Measurement Matrix Design for Compressive Sensing Based MIMO Radar

In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to a fusion center, where an L1-optimization problem is formulated and solved for target information. CS-based MIMO radar exploits the target sparsity in the angle-Doppler-range space and thus achieves the high localization performance of traditional MIMO radar but with many fewer measurements. The measurement matrix is vital for CS recovery performance. This paper considers the design of measurement matrices that achieve an optimality criterion that depends on the coherence of the sensing matrix (CSM) and/or signal-to-interference ratio (SIR). The first approach minimizes a performance penalty that is a linear combination of CSM and the inverse SIR. The second one imposes a structure on the measurement matrix and determines the parameters involved so that the SIR is enhanced. Depending on the transmit waveforms, the second approach can significantly improve SIR, while maintaining CSM comparable to that of the Gaussian random measurement matrix (GRMM). Simulations indicate that the proposed measurement matrices can improve detection accuracy as compared to a GRMM

Colocated MIMO radar using compressive sensing

We propose the use of compressive sensing (CS) in the context of a multi-input multioutput (MIMO) radar system that is implemented by a small scale network. Each receive node compressively samples the incoming signal, and forwards a small number of samples to a fusion center. At the fusion center, all received data are jointly processed to extract information on the potential targets via the CS approach. Since CS-based MIMO radar would require many fewer measurements than conventional MIMO radar for reliable target detection, there would be power savings during the data transmission to the fusion center, which would prolong the life of the wireless network. First, we propose a direction of arrival (DOA)-Doppler estimation approach. Assuming that the targets are sparsely located in the DOA-Doppler space, based on the samples forwarded by the receive nodes, the fusion center formulates an ℓ1-optimization problem, the solution of which yields the target DOA-Doppler information. The proposed approach achieves the superior resolution of MIMO radar with far fewer samples than required by conventional approaches. Second, we propose the use of step frequency to CS-based MIMO radar, which enables high range resolution, while transmitting narrowband pulses. For slowly moving targets, a novel approach is proposed that achieves significant complexity reduction by successively estimating angle-range and Doppler in a decoupled fashion and by employing initial estimates to further reduce the search space. Numerical results show that the achieved complexity reduction does not hurt resolution. Finally, we investigate optimal designs for the measurement matrix that is used to linearly compress the received signal. One optimality criterion amounts to decorrelating the bases that span the sparse space of the incoming signal and simultaneously enhancing signal-to-interference ratio (SIR). Another criterion targets SIRimprovement only. It is shown via simulations that, in certain cases, the measurement matrices obtained based on the aforementioned criteria can improve detection accuracy as compared to the typically used Gaussian random measurement matrix.Ph.D., Electrical Engineering -- Drexel University, 201

Discrete and Continuous Sparse Recovery Methods and Their Applications

Low dimensional signal processing has drawn an increasingly broad amount of attention in the past decade, because prior information about a low-dimensional space can be exploited to aid in the recovery of the signal of interest. Among all the different forms of low di- mensionality, in this dissertation we focus on the synthesis and analysis models of sparse recovery. This dissertation comprises two major topics. For the first topic, we discuss the synthesis model of sparse recovery and consider the dictionary mismatches in the model. We further introduce a continuous sparse recovery to eliminate the existing off-grid mismatches for DOA estimation. In the second topic, we focus on the analysis model, with an emphasis on efficient algorithms and performance analysis. In considering the sparse recovery method with structured dictionary mismatches for the synthesis model, we exploit the joint sparsity between the mismatch parameters and original sparse signal. We demonstrate that by exploiting this information, we can obtain a robust reconstruction under mild conditions on the sensing matrix. This model is very useful for radar and passive array applications. We propose several efficient algorithms to solve the joint sparse recovery problem. Using numerical examples, we demonstrate that our proposed algorithms outperform several methods in the literature. We further extend the mismatch model to a continuous sparse model, using the mathematical theory of super resolution. Statistical analysis shows the robustness of the proposed algorithm. A number-detection algorithm is also proposed for the co-prime arrays. By using numerical examples, we show that continuous sparse recovery further improves the DOA estimation accuracy, over both the joint sparse method and also MUSIC with spatial smoothing. In the second topic, we visit the corresponding analysis model of sparse recovery. Instead of assuming a sparse decomposition of the original signal, the analysis model focuses on the existence of a linear transformation which can make the original signal sparse. In this work we use a monotone version of the fast iterative shrinkage- thresholding algorithm (MFISTA) to yield efficient algorithms to solve the sparse recovery. We examine two widely used relaxation techniques, namely smoothing and decomposition, to relax the optimization. We show that although these two techniques are equivalent in their objective functions, the smoothing technique converges faster than the decomposition technique. We also compute the performance guarantee for the analysis model when a LASSO type of reconstruction is performed. By using numerical examples, we are able to show that the proposed algorithm is more efficient than other state of the art algorithms