Subspace Pursuit Algorithm Research Articles

On the conjugate gradient subspace pursuit algorithm

In this paper, a novel algorithm is proposed as the conjugate gradient subspace pursuit (CGSP). The main idea of CGSP is given to combine the subspace pursuit (SP) algorithm with the conjugate gradient method. Then, with mild assumption, the recovery guarantee condition is established, which implied that the algorithm can converge to an exact sparse solution after a finite number of iterations. Finally, the numerical simulation of CGSP is given. The simulation results show that the sparse signal satisfied the specific conditions can be recovered by CGSP with high probability and the high sampling rate, and CGSP has the best performance.

Long-Range Underwater Acoustic Channel Estimation

Long-range underwater acoustic communication (LR-UWAC) is an essential technique for applications such as the control of unmanned underwater vehicles, gliders, or tactical submarines for long-term monitoring tasks. While techniques for estimating the channel impulse response (CIR) of short-range UWAC have been successfully applied, this is not the case for LR-UWAC. Here, the main challenge is to handle the diverse channel structure, which can be of a sparse or a non-sparse structure. In this paper, we propose a robust channel estimator for LR-UWAC. Our solution includes a switching mechanism to classify the channel as either sparse or non-sparse. In its sparse form, the LR-UWAC channel is characterized by a long time delay spread, time-invariant characteristics, and a block structure. Thus, we propose a non-trivial combination of the block subspace pursuit and the distributed subspace pursuit algorithms to exploit the channel’s block structure. For non-sparse LR-UWAC channel structures, we approximate the received signal as Gaussian, and derive a maximum-likelihood (ML) estimator to separate the non-resolvable multipath. Extensive numerical simulation and results from two long-range sea experiments demonstrate the efficiency of our approach in identifying the channel’s structure, and to accurately estimate the channel compared to state-of-the-art benchmarks.

Doubly selective channel estimation and equalization based on ICI/ISI mitigation for OQAM-FBMC systems

Over a doubly selective channel, broadband transmission systems face challenges in channel estimation and equalization. High mobility causes inter-carrier interference (ICI), while multipath transmission induces inter-symbol interference (ISI). In this paper, we present a mitigation method of ICI/ISI for the offset quadrature amplitude-modulated filter bank multi-carrier (OQAM-FBMC) system. It features low inherent imaginary interference (IMI) sensitivity and high efficiency. Specifically, a pilot indices optimization algorithm and a sparse adaptive orthogonal subspace pursuit (SAOSP) algorithm are presented based on the 2-D channel modeling scheme. The guard pilots are first added to mitigate the effect of ICI. Then the index optimization and SAOSP algorithms are applied to achieve a high-accuracy estimation of sparse channel coefficients. In addition, a threshold judgment suboptimal minimum mean square error (MMSE) equalization method is presented based on the variability of the interference power. The method uses normalized interference power thresholds to estimate the ISI dimension and reduce the equalization data, thus mitigating the effect of ISI and achieving efficient equalization. To verify the above methods, single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) models are built. Simulation results indicate a 3-5 dB improvement in channel estimation accuracy. The suboptimal MMSE equalization results are close to the optimal MMSE with about four orders of magnitude reduction in complexity.

Temporal Correlation Enhanced Multiuser Detection for Uplink Grant-Free NOMA

Compressed sensing has been identified as a good candidate for user detection in grant-free non-orthogonal multiple access (NOMA) by exploiting the inherent sparsity of user activity. However, most of the existing works do not fully utilize the temporal correlation in NOMA and rely heavily on the unrealistic assumption that the number of active users is known in advance. To address these issues, we propose a temporal correlation enhanced multiuser detection scheme to achieve efficient and practical multiuser detection. Firstly, using 1 bit memory to piggyback the information whether the active users still have data to transmit, the base station can realize whether the active users in current time slot will turn to be silent or remain active. Then, to make explicit use of the temporal correlation of active user sets, a cross validation based adaptive subspace pursuit (CVASP) algorithm, is developed by utilizing the reported information on prior active users. The proposed CVASP is a highly practical algorithm that does not require any prior knowledge of the user sparsity level, as the cross validation technique could properly determine the stopping condition. Extensive simulation results demonstrate that the proposed mechanism could achieve a superier performance without requiring any prior knowledge.

Target parameter estimation for OTFS radar using sparse signal processing

In this paper, we consider a monostatic radar receiver for a joint communication and radar (JCR) system that transmits orthogonal time frequency space (OTFS) frames for target detection and parameter estimation. The circular prolate pulse shape (CPPS) is employed over the OTFS signal as it has lower out-of-band (OoB) power radiation in comparison with the rectangular pulse shaped (RPS) OTFS. The PAPR of CPPS OTFS signal shows lowest value for larger frame duration and hence the signal can be considered to be a good candidate for JCR system. In the Delay-Doppler (DD) domain, the radar channel is sparse and therefore, we model the target detection problem as a sparse recovery problem to generate target profiles with higher peak-to-sidelobe ratio (PSLR). The target detection is carried out in the DD domain, the time–frequency (TF) domain, and in the time domain (TD). Sparse signal recovery algorithms like the orthogonal matching pursuit (OMP) algorithm, the subspace pursuit (SP) algorithm, and the sparse Bayesian learning (SBL) based algorithm are used in target parameter estimation. The performance of these algorithms are compared in terms of their computational complexity, the root mean squared error (RMSE) in the estimates of range and velocity and PSLR value in the target profiles. Simulation results validate that the proposed CPPS OTFS based radar system could detect the targets accurately in all the three domains and produce target profiles with almost zero side lobes.

Second-Order Statistics-Aided Channel Estimation for Multipath Massive MIMO-OFDM Systems

This paper develops an efficient channel estimation algorithm based on second-order statistics of time division duplex (TDD) multiuser massive multiple-input multiple-output (MIMO) systems. The algorithm uses the received signal correlation to determine the most significant lags (MSLs) of the received signal. We first employ these MSLs to propose a novel set containing the channel’s four most significant taps (MSTs). Then, by using them, we propose an efficient semi-blind iterative algorithm called enhanced modified-subspace pursuit (EM-SP). It uses the set mentioned above and two theoretical results ( <xref ref-type="lemma" rid="lemma1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lemma 1</xref> and <xref ref-type="theorem" rid="theorem1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Theorem 1</xref> ) to estimate an arbitrary number of MSTs efficiently. Simulation results show that the normalized mean square error (NMSE) of the proposed EM-SP algorithm is much smaller than that of the subspace pursuit (SP) and orthogonal matching pursuit (OMP) algorithms at the cost of 0.3 % and 2 % more computational complexity for the channels with three and six nonzero paths, respectively. Moreover, the NMSE of it is very close to that of the optimal genie-aided least square algorithm.

Algorithms for Estimating Time-Locked Neural Response Components in Cortical Processing of Continuous Speech.

The Temporal Response Function (TRF) is a linear model of neural activity time-locked to continuous stimuli, including continuous speech. TRFs based on speech envelopes typically have distinct components that have provided remarkable insights into the cortical processing of speech. However, current methods may lead to less than reliable estimates of single-subject TRF components. Here, we compare two established methods, in TRF component estimation, and also propose novel algorithms that utilize prior knowledge of these components, bypassing the full TRF estimation. We compared two established algorithms, ridge and boosting, and two novel algorithms based on Subspace Pursuit (SP) and Expectation Maximization (EM), which directly estimate TRF components given plausible assumptions regarding component characteristics. Single-channel, multi-channel, and source-localized TRFs were fit on simulations and real magnetoencephalographic data. Performance metrics included model fit and component estimation accuracy. Boosting and ridge have comparable performance in component estimation. The novel algorithms outperformed the others in simulations, but not on real data, possibly due to the plausible assumptions not actually being met. Ridge had slightly better model fits on real data compared to boosting, but also more spurious TRF activity. Results indicate that both smooth (ridge) and sparse (boosting) algorithms perform comparably at TRF component estimation. The SP and EM algorithms may be accurate, but rely on assumptions of component characteristics. This systematic comparison establishes the suitability of widely used and novel algorithms for estimating robust TRF components, which is essential for improved subject-specific investigations into the cortical processing of speech.

Novel algorithm for flexible multibody systems with hybrid uncertainties

In this paper, a sparse polynomial chaos-Legendre metamodel based on compressed sensing is proposed to quantify the hybrid uncertainties in flexible multibody systems. Based on the fully parameterized beam elements of absolute nodal coordinate formulation, the differential-algebraic equations of the multibody system with hybrid uncertain parameters are established firstly. Secondly, the dynamical response of the multibody system can be expanded by using the polynomial chaos-Legendre metamodel, and the matrix form of dynamical response can be transformed into vector form by Kronecker product. Then, the coefficients of the polynomial are sparsely reconstructed by using the subspace pursuit algorithm. Finally, the effectiveness of sparse polynomial chaos-Legendre metamodel based on compressed sensing is verified through numerical examples. Especially, compared with the traditional methods, the sampling size of the proposed method is less than the number of degrees of freedom of unknown coefficients in the polynomial surrogate model. Therefore, the proposed sparse polynomial chaos-Legendre metamodel based on compressed sensing can effectively alleviate the “curse of dimensionality”.

A novel method for identification of synchronous resonance frequency of blades based on random arrangement of tip-timing probes

Blade tip-timing (BTT) signal suffers from the undersampling feature, which causes the high-frequency information to be aliased to the low-frequency band, especially the aliasing problem of the synchronous resonance frequency more serious. In order to realize the frequency identification of undersampled signals in synchronous resonance, a novel multiscale cyclic-reverse optimized arrangement (MC-ROA) method based on the random arrangement of tip-timing probes is proposed in this paper. Firstly, a sparse model for frequency recovery is built based on the link between the known undersampled signals and the unknown original signals in the frequency domain, and the subspace pursuit (SP) algorithm of compressive sensing (CS) is used for frequency recovery. Then, under the random arrangement of probes, the number of ideal probes is adjusted at multiple scales and the datum probes are selected cyclically to obtain multiple sets of solutions. Finally, the target frequency weights are used to overcome the limitations of the restricted isometry property (RIP) of the parameterized compression matrix to determine the optimal recovery frequency. The BTT experiments are given to verify the effectiveness of the proposed method.

Characteristics analysis of blade tip timing signals in synchronous resonance and frequency recovery based on subspace pursuit algorithm

Long-term high cycle fatigue vibration will lead to the reduction of life of the blade. Blade Tip Timing (BTT) technology is a research hotspot in the non-contact measurement of blades. Due to the limitation of the number of sensors, BTT signals present serious undersampled conditions. Identifying the frequency of blade vibration through the analysis of undersampled signals is the key problem of the current BTT technology. A sub-Nyquist technique, called multi-coset sampling (MCS), which is suitable for the BTT sampling model can be applied. In this paper, the characteristics of BTT signals under blade synchronous resonance are described and the deficiency of this feature in the recovery process using the orthogonal matching pursuit (OMP) algorithm is found. Based on the problem, the subspace pursuit (SP) algorithm adapted to this feature is proposed. The validity of the algorithm is verified by the blade rotation experiment. The advantage of this algorithm is that the synchronous resonance frequency of the blades can be recovered with a higher probability, which provides a new idea for the development of BTT technology.

Computing One-Bit Compressive Sensing via Double-Sparsity Constrained Optimization

One-bit compressive sensing gains its popularity in signal processing and communications due to its low storage costs and low hardware complexity. However, it has been a challenging task to recover the signal only by exploiting the one-bit (the sign) information. In this paper, we appropriately formulate the one-bit compressive sensing into a double-sparsity constrained optimization problem. The first-order optimality conditions for this nonconvex and discontinuous problem are established via the newly introduced <inline-formula><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula>-stationarity, based on which, a gradient projection subspace pursuit (GPSP) algorithm is developed. It is proven that GPSP can converge globally and terminate within finite steps. Numerical experiments have demonstrated its excellent performance in terms of a high order of accuracy with a high computational speed.

Compressive hard thresholding pursuit algorithm for sparse signal recovery

&lt;abstract&gt;&lt;p&gt;Hard Thresholding Pursuit (HTP) is one of the important and efficient algorithms for reconstructing sparse signals. Unfortunately, the hard thresholding operator is independent of the objective function and hence leads to numerical oscillation in the course of iterations. To alleviate this drawback, the hard thresholding operator should be applied to a compressible vector. Motivated by this idea, we propose a new algorithm called Compressive Hard Thresholding Pursuit (CHTP) by introducing a compressive step first to the standard HTP. Convergence analysis and stability of CHTP are established in terms of the restricted isometry property of a sensing matrix. Numerical experiments show that CHTP is competitive with other mainstream algorithms such as the HTP, Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP) algorithms both in the sparse signal reconstruction ability and average recovery runtime.&lt;/p&gt;&lt;/abstract&gt;

Joint User Activity Identification and Channel Estimation for Grant-Free NOMA: A Spatial–Temporal Structure-Enhanced Approach

Exploiting the sparse nature of user activity, compressed sensing (CS) has been a powerful technique to realize efficient user detection in grant-free nonorthogonal multiple access (NOMA). However, most of the existing CS-based multiuser detection schemes merely independently incorporate the temporal correlation in frame-based transmission or spatial correlation induced by multiantenna reception, leading to unsatisfactory user detection performance. Driven by the observation in the CS theory that the signal recovery performance could be enhanced by an increased number of sparse vectors with a common support set, in this article, we propose a novel joint user activity identification and channel estimation (JUICE) framework by integrating the temporal correlation of active user sets with multiantenna reception, which could achieve superior user detection performance. Specifically, we first formulate the JUICE as a Kronecker CS (KCS) problem to model the CS measurement process, by fully extracting the spatial-temporal structure of user activity. Then, based on the mined spatial-temporal structure of user activity, an adaptive subspace pursuit algorithm is developed, i.e., spatial-temporal structure enhanced adaptive subspace pursuit (STS-ASP), which could realize efficient multiuser detection. A distinct advantage of the proposed algorithm is that it does not require any prior knowledge (e.g., the number of active users and the noise level), by adaptively acquiring the number of active users and employing the cross-validation technique to appropriately terminate the iterative procedures. Extensive experimental evaluation is conducted, and the results corroborate the superiority of the proposed framework compared with the existing CS-based multiuser detection methods.

Compressive Sensing Based Massive Access for IoT Relying on Media Modulation Aided Machine Type Communications

A fundamental challenge of the large-scale Internet-of-Things lies in how to support massive machine-type communications (mMTC). This letter proposes a media modulation based mMTC solution for increasing the throughput, where a massive multi-input multi-output based base station (BS) is used for enhancing the detection performance. For such a mMTC scenario, the reliable active device detection and data decoding pose a serious challenge. By leveraging the sparsity of the uplink access signals of mMTC received at the BS, a compressive sensing based massive access solution is proposed for tackling this challenge. Specifically, we propose a structured orthogonal matching pursuit algorithm for detecting the active devices, whereby the block-sparsity of the uplink access signals exhibited across the successive time slots and the structured sparsity of media-modulated symbols are exploited for enhancing the detection performance. Moreover, a successive interference cancellation based structured subspace pursuit algorithm is conceived for data demodulation of the active devices, whereby the structured sparsity of media modulation based symbols found in each time slot is exploited for improving the detection performance. Finally, our simulation results verify the superiority of the proposed scheme over state-of-the-art solutions.

Millimeter Wave Massive MIMO Channel Estimation Using Subspace Pursuit Greedy Algorithm

Achieving high data rate communications and increasing system reliability are the essentials for 5G networks. Massive MIMO and millimeter wave (mmWave) communications along with the ongoing developments in the underlying infrastructure promise to sharply increase the aggregate capacity. The communication system harnessing the odds of the unused spectrum in mmWave bands is vulnerable to the extreme path loss that severely weakens the strength of the information-bearing signal. Nevertheless, exploiting hybrid beamforming and efficient high-speed channel estimation algorithm can help address this problem and create the communication systems required for 5G. Our main contribution in this paper is to propose a very high speed accurate greedy algorithm called Subspace Pursuit (SP) and we also compare the performance of this algorithm with two other greedy algorithms. Simulation results show that SP algorithm achieves a noticeable improvement in comparison with Orthogonal Matching Pursuit (OMP) and Regularized Orthogonal Matching Pursuit (ROMP) algorithms in terms of both the spectral efficiency and runtime.

De-noising low-frequency magnetotelluric data using mathematical morphology filtering and sparse representation

De-noising the magnetotelluric (MT) data using the conventional time-series editing methods is at the risk of losing low-frequency signals, especially the signal below 1 Hz. To overcome this deficiency, we propose a combinatorial method based on sparse representation and mathematical morphology filtering. First, the effective low-frequency signal is reconstructed using the mathematical morphological filtering (MMF) method and protected. Then, the residual noisy signal of high frequency is sparsely decomposed using the subspace pursuit (SP) algorithm to obtain noise-free high-frequency MT signals. Finally, the effective low-frequency signal is added to the de-noised high-frequency signal to get the full-band MT data. We evaluate the proposed method using a synthetic data set and two real data sets collected in Qiadam Basin, the northeastern part of the Tibetan Plateau. Experimental results demonstrate that the presented approach can be used to remove different kinds of cultural noises while preserve the low-frequency signal below 1 Hz. The evaluation results also indicate that the proposed method is superior to the conventional methods in terms of the signal-to-noise ratio (SNR), reconstruction error (E) and normalized cross-correlation (NCC).

A High-Throughput Subspace Pursuit Processor for ECG Recovery in Compressed Sensing Using Square-Root-Free MGS QR Decomposition

Sensor nodes in wireless body-area networks are expected to use compressed sensing (CS) for ultralow-power consumption. For signal recovery in CS systems, compared with the software implementation, the hardware processor has superiority on power, real-time ability, and so on. Although orthogonal matching pursuit (OMP) is conventionally selected in hardware implementations, its low recovery performance is still a problem. We propose to use the subspace pursuit (SP) algorithm that can achieve higher recovery performance with less iteration to implement the hardware processor. First, a new SP by a square-root-free method and a computation reuse scheme are proposed to reduce the SP’s complexity. Then, the fully paralleled architectures and elaborate pipelines are proposed to improve the processing throughput. Finally, we give an FPGA implementation prototype. Simulations compared with OMP show that the traditional SP can improve more than 8 dB on recovery performance or it can reduce more than 31% sampling paths in sensor nodes. These benefits are kept by our proposed SP because our improvement does not modify the algorithmic nature. Nevertheless, the significant complexity reduction is achieved by our proposal. The proposed SP processor can recover ECG signals with 28.2 dB and achieve the processing throughput of 44.4 K vectors/s.

On the joint design of compressed sensing and network coding for wireless communications

AbstractCompressed sensing and network coding techniques have seen a widespread interest in many disciplines during the last decade. Recently, a novel idea emerged for the combination of these areas in wireless communications to leverage the benefits from network coding while taking advantage of the correlations in the (sensory) data. The potential gains, such as lower latency for large‐scale sensing scenarios, reduced energy consumption, and a decrease in the amount of data during transmissions, are alluring to many use‐cases. However, a common issue one faces when joining both techniques is encountered in the fact that network coding is designed to operate over finite fields, whereas compressed sensing is mainly concerned with real numbers. This paper studies the impact of compressed sensing on network coding to enable one step decoding for the reconstruction of compressed data. We emphasize and discuss the design of the sensing and coding matrices, as well as the algorithms that enable accurate reconstructions. We employ the KL1p compressed sensing library and the NS3 simulator to evaluate this joint design. Our simulations show that using normalized coefficient matrices drawn from Gaussian distributions has higher efficiency and scalability including, but not limited to, multi‐hop networks, where the recoding feature of network coding can be exploited. Furthermore, the Subspace Pursuit algorithm outperforms the state‐of‐the‐art reconstruction algorithms, with respect to the reconstruction signal‐to‐noise ratio, by more than two folds compared to the other benchmark algorithms in cluster‐based Wireless Sensor Networks, where recoding using real network codes are involved.

On Recovery of Block Sparse Signals via Block Compressive Sampling Matching Pursuit

Compressive sampling matching pursuit (CoSaMP) is an efficient reconstruction algorithm for sparse signal. When the signal is block sparse, i.e., the non-zero elements are presented in clusters, some block sparse reconstruction algorithms have been proposed accordingly. In this paper, we present a new block algorithm based on CoSaMP, called block compressive sampling matching pursuit (BlockCoSaMP). Compared with CoSaMP algorithm, the proposed algorithm shows improved performance when sparse signal is presented in block form. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the performance of the CS algorithm, and Block restricted isometry property (Block RIP) is the extension of traditional RIP. Based on the Block RIP, we derive the sufficient condition to guarantee the convergence of Block-CoSaMP algorithm. In addition, the number of required iterations is obtained. Finally, simulation experiments show that with the increase of block length, the performance of Block-CoSaMP algorithm approaches to that of block subspace pursuit (Block-SP) algorithm. When the block length and sparsity are small, the performance of Block-CoSaMP algorithm is better than that of the CoSaMP, l 2 /l 1 norm and block orthogonal matching pursuit (BOMP) algorithms. Especially, when compared with CoSaMP and l 2 /l 1 norm algorithms, the proposed algorithm exhibits more obvious performance gain.

Compressed sensing for image reconstruction via back-off and rectification of greedy algorithm

Abstract Image reconstruction is an important research topic in the field of multimedia processing. It aims to represent a high-resolution image with highly compressed features that can be used to reconstruct the original image as well as possible, and has been widely used for image storage and transmission. Compressed Sensing (CS) is a commonly used approach for image reconstruction; however, CS currently lacks an efficient and accurate solving algorithm. To this end, we present an iterative greedy reconstruction algorithm for Compressed Sensing called back-off and rectification of greedy pursuit (BRGP). The most significant feature of the BRGP algorithm is that it uses a back-off and rectification mechanism to select the atoms and then obtains the final support set. Specifically, an intersection of support sets estimated by the Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP) algorithms is first set as the initial candidate support, and then a back-off and rectification mechanism is used to expand and rectify it. Experimental results show that the algorithm significantly outperforms conventional techniques for one-dimensional or two-dimensional compressible signals.