Hybrid GOMP–ROMP Algorithm for Sparse Channel Estimation in mmWave MIMO: Enhancing Convergence and Reducing Computational Complexity

Recently, technological developments have enhanced, the use of Millimeter-wave (mm-Wave) Multiple Input Multiple Output (MIMO) system in various communication applications and wireless sensor networks as channel estimation efficiency can be immensely improved with the help of this technological developments in Millimeter-wave MIMO system and wireless sensor network as well. Moreover, they can improve quality of communication services to a great extent. However, cell interference in Millimeter-wave (mm-Wave) MIMO system can produce a massive impact on spectral efficiency. Therefore, a Routing Enabled Channel Estimation (RECE) technique is presented in this article to minimize interference between cells. The proposed Channel Estimation technique improves channel capacity as well as spectral efficiency. Moreover, Normalized Mean Square Error (NMSE) is minimized heavily using proposed RECE technique. Here, main aim of this article is to reduce cell interference and channel estimation inside a cell by using route selection, beam selection, and spatial frequency estimation. Here, different scenarios and parameters are considered to evaluate performance efficiency of proposed RECE technique in terms of spectral efficiency, NMSE and SNR and compared against varied traditional channel estimation techniques. Moreover, it is clearly evident from performance results that the proposed channel estimation technique performs better than the other two methods.

In this paper, we present a novel method for the acquisition and compression of hyperspectral images based on two concepts - distributed source coding and compressive sensing. Compressive sensing (CS) is a signal acquisition method that samples at sub Nyquist rates which is possible for signals that are sparse in some transform domain. Distributed source coding (DSC) is a method to encode correlated sources separately and decode them together in an attempt to shift complexity from the encoder to the decoder. Distributed compressive sensing (DCS) is a new framework suggested for jointly sparse signals which we apply to the correlated bands of hyperspectral images. We compressively sense each band of the hyperspectral image individually and can then recover the bands separately or using a joint recovery method. We use the Orthogonal Matching Pursuit (OMP) for individual recovery and Simultaneous Orthogonal Matching Pursuit (SOMP) for joint decoding and compare the two methods. The latter is shown to perform consistently better showing that the Distributed Compressive Sensing method that exploits the joint sparsity of the hyperspectral image is much better than individual recovery.

Background: Doppler ultrasound is an important diagnostic tools used to view blood flow through the vessels. For the reconstruction we need to collect a large data to get a Doppler image with high performance. Objective: In this work, we propose an algorithm that combines compressed sensing (CS) and parallel computing to reconstruct the Doppler ultrasound signal and reduce the reconstruction time. Methods: Compressed sensing is a new sampling methods, appeared a few years ago, but it was used in different practical applications such as speeding up MRI scans by acquiring less data to achieve a given amount of resolution and Doppler ultrasound signal reconstruction using fewer measurements to achieve an image with high quality. The main idea of parallel signal/image reconstruction is to divide the main tasks into subtasks and solve them concurrently, in such way that total time can be divided between total tasks. Results: The reconstruction performed using Matlab on a personal computer running a Windows 7 operating system. Real and simulated Doppler data were used for the proposed algorithm validation. The result shows that as the number of cores increased the process time decreased. The image quality from serial programming is same as that a achieved by using parallel programming. The best quality of the image gain is when the 1-norm algorithm used. The lowest reconstruction time was obtained by combining the regularized orthogonal matching pursuit (ROMP) algorithm and parallel computing, with a reconstruction time less than 0.016 seconds when four cores were used and less than 0.034 seconds when two cores were used for 5% of the data. When 80% of the data used the reconstruction time for two cores was 0.109 and for four cores the time was 0.067. The best efficiency was achieved by parallelizing ROMP in two and four cores and the lowest efficiency achieved by parallelized CoSaMP algorithm. The excitation cost decreased with decreasing the numbers of cores. In all the reconstruction algorithms used to perform this work, four cores gave a lower excitation cost than those obtained with two cores. The lowest excitation cost was achieved via ROMP when four cores and fewer measurements were used (0.06) and higher cost gained by using 1-norm algorithm (12.42). The ROMP combined algorithm gives best result among all combined reconstruction algorithm used. Conclusion: We have demonstrated that it is possible to combine compressed sensing and parallel computing to reconstruct the Doppler ultrasound signal. The result of reconstructing the Doppler signal shows that combined algorithm leads to a reduction in reconstruction time and gives an image in realtime while reducing the computation complexity without affecting the image quality. Keywords: Doppler ultrasound signal, compressed sensing, multi-core processor, parallel computing, reconstruction, parfor.

Distributed compressed sensing techniques are applied to enhance sparse channel estimation performance in underwater acoustic multiband systems. The core idea is to use receptions from multiple sub-bands to enhance the detection of channel tap positions. A known variant of the orthogonal matching pursuit (OMP) algorithm based on the distributed compressed sensing principle is simultaneous orthogonal matching pursuit (SOMP). However, the impulse responses across multiple sub-bands may have different arrival structures, although they often show a certain level of similarity. To address such differences at the sub-bands, a multiple selection strategy is applied to select multiple candidates at individual sub-bands at each iteration. This is different from the conventional OMP and SOMP algorithms that select only one candidate at each iteration. When the multiple selection strategy is combined with the SOMP algorithm, the proposed algorithm is referred to as JB-MSSOMP algorithm. To take advantage of channel coherence between adjacent data blocks from different sub-bands, the multiple selection strategy is further used over time. This leads to JBT-MSSOMP algorithm. Computer simulations show improved channel estimation performance of the proposed JB-MSSOMP and JBT-MSSOMP algorithms over the OMP or SOMP algorithms. Communication data from a recent acoustic experiment demonstrates improved receiver performance with the proposed channel estimators.

Surface electromyography (sEMG) holds great potential in walking function evaluation. Compressed sensing (CS) leverages the sparsity of signals to decrease the number of samples required. In this study, a sEMG CS algorithm for spinal cord injury (SCI) patients based on regularized orthogonal matching pursuit (ROMP) was introduced. It was used to reconstruct multiple sEMG signals collected from SCI subjects. Its performance was compared with orthogonal matching pursuit (OMP). The impact of diverse measurement matrices on reconstruction accuracy was also evaluated. Results indicates that the combination of ROMP with a binary permuted block diagonal (BPBD) matrix outperforms the conventional OMP algorithm.

We present a theoretical analysis of the average performance of OMP for sparse approximation. For signals that are generated from a dictionary with $K$ atoms and coherence $\mu$ and coefficients corresponding to a geometric sequence with parameter $\alpha<1$, we show that OMP is successful with high probability as long as the sparsity level $S$ scales as $S\mu^2 \log K \lesssim 1-\alpha $. This improves by an order of magnitude over worst case results and shows that OMP and its famous competitor Basis Pursuit outperform each other depending on the setting.

Underwater acoustic channels typically exhibit clustered-sparse structure, and sparse channel recovery based on the clustered-sparse structure can achieve smaller structural error. We propose a novel clustered-sparse Bayesian model for sparse channel estimation in underwater acoustic (UWA) orthogonal frequency-division multiplexing (OFDM) communication systems. In this model, the sparsity and temporal correlation of channel impulse responses (CIRs) are controlled by a set of hyperparameters. For continuously transmitted OFDM blocks in one frame, the auto-regressive (AR) process is used to characterize temporal correlation of time-varying UWA channels, and different clusters are considered to have different AR model coefficients, as they are usually generated according to different transmission routes. A joint cluster partition and sparse Bayesian learning algorithm (JCP-SBL) is proposed to learn the clustered-sparse structure of UWA channels when the cluster partition is unknown. Results of numerical simulation and lake trial demonstrate the effectiveness of the JCP-SBL channel estimator in time-varying UWA channel, which achieve better channel estimation performance and lower bit error rate (BER) compared with the orthogonal matching pursuit (OMP), simultaneous OMP (SOMP) and temporal multiple sparse Bayesian learning (TMSBL).

We demonstrate a simple greedy algorithm that can reliably recover a vector v ? ?d from incomplete and inaccurate measurements x = ?v + e. Here, ? is a N x d measurement matrix with N<<d, and e is an error vector. Our algorithm, Regularized Orthogonal Matching Pursuit (ROMP), seeks to provide the benefits of the two major approaches to sparse recovery. It combines the speed and ease of implementation of the greedy methods with the strong guarantees of the convex programming methods. For any measurement matrix ? that satisfies a quantitative restricted isometry principle, ROMP recovers a signal v with O(n) nonzeros from its inaccurate measurements x in at most n iterations, where each iteration amounts to solving a least squares problem. The noise level of the recovery is proportional to ?{logn} ||e||2. In particular, if the error term e vanishes the reconstruction is exact.

Simultaneous orthogonal matching pursuit (SOMP) has been recently developed for hyperspectral image classification. It utilizes a joint sparsity model with the assumption that each pixel can be represented by a linear combination of labeled samples. We present an approach to improve the performance of SOMP based on a priori segmentation map. According to the map, we first build a local region where within-segment pixels are preserved while between-segment pixels are excluded. Hyperspectral pixels in the preserved region around the test pixel are then simultaneously represented by a linear combination of training samples, whose weights are recovered by solving a sparsity-constrained optimization problem. Finally, the label of the test pixel is determined to be the class that yields the minimal total residuals between the test samples and the approximations. Experimental results demonstrate that the proposed adaptive SOMP (ASOMP) is superior to some existing classifiers, such as the original SOMP and the recently proposed weighted-SOMP (WSOMP). For example, the ASOMP performed with an accuracy of 95.53% for the ROSIS University of Pavia data with 120 training samples per class, while SOMP obtained an accuracy of 87.61%, an improvement of approximately 8%.

Compressive sensing (CS) based cooperative trans­missions is investigated in cognitive radio networks (CRN). Energy efficiency based optimal relay selection is implemented to determine the measurement numbers in CS. Homotopy re­construction method that solves a bound constrained quadratic programming (BCQP) problem is studied for signal sparse reconstruction at secondary user destination (SUD) in CRN. Based on the determined measurement numbers, binary phase shift keying (BPSK) modulation signal is sparsely sampled by analog-to-information converters (AICs) equipped at the selected secondary user relays (SURs). The corresponding measurement matrix is constructed in CS-based cooperative transmissions. Homotopy reconstruction method is implemented to obtain dynamic update of the solution for BCQP problem. The updating critical value of homotopy parameter and the updating solution of the reconstructed signals' autocorrelation vector can be both achieved via iteration. Simulation results are presented to validate the effectiveness of the proposed approach. It is shown that, homotopy method recovers original signal approximately in low signal-to-noise ratio (SNR) region. Compared with orthogonal matching pursuit (OMP) reconstruction approach, it provides a balanced solution considering normalized mean square error (NMSE) performance versus computational complexity. More­over, spectrum sensing overhead plays significant role in CS based cooperative transmissions.

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.

Mitigating impulsive noise in airborne PLC: Introducing the S-SAMP-PV algorithm for MIMO OFDM systems

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.

Hybrid beamforming in transmitter and receiver can improve the spectral efficiency of millimeterwave (mmWave) multiple-input multiple-output (MIMO) communication system significantly, and can reduce the complexity of communication system. However, when the number of transmitted data streams is large, the existing designing schemes of hybrid beamforming, such as sparse approximation by orthogonal matching pursuit(OMP) algorithm, suffer from performance degradation. In this paper, we propose dictionary learning (DL) algorithm to perform the design of hybrid beamforming for mmWave MIMO system. Simulation result shows that the spectral efficiency of hybrid beamforming based on DL approaches that of optimal beamforming without constraint, which is far superior to the spectral efficiency of hybrid beamforming based on OMP. Moreover, the convergence property of the proposed algorithm is also verified.

We propose an efficient open-loop channel estimator for a millimeter-wave (mm-wave) hybrid multiple-input multiple-output (MIMO) system consisting of radio-frequency (RF) beamformers with large antenna arrays followed by a baseband MIMO processor. A sparse signal recovery problem exploiting the sparse nature of mm-wave channels is formulated for channel estimation based on the parametric channel model with quantized angles of departures/arrivals (AoDs/AoAs), called the angle grids. The problem is solved by the orthogonal matching pursuit (OMP) algorithm employing a redundant dictionary consisting of array response vectors with finely quantized angle grids. We suggest the use of non-uniformly quantized angle grids and show that such grids reduce the coherence of the redundant dictionary. The lower and upper bounds of the sum-of-squared errors of the proposed OMP-based estimator are derived analytically: the lower bound is derived by considering the oracle estimator that assumes the knowledge of AoDs/AoAs, and the upper bound is derived based on the results of the OMP performance guarantees. The design of training vectors (or sensing matrix) is particularly important in hybrid MIMO systems, because the RF beamformer prevents the use of independent and identically distributed random training vectors, which are popular in compressed sensing. We design training vectors so that the total coherence of the equivalent sensing matrix is minimized for a given RF beamforming matrix, which is assumed to be unitary. It is observed that the estimation accuracy can be improved significantly by randomly permuting the columns of the RF beamforming matrix. The simulation results demonstrate the advantage of the proposed OMP with a redundant dictionary over the existing methods such as the least squares method and the OMP based on the virtual channel model.