Conventional Compressive Sensing Algorithms Research Articles

Deep Learning-Based Channel Estimation for Massive MIMO With Hybrid Transceivers

Accurate and efficient estimation of the high dimensional channels is one of the critical challenges for practical applications of massive multiple-input multiple-output (MIMO). In the context of hybrid analog-digital (HAD) transceivers, channel estimation becomes even more complicated due to information loss caused by limited radio-frequency chains. The conventional compressive sensing (CS) algorithms usually suffer from unsatisfactory performance and high computational complexity. In this paper, we propose a novel deep learning (DL) based framework for uplink channel estimation in HAD massive MIMO systems. To better exploit the sparsity structure of channels in the angular domain, a novel angular space segmentation method is proposed, where the entire angular space is segmented into many small regions and a dedicated neural network is trained offline for each region. During online testing, the most suitable network is selected based on the information from the global positioning system. Inside each neural network, the region-specific measurement matrix and channel estimator are jointly optimized, which not only improves the signal measurement efficiency, but also enhances the channel estimation capability. Simulation results show that the proposed approach significantly outperforms the state-of-the-art CS algorithms in terms of estimation performance and computational complexity.

Strip-Map SAR Image Formulation Based on the Modified Alternating Split Bregman Method

Conventional compressive sensing (CS)-based imaging methods allow images to be reconstructed from a small amount of data, while they suffer from high computational burden even for a moderate scene. To address this problem, this paper presents a novel two-dimensional (2D) CS imaging algorithm for strip-map synthetic aperture radars (SARs) with zero squint angle. By introducing a 2D separable formulation to model the physical procedure of the SAR imaging, we separate the large measurement matrix into two small ones, and then the induced algorithm can deal with 2D signal directly instead of converting it into 1D vector. As a result, the computational load can be reduced significantly. Furthermore, thanks to its superior performance in maintaining contour information, the gradient space of the SAR image is exploited and the total variation (TV) constraint is incorporated to improve resolution performance. Due to the non-differentiable property of the TV regularizer, it is difficult to directly solve the induced TV regularization problem. To overcome this problem, an improved split Bregman method is presented by formulating the TV minimization problem into a sequence of unconstrained optimization problem and Bregman updates. It yields an accurate and simple solution. Finally, the synthesis and real experiment results demonstrate that the proposed algorithm remains competitive in terms of high resolution and high computational efficiency.

Multi-Channel Deep Networks for Block-Based Image Compressive Sensing

Incorporating deep neural networks in image compressive sensing (CS) receives intensive attentions in multimedia technology and applications recently. As deep network approaches learn the inverse mapping directly from the CS measurements, the reconstruction speed is significantly faster than the conventional CS algorithms. However, for existing network based approaches, a CS sampling procedure has to map a separate network model. This may potentially degrade the performance of image CS with block-wise sampling because of blocking artifacts, especially when multiple sampling rates are assigned to different blocks within an image. In this paper, we develop a multichannel deep network for block-based image CS by exploiting inter-block correlation with performance significantly exceeding the current state-of-the-art methods. The significant performance improvement is attributed to block-wise approximation but full image removal of blocking artifacts. Specifically, with our multichannel structure, the image blocks with a variety of sampling rates can be reconstructed in a single model. The initially reconstructed blocks are then capable of being reassembled into a full image to improve the recovered images by unrolling a hand-designed block based CS recovery algorithm. Experimental results demonstrate that the proposed method outperforms the state-of-the-art CS methods by a large margin in terms of objective metrics and subjective visual image quality. Our source codes are available at https://github.com/siwangzhou/DeepBCS.

Frequency selective millimeter‐wave channel estimation based on subspace enhancement algorithms

SummaryIn millimeter wave (mmW) communication systems, hybrid architecture, including the analog‐digital precoder and combiner matrices, is employed to take advantage of the multistream transceiver. In practice, mmW channel is assumed to be frequency‐selective, since the signal bandwidth is larger than the coherence bandwidth. Hence, orthogonal frequency‐division multiplexing signaling can be remedial. So far, most of the previous works on the frequency‐selective channel estimation have focused on the single measurement vector (SMV) form, whereas finding and exploiting the proper multimeasurement vector (MMV) model can improve upon the estimation procedure based on compressive sensing (CS) concepts. In fact, the estimation procedure based on the MMV model has a faster convergence speed than the SMV method specially, when the training frames are small. In this paper, we first extract the MMV model of the channel. In this model, the rank‐deficiency occurs as the number of training frames is less or equal to the sparsity level. Thus, the conventional estimation methods fail to provide the desirable performance. To overcome this issue, we propose two rank‐aware algorithms based on the enhancement of the observed signal subspace. The first algorithm assumes to know the sparsity level, while the second faces to the lack of knowledge about the sparsity level. The simulation results corroborate the fact that the proposed methods outperform the conventional CS algorithms such as Simultaneous Orthogonal Matching Pursuit.

Low-Overhead Hierarchically-Sparse Channel Estimation for Multiuser Wideband Massive MIMO

Numerical evidence suggests that compressive sensing (CS) approaches for wideband massive MIMO channel estimation can achieve very good performance with limited training overhead by exploiting the sparsity of the physical channel. However, analytical characterization of the (minimum) training overhead requirements is still an open issue. By observing that the wideband massive MIMO channel can be represented by a vector that is not simply sparse but has well defined structural properties, referred to as hierarchical sparsity, we propose low complexity channel estimators for the uplink multiuser scenario that take this property into account. By employing the framework of the hierarchical restricted isometry property, rigorous performance guarantees for these algorithms are provided suggesting concrete design goals for the user pilot sequences. For a specific design, we analytically characterize the scaling of the required pilot overhead with increasing number of antennas and bandwidth, revealing that, as long as the number of antennas is sufficiently large, it is independent of the per user channel sparsity level as well as the number of active users. These analytical insights are verified by simulations demonstrating also the superiority of the proposed algorithm over conventional CS algorithms that ignore the hierarchical sparsity property.

Enhanced 1-Bit Radar Imaging by Exploiting Two-Level Block Sparsity

Conventional compressive sensing (CS) aims at sparse signal recovery from the measurements with continuous values. Quantized CS (QCS) methods arise in digital implementations where quantization of the receiver data is performed prior to signal processing. The extreme case of QCS is the so-called 1-bit CS where each real-valued measurement maintains only the sign information with one bit. The 1-bit CS alleviates the burden of storage and transmission of large data volumes and reduces the cost of the analog-to-digital converter. Recently, the 1-bit CS has been successfully applied to inverse scattering and radar imaging. In high-resolution radar imaging scenarios, targets assume spatial extent and occupy clustering pixels. The real and imaginary components of a complex sparse signal are the projections of the same complex value onto two orthogonal axes and, therefore, share a joint sparsity pattern. In this paper, a new 1-bit CS algorithm, referred to as enhanced-binary iterative hard thresholding (E-BIHT), is proposed to improve quality of 1-bit radar imaging by exploiting the two-level block sparsity exhibited in the two properties of clustering and the joint sparsity pattern of the real and imaginary parts of the target image. Simulations and experimental results demonstrate that compared to commonly used 1-bit CS algorithms, the proposed E-BIHT provides more informative imaging resulting in higher target-to-clutter ratio.

NBI mitigation in DSSS communications via block sparse Bayesian learning

Abstract Narrowband interference (NBI) is a common interference pattern in direct-sequence spread-spectrum (DSSS) communications. NBI mitigation is a very important issue to ensure the effectiveness of DSSS communications. However, the existing NBI-mitigation algorithms for DSSS communications are confined to a high sampling rate. In order to solve this problem, compressive sensing (CS) is applied to NBI mitigation in DSSS communications, the impact of NBI on the reconstruction of the DSSS signal after compressed sampling is analyzed, and a newly emerged sparse approximation technique, block sparse Bayesian learning (BSBL), is utilized to estimate NBI in DSSS communications. An NBI-mitigation method in DSSS communications based on BSBL is proposed that uses the BSBL framework algorithm to reconstruct the NBI from the compressed signal and then cancels the interference in the time domain. After the NBI mitigation, the conventional CS algorithm is used to demodulate the DSSS signal in the compressed domain. In order to further improve the performance of the method, a filtering BSBL (FBSBL) framework is proposed using the block-sparsity feature of NBI and noise-like feature of the DSSS signal in the frequency domain. A DSSS communications NBI mitigation algorithm based on FBSBL_EM is designed. An equivalent measurement matrix is constructed use the constructed filtering matrix, which could reduce the noise and DSSS signal components in the procedure of compressed sampling. This leads to a highly accurate NBI reconstruction and further improves the NBI mitigation performance. The reported simulation results demonstrate that the proposed method is effective in cancelling the NBI in DSSS communications and significantly outperforms other conventional methods. A comprehensive analysis and comparison of the algorithm is presented and discussed. The results obtained in this study may be extended to other spread-spectrum communication systems, like the code-division multiple-access (CDMA) system.

A Compressive Sensing-Based Dynamic Estimation Algorithm in Unified Laser TTC System

Unified laser telemetry, tracking, and command (TTC) system on space platforms is increasingly utilized in space exploration for the reason that it takes advantage of the ultra-wideband laser signal, which is beneficial for high-speed command communication and high precision tracking and ranging. Unfortunately, its deployment is hindered by imprecise temporal synchronization because of high dynamic resulting from the movement of space platforms. This paper develops new compressive sensing (CS)-based dynamic estimation algorithm to address the dynamic estimation problem in spaceborne intensity modulation direct detection (IMDD)-based laser TTC systems. Specifically, we first design the sparsity in the transformation domain. On top of this design, a sparsity-aware algorithm for dynamic estimation through CS via sparse transformation is developed. To evaluate its performance, we conduct extensive simulations and the results demonstrate the effectiveness of the proposed algorithm in terms of good accuracy. Moreover, the analytical and simulation results show that the proposed algorithm exhibits better performance than conventional CS algorithms in terms of computational complexity, suggesting its attractiveness for spaceborne IMDD-based laser TTC systems.

Multihypothesis-Based Compressive Sensing Algorithm for Nonscanning Three-Dimensional Laser Imaging

The resolution of nonscanning three-dimensional (3-D) imaging systems is limited by the number and accuracy of the array sensors. Moreover, for space-continuous targets in practical situations, the echo pulses in time-of-flight systems overlap and traditional peak detection is no longer suitable for super-resolution applications. Hence, compressive sensing (CS) has been introduced to achieve super-resolution. However, most of the conventional CS algorithms cannot be used directly for 3-D image reconstruction. In this paper, we propose a novel super-resolution algorithm for nonscanning 3-D laser imaging based on CS reconstruction. To acquire the range information of space-continuous targets, an all-one projection is implemented in advance to estimate the spatial distribution of the targets; a range observation matrix composed of time-interval basis vectors is then constructed to obtain the peak values of each frame from overlapping echo pulses. Because of the spatial continuity of the targets, Tikhonov regularization is utilized to solve the ill-posed inverse problem. Furthermore, to enhance the reconstruction quality of the adjacent frames, multihypothesis prediction is used with displacement and diffusion models to estimate the motion of the contour line. Simulation results based on real data from the ASTER global digital elevation model demonstrate the effectiveness and high accuracy of the proposed algorithm for complex landforms.

Block-Wise Compressive Sensing Based Multiple Line Outage Detection for Smart Grid

Smart grids, which have the ability to detect and monitor necessary system parameters and user behaviors, have gradually become the development trend for future power networks. With increasing scale and access of new energy source, SGs become more unstable and vulnerable when changes of network topology occur abruptly. Among different kinds of abrupt changes, unexpected line outages may give rise to significant potential damages to SGs and lead to the very bad user experience. Thus, accurate and rapid detection of line outages turn into one of the important tasks and challenges in SGs. By utilizing the sparse property of line outages, compressive sensing (CS)-based line outage detection schemes have been proposed recently, in which the phase information collected from phasor measurement units is also fully utilized. In this paper, a novel block-wise CS (BW-CS)-based multiple line outage detection scheme is proposed for SGs. Firstly, by exploiting the sparsity of line outages and topology structure of the power grid, a novel reactance model is introduced, which makes the block-wise CS algorithm can be adopted. Then, by modifying one step of the conventional CS algorithm with the redefined element selection, criterion is modified to improve the recovery accuracy. Finally, the proposed scheme is extended into a three-phase power system. The simulation results show that our proposed BW-CS method can achieve superior precision with the similar complexity compared to the traditional methods.

The RIP and block-RIP analysis of Nyquist folding receiver for recovering signals.

Modern radar and communication systems require the detection and parameter estimation of signal under a broadband radio frequency (RF) environment. The Nyquist folding receiver (NYFR) is an efficient analog-to-information (A2I) architecture. It can use the compressive sensing (CS) techniques to break the limitations of the analog-to-digital converter (ADC). This paper demonstrates the restricted isometry property (RIP) of the NYFR deterministically by applying the Gershgorin circle theory. And, the NYFR suffers a poor RIP for the broadband signal, which will lead the conventional CS algorithms to be invalid. So, we derive the Fourier spectrum of the broadband signal, which covered multiple Nyquist zones and received by the NYFR. Then, the broadband signal can be regarded as the block-sparse signal. And, the block CS algorithms are applied for recovering the signal based on the analysis of the block-RIP. Finally, the simulation experiments demonstrate the validity of the findings.

Spatially correlated channel estimation based on block iterative support detection for massive MIMO systems

Downlink channel estimation with low pilot overhead is an important and challenging problem in massive multiple-input–multiple-output (MIMO) systems due to the substantially increased MIMO channel dimension. A block iterative support detection (block-ISD)-based algorithm for downlink channel estimation to reduce the pilot overhead is proposed, which is achieved by fully exploiting the block sparsity inherent in the block-sparse equivalent channel derived from the spatial correlations of MIMO channels. Furthermore, unlike conventional compressive sensing (CS) algorithms that rely on prior knowledge of the sparsity level, block-ISD relaxes this demanding requirement and is thus more practically appealing. Simulation results demonstrate that block-ISD yields better normalised mean square error (NMSE) performance than classical CS algorithms, and achieve a reduction of 84% pilot overhead compared with conventional channel estimation techniques.