Sub-Nyquist SAR Based on Pseudo-Random Time-Space Modulation

Sub-Nyquist sampling technology can ease the conflict between high resolution and wide swath in a synthetic aperture radar (SAR) system. However, the existing sub-Nyquist SAR imposes a constraint on the type of the observed scene and can only reconstruct the scene with small sparsity (i.e., number of significant coefficients). The information channel model of microwave imaging radar based on information theory, in which scene, echo, and the mapping relation between the two correspond to information source, sink, and channel, is built, and noisy-channel coding theorem explains the reason for the aforementioned under this model. To allow the wider application of sub-Nyquist SAR, this paper proposes sub-Nyquist SAR based on pseudo-random space-time modulation. This modulation is the spatial and temporal phase modulation to the traditional SAR raw data and can increase the mutual information of information source and sink so that the scenes with large sparsity can be reconstructed. Simulations of scenes with different sparsity, e.g., an ocean with several ships and urban scenes, were run to verify the validity of our proposed method, and the results show that the scenes with large sparsity can be successfully reconstructed.

[1]  Eva Lagunas Targarona,et al.  Compressive sensing based candidate detector and its applications to spectrum sensing and through-the-wall radar imaging , 2014 .

[2]  Naima Kaabouch,et al.  A performance comparison of measurement matrices in compressive sensing , 2018, Int. J. Commun. Syst..

[3]  J. Kong,et al.  Identification of Terrain Cover Using the Optimum Polarimetric Classifier , 2012 .

[4]  John C. Curlander,et al.  Synthetic Aperture Radar: Systems and Signal Processing , 1991 .

[5]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[6]  Ying Zhang,et al.  Information-Theoretic Characterization and Undersampling Ratio Determination for Compressive Radar Imaging in a Simulated Environment , 2015, Entropy.

[7]  Cormac Herley,et al.  Minimum rate sampling and reconstruction of signals with arbitrary frequency support , 1999, IEEE Trans. Inf. Theory.

[8]  Yue Gao,et al.  Reliable and Efficient Sub-Nyquist Wideband Spectrum Sensing in Cooperative Cognitive Radio Networks , 2016, IEEE Journal on Selected Areas in Communications.

[9]  Naima Kaabouch,et al.  Compressive sensing: Performance comparison of sparse recovery algorithms , 2018, 2017 IEEE 7th Annual Computing and Communication Workshop and Conference (CCWC).

[10]  Richard G. Baraniuk,et al.  Bayesian Compressive Sensing Via Belief Propagation , 2008, IEEE Transactions on Signal Processing.

[11]  Ian G. Cumming,et al.  Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation , 2005 .

[12]  Rongrong Wang,et al.  A null space analysis of the L1 synthesis method in dictionary-based compressed sensing , 2013 .

[13]  Li Wang,et al.  Minimum Rate Sampling and Spectrum-Blind Reconstruction in Random Equivalent Sampling , 2015, Circuits Syst. Signal Process..

[14]  Sergio Verdú,et al.  Fifty Years of Shannon Theory , 1998, IEEE Trans. Inf. Theory.

[15]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[16]  Terence Tao,et al.  The Dantzig selector: Statistical estimation when P is much larger than n , 2005, math/0506081.

[17]  Jonathan Weed,et al.  Approximately Certifying the Restricted Isometry Property is Hard , 2017, IEEE Transactions on Information Theory.

[18]  Antonio Iodice,et al.  Coprime Synthetic Aperture Radar (CopSAR): A New Acquisition Mode for Maritime Surveillance , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[19]  Qun Zhang,et al.  Compressed Sensing SAR Imaging Based on Centralized Sparse Representation , 2018, IEEE Sensors Journal.

[20]  Dong Yang,et al.  SAR Imaging With Undersampled Data via Matrix Completion , 2014, IEEE Geoscience and Remote Sensing Letters.

[21]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[22]  Raffaele Cerulli,et al.  Carousel greedy: A generalized greedy algorithm with applications in optimization , 2017, Comput. Oper. Res..

[23]  Thomas Strohmer,et al.  High-Resolution Radar via Compressed Sensing , 2008, IEEE Transactions on Signal Processing.

[24]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[25]  Aggelos K. Katsaggelos,et al.  Bayesian Compressive Sensing Using Laplace Priors , 2010, IEEE Transactions on Image Processing.

[26]  George Suciu,et al.  Access to RF White Spaces in Romania: Present and Future , 2015, Wireless Personal Communications.

[27]  H. Nyquist,et al.  Certain Topics in Telegraph Transmission Theory , 1928, Transactions of the American Institute of Electrical Engineers.

[28]  Emre Ertin,et al.  Sparsity and Compressed Sensing in Radar Imaging , 2010, Proceedings of the IEEE.

[29]  Yonina C. Eldar,et al.  Sub-Nyquist SAR via Fourier Domain Range-Doppler Processing , 2016, IEEE Transactions on Geoscience and Remote Sensing.

[30]  William Blackwell,et al.  A Single-Transceiver Compressive Reflector Antenna for High-Sensing-Capacity Imaging , 2016, IEEE Antennas and Wireless Propagation Letters.

[31]  Holger Rauhut,et al.  A Mathematical Introduction to Compressive Sensing , 2013, Applied and Numerical Harmonic Analysis.

[32]  Ke Yang,et al.  Informational Analysis for Compressive Sampling in Radar Imaging , 2015, Sensors.

[33]  Josiane Zerubia,et al.  Modeling SAR images with a generalization of the Rayleigh distribution , 2004, IEEE Transactions on Image Processing.

[34]  Justin K. Romberg,et al.  Compressive Sensing by Random Convolution , 2009, SIAM J. Imaging Sci..

[35]  Lawrence Carin,et al.  Bayesian Compressive Sensing , 2008, IEEE Transactions on Signal Processing.

[36]  R. Keith Raney,et al.  Precision SAR processing using chirp scaling , 1994, IEEE Trans. Geosci. Remote. Sens..

[37]  Maximiliano O. Sonnaillon,et al.  High-Frequency Digital Lock-In Amplifier Using Random Sampling , 2008, IEEE Transactions on Instrumentation and Measurement.

[38]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[39]  Wei Yu,et al.  Hybrid Digital and Analog Beamforming Design for Large-Scale Antenna Arrays , 2016, IEEE Journal of Selected Topics in Signal Processing.

[40]  Guoan Bi,et al.  Complex-Image-Based Sparse SAR Imaging and its Equivalence , 2018, IEEE Transactions on Geoscience and Remote Sensing.

[41]  Yonina C. Eldar,et al.  Sub-Nyquist Sampling of Short Pulses , 2010, IEEE Transactions on Signal Processing.

[42]  Aziza I. Hussein,et al.  Compressive Sensing Algorithms for Signal Processing Applications: A Survey , 2015 .

[43]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[44]  Robert J. Mailloux,et al.  Phased Array Antenna Handbook , 1993 .

[45]  K. Sarabandi Derivation of phase statistics from the Mueller matrix , 1992 .

[46]  Nathan A. Goodman,et al.  Processing of multiple-receiver spaceborne arrays for wide-area SAR , 2002, IEEE Trans. Geosci. Remote. Sens..

[47]  R.E. Ziemer,et al.  Digital and analog communication systems , 1981, Proceedings of the IEEE.

[48]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[49]  Paco López-Dekker,et al.  A Novel Strategy for Radar Imaging Based on Compressive Sensing , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[50]  Ruben Grigoryan,et al.  Acquisition of Multi-Band Signals via Compressed Sensing , 2015 .

[51]  J. Tropp,et al.  SIGNAL RECOVERY FROM PARTIAL INFORMATION VIA ORTHOGONAL MATCHING PURSUIT , 2005 .

[52]  Joachim H. G. Ender,et al.  On compressive sensing applied to radar , 2010, Signal Process..

[53]  Xiang-Gen Xia,et al.  Frequency determination from truly sub-Nyquist samplers based on robust Chinese remainder theorem , 2018, Signal Process..

[54]  Jie Zhang,et al.  Wideband Spectrum Sensing Based on Single-Channel Sub-Nyquist Sampling for Cognitive Radio , 2018, Sensors.

[55]  Xiaotao Huang,et al.  Segmented Reconstruction for Compressed Sensing SAR Imaging , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[56]  Ali Molaei,et al.  Compressive Reflector Antenna Phased Array , 2017 .

[57]  Rongrong Wang,et al.  A null space analysis of the L1 synthesis method in frame-based compressed sensing , 2013, ArXiv.

[58]  Juan Heredia Juesas,et al.  Single-transceiver compressive antenna for high-capacity sensing and imaging applications , 2015, 2015 9th European Conference on Antennas and Propagation (EuCAP).