Haijian Zhang

An Improved Auto-Calibration Algorithm Based on Sparse Bayesian Learning Framework

This letter considers the multiplicative perturbation problem in compressive sensing, which has become an increasingly important issue on obtaining robust performance for practical applications. The problem is formulated in a probabilistic model and an auto-calibration sparse Bayesian learning algorithm is proposed. In this algorithm, signal and perturbation are iteratively estimated to achieve sparsity by leveraging a variational Bayesian expectation maximization technique. Results from numerical experiments have demonstrated that the proposed algorithm has achieved improvements on the accuracy of signal reconstruction.

Novel Wideband DOA Estimation Based on Sparse Bayesian Learning With Dirichlet Process Priors

Direction of arrival (DOA) estimation methods based on joint sparsity are attractive due to their superiority of high resolution with a limited number of snapshots. However, the common assumption that signals from different directions share the spectral band is inappropriate when they occupy different bands. To flexibly deal with this situation, a novel wideband DOA estimation algorithm is proposed to simultaneously infer the band occupation and estimate high-resolution DOAs by leveraging the sparsity in the angular domain. The band occupation is exploited by exerting a Dirichlet process (DP) prior over the latent parametric space. Moreover, the proposed method is extended to deal with the off-grid problem by two schemes. One applies a linear approximation to the true dictionary and infers the hidden variables and parameters by the variational Bayesian expectation-maximization (VBEM) in an integrated manner. The other is the separated scheme where DOA is refined by a postsearching procedure based on the reconstructed results. Since the proposed schemes can automatically partition the sub-bands into clusters according to their underlying occupation, more accurate DOA estimation can be achieved by using the measurements within one cluster. Results of comprehensive simulations demonstrate that the proposed schemes outperform other reported ones.

Robust Frequency-Hopping Spectrum Estimation Based on Sparse Bayesian Method

This paper considers the problem of estimating multiple frequency hopping signals with unknown hopping pattern. By segmenting the received signals into overlapped measurements and leveraging the property that frequency content at each time instant is intrinsically parsimonious, a sparsity-inspired high-resolution time-frequency representation (TFR) is developed to achieve robust estimation. Inspired by the sparse Bayesian learning algorithm, the problem is formulated hierarchically to induce sparsity. In addition to the sparsity, the hopping pattern is exploited via temporal-aware clustering by exerting a dependent Dirichlet process prior over the latent parametric space. The estimation accuracy of the parameters can be greatly improved by this particular information-sharing scheme and sharp boundary of the hopping time estimation is manifested. Moreover, the proposed algorithm is further extended to multi-channel cases, where task-relation is utilized to obtain robust clustering of the latent parameters for better estimation performance. Since the problem is formulated in a full Bayesian framework, labor-intensive parameter tuning process can be avoided. Another superiority of the approach is that high-resolution instantaneous frequency estimation can be directly obtained without further refinement of the TFR. Results of numerical experiments show that the proposed algorithm can achieve superior performance particularly in low signal-to-noise ratio scenarios compared with other recently reported ones.

Structured sparsity-driven autofocus algorithm for high-resolution radar imagery

Recent development of compressive sensing has greatly benefited radar imaging problems. In this paper, we investigate the problem of obtaining enhanced targets such as ships and airplanes, where targets often exhibit structured sparsity. A novel structured sparsity-driven autofocus algorithm is proposed based on sparse Bayesian framework.The structured sparse prior is imposed on the target scene in a statistical manner. Based on a statistical framework, the proposed algorithm can simultaneously cope with structured sparse recovery and phase error correction problem. The focused high-resolution radar image can be obtained by iteratively estimating scattering coefficients and phase. Due to the structured sparse constraint, the proposed algorithm can desirably preserve the target region and alleviate over-shrinkage problem, compared to previous sparsity-driven auto-focus approaches.Moreover, to accelerate convergence rate of the algorithm, we propose to adaptively eliminate noise-only range cells in estimating phase errors. The selection is conveniently conducted based on the parameters controlling sparsity degree of the signal in the proposed hierarchical model.The simulated and real data experimental results demonstrate that the proposed algorithm can obtain more concentrated images with much smaller number of iterations, particularly in low SNR and highly under-sampling scenarios. HighlightsA novel structured sparsity-driven autofocus algorithm is proposed based on sparse Bayesian framework.To accelerate convergence rate of the algorithm, we propose to adaptively eliminate noise-only range cells in phase error estimation stage.The proposed algorithm can obtain more concentrated images with much smaller number of iterations, particularly in low SNR and highly under-sampling scenarios.

Robust time-varying filtering and separation of some nonstationary signals in low SNR environments

Conventional time-varying filtering is inefficient for severely spoiled signals because it requires discernible spectral content of the signal in time-frequency domain. Motivated by the time-frequency peak filtering (TFPF) algorithm, a robust time-varying filtering (RTVF) algorithm is proposed in this paper for the objectives of filtering and separating some nonstationary signals that contain strong noise. The performance of the TFPF based on windowed Wigner-Ville distribution is intrinsically limited by the linear constraint on the waveform of the received signal. The proposed RTVF significantly improves the filtering performance with low complexity by applying a sinusoidal time-frequency distribution, which allows a sinusoidal constraint on the signals waveform. The bias analysis of the RTVF is presented for some nonstationary signals with time-varying amplitude. Based on derived bias expressions, a criterion of optimal window size selection for implementation purpose is obtained. The RTVF can successfully decompose some multi-component signal into individual components based on an initial instantaneous frequency (IF) estimate of each component. Unlike existing time-varying filters, the RTVF is much less sensitive to the accuracy of the initial IF estimate. Computer simulations verify the theoretical analysis and demonstrate that the RTVF algorithm can achieve desirable performance of filtering and separation in low SNR environments. HighlightsThe proposed algorithm improves filtering performance for monocomponent signals.The proposed algorithm separates multicomponent signals into individual components.The requirement of high sampling rates is significantly relaxed.The proposed algorithm is implemented with low complexity.

Underdetermined blind separation of overlapped speech mixtures in time-frequency domain with estimated number of sources

Abstract Noise suppression and the estimation of the number of sources are two practical issues in applications of underdetermined blind source separation (UBSS). This paper proposes a noise-robust instantaneous UBSS algorithm for highly overlapped speech sources in the short-time Fourier transform (STFT) domain. The proposed algorithm firstly estimates the unknown complex-valued mixing matrix and the number of sources, which are then used to compute the STFT coefficients of corresponding sources at each auto-source time-frequency (TF) point. After that, the original sources are recovered by the inverse STFT. To mitigate the noise effect on the detection of auto-source TF points, we propose a method to effectively detect the auto-term location of the sources by using the principal component analysis (PCA) of the STFTs of noisy mixtures. The PCA-based detection method can achieve similar UBSS outcome as some filtering-based methods. More importantly, an efficient method to estimate the mixing matrix is proposed based on subspace projection and clustering approaches. The number of sources is obtained by counting the number of the resultant clusters. Evaluations have been carried out by using the speech corpus NOIZEUS and the experimental results have shown improved robustness and efficiency of the proposed algorithm.

DOA estimation of closely-spaced and spectrally-overlapped sources using a STFT-based MUSIC algorithm

The multiple signal classification (MUSIC) algorithm based on spatial time-frequency distribution (STFD) has been investigated for direction of arrival (DOA) estimation of closely-spaced sources. However, the limitations of the bilinear time-frequency based MUSIC (TF-MUSIC) algorithm lie in that it suffers from heavy implementation complexity, and its performance strongly depends on appropriate selection of auto-term location of the sources in time-frequency (TF) domain for the formulation of a group of STFD matrices, which is practically difficult especially when the sources are spectrally-overlapped. In order to relax these limitations, this paper aims to develop a novel DOA estimation algorithm. Specifically, we build a MUSIC algorithm based on spatial short-time Fourier transform (STFT), which effectively reduces implementation cost. More importantly, we propose an efficient method to precisely select single-source auto-term location for constructing the STFD matrices of each source. In addition to low complexity, the main advantage of the proposed STFT-MUSIC algorithm compared to some existing ones is that it can better deal with closely-spaced sources whose spectral contents are highly overlapped in TF domain. A short-time Fourier transform (STFT) based MUSIC algorithm is proposed.The proposed STFT-MUSIC algorithm has a low implementation complexity.A selection method of single-source time-frequency (TF) points in case of complex-valued mixing matrix is proposed.The STFT-MUSIC algorithm can be implemented with a small number of sensors in underdetermined cases.The STFT-MUSIC algorithm is especially suitable for closely-spaced and spectrally-overlapped sources.

IF extraction of multicomponent radar signals based on time-frequency gradient image

The estimation of multicomponent radar signals with overlapped instantaneous frequencies (IFs) in low SNR environments has been a challenging research topic. This paper proposes an IF estimation algorithm for spectrally overlapped radar signals which contain continuous and stepped IF laws. Firstly, we design a gradient image via the time-frequency distribution, based on which two ratio images are derived for detecting the IF segments of continuous and stepped radar components, respectively. Secondly, a graph to link the detected IF segments is constructed, and a Markov random field model is defined on the constructed graph. The final IF estimation process is transformed into the extraction of the best graph labeling. Numerical results are provided to demonstrate the robustness and efficiency of the proposed algorithm.

Time-varying filtering and separation of nonstationary FM signals in strong noise environments

Motivated by the existing time-frequency peak filtering (TFPF) algorithm, herein a robust time-varying filtering (RTVF) algorithm is proposed for filtering and separating multicomponent frequency modulation (FM) signals. The performance of the TFPF based on windowed Wigner-Ville distribution is limited by the linear constraint on the waveform of the received signal. The proposed RTVF significantly improves the filtering performance with low complexity by applying a sinusoidal time-frequency distribution, which allows a sinusoidal constraint on the signals waveform. The RTVF can successfully decompose a multicomponent signal into individual components based on an initial instantaneous frequency (IF) estimate of each component. Unlike existing time-varying filters, the RTVF is much less sensitive to the accuracy of the IF estimate, which can be gradually refined by performing an iterative RTVF procedure.

Frequency estimation of multiple sinusoids with three sub-Nyquist channels ☆

Abstract Frequency estimation of multiple sinusoids is significant in both theory and application. In some application scenarios, only sub-Nyquist samples are available to estimate the frequencies. A conventional approach is to sample the signals at several lower rates. In this paper, we address frequency estimation of the signals in the time domain through undersampled data. We analyze the impact of undersampling and demonstrate that three sub-Nyquist channels are generally enough to estimate the frequencies provided the undersampling ratios are pairwise coprime. We deduce the condition that leads to the failure of resolving frequency ambiguity when two coprime undersampling channels are utilized. When three-channel sub-Nyquist samples are used jointly, the frequencies can be determined uniquely and the correct frequencies are estimated. Numerical experiments verify the correctness of our analysis and conclusion.