Comparison of iterative sparse recovery algorithms

In this paper, joint compressed sensing (CS)-based estimation of transmit power, geographical location and frequency bands of active primary users (PUs) using three reconstruction algorithms, orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and iterative hard thresholding (IHT) methods is investigated. In the first simulations, the performances of OMP, CoSaMP and IHT methods are evaluated in different signal to noise ratios (SNRs) and different values of sparsity. The first experiment demonstrates that OMP is the high performance reconstruction algorithm but it needs a bit higher complexity. Moreover, two scenarios for decision-making is considered in fusion center (FC) and respected simulation results for two cases, ideal and non-ideal lossy channels between secondary users (SUs) and fusion center, are represented. Second experiments show that decision-making based on integrated reconstruction is more efficient than averaging on three separate reconstructions in both ideal and lossy channels.

Wearable ECG monitoring devices, often limited by power constraints, require efficient methods to reduce energy consumption and extend battery life for continuous health tracking. This work proposes a digital compressed sensing approach for ECG (DCS-ECG), featuring a suitable sensing matrix, effective sparse signal recovery algorithms, and an optimized number of bits for quantization (BM). The framework is designed to achieve high compression ratios (CR) with minimal signal distortion and parameter extraction without the reconstruction of the original signal. The following five sensing matrices are examined: deterministic block binary diagonal (DBBD) matrix, random binary (RBin) matrix, random Bernoulli (RBen) matrix, random Gaussian (RG) matrix, and random sparse fixed binary (RSB) matrix. These are paired with a sparsifying matrix (ψ), a hybrid of identity matrix (I), discrete sine transform matrix (S), and discrete cosine transform matrix (C) (i.e. ψ = [I S C]). The following five sparse reconstruction algorithms are evaluated: iterative hard thresholding (IHT) algorithm, orthogonal matching pursuit (OMP) algorithm, smoothed ℓ0 (SL0) algorithm, ℓ1 least square (L1LS) algorithm, and subspace matching pursuit (SMP) algorithm. The proposed DCS-ECG system was tested on ECG signals from the MIT-BIH arrhythmia database. The configuration using the DBBD sensing matrix and OMP recovery algorithm with the sparsifying matrix achieved a low average percentage of root mean square difference (PRD) of 3.75 ± 1.43% at CR = 12.5%, which also offers fast reconstruction. For CR = 12.5% and BM = 8, the CS measurement generation on the Arduino Due consumes 2.02 mJ, while reconstruction on the Raspberry Pi requires 1.13 J. The wireless transmission energy is 1.2973 J. Overall, the proposed CS-based system achieves an 86.24% total energy saving compared to the without CS approach, demonstrating its suitability for low-power IoT-enabled wearable edge ECG health monitoring applications.

In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise (WGN). We show that without any additional information in CS, the probability of error obtained using the signal reconstructed by four recovery algorithms: the basis pursuit denoising (BPDN) algorithm, the Dantzig selector, the orthogonal matching pursuit (OMP) method and the compressive sampling matching pursuit (CoSaMP) algorithm is always larger than the derived theoretical bound. Simulation results demonstrate the effectiveness of our result.

The orthogonal matching pursuit (OMP) algorithm is widely used because of its simple algorithmic structure, the linear magnitude of its computational complexity and other advantages. Algorithms of improved and extended OMP types are continually emerging. To make the OMP algorithm more suitable for the new transmission requirements of the fifth-generation (5G) network, the orthogonal matching pursuit with multiple users (OMP_mu) algorithm is proposed for cell-free massive multi-input multi-output (MIMO) networks with multiuser spatial index modulation. The OMP_mu algorithm considers the constraint condition for the sparsity of each user on the basis of each iterative search in the OMP algorithm until all users meet the constraint. The simulation results show that compared with the original OMP algorithm, the OMP_mu algorithm has a greatly improved demodulation performance. Compared with the orthogonal matching pursuit step-by-step (OMP_step) algorithm, which takes the user sparsity constraint condition into account in two steps, the OMP_mu algorithm greatly reduces the operation time and number of iterations while achieving a slightly better performance. The OMP_mu algorithm provides an effective reference for the application of spatial index modulation in cell-free massive MIMO networks.

In most scenes of through-the-wall imaging (TWI), the observation zone is spares. So the radar signals could be processed using Compressive Sensing (CS) technique. Existing greedy algorithms for CS, such as orthogonal Matching Pursuit (OMP) algorithm and Compressive Sampling Matching pursuit (CoSaMP), suffer from artifacts and low resolution respectively. To cover the shortage of existing algorithms, a modified Compressive Sampling Matching Pursuit algorithm is proposed. By using the orthogonality among selected basis-signals and backtracking strategy for basis-signals reevaluation, the proposed algorithm could reconstruct radar signal. Then the image of observation zone could be got using Delay and Sum (DAS) beamforming method. Measurement results demonstrate the effectiveness of the proposed algorithm.

The recovery algorithm is a crucial issue of the compressed sensing (CS). This paper presents a greedy algorithm called optimized orthogonal matching pursuit (OOMP) for sparse signal recovery. The OOMP algorithm improves the orthogonal matching pursuit (OMP) algorithm via providing the projection onto the subspace generated by the selected measurements and minimizing the corresponding residual error at each iteration. Compared with the OMP algorithm, the simulation results show that the proposed algorithm provides a better approximation of a given signal and reduces measurements needed to recover the signal accurately.

The upcoming wireless communication technologies increase the demand for spectrum, the dynamic spectrum allocation technique is a promising solution for the spectrum allocation. Spectrum sensing plays a key role in dynamic spectrum allocation, scanning through a wideband for the detection of spectrum holes which poses a problem of very high sampling rate and compressive sensing (CS) uses sub-Nyquist samples to addresses this problem. This paper proposes how orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and stage wise orthogonal matching pursuit (StOMP) signal reconstruction algorithms can be used for detection of spectrum holes. Simulation results reveal that the probability of detection of these algorithms is very high for the detection problem than for the estimation problem.KeywordsCognitive radioOrthogonal matching pursuitSpectrum sensingCompressive sensingWide band signal

Orthogonal matching pursuit (OMP) is a commonly used algorithm for recovery sparse signals due to its low complexity and simple implementation. We analyze the convergence property of OMP based on the restricted isometry property (RIP), and show that the OMP algorithm can exactly recover an arbitrary K-sparse signal using K steps provided that the sampling matrix Φ satisfies the RIP with parameter . In addition, we also give the convergence analysis of OMP for the case of inaccurate measurements. Moreover, a variant of OMP, referred to as multi-candidate OMP (MOMP) algorithm, is proposed to recover sparse signals, which can further reduce the computational complexity of OMP. The key point of MOMP is that at each step it selects multi-candidates adding to the optimal atom set, whilst OMP only selects one atom. We also present the convergence analysis of MOMP using the RIP. Finally, we testify the performance of the proposed algorithm using several numerical experiments.

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15° using OMP algorithms to by > 5° using the proposed NSRomp algorithm.

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm, without any loss of accuracy.

Multiphase flow measurements, based on tomographic imaging techniques, have made substantial progress in the past several years. In particular, ultrasonic tomographic reconstruction has shown its high potential in accurately measuring fluid fractions in a flow cross-section based on direct flow measurements. These types of measurements are very attractive as the system is nonradioactive, has direct contact to fluid, yet without flow obstruction. An ultrasonic tomographic multiphase flow meter (UTM) is being developed to capture the fluid flow rates and phase compositions in producing oil wells. The UTM aims to generate cross-sectional images of the flow inside the pipe. To recover these images, complex computations and high processing time are required, based on a limited amount of available data. For this purpose, compressive sensing (CS) reconstruction methods have shown great potential in overcoming the mentioned data quality and quantity issues. CS builds upon the fact that one can recover certain data of interest from potentially very few measurements. Many CS algorithms have been proposed in the literature. In this paper, we seek to find a suitable algorithm by comparing different CS algorithms in terms of the resulting recovered image quality. Specifically, we survey three algorithms in CS, namely basis pursuit, iterative soft thresholding (IST), and orthogonal matching pursuit (OMP). We also compare the results of the CS algorithms to that of a least-square based conventional algorithm. The numerical results show the superiority of CS recovery algorithms over the conventional approach, both qualitatively and quantitatively. The results also suggest that high image quality could potentially be achieved with less complex CS algorithms, i.e., the IST and OMP algorithms. As presented in the paper, our goal is to adapt CS reconstruction algorithms for images generated by the UTM, for the purpose of accurate quantification of oil, gas, and water phase fractions produced from different wells.

FOMP algorithm for Direction of Arrival estimation

Due to the broad bandwidth nature of the direct sequence spread spectrum (DSSS) signal, the application of narrowband interference (NBI) cancelation algorithms based on the Nyquist‐Shannon sampling theory are limited by the high sampling rate. To solve the sampling and processing difficulty in the traditional DSSS communication interference cancelation method, we used the compressive sensing (CS) to reduce the sampling rate of the DSSS communication system, and further proposed a compressed domain NBI elimination method in this study. We proved that NBI with a certain bandwidth and DSSS signal are both sparse in specific dictionaries and proposed the corresponding sparse dictionary construction method. Detailed analysis of the compressed domain features of NBI and the DSSS signal demonstrated that it is possible to extract the strong NBI components from the compressed measurements. Two compressed domain NBI cancelation algorithms were proposed based on this idea. The extracted NBI components were filtered out from the compressed measurements directly in the first algorithm, and then we achieved the DSSS signal demodulation in compressed domain using the separated DSSS signal components with the orthogonal matching pursuit (OMP) algorithm. A proposed extraction filter block sparse Bayesian learning (EFBSBL) framework algorithm was utilized to estimate the NBI from the compressed measurements in the second algorithm. The estimated NBI was eliminated from the received signal, and then we recompressed the DSSS signal after NBI cancelation and realized the DSSS signal demodulation in compressed domain with the OMP algorithm. Simulation results support our theoretical analysis results and reveal that the two proposed algorithms are both effective for NBI cancelation and significant interference cancelation performance are achieved.

In this paper, we present a novel architecture based on field-programmable gate arrays (FPGAs) for the reconstruction of compressively sensed signal using the orthogonal matching pursuit (OMP) algorithm. We have analyzed the computational complexities and data dependence between different stages of OMP algorithm to design its architecture that provides higher throughput with less area consumption. Since the solution of least square problem involves a large part of the overall computation time, we have suggested a parallel low-complexity architecture for the solution of the linear system. We have further modeled the proposed design using Simulink and carried out the implementation on FPGA using Xilinx system generator tool. We have presented here a methodology to optimize both area and execution time in Simulink environment. The execution time of the proposed design is reduced by maximizing parallelism by appropriate level of unfolding, while the FPGA resources are reduced by sharing the hardware for matrix-vector multiplication across the data-dependent sections of the algorithm. The hardware implementation on the Virtex6 FPGA provides significantly superior performance in terms of resource utilization measured in the number of occupied slices, and maximum usable frequency compared with the existing implementations. Compared with the existing similar design, the proposed structure involves 328 more DSP48s, but it involves 25,802 less slices and 1.85 times less computation time for signal reconstruction with N = 1024, K = 256, and m = 36, where N is the number of samples, K is the size of the measurement vector, and m is the sparsity. It also provides a higher peak signal-to-noise ratio value of 38.9 dB with a reconstruction time of 0.34 s, which is twice faster than the existing design. In addition, we have presented a performance metric to implement the OMP algorithm in resource constrained FPGA for the better quality of signal reconstruction.