Compared with the traditional transportation data, the transportation big data (TBD) is under the background of “Internet + traffic.” It is a great challenge for analyzing and processing TBD because of its complex and unstructured characteristics, such as sequence, strong relevance, accuracy, and closed loop. This Special Issue provides high-quality and up-to-date technology related to the application of SP and AI into TBD and their applications in the COVID-19 scenario and beyond and serves as a forum for researchers all over the world to discuss their works and recent advancements in the field, especially for defensing COVID-19 in public transportation.

Traditional range-instantaneous Doppler (RID) methods for maneuvering target imaging suffer from the problems of low resolution and poor noise suppression. We propose a new super-resolution inverse synthetic aperture radar (ISAR) imaging method based on deep-learning-assisted time–frequency analysis (TFA). Our deep neural network resembles the basic structure of a U-net with two additional convolutional-upsampling layers and$l_{1}$-norm loss function for super-resolution generation and noise suppression. The neural network is trained in advance to learn the mapping function between the low-resolution time–frequency spectrum inputs and their high-resolution references. Then, the linear TFA assisted by the pretrained network is integrated into the RID-based ISAR imaging system and is found to achieve sharply focused and denoised target image with super-resolution. Both the simulated and real radar data are used to evaluate the performance of the proposed method. Numerical experimental results demonstrate the superiority of the proposed ISAR imaging method over traditional ones.

Using the continuous-wave technology to replace the conventional pulse-mode, frequency-modulation continuous-wave (FMCW) synthetic aperture radar (SAR) has shown good potentials of reducing the weight of the system and the sensors' peak transmission power. In order to relax the requirements of data bandwidth and storage, and increase the swath, the SAR system will collect the downsampled data, which makes the traditional matched filtering (MF)-based method unable to recover the considered scene, leading to failed reconstruction. To solve this problem, this letter presents an FMCW SAR sparse imaging method based on the frequency-scaling algorithm (FSA). Experimental results on the real data show that compared with the MF-based FMCW SAR imaging algorithms, the proposed method can improve the recovered image performance effectively. For the sparse surveillance region, it can achieve accurate recovery even from the downsampled data. Because the computational complexity of the proposed method is in the same order as that of MF, the sparse imaging of large-scale scenes can also be realized in the FMCW SAR.

The papers in this special section focus on advanced signal processing and artificial intelligence (AI) technologies for industrial Big Data (IBD) powered by Industry 4.0. Modern industry has evolved from the traditional manufacturing industry to digital and intelligent industry. Huge amount of complex real-time data are generated from the thousands of industrial sensors in physical and man-made environments. Industrial big data (IBD) afford us an unprecedented opportunity to obtain an in-depth understanding of Internet of Things and facilitate data-driven approaches for industrial optimization and scheduling. The papers in this section collect the latest ideas and research on advanced signal processing and artificial intelligence (AI) technologies for IBD.

In recent years, the sparse signal processing technique has shown significant potential in synthetic aperture radar (SAR) imaging, such as image performance improvement and downsampled data-based image recovery. However, due to the huge computational complexity needed, the existing sparse SAR imaging methods, such as conventional observation matrix-based and azimuth-range decouple-based algorithms, are not able to achieve real-time processing, especially for the large-scale scenes, which seriously restricts its application in some fields, e.g., real-time monitoring and early warning. To solve this problem, this article presents a novel real-time sparse SAR imaging method, which can get a similar image performance to that obtained by the existing sparse imaging methods, to reduce the computational complexity to the same order as that required by matched filtering (MF)-based algorithms. This means that with the proposed method, real-time data processing for practical large-scale scene sparse reconstruction becomes possible. Experimental results based on simulated and real data along with a performance analysis are presented to validate the proposed real-time sparse imaging method.

In a multipath propagation environment, prevalent target localization methods are mainly based on the classical two-ray propagation model without considering other reflected waves. Because the received target echoes are considerably corrupted by multipath reflections in the case of complex terrain, these prevalent methods might fail to work or achieve poor performance. To solve this problem, we first consider a practical multipath propagation scenario to reveal the dynamic structural relationship of the spatial paths based on the spherical earth model. Subsequently, a target localization algorithm based on low-rank decomposition (LRD) and sparse representation (SR) framework is proposed. The proposed algorithm can effectively mitigate the effects of complex multipath interference without using any prior knowledge on the illuminated terrain and the reflecting paths. Experiments on synthetic data and real data validate the effectiveness of the proposed algorithm.

Obtained by wide band radar system, high resolution range profile (HRRP) is the projection of scatterers of target to the radar line-of-sight (LOS). HRRP reconstruction is unavoidable for inverse synthetic aperture radar (ISAR) imaging, and of particular usage for target recognition, especially in cases that the ISAR image of target is not able to be achieved. For the high-speed moving target, however, its HRRP is stretched by the high order phase error. To obtain well-focused HRRP, the phase error induced by target velocity should be compensated, utilizing either measured or estimated target velocity. Noting in case of under-sampled data, the traditional velocity estimation and HRRP reconstruction algorithms become invalid, a novel HRRP reconstruction of high-speed target for under-sampled data is proposed. The Laplacian scale mixture (LSM) is used as the sparse prior of HRRP, and the variational Bayesian inference is utilized to derive its posterior, so as to reconstruct it with high resolution from the under-sampled data. Additionally, during the reconstruction of HRRP, the target velocity is estimated via joint constraint of entropy minimization and sparseness of HRRP to compensate the high order phase error brought by the target velocity to concentrate HRRP. Experimental results based on both simulated and measured data validate the effectiveness of the proposed Bayesian HRRP reconstruction algorithm.

The classical solution to an underdetermined system of linear equations mainly has two opposite directions, which lead to either a large ℓ2-norm sparse solution or a non-sparse minimum ℓ2-norm solution. In this paper, we systematically show that by modifying the well-known basic matching pursuit algorithm originally proposed to identify the sparse solution, an alternative solution between the two classical ones could be obtained. The modified algorithm, termed as random matching pursuit (RMP), is then used to create a novel image watermarking framework. Compared to conventional systems, the security is substantially improved by the use of random over-complete dictionaries and the order parameter of RMP. Capacity can also be increased thanks to the transform with over-complete dictionaries that could expand signal dimension. Meanwhile, imperceptibility and robustness properties of the proposed design framework are not compromised. The classical spread spectrum and improved spread spectrum techniques are applied to the proposed framework for practical implementations. The novelty and effectiveness of the proposed systems are supported by rigorous performance analysis and experimental results using an image data set. This paper reveals the potential of using over-complete dictionaries in multimedia watermarking systems, which theoretically leads to the exploration of alternative candidates among the infinite solutions to underdetermined linear systems other than minimum ℓ2-norm and sparse ones.

Frequency-modulation continuous-wave (FMCW) synthetic-aperture radar (SAR) can minimize the peak transmission power of sensors and reduce the size and weight of the systems. Wavenumber domain algorithm (WDA) is an accurate focusing method for SAR imaging. By using the exact signal form to compensate the phase error, WDA can achieve exact scene recovery from high-squint and long aperture data as long as the platform velocity is stable. In this paper, we introduce WDA to FMCW SAR and discuss the WDA-based FMCW SAR sparse imaging method. There are two main contributions of this paper: 1) a motion compensation-based WDA imaging method is introduced to correct the motion error that is often associated in practical airborne FMCW SAR data and 2) a novel WDA-based FMCW SAR sparse imaging method is developed to further improve the performance of recovered image. Compared with the typical WDA algorithm, the sparse imaging method can suppress the noise and sidelobes and perform the sparse scene recovery from the downsampled data. Experimental results via simulated and real airborne data verify the presented WDA-based FMCW SAR imaging methods.

This paper proposes a new scheme of motion parameter estimation and relocation for airborne three-channel circular stripmap synthetic aperture radar (CSSAR)-ground moving target indication (GMTI) systems. Compared with the conventional straight-path SAR, the parameter estimation of a target is more challenging because the target's range history and signal model are more complicated due to the complexity of the relative motion between CSSAR and ground moving target. In this paper, the signal model of a ground moving target and the expression for its along-track interferometric (ATI) phase from the environment of airborne three-channel CSSAR are derived. The coupling effect among the target's motion and position parameters is also figured out. Then, a scheme of motion parameter estimation and relocation is proposed. The proposed scheme utilizes the ATI phase and the quadratic-term coefficient in the range equation to estimate the target's motion and position parameters and utilizes an iterative strategy to address the coupling effect among these parameters. Numerical simulations are conducted to validate the satisfactory performance achieved by the proposed algorithm.

For sparse aperture (SA) radar echoes, the coherence between the undersampled pulses is destroyed, which challenges the effectiveness of the traditional autofocusing and scaling in inverse synthetic aperture radar (ISAR) imaging. A novel Bayesian ISAR autofocusing and scaling algorithm for sparse aperture is proposed, which utilizes Laplacian scale mixture, as the sparse prior of ISAR image, and variational Bayesian inference based on the Laplacian approximation to derive its posterior. In addition, it learns the phase error, rotational velocity, and center of target from radar echo automatically during the reconstruction of ISAR image, so as to achieve ISAR autofocusing and scaling for SA. Because the parameters learning is not easy to converge with the undersampled data, a modified Newton method based on joint constraint of entropy and sparsity is proposed to guarantee fast convergence in a right direction. Experimental results based on both simulated and measured data validate the robustness of the proposed ISAR imaging algorithm against SA and noise.

Using sparse signal processing to replace matched filtering (MF) in synthetic aperture radar (SAR) imaging has shown significant potential to improve image quality. Due to the huge computational cost needed, it is difficult to apply conventional observation-matrix-based sparse SAR imaging method for large-scene reconstruction. The azimuth-range decouple method is able to minimize the computational complexity and achieve image performance similar to that obtained by the observation-matrix-based algorithm. However, there still exist two difficult problems in sparse SAR imaging, i.e., real-time processing and lack of raw data. To solve these problems, this paper presents a novel complex-image-based sparse SAR imaging method. It is found that if the input MF-recovered SAR complex image is obtained via fully sampled raw data, the proposed method can achieve an identical high-resolution image to that obtained by the azimuth-range decouple algorithm. The computational complexity is also decreased to the same order as that of MF, which makes the real-time sparse SAR imaging become possible. In addition, it should be noted that even though without raw data, the proposed method can still obtain impressive sparse recovery performance by using only the available complex image. Performance analysis and experimental results on real data validate the proposed method.

In this letter, a new spectrum-oriented fast factorized backprojection (FFBP) algorithm is proposed for synthetic aperture radar (SAR) imaging on a maneuvering platform. Specifically, an analytical SAR image spectrum is derived in a novel quasi-polar coordinate system based on the FFBP, which makes it easy to incorporate with an autocalibration process for both systematic and nonsystematic errors. Different from the conventional FFBP algorithms developed in polar grid, the proposed algorithm devised in quasi-polar gird conducts the motion-induced phase error as a space-invariant component, which will definitely facilitate the phase autofocusing process during the FFBP recursions. Subsequently, a phase autofocusing process is incorporated in the resultant SAR image formation algorithm. Simulations and discussions are presented to show the focusing quality improvement made by the proposed algorithm.

This paper deals with the issue of ground moving target imaging and motion parameter estimation with an airborne dual-channel circular stripmap synthetic aperture radar (CSSAR) system. Although several methods of ground moving target motion parameter estimation have been proposed for the conventional airborne linear stripmap SAR, they cannot be applied to airborne CSSAR because the range history of a ground moving target for airborne CSSAR is different than that for airborne linear stripmap SAR. In this paper, the moving target's range history for airborne dual-channel CSSAR and the target signal model after the displaced phase center antenna processing are derived, and a new ground moving target imaging and motion parameter estimation algorithm is developed. In this algorithm, the estimation of baseband Doppler centroid and its compensation are first performed. Then focusing is implemented in the 2-D frequency domain via phase multiplication, and the target is focused in the SAR image without azimuth displacement due to the compensation of the Doppler shift caused by its motion. Finally, the target's motion parameters are estimated with its Doppler parameters and its position in the SAR image. Numerical simulations are conducted to validate the derived range history and the performance of the proposed algorithm.

Because of flexible geometric configuration and trajectory designation, time-domain algorithms become popular for unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) applications. In this paper, a new quasi-polar-coordinate-based fast factorized back-projection (FFBP) algorithm combined with data-driven motion compensation is proposed for miniature UAV-SAR imaging. By utilizing wavenumber decomposition, the analytical spectrum of a quasi-polar grid image is obtained, where the phase errors arising from the trajectory deviations can be conveniently investigated and the phase autofocusing can be compatibly incorporated. Different from the conventional FFBP based on a polar coordinate system, the proposed algorithm operates in a quasi-polar coordinate system, where the phase errors become spacial invariant and can be accurately estimated and easily compensated. Moreover, the relationship between phase errors and nonsystematic range cell migration (NsRCM) is revealed according to the analytical image spectrum, based on which the NsRCM correction is developed to further improve the image focusing quality for high-resolution SAR applications. Promising experimental results from the raw data experiments of miniature UAV-SAR test bed are presented and analyzed to validate the advantages of the proposed algorithm.

Spherical harmonics root-MUSIC (MUltiple SIgnal Classification) technique for source localization using spherical microphone array is presented in this paper. Earlier work on root-MUSIC is limited to linear and planar arrays. Root-MUSIC for planar array utilizes the concept of manifold separation and beamspace transformation. In this paper, the Vandermonde structure of array manifold for a particular order is proved. Hence, the validity of root-MUSIC in the spherical harmonics domain is confirmed. The proposed method is evaluated by using simulated experiments on source localization. Root mean square error analysis and statistical analysis are presented. The experimental measures at various signal to noise ratios (SNRs) show the robustness of the proposed method. The method is also verified by using experiment on real signal acquired over spherical microphone array.

Recently, compressive sensing theory has been successfully applied in inverse synthetic aperture radar (ISAR) imaging. However, the issue of maneuvering target imaging from compressive sampling data has not been sufficiently addressed because it is difficult to jointly deal with both sparse imaging and motion compensation under compressive sampling. In this paper, we develop a novel algorithm of high-resolution ISAR imaging for maneuvering targets from compressive sampling data. In this algorithm, a non-uniform scaled Fourier dictionary is constructed to represent the maneuverability. A hierarchical statistical model is utilized to encode the sparsity of ISAR image. Then, ISAR imaging joint with motion estimation is solved by using a parametric sparse Bayesian leaning (P-SBL) method, including sparse imaging and dictionary learning. Finally, experiments are performed to confirm the effectiveness of the proposed method by using the simulated and measured data.

In this paper, the analytic expression of synthetic aperture radar (SAR) image spectrum in the polar grid system is derived based on the wavenumber analysis. By revealing the relationship between wavenumber variable and image spectrum in the polar system, we can better understand the mechanism of fast factorized BP (FFBP) processing. Moreover, the form of phase error in spectral domain can be possibly revealed which will facilitate motion compensation and autofocusing in FFBP processing. Simulation results are presented and analyzed to demonstrate the validity of the derived spectrum.

The authors study the performance of protograph low‐density parity‐check (LDPC) codes over two‐dimensional (2D) intersymbol interference (ISI) channels in this study. To begin with, the authors propose a modified version of finite‐length (FL) extrinsic information transfer (EXIT) algorithm so as to facilitate the convergence analysis of protograph codes. Exploiting the FL‐EXIT analyses, the authors observe that the protograph codes optimised for 1D ISI channels, e.g. the 1D‐ISI protograph code, cannot maintain their advantages in the 2D‐ISI scenarios. To address this problem, the authors develop a simple design scheme for constructing a family of rate‐compatible improved protograph (RCIP) codes particularly for 2D‐ISI channels, which not only outperform the 1D‐ISI protograph code, but also are superior to the regular column‐weight‐3 code and optimised irregular LDPC codes in terms of the convergence speed and error performance. More importantly, such RCIP codes benefit from relatively lower error‐floor as well as linear encoding and fast decoding. Thanks to these advantages, the proposed RCIP codes stand out as better alternatives in comparison with other error‐correction codes for ultra‐high‐density data storage systems.

Forward velocity extraction is a very important process for obtaining a high-quality unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) image. Because of the constraints of low flying altitude and small platform size, the flight path of the UAV is easily disturbed by the atmospheric turbulence. The complex motion error of the UAV's flight path makes the forward velocity difficult to be extracted from raw SAR data. To address this problem, an adaptive notch filtering (ANF)-based approach for forward velocity extraction is proposed. Based on the kinetic characteristics of the UAV, the variation of Doppler centroid frequency is analyzed and exploited to remove most components of the cross-track acceleration in the low-frequency range. Then, by regarding the forward velocity component as a narrow-band component, ANF processing is employed to extract it from the estimated Doppler rate. Comparing with the methods reported in the literature, the ANF method can achieve higher accuracy and efficiency due to its excellent notching performance and strong suppression for narrow-band signals. Promising results from raw data experiments are presented to demonstrate the validity and superiority of the proposed method.

We present a novel framework of performing multimedia data hiding using an over-complete dictionary, which brings compressive sensing to the application of data hiding. Unlike the conventional orthonormal full-space dictionary, the over-complete dictionary produces an underdetermined system with infinite transform results. We first discuss the minimum norm formulation (ℓ2-norm) which yields a closed-form solution and the concept of watermark projection, so that higher embedding capacity and an additional privacy preserving feature can be obtained. Furthermore, we study the sparse formulation (ℓ2-norm) and illustrate that as long as the ℓ0-norm of the sparse representation of the host signal is less than the signal's dimension in the original domain, an informed sparse domain data hiding system can be established by modifying the coefficients of the atoms that have not participated in representing the host signal. A single support modification-based data hiding system is then proposed and analyzed as an example. Several potential research directions are discussed for further studies. More generally, apart from the ℓ2- and ℓ0-norm constraints, other conditions for reliable detection performance are worth of future investigation.

In this paper, a novel synthetic aperture radar (SAR) ground moving target imaging (GMTIm) algorithm is presented within a parametric and dynamic sparse Bayesian learning (SBL) framework. A new time-frequency representation, which is known as Lv's distribution (LVD), is employed on the moving targets to determine the parametric dictionary used in the SBL framework. To combat the inherent accuracy limitations of the LVD and extrinsic perturbation errors, a dynamical refinement process is further developed and incorporated into the SBL framework to obtain highly focused SAR image of multiple moving targets. An emerging inference technique, which is known as variational Bayesian expectation-maximization, is applied to achieve an efficient Bayesian inference for the focused SAR moving target image. A remarkable advantage of the proposed algorithm is to provide a fully posterior distribution (Bayesian inference) for the SAR moving target image, rather than a poor point estimate used in conventional methods. Because of utilizing high-order statistical information, the error propagation problem is desirably ameliorated in an iterative manner. The perturbations, known as the multiplicative phase error and additive clutter and noise, are both well adjusted for further improving the image quality. Experimental results by using simulated spotlight-SAR data and real Gotcha data have demonstrated the superiority of the proposed algorithm over other reported ones.

This paper presents a new SAR ground moving target imaging (GMTIm) algorithm based on an unified framework of Keystone transformation (KT). To combat the inherent range-azimuth coupling, an tandem two-step strategy is designed, where the range decoupling is implemented by polar format algorithm (PFA) and the azimuth decoupling is finished by an novel time-frequency representation method that is Lv's distribution (LVD). We show, mathematically, that the azimuth resampling of PFA has inherently the same mechanism as the KT, and also, the LVD achieves the optimal performance when it is performed in accordance with the KT principle. Therefore, multiple moving targets can be imaged simultaneously. Focused targets' responses can be obtained in both range and azimuth dimensions. Isotropic point target simulation is designed, and experiments are carried out to validate our proposed SAR-GMTIm algorithm.

In this paper, we investigate the performance of the protograph low-density parity-check (LDPC) codes concatenated with space-time block code (STBC) over Rayleigh fading channels. We firstly extend the modified protograph extrinsic information transfer (PEXIT) algorithm in order to analyze the convergence performance of protograph codes. Based on the extended PEXIT algorithm and Gaussian approximation, we further derive the asymptotic bit-error-rate (BER) expression of protograph codes. Utilizing the PEXIT algorithm, theoretical and simulated BERs, we compare the performance of two classical protograph codes, i.e., accumulate-repeat-by-3-accumulate (AR3A) code and accumulate-repeat-by-4-jagged-accumulate (AR4JA) code, regular LDPC code, and optimized irregular LDPC codes, and illustrate that the AR3A code is superior to other three codes. Additionally, we discuss the impact of the number of receive antennas (i.e., NR) on the system performance and verify that the theoretical analyses hold as NR varies. As a result, the AR3A code stands out as a good candidate for wireless communication applications with multiple antennas.

This paper presents a new ground moving target imaging (GMTIm) algorithm for airborne synthetic aperture radar (SAR) based on a novel time-frequency representation (TFR), Lv's distribution (LVD). We first analyze generic moving target signatures for a multichannel SAR and then derive the analytical spectrum of a point target moving at a constant velocity by a polar format algorithm for SAR image formation. SAR motion deviation from a predetermined flight track is considered to facilitate airborne SAR applications. LVD, as a recently developed TFR for the analysis of multicomponent linear-frequency-modulated signal, is adopted to represent the target kinematic spectrum in the Doppler centroid frequency and chirp rate domain. As a result, the proposed SAR-GMTIm algorithm is capable of imaging multiple moving targets even when they are located at the same range resolution cell. Some practical issues such as imaging maneuvering targets and small/weak targets are discussed to enhance the applicability of the proposed algorithm. Simulation results with isotropic point moving targets are presented to validate the effectiveness and superiority of the proposed algorithm. Raw data collected by an airborne multichannel SAR are also used to verify the performance improvement made by the proposed algorithm.

We investigate the performance of the protograph low-density parity-check (LDPC) codes over Nakagami block-fading (BF) channels with multiple receive antennas. Using the modified protograph extrinsic information transfer (PEXIT) algorithm, we observe that the existing protograph LDPC codes, which have been shown to possess excellent error performance over additive white Gaussian noise channels, cannot perform well over non-ergodic BF channels. To address this problem, a simple design scheme is proposed to construct three new root-protograph (RP) LDPC codes, i.e., the regular RP code, the improved RP1 (IRP1) code, and the IRP2 code. The convergence analysis, error-performance analysis, and simulated results show that the three proposed RP codes outperform the existing protograph LDPC codes and regular quasi-cyclic LDPC code. Furthermore, the IRP1 code and the IRP2 code are superior to the regular RP code and the regular root-LDPC code and exhibit outage-limit-approaching error performance. Consequently, these two proposed IRP codes appear to be better alternatives as compared to other error-correction codes for slowly-varying wireless communication systems.

This paper considers the problem of estimating multiple frequency hopping signals with unknown hopping pattern. By segmenting the received signals into overlapped measurements and leveraging the property that frequency content at each time instant is intrinsically parsimonious, a sparsity-inspired high-resolution time-frequency representation (TFR) is developed to achieve robust estimation. Inspired by the sparse Bayesian learning algorithm, the problem is formulated hierarchically to induce sparsity. In addition to the sparsity, the hopping pattern is exploited via temporal-aware clustering by exerting a dependent Dirichlet process prior over the latent parametric space. The estimation accuracy of the parameters can be greatly improved by this particular information-sharing scheme and sharp boundary of the hopping time estimation is manifested. Moreover, the proposed algorithm is further extended to multi-channel cases, where task-relation is utilized to obtain robust clustering of the latent parameters for better estimation performance. Since the problem is formulated in a full Bayesian framework, labor-intensive parameter tuning process can be avoided. Another superiority of the approach is that high-resolution instantaneous frequency estimation can be directly obtained without further refinement of the TFR. Results of numerical experiments show that the proposed algorithm can achieve superior performance particularly in low signal-to-noise ratio scenarios compared with other recently reported ones.

Compressive sensing (CS) based Inverse Synthetic Aperture Radar (ISAR) imaging exploits the sparsity of the target scene to achieve high resolution and effective denoising with limited measurements. This paper extends the CS based ISAR imaging to further include the continuity structure of the target scene within a Bayesian framework. A correlated prior is imposed to statistically encourage the continuity structures in both the cross-range and range domains of the target region and the Gibbs sampling strategy is used for Bayesian inference. Because the resulted method requires to recover the whole target scene at a time with heavy computational complexity, an approximate strategy is proposed to alleviate the computational burden. Experimental results demonstrate that the proposed algorithm can achieve substantial improvements in terms of preserving the weak scatterers and removing noise over other reported CS based ISAR imaging algorithms.

Motivated by the existing time-frequency peak filtering (TFPF) algorithm, herein a robust time-varying filtering (RTVF) algorithm is proposed for filtering and separating multicomponent frequency modulation (FM) signals. The performance of the TFPF based on windowed Wigner-Ville distribution is limited by the linear constraint on the waveform of the received signal. The proposed RTVF significantly improves the filtering performance with low complexity by applying a sinusoidal time-frequency distribution, which allows a sinusoidal constraint on the signal's waveform. The RTVF can successfully decompose a multicomponent signal into individual components based on an initial instantaneous frequency (IF) estimate of each component. Unlike existing time-varying filters, the RTVF is much less sensitive to the accuracy of the IF estimate, which can be gradually refined by performing an iterative RTVF procedure.

Transform domain communication system (TDCS) has been proposed to establish a communication link with a low probability of interception by synthesising an adaptive waveform containing energy only in the unused frequency bands. However, this communication system suffers from a low spectral efficiency. To improve its spectral efficiency, a unified modulation framework for a TDCS is proposed in this study to embrace the previously reported modulation schemes under one framework. The resulting spectral efficiency is higher compared to these previous schemes. Also, to combat the slow channel fading, a TDCS system using two transmit antennas and one receive antenna with the proposed modulation scheme is presented. Simulation results show that the multiple‐antenna system improves the performance dramatically compared to the single antenna system under the slow fading environment.

To support interference-free quasi-synchronous code-division multiple-access (QS-CDMA) communication with low spectral density profile in a cognitive radio (CR) network, it is desirable to design a set of CDMA spreading sequences with zero-correlation zone (ZCZ) property. However, traditional ZCZ sequences (which assume the availability of the entire spectral band) cannot be used because their orthogonality will be destroyed by the spectrum hole constraint in a CR channel. To date, analytical construction of ZCZ CR sequences remains open. Taking advantage of the Kronecker sequence property, a novel family of sequences (called "quasi-ZCZ" CR sequences) which displays zero cross-correlation and near-zero auto-correlation zone property under arbitrary spectrum hole constraint is presented in this paper. Furthermore, a novel algorithm is proposed to jointly optimize the peak-to-average power ratio (PAPR) and the periodic auto-correlations of the proposed quasi-ZCZ CR sequences. Simulations show that they give rise to single-user bit-error-rate performance in CR-CDMA systems which outperform traditional non-contiguous multicarrier CDMA and transform domain communication systems; they also lead to CR-CDMA systems which are more resilient than non-contiguous OFDM systems to spectrum sensing mismatch, due to the wideband spreading.

This letter addresses the recovery of hierarchical sparse signals in a Bayesian framework. Hierarchical sparse signals exhibit two levels of sparsity, i.e., block-sparsity among different blocks and internal sparsity within each individual block. As in sparse Bayesian learning, each component of the coefficient vector is firstly modeled as a Gaussian distributed variable with zero mean. To enforce the two-level hierarchical sparsity, the variance is further modeled by two classes of hidden variables controlling the block-sparsity and the internal sparsity, respectively. Finally, variational Bayesian inference is used to recover the coefficient vector from the noise corrupted data. Numerical simulation and experimental results show that the proposed method outperforms those recently reported recovery methods.

This paper presents a novel inverse synthetic aperture radar (ISAR) imaging method by exploiting the inherent continuity of the scatterers on the target scene to obtain enhanced target images within a Bayesian framework. A simplified radar system is utilized by transmitting the sparse probing frequency signal, where the ISAR imaging problem can be converted to deal with underdetermined linear inverse scattering. Following the Bayesian compressive sensing (BCS) theory, a hierarchical Bayesian prior is employed to model the scatterers in the range-Doppler plane. In contrast to the independent prior on each scatterer in the conventional BCS, a correlated prior is proposed to statistically encourage the continuity structure of the scatterers in the target region. To overcome the intractability of the posterior distribution, the Gibbs sampling strategy is used for Bayesian inference. The parameters of the signal model are inferred efficiently from samples obtained by the Gibbs sampler. Because the proposed method is a data-driven learning process, the tedious parameter tuning process required by the convex optimization-based approaches can be avoided. Both the synthetic and the experimental results demonstrate that the proposed algorithm can achieve substantial improvements in the scenarios of limited measurements and low signal-to-noise ratio compared with other reported algorithms for ISAR imaging problems.

For inverse synthetic aperture radar imagery, the inherent sparsity of the scatterers in the range-Doppler domain has been exploited to achieve a high-resolution range profile or Doppler spectrum. Prior to applying the sparse recovery technique, preprocessing procedures are performed for the minimization of the translational-motion-induced Doppler effects. Due to the imperfection of coarse motion compensation, the autofocus technique is further required to eliminate the residual phase errors. This paper considers the phase error correction problem in the context of the sparse signal recovery technique. In order to encode sparsity, a multitask Bayesian model is utilized to probabilistically formulate this problem in a hierarchical manner. In this novel method, a focused high-resolution radar image is obtained by estimating the sparse scattering coefficients and phase errors in individual and global stages, respectively, to statistically make use of the sparsity. The superiority of this algorithm is that the uncertainty information of the estimation can be properly incorporated to obtain enhanced estimation accuracy. Moreover, the proposed algorithm achieves guaranteed convergence and avoids a tedious parameter-tuning procedure. Experimental results based on synthetic and practical data have demonstrated that our method has a desirable denoising capability and can produce a relatively well-focused image of the target, particularly in low signal-to-noise ratio and high undersampling ratio scenarios, compared with other recently reported methods.

The estimation of the mixing matrix as well as the number of sources in blind source separation are two challenging problems. This paper proposes an effective estimation method to solve these two problems for underdetermined blind separation of overlapped sources in short-time Fourier transform (STFT) domain. Our study considers the blind estimation of the mixing matrix based on subspace projection as well as clustering methods, and the number of sources can be therefore estimated by counting the columns of the estimated mixing matrix. The proposed estimation method is noise-robust and suitable for the sources whose spectral contents are highly overlapped in STFT domain. Numerical results on speech sources are presented to illustrate the effectiveness and robustness of the proposed method.

The detection and estimation of harmonic sinusoidal signals with multiple unknown fundamental frequencies are of great importance in many applications. In this paper, a cascaded sparse processing method is proposed for joint recovery and order estimation of harmonic sinusoidal signals. The cascaded sparse processing is performed by the following two steps. Firstly, group Lasso method is applied to estimate and recover the fundamental frequencies based on the characteristics of the block-sparsity of the harmonics. Then, Lasso estimator is used for each block corresponding to its fundamental frequency for further noise suppression. The theoretical conditions under which the proposed method can give a correct estimate of the signal support is derived under the Fourier basis. Simulation results of the proposed method are given to show the desirable performance.

In this paper, the access strategy for spectrum-sharing based two-tier networks is investigated. By exploring the motivations of the home base station (HBS) and the macrocell user (MU), we propose a Stackelberg game based approach, which enables them to improve their performances by establishing direct links. The proposed approach copes with the distributed nature of the user-deployed small cell networks, and requires no inter-cell coordinations. Experimental results show that the proposed approach can guarantee the capacity gain of the small cells, while improving the energy efficiency of the macrocell users. Furthermore, by adjusting the objective function, the benefits of open access can be balanced between the capacity gain of small cells and the energy efficiency improvement of the MUs. Therefore it can be applied flexibly for various design purposes.

Transform domain communication system (TDCS), as an overlay cognitive radio communication system, has been proposed to obtain a low probability of interception by using spectrum bin nulling to synthesise an adaptive waveform corresponding to the spectrum sensing output. However, its low spectral efficiency limits potential practical applications. In this study, an efficient modulation scheme, namely quadrature cyclic code shift keying (Q‐CCSK), is proposed for TDCSs by generating another fundamental modulation waveform as the data‐bearing quadrature branch. Although using Q‐CCSK doubles the spectral efficiency for TDCSs, the instinct inter‐branch interference arises from the added quadrature branch. Through the orthogonality analysis, it is proven that the two branches (in‐phase and quadrature‐ branches) are still satisfied the property of quasi‐orthogonality. Moreover, the performances of TDCSs employing Q‐CCSK in additive white Gaussian noise (AWGN) and multipath fading channels are discussed, respectively. Analytical and simulation results demonstrate that, compared with conventional schemes, the TDCS employing Q‐CCSK can double the spectral efficiency with comparable systematic performance.

This letter considers the multiplicative perturbation problem in compressive sensing, which has become an increasingly important issue on obtaining robust performance for practical applications. The problem is formulated in a probabilistic model and an auto-calibration sparse Bayesian learning algorithm is proposed. In this algorithm, signal and perturbation are iteratively estimated to achieve sparsity by leveraging a variational Bayesian expectation maximization technique. Results from numerical experiments have demonstrated that the proposed algorithm has achieved improvements on the accuracy of signal reconstruction.

For overlay cognitive radio networks (CRNs), transform domain communication system (TDCS) has been proposed to support multiuser communications through spectrum bin nulling and frequency domain spreading. In TDCS-based CRNs, each user is assigned a specific pseudorandom spreading sequence. However, the existence of multiuser interference (MUI) is one of main concerns, due to the non-zero cross-correlations between any pair of TDCS signals. In this paper, a novel framework of TDCS-based CRNs with the joint design of sequences and modulation schemes is presented to realize MUI avoidance. With the uncertainty of spectrum sensing results in CRNs, we first introduce a unique sequence design through two-dimensional time-frequency synthesis and obtain a class of almost perfect sequences whose periodic auto-correlation and cross-correlations are identically zero for most circular shifts. These correlation properties are further exploited in conjunction with a specially-designed cyclic code shift keying in order to achieve the advantage of MUI avoidance. Numerical results demonstrate that the proposed TDCS-based CRNs are well suited for decentralized networks against the near-far problem.

This study presents a cluster-based transform domain communication system (TDCS) to improve spectrum efficiency. Unlike the utilities of clusters in orthogonal frequency division multiplex systems, the cluster-based TDCS framework divides entire unoccupied spectrum bins into L clusters, where each one represents a data stream independently, to achieve L times of spectrum efficiency compared to that of the traditional one. Among various schemes of spectrum bin spacing and allocation, the TDCS with random allocation scheme appears to be an ideal candidate to significantly improve spectrum efficiency without seriously degrading power efficiency. In multipath fading channel, the coded TDCS with random allocation scheme achieves robust bit error rate (BER) performance owing to a large degree of frequency diversity. Furthermore, this study shows that the smaller spectrum bin spacing should be configured for the cluster-based TDCS to achieve higher spectrum efficiency and more robust BER performance.

This paper studies spatial spectrum sharing (SSS) based multi-user cognitive radio (CR) networks that allow secondary users (SU) to access the licensed spectrum as long as the interference powers of primary users (PU) to be lower than a certain threshold. Although recent results have shown that multi-hop relaying has a great potential on improving the performance of CR networks, finding effective methods to control and manage SUs to achieve the optimal performance is still a challenging problem. In this paper, we model CR networks as a non-cooperative game in which each SU obtains benefits through both spectrum sharing by paying prices to PUs and multi-hop relaying by paying price to nearby SUs. Optimal power allocation methods for SUs are investigated under different assumptions and pricing functions. The conditions under which the optimal Nash Equilibrium (NE) is obtained when all SUs use multi-hop relaying are discussed. Our results are extended into large multi-user CR networks with K source-to-destination pairs. Two distributed algorithms are proposed. The first one is a sub-gradient based power allocation algorithm in which SUs can iteratively adjust their transmit powers to approach the payoff of a NE. The other one is a Q-learning based relay selection algorithm which enables each SU to iteratively search for a NE-achieving relaying scheme.

This paper studies the power control problem for spectrum sharing based cognitive radio (CR) networks with multiple secondary source-to-destination (SD) pairs. A simple distributed algorithm is proposed for the secondary users (SUs) to iteratively adjust their transmit powers to improve the performance of the network. The proposed algorithm does not require each SU (or PU) to negotiate with other SUs (or PUs) during the communication. It is proved that the proposed algorithm can obtain a time average performance as good as that achieved when the Nash equilibrium (NE) is chosen in hindsight. More specifically, the average performance of CR networks will converge to an ε-Nash equilibrium at a rate of Tε= O (exp (1/ε)). A sub-optimal algorithm is also introduced to further improve the convergence rate to Tε'/log Tε'= O (1/ε'). Numerical results are presented to show the performance of the proposed algorithms under different settings.

This paper studies the uncertainty principle of the second-order local polynomial Fourier transform (LPFT). It shows that the uncertainty product of the LPFT is time-independent when the Gaussian window is used to segment the signal. Meanwhile when the extra parameter is estimated correctly, the uncertainty product of the LPFT becomes a constant. Compared to the short-time Fourier transform and the Wigner-Ville distribution, it shows that the LPFT provides a better resolution of signal presentation in the time-frequency domain. Simulation for a speech signal is also given to confirm that the LPFT is capable of revealing more spectrum details when the frequency contents change dramatically.

This paper studies the effects of cross-terms in the local polynomial periodograms (LPP) by defining and examining the cross local polynomial periodogram (CLPP) and the time-frequency correlative coefficients (TFCC). Our observations show that the cross-terms of signal components can be ignored if they do not intersect and the window length used in the LPP is sufficient. In addition, the TFCC is useful for the analysis of time-frequency coherency between LFM signals and gives us a parametric measure on the amount of the cross-terms in the LPP.

Abstract A new algorithm of adaptive subcarrier allocation and bit loading (A‐SABL) is proposed for simultaneous voice and data transmission in multiuser OFDM systems. The algorithm takes advantage of the frequency diversity and the voice/data transmission requirements to dynamically assign the number of subcarriers and bits/per symbol on each subcarrier for each user in a single cell. Due to the strict delay requirement of voice service, the subcarriers with low channel gains are assigned for voice transmission with a small number of bits per symbol to guarantee its required bit‐error‐rate (BER) and transmission rate. Based on the remaining subcarriers with high channel gains and the transmission power, the throughput of data transmission is then maximized by loading as many bits as possible on each subcarrier to achieve the required transmission bit rate and BER. Theoretical analysis and simulation on the proposed algorithm show that a better performance is obtained than previously reported schemes. Copyright © 2008 John Wiley & Sons, Ltd.

This letter presents a fast algorithm for the sequency-ordered complex Hadamard transform (SCHT) based on the decomposition method of decimation-in-sequency. To support high-speed real-time applications, a pipelined hardware structure is also proposed to deal with sequentially presented input/output data streams. This structure achieves a full hardware utilization and requires only complex adder/subtracters and complex data stores for an N-point SCHT.

This paper presents efficient algorithms for the analysis of non-stationary multi-component signals based on modified local polynomial time frequency transform. The signals to be analyzed are divided into a number of segments and the desired parameters are estimated in each segment for computing modified local polynomial time frequency transform. Compared to other reported algorithms, the length of overlap between consecutive segments is reduced to minimize the overall computational complexity. The concept of adaptive window lengths is also employed to achieve a better time-frequency resolution for each component.

This letter derives a computationally efficient sequential Monte Carlo solution for blind detection of direct-sequence code-division multiple-access systems over multipath fading channels by decomposing the observed data into a number of signal components. Then the parameters of each component can be estimated by the sequential importance sampling and Kalman filtering. In comparison with other similar receivers, simulation results demonstrate that the proposed solution achieves the desirable performance with a significantly reduced computational complexity

This paper presents the application of sequential Monte Carlo (SMC) methodology for blind detection in wireless DS-CDMA systems over fading channels. A novel blind Cholesky-SMC receiver based on the techniques of Cholesky factorization and sequential importance sampling is developed for differentially encoded DS-CDMA systems. With simulated results, the promising performance of the proposed receiver is demonstrated for the both the systems over the flat fading channels and frequency-selective fading channels.

Group-blind multiuser detectors for uplink code-division multiple-access (CDMA) were recently developed by Wang and Host-Madsen. These detectors make use of the spreading sequences of known users to construct a group constraint to suppress the intracell interference. However, such techniques demand the estimation of the multipath channels and the delays of the known users. In this paper, several improved blind linear detectors are developed for CDMA in fading multipath channels. The proposed detectors utilize the correlation information between consecutively received signals to generate the corresponding group constraint. It is shown that by incorporating this group constraint, the proposed detectors can provide different performance gains in both uplink and downlink environments. Compared with the previously reported group-blind detectors, our new methods only need to estimate the multipath channel of the desired user and do not require the channel estimation of other users. Simulation results demonstrate that the proposed detectors outperform the conventional blind linear multiuser detectors.

With the known knowledge of the instantaneous channel gains in the uplink of multiuser OFDM/CDMA systems, adaptive bit loading algorithms are proposed to minimize the interference from an individual user. The performance of the proposed algorithm is studied in a multiuser frequency selective fading environment in terms of bit error rate, system capacity and capability of supporting high data rates. The results show that the proposed algorithm outperforms the previously reported algorithms.

This paper proposes a blind channel estimation scheme for long code DS-CDMA systems with multipath fading channel. The Toeplitz displacement method is used to remove the effects of channel noise and interferences before the correlation matching approach is adopted to estimate the channel parameters. Simulation results show that the proposed method has better MSE performance and more robust against the near-far problem.

This paper presents a new algorithm of blind adaptive space-time multiuser detection for synchronous CDMA systems with antenna arrays. In contrast to previously reported spatial diversity detectors which use the decorrelating or minimum mean square (MMSE) detector for each receiving antenna, our algorithms employ the known signature waveform to estimate the combining vector for the desired user. Therefore, we only need to resolve the decorrelating detector or MMSE detector once by combining the array outputs with estimated combining vector. The new algorithm can provide the same performance improvement as that offered by the conventional spatial diversity multiuser detectors with significant savings on computational complexity

An analytic method is used to extend the sound impulse response of a room. It is based on the extrapolation theory for band-limited signals. Only two matrix operations are needed for extending a discrete impulse response. Due to the approximation of the geometrical acoustic model of the observed data and the computation errors, the problem may be ill-conditioned. The optimum regularization method is used to solve the ill-posed problem. For discrete signals, the extrapolation is not unique, therefore additional constraints are used to obtain the admissible result. The method is evaluated with a set of psychoacoustic experiments. The evaluations are made on five psychological characteristics, and a general conclusion is given based on general fuzzy clustering.

A general method is proposed to factor a discrete W transform (DWT) into lifting steps and additions. Then, based on the relationships among various types of discrete sinusoidal transforms, other types of transforms such as the discrete Fourier transform (DFT) and discrete cosine transform (DCT) are factored into lifting steps and additions. After approximating the lifting matrices, we get various types of new integer discrete transforms such as IntDWT, IntDFT and IntDCT which are floating-point multiplication free. Transforms which map integer to integer are also proposed. Fast algorithms are given for the new transforms and their computational complexities are analyzed. Based on a polynomial transform and an index mapping, multi-dimensional integer transforms are presented with especially low computational complexity.

The harmonic transform is designed for harmonic signals, which are composed of a base tone and some harmonics (e.g., voiced speech). As a generalization of the Fourier transform, the harmonic transform represents signals by the sum of a base tone and some harmonics, which may give more concise results for harmonic signals than the Fourier transform. Some experiments of speech signals are used to demonstrate the advantages of the harmonic transform on harmonic signal processing.

An efficient blind adaptive multiuser detector based on the modified RLS algorithm is proposed for synchronous DS-CDMA systems over a flat fading channel with large spreading sequences. We first properly decompose the optimal weight vector associated with the original code of the desired user into several adaptive weight subvectors. A modified adaptive algorithm based on the conventional RLS algorithm is derived to update the weight subvectors. Simulation results show that the proposed detector achieves better performance than the adaptive detector using conventional RLS algorithm especially for DS-CDMA systems with large processing gains. In addition, it is computationally efficient and robust against the near-far problem.

Polynomial algorithms for multidimensional discrete Hartley transform (MD-DHT) are proposed. Based on the multidimensional polynomial Transform, the MD-DHT is converted into a series of one-dimensional type-II discrete W transforms (DWT). The algorithms are clearly described and detailed analysis of the computational complexity is also presented, The proposed algorithm achieves considerable savings on the number of operations. The number of multiplications for computing an r-dimensional DHT is only 1/r times that needed by the row-column method. The number of additions is also reduced considerably.

A novel adaptive harmonic fractional Fourier transform is proposed for analysis of voiced speech signals. It provides a higher concentration than STFT and avoids the cross interference components produced by the Wigner-Ville distribution and other bilinear representation. The proposed method rotates the base tone and harmonics in time-frequency domain. After the rotation, base tone and harmonics become parallel to the time axis in time-frequency domain so that a high concentration can be achieved.

We propose an instantaneous amplitude (IA) based model for speech signal representation. This can avoid the difficulty in dealing with the time-varying phases and allows us to perform an optimization procedure easily such that the synthetic signal can be made as close to the original one as possible. A simplified frequency picking algorithm is derived to shorten the processing time while still maintaining the quality of the synthetic speech. Experiments show that the synthetic speech with the developed technique is of toll quality and almost perceptually indistinguishable from the original speech. Initial work on the coding of the parameters, for a 16 kHz sampled speech, for the IA model is done and a toll quality synthesized speech at a bit rate of 40 kbps is achieved.

This paper studies the performance of antenna diversity reception with selection combining (SC) and maximal ratio combining (MRC) in a correlated Rayleigh fading environment. Simple PDF expressions are derived for the output SNR of the SC and MRC diversity receivers. Based on the PDF, the average BERs for DPSK and NCFSK modulation are calculated to show the effects of the correlation. Moreover, the relationship between the average BER and the diversity antennas' separation is given. The presented numerical results show that SC and MRC diversity reception can achieve a good performance only if the distance between two diversity antennas is larger than 0.3/spl lambda/.

The system capacity determined by the outage probability of a multi-beam LEO system with CDMA and FDMA/TDMA is analyzed. In the case of CDMA, all possible multiple access interference is taken into account by a comprehensive interference analysis model including the effects of channel fading and shadowing, power control, practical spot beam antenna gains and imperfect equalization of the antenna pattern across a cell region. The results indicate that in LEO systems the CDMA capacity is significantly reduced because of the power control imperfections and the fact that multiple access interference is much more severe than that in terrestrial systems. A comparison with FDMA/TDMA shows that the capacity of an FDMA/TDMA system is comparable to a CDMA one for the LEO satellite systems.

In this paper, we consider maximum likelihood estimation of multipath channel parameters in asynchronous direct-sequence code-division multiple access communication systems. The proposed algorithm is based on the training sequence which is transmitted by the desired user. By modeling the interfering signals as unknown colored Gaussian noise, the multiuser estimation problem is decomposed into a series of single user problems. Simulation results show that the proposed estimator is efficient and robust against the near-far problem and channel fading.

The fractal dimension has been studied as a feature for texture analysis. It has been found that the fractal dimension is not an effective image texture measure but little is known about the reasons for the fractal dimension failing to be effective for texture analysis. This paper investigates into the underlying causes why the fractal dimension is not an effective image texture feature. Four mathematical properties have been identified which are responsible for the fractal dimension's ineffectiveness. The experimental results show that while the fractal dimension itself is hardly an effective feature for texture classification, it can considerably enhance other feature sets.

A novel adaptive harmonic fractional Fourier transform is proposed for analysis of voiced speech signals. It provides a higher concentration than the short time Fourier transform (STFT) and avoids the cross interference components produced by the Wigner-Ville distribution and other bilinear representations. The proposed method rotates the base tone and harmonics in time-frequency domain. After the rotation, base tone and harmonics become in parallel to the time axis in time-frequency domain so that a high concentration can be achieved.

Bit error probability of a CDMA-based multispot beam LEO system with imperfect power control over Rice-lognormal channels is calculated in this paper. The power control error is assumed to be a lognormal random variable. In the model, the multiple access interference due to all users seen by the serving satellite of the user-of-interest is taken into account, which is more realistic and differs from other reported work (Monk and Milstein 1995; Vojcic et al., 1994) in which only part of all possible interference was considered. The numerical results show that the power control error has a significant effect on the system performance.

An analysis of the delay requirements for rational sampling rate conversion systems is presented. Two transformation rules are derived to minimize the total number of delay units in the system. Using the two rules, a parameter formalized three-dimensional structure with minimum delay requirements can be achieved. This structure is particularly suited to a time multiplexed implementation which allows fewer arithmetic operators and data stores to be built in hardware as compared with a direct implementation of the polyphase structure.>