Implementation of Compact Hardware Accelerators for Ring-Binary-LWE-based Post-quantum Cryptography

Post-quantum cryptography (PQC) has recently drawn substantial attention from various communities owing to the proven vulnerability of existing public-key cryptosystems against the attacks launched from well-established quantum computers. The Ring-Binary-Learning-with-Errors (RBLWE), a variant of Ring-LWE, has been proposed to build PQC for lightweight applications. As more Field-Programmable Gate Array (FPGA) devices are being deployed in lightweight applications like Internet-of-Things (IoT) devices, it would be interesting if the RBLWE-based PQC can be implemented on the FPGA with ultra-low complexity and flexible processing. However, thus far, limited information is available for such implementations. In this article, we propose novel RBLWE-based PQC accelerators on the FPGA with ultra-low implementation complexity and flexible timing. We first present the process of deriving the key operation of the RBLWE-based scheme into the proposed algorithmic operation. The corresponding hardware accelerator is then efficiently mapped from the proposed algorithm with the help of algorithm-to-architecture implementation techniques and extended to obtain higher-throughput designs. The final complexity analysis and implementation results (on a variety of FPGAs) show that the proposed accelerators have significantly smaller area-time complexities than the state-of-the-art designs. Overall, the proposed accelerators feature low implementation complexity and flexible processing, making them desirable for emerging FPGA-based lightweight applications.

Low-complexity amplitude-division irregular QAM formats for short-reach unamplified coherent optical systems.

A low-complexity scheme is proposed to realize irregular uniform quadrature amplitude modulation (QAM) formats with Gray mapping, which are named amplitude-division irregular QAM (AD-Ir-QAM) formats. Compared to conventional probabilistic shaping (PS) with the Maxwell-Boltzmann (MB) distribution (PS-MB), irregular QAM formats show a smaller peak-to-average power (PAPR) and achieve a better performance in systems with the peak-power constraint. Compared with irregular QAM formats realized by PS (PS-Ir-QAM), AD-Ir-QAM formats realize a more flexible rate adaptation and have a lower implementation complexity. Experimental results obtained in an unamplified coherent optical system show that, at a generalized mutual information (GMI) of 4.5 bits/2D-symbol, AD-Ir-100QAM achieves gains of 2.1 and 0.5 dB in the power budget over PS-MB-100QAM and PS-Ir-100QAM, respectively.

Greedy Integration Based Multi-Frame Detection Algorithm in Radar Systems

In this paper, we address the problem of detection and tracking of dim targets in radar systems through the use of multi-frame detection (MFD) techniques. We first study the energy expansion problem during multi-frame integration for classical MFD methods, which shows that the extended energy peak envelope poses a great challenge for target detection in nonhomogeneous backgrounds and multi-target cases. Next, a greedy integration based MFD algorithm is proposed, which separates the overall multi-frame joint maximization into two processes of confidence building and extended energy suppression. The proposed algorithm can eliminate the energy expansion intrinsically and achieve better detection performance with a lower implementation complexity. In addition, we extend the proposed algorithm to radar systems by deriving the accurate nonlinear conversion relationships between target states of Cartesian coordinates and echo measurements of polar coordinates. In radar scenarios, the proposed algorithm is capable to make detection adaptively after multi-frame integration through the use of traditional constant false alarm rate (CFAR) procedures. Finally, numerical results and tests with real radar data are presented to demonstrate the effectiveness of the proposed algorithm.

Constant Weight Codes With Gabor Dictionaries and Bayesian Decoding for Massive Random Access

This paper considers a general framework for massive random access based on sparse superposition coding. We provide guidelines for the code design and propose the use of constant-weight codes in combination with a dictionary design based on Gabor frames. The decoder applies an extension of approximate message passing (AMP) by iteratively exchanging soft information between an AMP module that accounts for the dictionary structure, and a second inference module that utilizes the structure of the involved constant-weight code. We apply the encoding structure to (i) the unsourced random access setting, where all users employ a common dictionary, and (ii) to the “sourced” random access setting with user-specific dictionaries. When applied to a fading scenario, the communication scheme essentially operates non-coherently, as channel state information is required neither at the transmitter nor at the receiver. We observe that in regimes of practical interest, the proposed scheme compares favorably with state-of-the art schemes, in terms of the (per-user) energy-per-bit requirement, as well as the number of active users that can be simultaneously accommodated in the system. Importantly, this is achieved with a considerably smaller size of the transmitted codewords, potentially yielding lower latency and bandwidth occupancy, as well as lower implementation complexity.

Genetic Algorithm Aided Compressed Sensing Detector for Differential Space-Time Media-Based Modulation

Differential spatial modulation (DSM) is a multi-antenna technique that does not require channel state information (CSI). However, DSM has a deficiency of low spectral efficiency (SE). In this paper, a differential space-time media-based modulation (DSTMBM) system is proposed. The DSTMBM system equips radio frequency (RF) mirrors to transmit additional bits, which leads to an improvement of SE. Simulation results show that the bit error rate (BER) performance of DSTMBM is about 4dB better than that of DSM under the same parameters. For low-complexity implementation, a genetic algorithm aided compressed sensing (GA-CS) detector is tailored to the DSTMBM system. Compared with the state-of-the-art low-complexity detector with the best performance in differential systems, the GA-CS detector achieves a complexity reduction of 3 orders of magnitude when the transmit matrix dimension is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$8\times 8$</tex-math></inline-formula> , at the cost of only around 1dB in terms of BER performance. Furthermore, the complexity of GA-CS detector does not grow exponentially with the matrix dimension.

Accelerating QTMT-based CU partition and intra mode decision for versatile video coding

The H.266/VVC achieves about 50% bitrate saving compared to its predecessor H.265/HEVC at the expense of exponentially increased computational complexity. The most efficient but complex technique for H.266/VVC intra frame coding is the QuadTree with a nested Multi-type Tree encoding structure (QTMT), which usually requires traversing the Rate-Distortion (R-D) cost of each partition and each mode for the best option. To alleviate such computational burden while preserving the coding efficiency as much as possible, this paper develops a multi-feature guided Fast CU Partition (FCP) and Laplacian guided Fast Mode Selection (FMS) to accelerate the intra QTMT decision together. For FCP, we regard the CU partition as a classification problem and adopt the Support Vector Machine (SVM) for its low-complexity implementation; after evaluating the contribution of a set of features, three representative features of video textures are selected and used to train the SVM model. Additionally, an advanced technique is applied by adopting a soft decision in SVM for a more flexible trade-off between the complexity and R-D performance. For FMS, we utilize the Laplace operator to determine the most probable directions of the current CU and skip half of the candidate modes for runtime saving. Experimental results demonstrate that the proposed FCP reduces the encoding time of H.266/VVC by 51.03% with 1.65% Bjøntegaard Delta Bit-Rate (BDBR) increase; the proposed FMS reduces the encoding time by 12.68% with 0.09% BDBR loss. Their direct combination and advanced combination finally lead to 54.84% encoding time reduction with 1.74% BDBR increase and 40.39% encoding time reduction with 1.33% BDBR increase, respectively, outperforming state-of-the-art approaches significantly.

Diffusion Partitioned-Block Frequency-Domain Adaptive Filter Over Multitask Networks

As a generalization of the frequency-domain adaptive filter (FDAF) algorithm, partitioned-block frequency-domain adaptive filter (PBFDAF) results in minimal signal path delay. In this brief, we propose the diffusion normalized PBFDAF algorithm based on an unsupervised clustering strategy to address the low complexity implementation issues in multitask networks. Each node adaptively adjusts the combination weight coefficients by minimizing the instantaneous mean square deviation (MSD) in frequency-domain. The simulation results demonstrate that the proposed algorithm achieves superior performance.

Beam multiply and sum: A tradeoff between delay and sum and filtered delay multiply and sum beamforming for ultrafast ultrasound imaging

The delay and sum (DAS) has been the popular beamforming algorithm for image reconstruction in ultrafast ultrasound imaging systems due to its low complexity implementation. However, to improve the lower contrast and resolution in images reconstructed using DAS, there have been many adaptive and non-linear beamforming algorithms developed in the recent past. One of the popular non-linear algorithms proposed in the literature, filtered delay multiply and sum (F-DMAS) is sensitive to off-axis clutters and produces artifacts that result in the degradation of the overall image quality along with a possible dynamic range alteration. In this work, a novel approach to combining the strengths of DAS and F-DMAS algorithms is proposed. The proposed approach referred to as beam multiply and sum (BMAS), employs a DAS beamformer in multiple sub-apertures at receive to form the sub-aperture beams and cross multiplies them using a multiply and sum architecture to enhance the spatial coherence and suppress the clutter artifacts. An exhaustive performance comparison in terms of dynamic range alteration, resolution, and contrast of the BMAS is performed with standard in-silico and in-vitro datasets. The results suggest that the proposed approach outperforms the DAS and F-DMAS beamformers in most cases. More than the proposal of a novel beamforming algorithm, to the best of our knowledge, the approach is the first attempt of its kind towards the possibility of the co-existence of two or more beamformers in an ultrasound imaging system. With optimal tuning, it could provide a good trade-off between the effects of improved resolution and improved contrast while keeping the dynamic range linearity unaltered.

An efficient image compression architecture based on optimized 9/7 wavelet transform with hybrid post processing and entropy encoder module

Satellite communication is popular due to the advancement in storing and transmitting satellite images. Image compression can be defined as the science of lowering the number of bits necessary to represent an image. In satellite image processing, image degradation is considered a challenging problem. The Consultative Committee for Space Data Systems (CCSDS) Image Data Compression (IDC) standard CCSDS-122.0-B-1 is the transformation-dependent image compression method developed especially for usage in on-board space platforms. It holds de-correlation, quantization and entropy encoding phases. This paper introduces a new optimized memory organization for Discrete Wavelet Transform (DWT) to perform spatial de-correlation with fewer memory requirements on an FPGA device. Also, the proposed optimized DWT is integrated with a hybrid post-processing and entropy encoder module to reduce the spatial redundancies between the wavelet coefficients and compress the de-correlated data with high compression performance. A high-throughput hardware implementation of the Binary arithmetic entropy Coder (BAEC) is also provided to perform lossless compression with low implementation complexity. To provide the convenience and compactness, the proposed system will be implemented in the Xilinx working platform by developing a Verilog code. The proposed model is then evaluated on the Arty Z7–20 development board. The proposed approach is analyzed on different performance parameters such as throughput and frequency. The proposed design allowed a maximum operating frequency of 250 MHz, leading to a throughput of 156.25 Msamples/sec on Zynq. In addition, the structure of the proposed method overtakes the conventional design in terms of memory requirements and area.

Hybrid Analog and Digital Beamforming for RIS-Assisted mmWave Communications

Reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) communications has been envisioned as a prominent technology for future wireless networks, since it is capable of simultaneously providing abundant spectrum resources and favorable propagation environments. The small wavelength at mmWave bands also enables the widespread use of large antenna arrays, of which the hybrid beamforming structure has emerged as a cost-effective solution. In this paper, we aim to minimize the sum-mean-square-error (sum-MSE) in the RIS-assisted mmWave multiuser multiple input multiple output (MU-MIMO) system by jointly optimizing the hybrid analog-digital precoders and the RIS reflection matrix. We demonstrate that the role of RIS in assisting mmWave communications can be completely replaced by a large-scale Kronecker-structured hybrid array. Moreover, an accelerated Riemannian gradient algorithm using majorization minimization technique is proposed to tackle the unit-modulus constrained analog precoder/RIS design. Under the assumption of perfect channel state information (CSI), we firstly consider the single-user MIMO (SU-MIMO) setup and propose an effective alternating minimization (AM) procedure to characterize the system performance limit. Moreover, a two-stage scheme is developed for low-complexity implementation. This AM procedure is then extended to the general MU-MIMO scenario. In addition, we develop a novel enhanced regularized zero-forcing (ERZF) scheme for simultaneously combating strong noise in the low-SNR regime and mitigating multi-user interference (MUI) in the high-SNR regime. The optimality of our proposed algorithms is validated for some simplified practical scenarios. Numerical results illustrate that the proposed algorithms outperform existing benchmark schemes in terms of the actual complexity and performance.

Low Complexity Implementation of OTFS Transmitter using Fully Parallel and Pipelined Hardware Architecture

Low Complexity Implementation of OTFS Transmitter using Fully Parallel and Pipelined Hardware Architecture

Designing the Signal Quality Monitoring Algorithm Based on Chip Domain Observables for BDS B1C/B2a Signals under the Requirements of DFMC SBAS

To guarantee the integrity of a global navigation satellite system (GNSS) for safety-critical users, a satellite-based augmentation system (SBAS) makes use of the integrity monitoring architecture, of which the signal quality monitor (SQM) is an important component to address the potential risks caused by satellite-induced signal anomalies. Due to the introduction of dual-frequency multi-constellation (DFMC) techniques in 2025, the ranging uncertainty will be reduced by the elimination of first-order ionospheric delay, but the biases measured in each individual signal will be inflated by the ionosphere-free combinations. Moreover, multiple modulations of DFMC signals might introduce applicability uncertainty of a traditional SQM method that has been protecting GPS L1C/A signal only. Thus, higher requirements are put forward for future SQM methods in detection sensitivity and modulation independence. This paper first proposes a design methodology for the SQM algorithm for BDS B1C/B2a signals, which could be easily extended to the DF combinations of other GNSS core constellations. Then, by comparing the performances of SQM baseline algorithms based on traditional multi-correlator and emerging chip domain observables (CDOs), respectively, the superiority of CDO-based SQM is declared. Detailed design iterations are further discussed, including the algorithm practicalization with optimizing code-phase bin length and lowering sampling frequency, as well as the metric simplification, to promote the overall performance while preserving a lower implementation complexity. Ultimately, a CDO-based SQM algorithm for BDS B1C/B2a signals is reached, which would be considered as an effective candidate in new generation DFMC SBASs.

Efficient Hybrid A/D Beamforming for Millimeter-Wave Systems Using Butler Matrices

Hybrid analog/digital (A/D) beamforming architectures are low complexity alternatives to fully digital designs in large antenna setups. Recent research efforts have been set out to find low-complexity algorithms, which have low implementation complexity in the analog domain. In this paper, we propose a two-stage hybrid precoding design assuming hardware constraints that avoid the use of adaptive phase-shifters (PSs) by introducing a novel combination of Butler matrices (BMs) to feed a uniform planar array (UPA). With several fixed beams, we propose an algorithm to design the analog precoding matrix in the first stage, while in the second stage, hybrid-beamforming (HBF)-weighted minimum mean square error (WMMSE) is proposed for baseband precoding by taking into account the analog precoding matrix designed in the first stage. The proposed algorithm shows fast convergence, thanks to the analog precoder design, which helps the HBF-WMMSE algorithm to converge within a few iterations. Compared with the classical matched filter (MF) and minimum mean square error (MMSE) solutions, HBF-WMMSE outperforms the latter in terms of sum-rate, especially in the low signal-to-noise-ratio (SNR) regime. Simulation results further show that the partially connected Butler matrices (PCBMS) approach implemented with fixed-PSs exhibit superior energy-efficiency while maintaining higher spectral-efficiency as compared to the partially connected analog phase shifting (PCAPS) network implemented with variable-PSs.

Free-Space Optical Communication Based on Mode Diversity Reception Using a Nonmode Selective Photonic Lantern and Equal Gain Combining

This paper experimentally investigates the perform-ance of free-space optical (FSO) communication based on mode diversity reception (MDR) using nonmode selective photonic lantern (NSPL) and equal gain combining (EGC). By employing a mode demultiplexer and combining technology in the receiver, the bit error rate (BER) and outage performance of FSO communication system can be significantly improved. However, different from diversity system with multiple receive apertures, the branches in mode diversity system are non-independent fading signals, which are influenced by not only atmospheric but also the modal crosstalk of mode demultiplexer. Therefore, we take into consideration the difference of mode demultiplexer and study four schemes for FSO mode diversity reception system: 1) NSPL with equal gain combining (NSPL-EGC), 2) NSPL with maximal ratio combining (NSPL-MRC), 3) mode selective photonic lantern with equal gain combining (MSPL-EGC), and 4) mode selective photonic lantern with equal gain combining (MSPL-MRC). Experimental results show that NSPL-EGC is the most suitable scheme for MDR with low implementation complexity, and the performance difference is less than 1 dB compared with the one using MRC at BER = 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> under turbulence from weak to strong.

Discrete-modulation continuous-variable quantum key distribution with a high key rate

Discrete-modulation continuous-variable (CV) quantum key distribution has the potential for large-scale deployment in secure quantum communication networks owing to its low implementation complexity and compatibility with the current coherent optical telecommunication. However, current discrete-modulation protocols require relatively large constellation sizes to achieve a key rate comparable to that of the Gaussian modulation. Here, we show that a high key rate comparable to the Gaussian modulation can be achieved using only ten or so coherent states by implementing suitable key map and numerical convex optimization techniques. Specifically, the key rate of the two-ring constellation with 12 coherent states (four states in the inner ring and eight states in the outer ring) can reach 2.4 times of that of original quadrature phase shift keying and 70% of the Gaussian modulation protocol at 50 km. Such an approach can easily be applied to existing systems, making the discrete-modulation protocol an attractive alternative for high-rate and low-cost applications in secure quantum communication networks.

Digital Twin-Aided Orchestration of Mobile Edge Computing With Grant-Free Access

Digital twin-aided (DT) edge computing is investigated, where users utilize grant-free random access with adaptive rate to offload their tasks to the edge server. A novel, with lower implementation complexity, probabilistic partial offloading scheme is introduced, while each device is assumed to have an infinite buffer to store its tasks. The aim of the proposed work is to minimize the average delay of the partial offloading. To that end, the average delay of waiting in the queue, the delay of offloading, and the local computation delay are extracted by using queuing theory tools. Then, the non-convex problem of minimizing the average delay of all clients is formulated, while taking into account DT imperfections. Successive convex approximation (SCA), alternating optimization (AO), and various algebraic manipulations are utilized to transform the problem into an equivalent convex problem with tractable solution. Finally, simulation results showcase the value of the proposed analysis and offer important insights for the proposed DT-aided edge network. Specifically, the proposed partial offloading scheme is shown to be more delay efficient compared to both local computing and full offloading, particularly, for greater task generation rates at the users. Also, the impact of the DT imperfections at the average delay is shown to be more notable as the number of users, or the tasks’ size, increases.

Performance Analysis of Intelligent Reflecting Surface Assisted Opportunistic Communications

Intelligent reflecting surfaces (IRSs) are a promising technology for enhancing coverage and spectral efficiency, both in the sub-6 GHz and the millimeter wave (mmWave) bands. Existing approaches to leverage the benefits of IRS involve the use of a resource-intensive channel estimation step followed by a computationally expensive algorithm to optimize the reflection coefficients at the IRS. In this work, focusing on the sub-6 GHz band of communications, we present and analyze several alternative schemes, where the phase configuration of the IRS is randomized and multi-user diversity is exploited to opportunistically select the best user at each point in time for data transmission. We show that the throughput of an IRS assisted opportunistic communication (OC) system asymptotically converges to the optimal beamforming-based throughput under fair allocation of resources, as the number of users gets large. We also introduce schemes that enhance the rate of convergence of the OC rate to the beamforming rate with the number of users. For all the proposed schemes, we derive the scaling law of the throughput in terms of the system parameters, as the number of users gets large. Following this, we extend the setup to wideband channels via an orthogonal frequency division multiplexing (OFDM) system and discuss two OC schemes in an IRS assisted setting that clearly elucidate the superior performance that IRS aided OC systems can offer over conventional systems, at very low implementation cost and complexity.

A Framework for Hardware Impairments-Aware Multi-Antenna Transceiver Design in IoT Systems via Majorization–Minimization

In view of the nonideality of communication links in the Internet of Things (IoT) originating from transceiver hardware impairments, in this article, we introduce a general framework for hardware impairments-aware multiantenna transceiver design, which considers different availabilities of CSI at the transmitter (CSIT) and the receiver (CSIR). The well-known Kronecker model is applied to characterize stochastic channel state information (CSI) errors. For each case, we aim to minimize the (average) total mean square error (MSE) of all data streams subject to the practical per-antenna power constraints. To address the nonconvexity of the formulated problem, we propose an efficient majorization–minimization (MM)-based iterative algorithm to transform the original problem into a series of convex subproblems with semiclosed-form optimal solutions. For low-complexity implementation, we also develop an alternative scheme for directly finding a high-quality suboptimal solution by considering both worst case hardware impairments and worst case CSI errors. In particular, since an explicit expression of the average total MSE for the perfect CSIR and imperfect CSIT case is hard to derive, we instead optimize its effective upper and lower bounds. The prospective applications of our work in the two currently popular multiple-input–multiple-output (MIMO) IoT scenarios are then discussed. Furthermore, we fundamentally reveal the MSE floor effect caused by both hardware distortion and CSI imperfection in the high-SNR regime. Numerical results illustrate the excellent average total MSE and average bit error rate (BER) performance of our proposed algorithms over the adopted benchmark schemes.

Joint Intra/Inter-Slot Code Design for Unsourced Multiple Access in 6G Internet of Things

Unsourced multiple access (UMA) is the technology for massive, low-power, and uncoordinated Internet-of-Things in the 6G wireless system, improving connectivity and energy efficiency on guaranteed reliability. The multi-user coding scheme design is a critical problem for UMA. This paper proposes a UMA coding scheme based on the T-Fold IRSA (irregular repetition slotted Aloha) paradigm by using joint Intra/inter-slot code design and optimization. Our scheme adopts interleave-division multiple access (IDMA) to enhance the intra-slot coding gain and the low-complexity joint intra/inter-slot SIC (successive interference cancellation) decoder structure to recover multi-user payloads. Based on the error event decomposition and density evolution analysis, we build a joint intra/inter-slot coding parameter optimization algorithm to minimize the SNR (signal-to-noise ratio) requirement at an expected system packet loss rate. Numerical results indicate that the proposed scheme achieves energy efficiency gain by balancing the intra/inter-slot coding gain while maintaining relatively low implementation complexity.

SDFnT-Based Parameter Estimation for OFDM Radar Systems with Intercarrier Interference

The orthogonal frequency division multiplexing (OFDM) radar suffers from severe performance degradation in range-velocity estimation in high mobility scenarios. In this paper, a novel intercarrier interference (ICI)-free parameter estimation method for OFDM radar is proposed. By employing a scale discrete Fresnel transform (SDFnT), the OFDM radar signals are converted to the scale Fresnel domain, and the orthogonality of subcarriers can be recovered with the optimal scale factor. Furthermore, due to the compatibility of the SDFnT and the discrete Fourier Transform (DFT), the proposed method has low computational complexity and high feasibility for OFDM radar implementation. Simulation results show that the proposed SDFnT-based scheme effectively eliminates the ICI effect for single and multiple targets and achieves high accuracy delay-Doppler estimation for OFDM radar systems in circumstances of high velocity and low SNR with consistency and robustness.