Sparse modeling is one of the most active research areas in engineering and science. The technique provides solutions from far fewer samples exploiting sparsity, that is, the majority of the data are zero. This paper reviews sparse modeling in radio techniques. The first half of this paper introduces direction-of-arrival (DOA) estimation from signals received by multiple antennas. The estimation is carried out using compressed sensing, an effective tool for the sparse modeling, which produces solutions to an underdetermined linear system with a sparse regularization term. The DOA estimation performance is compared among three compressed sensing algorithms. The second half reviews channel state information (CSI) acquisitions in multiple-input multiple-output (MIMO) systems. In time-varying environments, CSI estimated with pilot symbols may be outdated at the actual transmission time. We describe CSI prediction based on sparse DOA estimation, and show excellent precoding performance when using the CSI prediction. The other topic in the second half is sparse Bayesian learning (SBL)-based channel estimation. A base station (BS) has many antennas in a massive MIMO system. A major obstacle for using the massive MIMO system in frequency-division duplex mode is an overhead for downlink CSI acquisition because we need to send many pilot symbols from the BS and to get the feedback from user equipment. An SBL-based channel estimation method can mitigate this issue. In this paper, we describe the outline of the method, and show that the technique can reduce the downlink pilot symbols.

Direction of arrival (DOA) estimation as a fundamental issue in array signal processing has been extensively studied for many applications in military and civilian fields. Many DOA estimation algorithms have been developed for different application scenarios such as low signal-to-noise ratio (SNR), limited snapshots, etc. However, there are still some practical problems that make DOA estimation very difficult. One of them is the correlation between sources. In this paper, we develop a sparsity-based method to estimate the DOA of coherent signals with sparse linear array (SLA). We adopt the off-grid signal model and solve the DOA estimation problem in the sparse Bayesian learning (SBL) framework. By considering the SLA as a ‘missing sensor’ ULA, our proposed method treats the output of the SLA as a partial output of the corresponding virtual uniform linear array (ULA) to make full use of the expanded aperture character of the SLA. Then we employ the expectation-maximization (EM) method to update the hyper-parameters and the output of the virtual ULA in an iterative manner. Numerical results demonstrate that the proposed method has a better performance in correlated signal scenarios than the reference methods in comparison, confirming the advantage of exploiting the extended aperture feature of the SLA.

In sparsity-based optimization problems for two dimensional (2-D) direction-of-arrival (DOA) estimation using L-shaped nested arrays, one of the major issues is computational complexity. A 2-D DOA estimation algorithm is proposed based on reconsitution sparse Bayesian learning (RSBL) and cross covariance matrix decomposition. A single measurement vector (SMV) model is obtained by the difference coarray corresponding to one-dimensional nested array. Through spatial smoothing, the signal measurement vector is transformed into a multiple measurement vector (MMV) matrix. The signal matrix is separated by singular values decomposition (SVD) of the matrix. Using this method, the dimensionality of the sensing matrix and data size can be reduced. The sparse Bayesian learning algorithm is used to estimate one-dimensional angles. By using the one-dimensional angle estimations, the steering vector matrix is reconstructed. The cross covariance matrix of two dimensions is decomposed and transformed. Then the closed expression of the steering vector matrix of another dimension is derived, and the angles are estimated. Automatic pairing can be achieved in two dimensions. Through the proposed algorithm, the 2-D search problem is transformed into a one-dimensional search problem and a matrix transformation problem. Simulations show that the proposed algorithm has better angle estimation accuracy than the traditional two-dimensional direction finding algorithm at low signal-to-noise ratio and few samples.

Restoration is an important area in improving the visual quality, and lays the foundation for accurate object detection or terrain classification in image analysis. In this paper, we introduce Beta process priors into hierarchical sparse Bayesian learning for recovering underlying degraded hyperspectral images (HSI), including suppressing the various noises and inferring the missing data. The proposed method decomposes the HSI into the weighted summation of the dictionary elements, Gaussian noise term and sparse noise term. With these, the latent information and the noise characteristics of HSI can be well learned and represented. Solved by Gibbs sampler, the underlying dictionary and the noise can be efficiently predicted with no tuning of any parameters. The performance of the proposed method is compared with state-of-the-art ones and validated on two hyperspectral datasets, which are contaminated with the Gaussian noises, impulse noises, stripes and dead pixel lines, or with a large number of data missing uniformly at random. The visual and quantitative results demonstrate the superiority of the proposed method.

Reliable wireless communication often requires accurate knowledge of the underlying multipath channels. Numerous measurement campaigns have shown that physical multipath channels tend to exhibit a sparse structure. Conventional blind channel identification (BCI) strategies such as the least squares, which are known to be optimal under the assumption of rich multipath channels, are ill-suited to exploiting the inherent sparse nature of multipath channels. Recently, l1-norm regularized least-squares-type approaches have been proposed to address this problem with a single parameter governing all coefficients, which is equivalent to maximum a posteriori probability estimation with a Laplacian prior for the channel coefficients. Since Laplace prior is not conjugate to the Gaussian likelihood, no closed form of Bayesian inference is possible. Following a different approach, this paper deals with blind channel identification of a single-input multiple-output (SIMO) system based on sparse Bayesian learning (SBL). The inherent sparse nature of wireless multipath channels is exploited by incorporating a transformative cross relation formulation into a general Bayesian framework, in which the filter coefficients are governed by independent scalar parameters. A fast iterative Bayesian inference method is then applied to the proposed model for obtaining sparse solutions, which completely eliminates the need for computationally costly parameter fine tuning, which is necessary in the l1-norm regularization method. Simulation results are provided to demonstrate the superior effectiveness of the proposed channel estimation algorithm over the conventional least squares (LS) scheme as well as the l1-norm regularization method. It is shown that the proposed algorithm exhibits superior estimation performance compared to both LS and l1-norm regularization methods.

Because accurate position information plays an important role in wireless sensor networks (WSNs), target localization has attracted considerable attention in recent years. In this paper, based on target spatial domain discretion, the target localization problem is formulated as a sparsity-seeking problem that can be solved by the compressed sensing (CS) technique. To satisfy the robust recovery condition called restricted isometry property (RIP) for CS theory requirement, an orthogonalization preprocessing method named LU (lower triangular matrix, unitary matrix) decomposition is utilized to ensure the observation matrix obeys the RIP. In addition, from the viewpoint of the positioning systems, taking advantage of the joint posterior distribution of model parameters that approximate the sparse prior knowledge of target, the sparse Bayesian learning (SBL) approach is utilized to improve the positioning performance. Simulation results illustrate that the proposed algorithm has higher positioning accuracy in multi-target scenarios than existing algorithms.

We propose a cooperative compressed spectrum sensing scheme for correlated signals in wideband cognitive radio networks. In order to design a reconstruction algorithm which accurately recover the wideband signals from the compressed samples in low SNR (Signal-to-Noise Ratio) environments, we consider the multiple measurement vector model exploiting a sequence of input signals and propose a cooperative sparse Bayesian learning algorithm which models the temporal correlation of the input signals. Simulation results show that the proposed scheme outperforms existing compressed sensing algorithms for low SNRs.