Subspace Pursuit Algorithm Research Articles

Joint Channel Estimation and Multiuser Detection for Uplink Grant-Free NOMA

Grant-free non-orthogonal multiple access is an emerging research topic in machine-type communications, which is used to reduce signaling overhead. In this context, this letter introduces a novel joint channel estimation (CE) and multiuser detection (MUD) framework for the frame based multi-user transmission scenario where users are (in)active for the duration of a frame. First, considering the inherent frame-wise joint sparsity of the pilot and data phases in the entire frame, we formulate the multiple measurement vector-compressive sensing (MMV-CS) framework. Then, transfer the MMV-CS to a block-sparse single measurement vector-CS (BS-SMV-CS) model. Finally, to make explicit use of the block sparsity inherent in the BS-SMV-CS model and consider that the user sparsity level should be unknown for receiver, an enhanced subspace pursuit (SP) algorithm is developed, i.e., block sparsity adaptive SP. Superior performance of the proposed joint CE and MUD framework is demonstrated by simulation results.

Compressive sensing-based vibration signal reconstruction using sparsity adaptive subspace pursuit

Wireless sensors produce large amounts of data in long-term online monitoring following the Shannon–Nyquist theorem, leading to a heavy burden on wireless communications and data storage. To address this problem, compressive sensing which allows wireless sensors to sample at a much lower rate than the Nyquist frequency has been considered. However, the lower rate sacrifices the integrity of the signal. Therefore, reconstruction from low-dimension measurement samples is necessary. Generally, the reconstruction needs the information of signal sparsity in advance, whereas it is usually unknown in practical applications. To address this issue, a sparsity adaptive subspace pursuit compressive sensing algorithm is deployed in this article. In order to balance the computational speed and estimation accuracy, a half-fold sparsity estimation method is proposed. To verify the effectiveness of this algorithm, several simulation tests were performed. First, the feasibility of subspace pursuit algorithm is verified using random sparse signals with five different sparsities. Second, the synthesized vibration signals for four different compression rates are reconstructed. The corresponding reconstruction correlation coefficient and root mean square error are demonstrated. The high correlation and low error result mean that the proposed algorithm can be applied in the vibration signal process. Third, implementation of the proposed approach for a practical vibration signal from an offshore structure is carried out. To reduce the effect of signal noise, the wavelet de-noising technique is used. Considering the randomness of the sampling, many reconstruction tests were carried out. Finally, to validate the reliability of the reconstructed signal, the structure modal parameters are calculated by the Eigensystem realization algorithm, and the result is only slightly different between original and reconstructed signal, which means that the proposed method can successfully save the modal information of vibration signals.

Downlink compressive channel estimation with support diagnosis in FDD massive MIMO

Downlink channel state information (CSI) is critical in a frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) system. We exploit the reciprocity between uplink and downlink channels in angular domain and diagnose the supports of downlink channel from the estimated uplink channel. While the basis mismatch effects will damage the sparsity level and the path angle deviations between uplink and downlink transmission paths will induce differences in channel supports, a downlink support diagnosis algorithm based on the DBSCAN (density-based spatial clustering of applications with noise) which is widely used in machine learning is presented. With the diagnosed supports of downlink channel in angular domain, a weighted subspace pursuit (SP) channel estimation algorithm for FDD massive MIMO is proposed. The restricted isometry property (RIP)-based performance analysis for the weighted SP algorithm is given out. Both the analysis and the simulation results show that the proposed downlink channel estimation with diagnosed supports is superior to the standard iteratively reweighted least squares (IRLS) and SP without channel priori or with the assumption of the common supports for uplink and downlink channels in angular domain.

Fluorescence Molecular Imaging and Tomography of Matrix Metalloproteinase-Activatable Near-Infrared Fluorescence Probe and Image-Guided Orthotopic Glioma Resection.

Malignant gliomas are major causes of cancer-related mortality and morbidity. Traditional surgery usually leads to incomplete resection of gliomas resulting in the high incidence of tumor recurrence. Advanced medical imaging technology, such as fluorescence imaging-guided surgery, combined with tumor-specific imaging probes allows the identification of tumor margins and improved surgery. However, there are two pressing issues that need to be addressed: first, few fluorescence imaging probes can specifically target gliomas; second, fluorescence molecular imaging (FMI) cannot get the in-depth information of deep-seated gliomas; both of which affect the complete removal of the gliomas. In this study, the biodistribution of smart matrix metalloproteinase (MMP) targeting near-infrared (NIR) fluorescent probe MMPSense 750 FAST (MMP-750) was examined in both U87MG-GFP-fLuc glioma xenograft and orthotopic mouse models using FMI. Then, CT and FMI images of orthotopic gliomas were acquired for the reconstruction of fluorescence molecular tomography (FMT) using a randomly enhanced adaptive subspace pursuit (REASP) algorithm. Furthermore, the resection of orthotopic glioma was performed using the fluorescence surgical navigation system after the injection of the MMP-750 probe. After surgery, bioluminescence imaging (BLI) and hematoxylin and eosin staining were carried out to confirm the precision resection of the tumor. FMI results showed that the MMP-750 probe can specifically target U87MG glioma in vivo. FMT presented the spatial information of the orthotopic glioma using the REASP reconstruction algorithm. Furthermore, MMP-750 could effectively delineate the tumor margin during glioma surgery leading to a complete resection of the tumors. The smart MMP-750 specifically targets the glioma and FMT of MMP-750 provides 3D information for the spatial localization of the glioma. MMP-750 can work as an ideal fluorescence probe for guiding the intraoperative surgical resection of the glioma, possessing clinical translation.

Priori-Information Hold Subspace Pursuit: A Compressive Sensing-Based Channel Estimation for Layer Modulated TDS-OFDM

Time-domain synchronous orthogonal frequency division multiplexing (TDS-OFDM) has been widely recognized as a fundamental OFDM block transmission scheme because of its advantages in spectral efficiency. However, it suffers from severe performance loss under strong frequency selective channels and thus has difficulty supporting high-order modulations such as 256QAM. In this paper, we proposed a compressive sensing (CS)-based channel estimation (CE) algorithm for layer modulated TDS-OFDM (LM-TDS-OFDM). In the proposed CE algorithm, the low-order modulated symbols will be recovered and then sent to a feedback loop for precise CE. The priori-information hold subspace pursuit algorithm is investigated to achieve accurate estimation of channel. Analyses and simulations show that the proposed algorithm can successfully obtain high-accuracy CE and significantly reduce the computational complexity. Based on the proposed CE scheme, LM-TDS-OFDM can well support 256QAM transmission under severe channel conditions.

Subspace Pursuit for Sparse Signal Reconstruction in Wireless Sensor Networks

Subspace pursuit (SP) algorithm provides the two most important features of greedy algorithms. It has lowest computational complexity in comparison to other greedy algorithms such as OMP and ROMP. It provides the reconstruction quality of same order as that of linear programming techniques for very sparse signals. SP algorithm estimates the sparse signal step by step, in an iterative fashion. The presented analysis shows that SP exactly recovers the sparse signals for temporally correlated data collected during real-time experimentation using NI WSN platform. The efficacy of recovered signal is analyzed using the parameters of peak signal to noise ratio and root mean square error.

Mobility-Aware Reconstruction Algorithm for Correlated Nonzero Neighborhood Structured Downlink Channel in Massive MIMO

This paper investigates downlink (DL) channel estimation of frequency division duplex (FDD) massive multiple-input-multiple-output (MIMO) with a finite number of base station (BS) antennas. Based on the performance analysis of DL channel in FDD, it is demonstrated that the interference effect cannot be ignored in the finite region. Also, excessive training overhead is required in conventional channel estimation methods when the number of BS antennas goes large. Therefore, it is necessary to design an algorithm for alleviating the interference in addition to the reduction of pilot overhead. In this paper, a general model is presented to exploit certain sparsity structure of massive MIMO channel in beam domain, which is called nonzero-neighborhood (NZN) structure. Considering the smooth variation of channel paths during two consecutive estimation intervals, a compressed sensing-based algorithm is proposed to efficiently estimate and track NZN-structured DL channel. The convergence behavior and computational complexity of the proposed mobility-aware subspace pursuit (MA-SP) algorithm are analyzed based on restricted isometric property. It is demonstrated that the application of proposed MA-SP algorithm efficiently reduces the required pilot length in channel estimation. Interference analysis shows that inter-cell interference is considerably alleviated in the proposed channel estimation phase without any prior information about interference. Simulation results demonstrate the effectiveness of the proposed MA-SP technique compared with the previous methods.

Efficient Multi-User Detection for Uplink Grant-Free NOMA: Prior-Information Aided Adaptive Compressive Sensing Perspective

Non-orthogonal multiple access (NOMA) is an emerging research topic in the future fifth generation wireless communication networks, which is expected to support massive connectivity for massive machine-type communications (mMTC). Due to the sporadic communication nature of mMTC, the grant-free transmission methodology is highly expected in uplink NOMA systems, to drastically reduce the transmission latency and signaling overhead. Exploiting the inherent sparsity nature of user activity, compressive sensing (CS) techniques have been applied for efficient multi-user detection in the uplink grant-free NOMA. In this paper, we propose a prior-information-aided adaptive subspace pursuit (PIA-ASP) algorithm to improve the multi-user detection performance. In this algorithm, a parameter evaluating the quality of the prior-information support set is introduced, in order to exploit the intrinsically temporal correlation of active user support sets in several continuous time slots adaptively. Then, to mitigate the incorrect estimation effect of the prior support quality information, a robust PIA-ASP algorithm is further proposed, which adaptively exploits the prior support based on the corresponding support quality information in a conservative way. It is noted that both of the two proposed algorithms do not require the knowledge of the user sparsity level, while most of the state-of-the-art CS-based multi-user detection algorithms usually need. Moreover, for the two proposed algorithms, the upper bound of the signal detection error and the computational complexity is derived. Simulation results demonstrate that the two proposed algorithms are capable of achieving much better performance than that of the existing CS-based multi-user detection algorithms with a similar computational complexity.

Jittered chirp sequence waveform in combination with CS‐based unambiguous Doppler processing for automotive frequency‐modulated continuous wave radar

The chirp sequence waveform is one of the most commonly used waveforms for automotive frequency-modulated continuous wave radars. When a chirp sequence waveform is applied, the range-Doppler processing method based on two-dimensional fast Fourier transform can be used to extract the range and velocity parameters of multiple targets from the beat signals. However, conventional chirp sequence waveforms suffer from the Doppler ambiguity problem, which results in ambiguities in velocity measurement. In this study, the authors propose a novel jittered chirp sequence waveform. In the proposed waveform, the initial times of the chirps are randomly jittered. According to the compressed sensing theory, they establish the parameter design principle for the new waveform, and apply sparse recovery method to achieve unambiguous Doppler processing. Subspace pursuit algorithm is recommended as the suitable sparse recovery method for Doppler processing due to its low complexity and stable recovery performance. The effectiveness of the proposed waveform and its corresponding signal processing method are verified by simulation and experimental results.

An improved stopping condition guarantee recovery of sparse signal via Subspace Pursuit method

The Subspace Pursuit (SP) algorithm is one of greedy pursuit methods which is used to reconstruct of K-sparse signal. Unlike existing condition produced by Dai and Milenkovic in 2004 that suggests the residual value of current iteration is reduced from the previous iteration, our approach eliminates useless information by reducing the number of iterations used to detect the correct support set. This operation is done by suggesting a new halting condition that can capture the best support set which can give the best representation of the reconstructed signal. The new halting conditions enhanced the SP algorithm to low computational complexity and reconstruction accuracy of the sparse signal.A mathematically proven for two halt condition: noiseless setting, and noisy setting for signal affected by Gaussian noise. An error bound relation also is driven.In this paper, we try also to relax the restricted isometry constant RIC value to narrows the gap between the known bounds and ultimate performance, which it produced by Dai.Simulation results show that the new halting condition can overpass best results produce by earlier iteration and rise time consume. Our new halting condition can catch this earlier iteration and enhanced SP algorithm results.

Near-Optimal Signal Detector Based on Structured Compressive Sensing for Massive SM-MIMO

Massive spatial modulation (SM)-MIMO, which employs massive low-cost antennas but few power-hungry transmit radio frequency (RF) chains at the transmitter, is recently proposed to provide both high spectrum efficiency and energy efficiency for future green communications. However, in massive SM-MIMO, the optimal maximum likelihood (ML) detector has the prohibitively high complexity, while state-of-the-art low-complexity detectors for conventional small-scale SM-MIMO suffer from an obvious performance loss. In this paper, by exploiting the structured sparsity of multiple SM signals, we propose a low-complexity signal detector based on structured compressive sensing (SCS) to improve the signal detection performance. Specifically, we first propose the grouped transmission scheme at the transmitter, where multiple SM signals in several continuous time slots are grouped to carry the common spatial constellation symbol to introduce the desired structured sparsity. Accordingly, a structured subspace pursuit (SSP) algorithm is proposed at the receiver to jointly detect multiple SM signals by leveraging the structured sparsity. In addition, we also propose the SM signal interleaving to permute SM signals in the same transmission group, whereby the channel diversity can be exploited to further improve the signal detection performance. Theoretical analysis quantifies the performance gain from SM signal interleaving, and simulation results demonstrate the near-optimal performance of the proposed scheme.

Weighted compressive sensing based uplink channel estimation for time division duplex massive multi‐input multi‐output systems

In this paper, the channel estimation problem for the uplink massive multi-input multi-output (MIMO) system is considered. Motivated by the observations that the channels in massive MIMO systems may exhibit sparsity and the channel support changes slowly over time, we propose one efficient channel estimation method under the framework of compressive sensing. By exploiting the channel impulse response (CIR) estimated from the previous OFDM symbol, we firstly estimate the probabilities that the elements in the current CIR are nonzero. Then, we propose the probability-weighted subspace pursuit (PWSP) algorithm exploiting these probability information to efficiently reconstruct the uplink massive MIMO channel. Moreover, noting that the massive MIMO systems also share a common support within one channel matrix due to the shared local scatterers in the physical propagation environment, an antenna collaborating method is exploited for the proposed method to further enhance the channel estimation performance. Simulation results show that compared to the existing compressive sensing methods, the proposed methods could achieve higher spectral efficiency as well as more reliable performance over time-varying channel.

An Adaptive Joint Sparsity Recovery for Compressive Sensing Based EEG System

The last decade has witnessed tremendous efforts to shape the Internet of things (IoT) platforms to be well suited for healthcare applications. These platforms are comprised of a network of wireless sensors to monitor several physical and physiological quantities. For instance, long-term monitoring of brain activities using wearable electroencephalogram (EEG) sensors is widely exploited in the clinical diagnosis of epileptic seizures and sleeping disorders. However, the deployment of such platforms is challenged by the high power consumption and system complexity. Energy efficiency can be achieved by exploring efficient compression techniques such as compressive sensing (CS). CS is an emerging theory that enables a compressed acquisition using well-designed sensing matrices. Moreover, system complexity can be optimized by using hardware friendly structured sensing matrices. This paper quantifies the performance of a CS-based multichannel EEG monitoring. In addition, the paper exploits the joint sparsity of multichannel EEG using subspace pursuit (SP) algorithm as well as a designed sparsifying basis in order to improve the reconstruction quality. Furthermore, the paper proposes a modification to the SP algorithm based on an adaptive selection approach to further improve the performance in terms of reconstruction quality, execution time, and the robustness of the recovery process.

On the number of iterations for convergence of CoSaMP and Subspace Pursuit algorithms

In compressive sensing, one important parameter that characterizes the various greedy recovery algorithms is the iteration bound which provides the maximum number of iterations by which the algorithm is guaranteed to converge. In this letter, we present a new iteration bound for the compressive sampling matching pursuit (CoSaMP) algorithm by certain mathematical manipulations including formulation of appropriate sufficient conditions that ensure passage of a chosen support through the two selection stages of CoSaMP, “Augment” and “Update”. Subsequently, we extend the treatment to the subspace pursuit (SP) algorithm. The proposed iteration bounds for both CoSaMP and SP algorithms are seen to be improvements over their existing counterparts, revealing that both CoSaMP and SP algorithms converge in fewer iterations than suggested by results available in literature. • Presents new iteration bounds for CoSaMP and subspace pursuit (SP) algorithms. • Proposed bounds are lesser than their counterparts existing in literature. • The reduction is significant for moderately large K , i.e., system sparsity. • New results on convergence behavior of CoSaMP and SP algorithms presented.

Structured Compressive Sensing-Based Spatio-Temporal Joint Channel Estimation for FDD Massive MIMO

Massive MIMO is a promising technique for future 5G communications due to its high spectrum and energy efficiency. To realize its potential performance gain, accurate channel estimation is essential. However, due to massive number of antennas at the base station (BS), the pilot overhead required by conventional channel estimation schemes will be unaffordable, especially for frequency division duplex (FDD) massive MIMO. To overcome this problem, we propose a structured compressive sensing (SCS)-based spatio-temporal joint channel estimation scheme to reduce the required pilot overhead, whereby the spatio-temporal common sparsity of delay-domain MIMO channels is leveraged. Particularly, we first propose the non-orthogonal pilots at the BS under the framework of CS theory to reduce the required pilot overhead. Then, an adaptive structured subspace pursuit (ASSP) algorithm at the user is proposed to jointly estimate channels associated with multiple OFDM symbols from the limited number of pilots, whereby the spatio-temporal common sparsity of MIMO channels is exploited to improve the channel estimation accuracy. Moreover, by exploiting the temporal channel correlation, we propose a space-time adaptive pilot scheme to further reduce the pilot overhead. Additionally, we discuss the proposed channel estimation scheme in multi-cell scenario. Simulation results demonstrate that the proposed scheme can accurately estimate channels with the reduced pilot overhead, and it is capable of approaching the optimal oracle least squares estimator.

Efficient Downlink Channel Estimation Scheme Based on Block-Structured Compressive Sensing for TDD Massive MU-MIMO Systems

In this letter, an efficient channel estimation approach based on the emerging block-structured compressive sensing is proposed for the downlink massive multiuser (MU) MIMO system. By exploiting the block sparsity of channel matrix and channel reciprocity in TDD mode, the auxiliary information based block subspace pursuit (ABSP) algorithm is proposed to recover the downlink channels, where the path delays acquired from uplink training is utilized as the auxiliary information. Unlike traditional approaches where the channel estimation overhead is proportional to the number of BS antennas, the proposed approach could provide an accurate channel estimation approaching the performance bound while reduce the pilot overhead by nearly one-third.

Hybrid matching pursuit for distributed through-wall radar imaging

In this paper, we consider the problem of through-wall radar imaging (TWRI) with an antenna array and develop a distributed greedy algorithm named hybrid matching pursuit (HMP). By dividing all the antenna phase centers into some groups, the task of TWRI can be formulated as a problem of jointly sparse signal recovery based on distributed data subsets. In TWRI applications, existing distributed greedy algorithms such as the simultaneous orthogonal matching pursuit (SOMP) algorithm and the simultaneous subspace pursuit (SSP) algorithm suffer from high artifacts and low-resolution, respectively. The proposed HMP algorithm aims to combine the strengths of SOMP and SSP (i.e., the orthogonality among selected basis-signals and the backtracking strategy for basis-signal reevaluation) and, accordingly, to reconstruct high-resolution radar images with no visible artifacts. Experimental results on real through-wall radar data show that, compared to existing greedy methods, the proposed HMP algorithm significantly improves the radar image quality, at the cost of increased computational complexity.

Sparsity-Aware Adaptive Channel Estimation Based on SNR Detection

Time domain synchronous orthogonal frequency division multiplexing OFDM (TDS-OFDM) has a higher spectral efficiency and faster synchronization than standard cyclic prefix OFDM, but suffers from the performance loss over multipath fading channels due to severe interblock-interference. Recently, compressive sensing (CS) is explored to solve those problems, but it heavily relies on the sparsity level of the channel, which is unknown in practice. In this paper, a signal-to-noise ratio-based sparsity estimation method is proposed to detect the sparsity level of the channel. Then we propose the priori aided subspace pursuit algorithm if the channel sparsity meets the theoretical CS model, otherwise we use an improved iterative channel estimation method with the help of the channel sparsity. Simulation results demonstrate that the proposed scheme could improve the robustness and performance of TDS-OFDM systems compared with the conventional iterative methods or recently proposed CS based methods.

An Improved Subspace Pursuit Algorithm with Threshold Matrix

An Improved Subspace Pursuit Algorithm with Threshold Matrix

Improved Analysis for Subspace Pursuit Algorithm in Terms of Restricted Isometry Constant

In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing with the well-known $\ell_1$-minimization. Restricted isometry property (RIP) and restricted isometry constant (RIC) of measurement matrices which ensure the convergency of iterative algorithms play key roles for the guarantee of successful reconstructions. In this paper, we show that for the $s$-sparse recovery, the RICs are enlarged to $\delta_{3s}<0.4859$ for SP and $\delta_{4s}<0.5$ for CoSaMP, which improve the known results significantly. The proposed results also apply to almost sparse signal and corrupted measurements.