Blind signals separation in wireless communications based on Compressive Sensing

Compressed sensing (CS) is a sparse signal sampling methodology for efficiently acquiring and reconstructing a signal from relatively few measurements. Recent work shows that CS is well-suited to be applied to problems in genomics, including probe design in microarrays, RNA interference (RNAi), and taxonomic assignment in metagenomics. The principle of using different CS recovery methods in these applications has thus been established, but a comprehensive study of using a wide range of CS methods has not been done. For each of these applications, we apply three hitherto unused CS methods, namely, l1-magic, CoSaMP, and l1-homotopy, in conjunction with CS measurement matrices such as randomly generated CS m matrix, Hamming matrix, and projective geometry-based matrix. We find that, in RNAi, the l1-magic (the standard package for l1 minimization) and l1-homotopy methods show significant reduction in reconstruction error compared to the baseline. In metagenomics, we find that l1-homotopy as well as CoSaMP estimate concentration with significantly reduced time when compared to the GPSR and WGSQuikr methods.

Compressive sensing (CS) can reduce the number of data transmissions and balance the traffic load throughout networks. However, the total number of data transmissions required in CS method is still large. It is observed that there are many zero elements in the measurement matrix. In each round of data transmission in CS method, the sensor nodes corresponding to the zero elements in the measurement matrix do not have their own data to transmit. To further reduce the number of data transmissions in the network, we aim to compute a data gathering tree by taking advantages of these zero elements in the measurement matrix, such that the total number of data transmissions is minimized. We formulate the problem as linear programming with boolean variables. The problem is NP-hard. We propose heuristic algorithm to compute the Minimum Transmission Tree (MTT) for data gathering in CS methods. The MTT algorithm constructs a spanning tree by iteratively including the edge whose average incremental transmission cost is minimum. The simulation results demonstrate that our algorithm can reduce the number of transmissions significantly, compared with the methods using minimum spanning tree (MST), shortest path tree and the CS method with nonzero measurement coefficient using MST.

Compressive sensing (CS) is one of the effective data compression methods where a small number of measurements of a sparse signal is required to have an exact recovery. In Compressive sensing technique, the data is acquired and compressed at the same time. CS concept allows capturing only fewer sparse and compressible signal which contains only useful information that helps to recover a proper signal. In this paper, image compression is performed with compressive sensing concept. The different basis matrices and sensing matrices are considered which satisfy the Restricted Isometric Property (RIP) and Independent and Identically Distributed (IID). The hardware implementation of CS is covered to have real-time compression for various image-based applications. The performance is observed regarding SNR, compression ratio, and correlation. The reconstruction algorithms are implemented on MATLAB platform. The obtained results show satisfactory performance for CS based image compression.

An efficient algorithm for blind separation of binary symmetrical signals is proposed, which don’t depend on the statistical characteristics of source signals. The mixture matrix is estimated accurately by using the relations of sensor signals in case of no noise and it is also proved in this paper, and the estimated mixture matrix is a primary column transformation of the original mixture matrix by the algorithm, through which the source signals are recovered by permutations and sign changes of their rows. In practice, they can be corrected by introducing headers in the bit-streams and differently encoding them. The algorithm is shown simple and efficient in last simulations.

In correlation‐based signal separation algorithms, the received mixed signals are fed to a de‐coupling system designed to minimize the output cross‐correlation functions. If minimizaion is perfect, each of the system's outputs carries only one signal independent of the others. In these algorithms, the computation burden of the output cross‐correlation functions normally slows down the separation algorithm. This paper, describes a computationally efficient method for off‐line pre‐computation of the needed cross‐correlation functions. Explicit formulas have been derived for the output cross‐correlation functions in terms of the received input signals and the de‐coupling system parameters. Then, it is shown that signal separation amounts to the least‐squares solution of a system of linear equations describing these output cross‐correlation functions, evaluated over a batch of lags. Next, a fast RLS‐type adaptive algorithm is devised for on‐line signal separation. In this respect, an algorithm is derived for updating the de‐coupling parameters as data comes in. This update is achieved recursively, along the negative of the steepest descent directions of an objective cost function describing the output cross‐correlation functions over a batch of lags, subject to equal output power constraints. Illustrative examples are given to demonstrate the effectiveness of the proposed algorithms. Copyright © 2002 John Wiley & Sons, Ltd.

Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are nonnegative and mutual statistically dependent signals. When the observations are nonnegative linear combinations of nonnegative sources, the correlation coefficients of the observations are larger than these of source signals. In this letter, a novel Nonnegative Matrix Factorization (NMF) algorithm with least correlated component constraints to blind separation of convolutive mixed sources is proposed. The algorithm relaxes the source independence assumption and has low-complexity algebraic computations. Simulation results on blind source separation including real face image data indicate that the sources can be successfully recovered with the algorithm.

By means of compressive sensing (CS) technique, this paper considers the collection of sensor data with spatiotemporal correlations in wireless sensor networks (WSNs). In energy-constrained WSNs, one-dimensional CS methods need a lot of data transmissions since they are less applicable in fully exploiting the spatiotemporal correlations, while the Kronecker CS (KCS) methods suffer performance degradations when the signal dimension increases. In this paper, an appropriate sensing matrix as well as an efficient sensing method is proposed to further reduce the data transmissions without the loss of the recovery performance. Different matrices for the temporal signal of each sensor node are separately designed. The corresponding energy-efficient data gathering method is presented, which only transmitting a subset of sensor readings to recover data of the entire WSN. Theoretical analysis indicates that the sensing structure could have the relatively small mutual coherence according to the selection of matrix. Compared with the existing spatiotemporal CS (CS-ST) method, the simulation results show that the proposed efficient measurement method could reduce data transmissions by about 25% with the similar recovery performance. In addition, compared with the conventional KCS method, for 95% successful recovery, the proposed sensing structure could improve the recovery performance by about 20%.

The validity of the compressed sensing (CS) is premised on the sparsity of the signals. In general, a signal is sparse if it can be linearly represented by few column combinations of a certain basis matrix. However, when signals exhibit some complex structure, or in other words, are difficult or inconvenient to be linearly represented, existing many CS methods may suffer from poor performance. In this paper, by introducing a sample set and the widely used kernel trick to CS, we investigate a sample based nonlinear compressed sensing (SNCS) model. In particular, with the help of kernel trick, our SNCS model can capture the nonlinear sparse structure of signals, and hence leads to a better performance than that of the traditional CS. On the other hand, due to the introduction of sample set, our SNCS model performs again better than a recent emerged kernel trick compressed sensing (KTCS) model. What's more, the optimization problem induced by our SNCS model still keeps concise and is easily solved by traditional CS methods.

The problem of blind separation of signals in a post-nonlinear mixture is addressed in this paper. A post-nonlinear mixture is formed by a component-wise nonlinear distortion of a linear mixture. Hence, a nonlinear adjusting part, placed in front of the linear separation structure, is needed to compensate for the distortion in separating such signals. The learning rules for the post-nonlinear separation structure are derived by a maximum likelihood approach. An algorithm for the blind separation of post-nonlinearly mixed suband super-Gaussian signals is proposed, based on some previous works. Multilayer perceptrons are used in this algorithm to model the nonlinear part of the separation structure. The algorithm switches between sub- and super-Gaussian probability models during learning according to a stability condition, and it operates in a block-adaptive manner. The effectiveness of the algorithm is verified by experiments on artificial and natural signals.

Blind signal separation method is the method that the source signals are obtained by separating only the mixed signals. Generally, separation precision is lower when the basic method of blind signal separation is used for the sound signals. It is the cause that the power of the sound signals is concentrated in the low-frequency band. For the problem, we already considered that the method of the blind signal separation using QMF. Specifically, the mixed signals are divided into two frequency bands, and we perform suitable separation for each two bands. As the result, the conventional method has higher separation precision than the basic method. However, in the low-frequency band, power spectrum is not constant for frequency. Therefore, it is expected that the separation precision is higher than the conventional method by performing the suitable separation for each of signals based on the division to several narrow frequency bands on the low-frequency band. Then, in this paper, we propose the method that has higher separation precision and we evaluate the proposed method by computer simulation.

Synthesis of sparse planar arrays can effectively reduce hardware costs and computational complexity in phased array 3-D imaging sonar systems. Traditional stochastic methods, such as simulated annealing, require multiple experiments and parameter adjustments to obtain optimal results. Methods based on compressed sensing (CS) can overcome this defect. However, when applied to large arrays, CS methods require vast computational complexity and may not obtain optimal sparse results because of violating the restricted isometry property. To make CS methods more practical, a distributed convex optimization CS method is proposed here for the sparse planar array synthesis in 3-D imaging sonar systems. This method is based on the CS theory, solving the minimum number of active elements under certain beam pattern constraints using the iterative reweighted l 1-norm minimization algorithm. Then, a multistage distributed framework is proposed to decompose the array into multistage subarrays, and the array synthesis is performed sequentially for each stage subarray to reduce computational complexity and obtain higher sparsity rates. Some applications of sparse planar array synthesis are employed to evaluate the efficiency of the proposed method.

Functional near- infrared spectroscopy (fNIRS) as an emerging optical neuroimaging technique has attracted the interest and attention of many investigators. With the growth of fNIRS data volume, effective data compression methods are urgent. Compressive sensing (CS) has been demonstrated a promising tool to deal with biomedical data. However, whether the compressibility of fNIRS data can discriminate different brain states is unclear. In this study, the fNIRS signals from fifteen attention-deficit/hyperactivity disorder (ADHD) children and fifteen typically developing (TD) children were recorded during an N-back task and a Go/NoGo task respectively. A block sparse Bayesian learning-based CS method was used to reconstruct the compressed fNIRS data. To assess the performance of the CS method, we adopted two metrics, structural similarity index (SSIM) and mean squared error (MSE), both of them effective in evaluating the compressibility of fNIRS data. Then, the two metrics were analyzed to discriminate the brain states of ADHD children and TD children during the two tasks using the multivariate pattern analysis (MVPA) method. As indicated by the results, the CS method could reconstruct the compressed fNIRS data with a high reconstruction quality at different compression ratio ([Formula: see text] and [Formula: see text]). Furthermore, the MVPA method could distinguish different brain states with high accuracy, and identify that the prefrontal cortex is a key brain region for distinguishing ADHD vs. TD or N-back vs. Go/NoGo. These findings indicated that CS is very promising for the storage and transmission of massive fNIRS data, and the compressibility of fNIRS data is a potential biomarker for the diagnosis of ADHD.

With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional optimization-based methods and the speed of recent network-based ones. Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general $$ norm CS reconstruction model. To cast ISTA into deep network form, we develop an effective strategy to solve the proximal mapping associated with the sparsity-inducing regularizer using nonlinear transforms. All the parameters in ISTA-Net (e.g. nonlinear transforms, shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than being hand-crafted. Moreover, considering that the residuals of natural images are more compressible, an enhanced version of ISTA-Net in the residual domain, dubbed ISTA-Net+, is derived to further improve CS reconstruction. Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and network-based CS methods by large margins, while maintaining fast computational speed. Our source codes are available: http://jianzhang.tech/projects/ISTA-Net.

Compressive sensing (CS) is an innovative approach to simultaneously measure and compress signals such as biomedical signals that are sparse or compressible. A major effort in CS is to design a measurement matrix that can be used to encode and compress such signals. The measurement matrix structure has a direct impact on the computational and storage costs as well as the recovered signal quality. Sparse measurement matrices (i.e. with few non-zero elements) may drastically reduce these costs. We propose a permuted Kronecker-based sparse measurement matrix for sensing and data recovery in CS applications. In our study, we use three classes of sub-matrices (normalized Gaussian, Bernoulli, and BCH-based matrices) to create the proposed measurement matrix. Using ECG signals from the MIT-BIH Arrhythmia database, we show that the reconstructed signal quality is comparable to the ones achieved using well known CS methods. Our methodology results in an overall reduction in storage and computations, both during the sensing and recovery process. This approach can be generalized to other classes of eligible measurement matrices in CS.

Recently, the use of unmanned aerial vehicles for both reconnaissance and fire strikes has been increasing. The control of such vehicles and the transmission of telemetry information are carried out using a combined command and telemetry radio link and frequency hopping spread spectrum technology. In such conditions, the task of developing automatic algorithms for detecting and separating radio links for portable radio monitoring devices becomes especially relevant. The aim of this work is to extend the capabilities of portable radio monitoring devices to detect unmanned aerial vehicles’ radio signals in sophisticated electronic environment by automating signal processing. Formally, the research task is to detect and separate several frequency hopping spread spectrum signals in same frequency band. To solve this task, it is first necessary to detect the frequency channels and estimate frequency and, if necessary, temporal and modulation parameters of the signals in these channels. Estimates of signal parameters values are recorded in associative arrays. The paper proposes a scheme of the algorithm for automatic detection and separation of signals with frequency hopping spread spectrum, as well as the structure of the array with the results of frequency band analysis. In the study of developed algorithm, we considered the practically important option of separating radio links with frequency hopping spread spectrum by the spectral width of the frequency element and the value of the signal-to-noise ratio in the frequency channel, since these features can be quite easily distinguished in the frequency domain. The radio links separation was performed by cluster analysis of scatter plots of parameter pairs estimates using a Gaussian mixture model. The developed algorithm can be implemented in existing and prospective portable radio monitoring devices to automatically detect and determine the number of unmanned aerial vehicles by their radio links signals, in particular, under conditions of a priori uncertainty about the values of signal parameters.