In order to achieve rate-compatible RM codes, two most effective ways are puncturing and shortening. In this paper, puncturing schemes are studied. Different from the existing spherical puncturing, puncturing schemes which do no change the Plotkin structure of RM codes are proposed, enabling existing decoding techniques be readily accessible. The proposed puncturing schemes are based on Hamming weights of column indices of the generator matrix of RM codes. When Hamming weights of column indices (also determining the column weights, CW) are the same, different strategies are proposed, producing four different puncturing strategies, called CW-IV, CW-LSB, CW-MSB, and CW-MSB-Sym, respectively. Analysis is performed to show the union bound on error performance of RM codes with puncturing. Theoretically, it also shows that the punctured first 1st-order subcode can have potentially better performance than the non-puncturing case if puncturing is properly designed. Simulation results show that the proposed puncturing strategies outperform random and quasi-uniform puncturing (QUP) schemes in terms of block error rate (BLER). Union bound results also confirm that the first 1st-order subcode shows better performance than the original non-puncturing case. This fact indicates a more efficient transmission scheme of RM codes: transmitting part of the original codeword to increase the spectrum efficiency while achieving a better BLER performance under recursive list decoding.

Most existing deep learning-based trajectory prediction algorithms heavily rely on human expertise, involving iterative manual tuning of their architectures and parameters to tailor prediction models for specific tasks or scenarios. This approach is not only complex to implement and inefficient, but also struggles to balance inference speed with prediction accuracy. To address this challenge, this paper innovatively proposes an improved heterogeneous multi-agent trajectory prediction algorithm utilizing graph neural architecture search. This method automatically conducts an end-to-end graph architecture search to obtain an optimal trajectory prediction model. To enhance model interpretability and its heterogeneous awareness of diverse scenarios, we design a physics- and risk-interaction-based guidance mechanism to steer the architecture search process. Furthermore, we construct a novel neural architecture search loss function, SocialMI-Loss, which comprehensively considers multiple factors such as prediction accuracy, driving region semantic constraints, and model complexity. This function is intended to guide the learning of the trajectory predictor, achieving a harmonious balance between accuracy and computational complexity. A comprehensive series of comparative experiments conducted on three large-scale autonomous driving datasets (nuScenes, Argoverse, and ApolloScape) consistently demonstrates the superior performance of our proposed method. Experimental results indicate that our framework achieves performance comparable to current state-of-the-art methods, while its automatically searched architecture remains remarkably lightweight. Our code is available at:https://github.com/Tu5tra/TrajGNAS.

Faster-than-Nyquist (FTN) technique promises higher capacity and spectral efficiency for wireless communications. However, existing FTN studies over doubly-selective fading (DSF) channels separate channel-induced inter-symbol interference (channel-ISI) and FTN-induced ISI (FTN-ISI) to simplify cancellation. In practical DSF scenarios, the inherent coupling between FTN-ISI and channel-ISI causes significant performance degradation in conventional detection algorithms. To address this limitation, we first derive a practical FTN transmission model over DSF channels and construct the corresponding coupled interference matrix. Considering that data detection relies on efficient channel estimation, we propose a channel estimation algorithm with joint recovery of resolvable subpath parameters. This algorithm decomposes propagation paths into resolvable subpaths with independent delay-Doppler characteristics, achieving enhanced estimation accuracy through joint gain-phase optimization. Finally, building on the derived transceiver model and coupled interference matrix, we propose a whitening-enhanced orthogonal approximate message passing (WE-OAMP) algorithm that suppresses coupled interference through iterative linear-nonlinear estimation while maintaining spectral compactness. This algorithm constructs a whitening matrix using the FTN-ISI matrix to suppress noise correlation, and then performs detection through iterative linear and nonlinear estimation. Simulation results validate that the WE-OAMP algorithm outperforms benchmark algorithms in terms of bit error rate performance, especially in coded systems. Furthermore, we derive the achievable capacity of FTN signaling with WE-OAMP detection, demonstrating capacity improvement compared to Nyquist systems.

We investigate the performance of an active reconfigurable intelligent surface (RIS)-assisted mixed radio frequency (RF)-terahertz (THz) relaying system, where the RF signal reaches the relay through the active RIS and is then transmitted to the user via the THz channel. Under this scenario, we analyze the system performance with the relay employing amplify-and-forward (AF) and decode-and-forward (DF) protocols. More specifically, we derive the exact expressions for the cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) for both relaying protocols. Based on this, we obtain the exact expressions for the outage probability, average bit error rate (ABER), and average channel capacity (ACC). Furthermore, to gain deeper insights, we derive the asymptotic expressions at high SNRs and obtain diversity order (DO) of the system. Moreover, we extend the analysis to the variable gain relaying scheme. The findings reveal that the DOs for both relaying protocols are determined by the THz channel parameters, and the DO under the AF relaying protocol is twice that of the DF relaying protocol. Finally, we validate that active RIS (A-RIS) can more effectively assist the performance of the mixed RF-THz relaying system compared to passive RIS.

System modeling in distributed adaptive networks remains challenging under sensor aging-induced nonlinear data censoring and non-Gaussian interference. This brief proposes a robust hierarchical control framework that incorporates a Laguerre-based random Fourier filter to capture network nonlinearities. To address censored measurements and impulsive noise, a robust Laguerre RFF Diffusion Hierarchical (LRFF-DH) algorithm is developed. It leverages maximum likelihood estimation to correct bias and introduces a connectivity-adaptive robustness strategy based on node connectivity, enhancing edge-node resilience while reducing computational load on critical nodes. Simulations on a 20-node ad-hoc network verify the algorithm's effectiveness in interference suppression and mean squared error reduction under complex nonlinear conditions.

To better understand whale vocalizations, it is essential to simultaneously extract the components of whistles and clicks. However, prevailing methods in whale signal processing have focused on analyzing individual whistles or clicks. In this letter, we propose a novel method for separating whistles and clicks, even when these components overlap. This method combines a time-frequency (TF)-varying Gaussian window with the synchro-compensating Chirplet transform to achieve variable anisotropy, concentrating the TF energy along the ridges of the whistle and click components in the TF representation (TFR) and computing their directional angles. By using the enhanced TFR and these directional angles, a bidirectional ridge splitter is developed to separate the components of overlapping whistles and clicks. The effectiveness of this method is validated through comparative experiments using both simulated and real whale signals.

Existing channel estimation and data detection methods for faster-than-Nyquist (FTN) transmission over frequency-selective fading channels primarily face three key challenges: high pilot and guard interval overhead, low channel estimation accuracy, and long distances in satellite communication systems. To address the first two issues, we design a low-overhead frame structure based on circular convolution and, accordingly, propose a low-overhead precoding-driven channel estimation (PD-CE) algorithm. The proposed algorithm leverages circular convolution to suppress inter-block interference (IBI) from the channel with minimal guard intervals and eliminate FTN-induced IBI without guard intervals, significantly reducing pilot and guard overhead. Meanwhile, the limited guard interval mitigates noise enhancement, enabling PD-CE to achieve superior channel estimation accuracy over existing estimation methods. The third challenge arises from the imperfect channel state information obtained at the transmitter. To enhance the robustness in satellite communication systems, we design a precoding matrix based on the minimum mean square error (MMSE) criterion, introducing a low-overhead precoding-driven channel estimation and data detection (MMSE-PD-CEDD) algorithm for interference suppression. Simulation results indicate that, even under channel estimation error, the proposed MMSE-PD-CEDD algorithm exhibits superior interference resistance compared to existing algorithms, while its bit error rate performance loss remains within an acceptable range relative to the Nyquist criterion.

This work proposes deploying stacked intelligent metasurface (SIM) on individual Internet of Things (IoT) devices to enhance the uplink transmission capability under a finite blocklength (FBL) regime. Aiming to maximize the achievable sum rate, a joint transmit power allocation, SIM phase shifts, and receiving beamforming design optimization problem is formulated. By decomposing the original problem into three sub-problems, reducing the intractable quadratic fraction of signal-to-interference-plus-noise ratio (SINR), the nonconvex channel dispersion function, and the constant modulus constraints to linear forms, we propose an iterative algorithm to obtain the solutions. Numerical results demonstrate that in a multi-user uplink FBL network, the incorporation of SIM yields approximately a 40% enhancement in the sum rate. The optimization of phase shifts leads to an improvement of nearly 70% in the sum rate compared to a random phase setting scheme, highlighting the crucial role of proper phase shift configuration in realizing the significant performance gains offered by SIM. The performance of the proposed algorithm is validated to be close to the slack upper bound. Furthermore, with the same total number of metasurface elements, the multi-layer SIM performs better than the traditional single-layer RIS, which reveals the advantages of multi-layer structure.

Detecting ships in synthetic aperture radar (SAR) imagery is a pivotal task for marine surveillance and security. Although many deep learning (DL) methods have been proposed for SAR ship detection, they still lack the ability to explore intrinsic scattering features, and their ship target detection capabilities necessitate further enhancements in complex labile environments, especially for small ships. For this reason, this letter proposes a dual branch scattering feature fusion network (SFFNet). First, scattering center feature maps are reconstructed, and then, we design a scattering feature attention fusion module (SFAFM) in view of reconstructed feature maps, which can enhance the prominent feature extraction ability of the network. Moreover, the backbone feature extraction architecture incorporates a dense depthwise block (DDWB) aimed at more effectively fostering information interactions for scattering features and improving the efficiency of the network. To validate the efficacy of the SFFNet, comprehensive experiments were conducted on two public datasets, namely, HRSID and LS-SSDD-v1.0, and experimental results indicated that the detection accuracy reached 98.3%, and the false detection rate decreased to 0.21%. The proposed method can achieve superior performance when benchmarked against other state-of-the-art detection methods.

This letter presents a Direction-of-arrival (DOA) estimation algorithm in passive sensing systems with Reconfigurable Intelligent Surface (RIS). In order to improve the estimation accuracy in non-Gaussian noise and access point (AP) interference environments, a joint logarithmic function and atomic norm (LFAN) constrained DOA estimation method is proposed, analyzed, and discussed in detail. The proposed LFAN effectively mitigates impulsive noise and AP interference to achieve precise estimation through a minimization problem using logarithmic function and atomic norm constraints. Simulation results show that the proposed LFAN outperforms existing algorithms in terms of estimation performance.

Reconfigurable Intelligent Surface (RIS) can obtain huge passive beamforming gains. However, due to imperfect hardware and deployment environments, RIS is subject to hardware impairments (HWI) and partial elements blockage, resulting in a significant loss of gain. Hence, RIS array diagnosis is of great significance for normal operations of the RIS system. We consider a RIS assisted millimeter-wave (mmWave) communication system where some RIS elements suffer from HWI. A conjugate gradient complex soft threshold (CG-CST) algorithm is proposed to diagnose the RIS array, reducing the overhead and increasing the diagnostic accuracy. Furthermore, the proposed CG-CST algorithm is effective in both single-input single-output (SISO) systems and systems with multiple antennas. Numerical results confirm that the presented CG-CST algorithm has superior performance compared to existing methods.

Several approaches for estimating the direction of arrival (DOA) are traditionally developed assuming Gaussian noise, making them highly sensitive to outliers. Therefore, when confronted with impulsive noise, the performance of these methods may significantly deteriorate. In this letter, we characterize impulsive noise as Gaussian noise mixed sparse outliers. By exploiting their statistical differences, we propose an innovative DOA estimation technique within the framework of sparse signal recovery (SSR). Unlike common robust loss functions, such as$\ell _{1}$and$\ell _{p}$norms, we combine the$\ell _{2}$-norm with the Minimax Logarithmic Concave function as the loss function. Furthermore, to address the issue of grid mismatch, we utilize an alternating optimization approach to acquire the grid deviations, with the aid of rough DOA estimations and estimated outliers. Simulation results indicate that the proposed technique exhibits robustness against large outliers.

Synthetic aperture radar (SAR) target detectors based on deep learning have difficulty finding a good balance between accuracy and speed. Current pruning methods are usually used for backbone consistent pruning and seldom directly for the whole structure of deep learning target detectors; therefore, for edge-end applications, this article proposes a new full-link general automatic pruning algorithm for SAR target detectors, referred to as SARGap. First, SARGap automatically analyzes the network structure by creating a dependency graph, divides the pair-coupled network structure into the same group, and prunes the same channel for the same group of network structures so that the algorithm can be applied to a variety of complex target detectors. Second, an automatic pruning rate search method (APRS) is designed to search for the optimal pruning rate of each group of network structures in the target detector. Finally, to find a good balance between precision and speed in the automatic search of the pruning rate, a multiobjective optimization loss function (MOOL) is constructed as the APRS objective function. A series of experiments based on SSDD and HRSID, two large-scale SAR target detection datasets, are carried out to prove the superiority of this method. Using Yolov5s as the baseline, SARGap can compress parameters by 84.29%/82.86% and flops by 80.50%/81.93% on two datasets with almost no loss of accuracy. In addition, SARGap can be applied to any deep learning target detector and match hardware computing resources to achieve optimal full-link pruning.

In this work, we propose a voxel-based single-stage fine-grained and efficient point cloud 3D object detection algorithm to address the inadequate granularity in point cloud feature extraction tasks and the imbalance between efficiency and accuracy in single-stage point cloud 3D object detection scenarios. We develop a lightweight multibranch cross-sparse convolution network (LMCCN) that is designed to preserve the feature granularity of the original point cloud while achieving enhanced extraction efficiency. Additionally, we introduce a compact fine-grained self-attention augmented bird’s eye view (BEV) feature extraction module (CFSAM). This module aims to further refine BEV features, enabling the acquisition of both locally and globally enhanced features and thereby augmentingthe perceptual capabilities of the constructed model. Without bells and whistles, the proposed method attains excellent performance on many autonomous driving benchmarks, with detection accuracies of up to 81.67% on KITTI, 72.74% on ONCE, and 84.00% on nuScenes. Moreover, it reaches a peak detection speed of 46.08 FPS, effectively balancing accuracy with speed.

This paper investigates physical layer secure communication in a wideband wireless system, where a base station (BS) equipped with an extremely large scale antenna array (ELAA) transmits confidential information to a legitimate receiver under the threat of a potential eavesdropper. Due to the high carrier frequency and large antenna aperture, both the receiver and eavesdropper lie in the near-field region of the BS. In order to mitigate the beam split effect and reduce the hardware cost, a true-time delayer-based hybrid beamfocusing architecture is designed. Then, a nonconvex sum secrecy capacity maximization problem (SSCM) is formulated for securing wideband communications. Based on alternating optimization, the SSCM is decomposed into three subproblems solved iteratively for designing the digital beamfocusing vectors, time delay matrices, and phase shift matrices on each subcarrier, respectively. Simulation results show that the proposed scheme yields significantly high secrecy capacity compared to benchmarks, which validates the effectiveness of our scheme in enhancing secure wideband communications and mitigating the beam split effects.

To improve the accuracy of modulated signal recognition in variable environments and reduce the impact of factors such as lack of prior knowledge on recognition results, researchers have gradually adopted deep learning techniques to replace traditional modulated signal processing techniques. To address the problem of low recognition accuracy of the modulated signal at low signal-to-noise ratios, we have designed a novel modulation recognition network of multi-scale analysis with deep threshold noise elimination to recognize the actually collected modulated signals under a symmetric cross-entropy function of label smoothing. The network consists of a denoising encoder with deep adaptive threshold learning and a decoder with multi-scale feature fusion. The two modules are skip-connected to work together to improve the robustness of the overall network. Experimental results show that this method has better recognition accuracy at low signal-to-noise ratios than previous methods. The network demonstrates a flexible self-learning capability for different noise thresholds and the effectiveness of the designed feature fusion module in multi-scale feature acquisition for various modulation types.

The squared sine adaptive (SSA) algorithm is presented for identification scenarios, such as acoustic-echo cancellation (AEC) applications, in non-Gaussian environments. To devise the SSA algorithm, a novel cost function is constructed by exerting a sliding window-type squared sine function on the estimation error vector, which provides robustness in impulsive-noise environments and speeds up convergence when the input is colored. Theoretical results are presented for predicting the mean-weight, convergence, transient excess-mean-square-error (EMSE), and tracking behaviour. Moreover, the minimum EMSE and the optimum step size for tracking are presented. The computational complexity of the SSA algorithm has also been investigated. Numerical experiments demonstrate that results of the theoretical analysis match the simulated results very well and the proposed SSA algorithm outperforms known algorithms in AEC applications.

Most of the existing deep learning-based SAR target detection algorithms rely on manual experience to repeatedly adjust structures and parameters to design models suitable for specific scenarios or tasks. The implementation of the above methods is complicated, the design efficiency is low, and it is difficult to ensure the balance between accuracy and complexity. We innovatively propose a hardware-aware SAR target detection algorithm via multiobjective neural architecture search (NAS), referred to as SARNas. First, we design a flexible and efficient search space, a supernet search strategy and a subnet contribution evaluation strategy. Furthermore, we construct a new NAS loss function, called SARMI-Loss, to guide the learning of a SAR object detector that balances accuracy and computational complexity. Our SAR-Nas method can address the resource limitations of edge devices and automatically search for the optimal SAR target detector in an end-to-end manner for any deep learning-based SAR baseline model. A series of comparative experiments on three SAR image object detection datasets (SSDD, HRSID and MSAR) demonstrate the superiority of our method. The experimental results with YOLOV5 as the benchmark model show that the detection accuracy of the target detection networks automatically found by using the SARNas method on the SSDD, HRSID, and MSAR datasets can reach 98.5%, 92.8%, and 91.8% in mean average precision (mAP) with only 2.31M, 1.99M, 2.21M parameters, respectively. The number of model parameters is reduced by 88.9%, 90.46%, and 68.5%, respectively, and the inference speed is increased by 51.6%, 46.1%, and 13.9% without losing accuracy.

In recent years, deep learning has been widely used in remote sensing, especially in the field of synthetic aperture radar (SAR) image target detection. However, all of these deep learning models continue increasing the network’s depth and width without maintaining a good balance between accuracy and speed. Therefore, in this article, we propose a hybrid representation learning-enhanced SAR target detection algorithm based on the unique features of SAR images from a lightweight perspective called HRLE-SARDet. First, we design a lightweight and scattering feature extraction backbone that is more suitable for SAR image data. Second, for the multiscale feature discrepancy, we design a new multiscale feature fusion neck. Next, to better extract the scattering information from small targets of SAR images and improve the detection accuracy, we design a lightweight hybrid representation learning enhancement module. Finally, to better fit target detection for SAR image datasets, we redesign a more flexible loss function, which allows for an easy adjustment of the importance of polynomial bases according to the target task and dataset. Extensive experimental results on three SAR image ship target datasets (SSDD, AIR-SARShip-2.0, and HRSID) and a newly released large multiclass target SAR dataset (MSAR-1.0) show that our HRLE-SARDet achieves 98.4%, 79.2%, 92.5%, and 88.4% mean average precision (mAP) with only 1.09 M parameters and 2.5 G floating-point operations (FLOPs) on the SSDD, AIR-SARShip-2.0, HRSID, and MSAR-1.0 datasets, respectively, which is an excellent performance.

Oriented object detection in remote sensing images (RSI) has received more and more attention due to its broader applicability in natural scenes relative to horizontal bounding boxes. The complex scenes and multi-scale targets in remote sensing images make it often difficult for existing studies to extract key features of the targets effectively. At the same time, due to the problem of feature inconsistency in different layers, the direct fusion of these features is likely to cause feature conflicts, resulting in degradation of detection accuracy. To solve these problems, the dual-path multi-head feature enhancement detector (DP-MHFE Det), which contains two novel architectures, is proposed in this letter. The dual-path rotation feature aggregation module (DP-RFAM) improves the feature extraction capability of the network for rotating objects through dual-path structure and deformable convolution (DCN). To use these features effectively, the multi-head multi-level feature fusion enhancement network (MMFFENet) is proposed to guide the feature layers to learn and retain the key features they need autonomously, and then enhance their features according to the characteristics of different subtasks. Experiments conducted on two remote sensing datasets, DOTA and HRSC2016, show that DP-MHFE Det is faster than almost all detection methods compared to the state-of-the-art methods while showing strong competitiveness in accuracy.

A novel sparse array (SA) structure is proposed based on the maximum inter-element spacing (IES) constraint (MISC) criterion. Compared with the traditional MISC array, the proposed SA configurations, termed as improved MISC (IMISC) has significantly increased uniform degrees of freedom (uDOF) and reduced mutual coupling. In particular, the IMISC arrays are composed of six uniform linear arrays (ULAs), which can be determined by an IES set. The IES set is constrained by two parameters, namely the maximum IES and the number of sensors. The uDOF of the IMISC arrays is derived and the weight function of the IMISC arrays is analyzed as well. The proposed IMISC arrays have a great advantage in terms of uDOF against the existing SAs, while their mutual coupling remains at a low level. Simulations are carried out to demonstrate the advantages of the IMISC arrays.

In this paper, a general sparse array (SA) design principle, called uniform linear array (ULA) fitting, is proposed. It uses concatenation of sub-ULAs to design SAs with feasible difference coarrays (DCAs). Motivation for the ULA fitting is that the nested array and coprime array are in fact the examples of concatenations of two sub-ULAs which provide good properties. The polynomial model is utilized to investigate the case when an SA is composed of multiple sub-ULAs. An example of SA designed via ULA fitting is presented, and it attests that the ULA fitting enables to design SAs with closedform expressions, low coupling leakage and long consecutive DCA.

Correntropy is a local similarity measure defined in kernel space, and the maximum correntropy criterion (mcc) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with the center located at zero. However, the zero-mean Gaussian function may not be a good choice for many practical applications. In this letter, we propose an extended version of correntropy, whose center can be located at any position. Accordingly, we propose a new optimization criterion called maximum correntropy criterion with variable center (MCC-VC). We also propose an efficient approach to optimize the kernel width and center location in the MCC-VC. Simulation results of regression with linear-in-parameter (LIP) models confirm the desirable performance of the new method.

In this paper, a correntropy induced metric (CIM) criterion based set-membership NLMS (SM-NLMS) algorithm is proposed and its derivation is given in detail for estimating a sparse channel identification system. In the proposed algorithm, the CIM is utilized to exploit the sparsity-aware property of the sparse broadband multiple-path channels to achieve a better channel state information (CSI). Moreover, the proposed CIM criterion based SM-NLMS (CIMSM-NLMS) algorithm is carried out by mimicking a modified cost function under a restricted condition of CIM. The channel estimation performance of the proposed CIMSM-NLMS algorithm obtained by computer simulation is provided for appraising a sparse channel. The achieved simulation results reveal that the proposed CIMSM-NLMS algorithm is stable and outperforms the conventional SM-NLMS and sparse NLMS, LMS and SM-NLMS algorithms in terms of both the convergence and steady-state misalignment.

An improved norm-constrained set-membership normalized least mean square (INCSM-NLMS) algorithm is proposed for adaptive sparse channel estimation (ASCE). The proposed INCSM-NLMS algorithm is implemented by incorporating an lp -norm penalty into the cost function of the traditional set-membership normalized least mean square (SM-NLMS) algorithm, which is also denoted as lp -norm penalized SM-NLMS (LPSM-NLMS) algorithm. The derivation of the proposed LPSM-NLMS algorithm is given theoretically, resulting in a zero attractor in its iteration. By using this proposed zero attractor, the convergence speed is effectively accelerated and the channel estimation steady-state error is also observably reduced in comparison with the existing popular SM-NLMS algorithms for estimating exact sparse multipath channels. The estimation behaviors are investigated via a typical sparse wireless multipath channel, a typical network echo channel, and an acoustic channel. The computer simulation results show that the proposed LPSM-NLMS algorithm is better than those corresponding sparse SM-NLMS and traditional SM-NLMS algorithms when the channels are exactly sparse.

A norm combination penalized set-membership NLMS algorithm with l0 and l1 independently constrained, which is denoted as l0 and l1 independently constrained set-membership (SM) NLMS (L0L1SM-NLMS) algorithm, is presented for sparse adaptive multipath channel estimations. The L0L1SM-NLMS algorithm with fast convergence and small estimation error is implemented by independently exerting penalties on the channel coefficients via controlling the large group and small group channel coefficients which are implemented by l0 and l1 norm constraints, respectively. Additionally, a further improved L0L1SM-NLMS algorithm denoted as reweighted L0L1SM-NLMS (RL0L1SM-NLMS) algorithm is presented via integrating a reweighting factor into our L0L1SM-NLMS algorithm to properly adjust the zero-attracting capabilities. Our developed RL0L1SM-NLMS algorithm provides a better estimation behavior than the presented L0L1SM-NLMS algorithm for implementing an estimation on sparse channels. The estimation performance of the L0L1SM-NLMS and RL0L1SM-NLMS algorithms is obtained for estimating sparse channels. The achieved simulation results show that our L0L1SM- and RL0L1SM-NLMS algorithms are superior to the traditional LMS, NLMS, SM-NLMS, ZA-LMS, RZA-LMS, and ZA-, RZA-, ZASM-, and RZASM-NLMS algorithms in terms of the convergence speed and steady-state performance.

A low-complexity norm-adaption least-mean-square/fourth (LCNA-LMS/F) algorithm is proposed to exploit the sparse properties of the wireless multi-path channel in this paper. The proposed LCNA-LMS/F algorithm is realized by using a segment function instead of the reweighting factor in the reweighted norm-adaption least-mean-square/fourth (RNA-LMF) algorithm to remove the division operation, which can reduce the computational complexity. The channel estimation behaviors of the proposed LCNA-LMS/F algorithm are investigated over a sparse channel and the computer simulation results show that the proposed LCNA-LMS/F algorithm achieves superior performance with respect to the convergence speed and the steady-state error floor compared with the conventional least-mean-square/fourth (LMS/F) and its sparsity forms.