Optimization of Sparse Cross Array Synthesis via Perturbed Convex Optimization

Three-dimensional (3-D) imaging sonar systems require large planar arrays, which incur hardware costs. In contrast, a cross array consisting of two perpendicular linear arrays can also support 3-D imaging while dramatically reducing the number of sensors. Moreover, the use of an aperiodic sparse array can further reduce the number of sensors efficiently. In this paper, an optimized method for sparse cross array synthesis is proposed. First, the beamforming of a cross array based on a multi-frequency algorithm is simplified for both near-field and far-field. Next, a perturbed convex optimization algorithm is proposed for sparse cross array synthesis. The method based on convex optimization utilizes a first-order Taylor expansion to create position perturbations that can optimize the beam pattern and minimize the number of active sensors. Finally, a cross array with 100 + 100 sensors is employed from which a sparse cross array with 45 + 45 sensors is obtained via the proposed method. The experimental results show that the proposed method is more effective than existing methods for obtaining optimum results for sparse cross array synthesis in both the near-field and far-field.

[1]  J. Hooker,et al.  Optimal Thinning Levels in Linear Arrays , 2010, IEEE Antennas and Wireless Propagation Letters.

[2]  Peng Chen,et al.  Optimized Simulated Annealing Algorithm for Thinning and Weighting Large Planar Arrays in Both Far-Field and Near-Field , 2011 .

[3]  Kim-Chuan Toh,et al.  Solving semidefinite-quadratic-linear programs using SDPT3 , 2003, Math. Program..

[4]  Giancarlo Prisco,et al.  Maximally Sparse, Steerable, and Nonsuperdirective Array Antennas via Convex Optimizations , 2016, IEEE Transactions on Antennas and Propagation.

[5]  Renato D. C. Monteiro,et al.  Primal-Dual Path-Following Algorithms for Semidefinite Programming , 1997, SIAM J. Optim..

[6]  Andrea Massa,et al.  Sparsening Conformal Arrays Through a Versatile $BCS$-Based Method , 2014, IEEE Transactions on Antennas and Propagation.

[7]  R. K. Hansen,et al.  The application of real time 3D acoustical imaging , 1998, IEEE Oceanic Engineering Society. OCEANS'98. Conference Proceedings (Cat. No.98CH36259).

[8]  Jianjiang Zhou,et al.  A hybrid algorithm of orthogonal perturbation method and convex optimization for beamforming of sparse antenna array , 2020 .

[9]  Hong Zhou,et al.  A Low-Complexity Real-Time 3-D Sonar Imaging System With a Cross Array , 2016, IEEE Journal of Oceanic Engineering.

[10]  Butrus T. Khuri-Yakub,et al.  Minimally Redundant 2-D Array Designs for 3-D Medical Ultrasound Imaging , 2009, IEEE Transactions on Medical Imaging.

[11]  G. Buttazzoni,et al.  Synthesis of sparse arrays radiating shaped beams , 2016, 2016 IEEE International Symposium on Antennas and Propagation (APSURSI).

[12]  A. Trucco,et al.  Three-dimensional image generation and processing in underwater acoustic vision , 2000, Proceedings of the IEEE.

[13]  Tao Dong,et al.  Synthesis of planar sparse arrays by perturbed compressive sampling framework , 2016 .

[14]  Dongdong Zhao,et al.  Optimized Design for Sparse Cross Arrays in Both Near-Field and Far-Field , 2019, IEEE Journal of Oceanic Engineering.

[15]  Shinji Hara,et al.  Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices , 1997, SIAM J. Optim..

[16]  Robert J. Vanderbei,et al.  An Interior-Point Method for Semidefinite Programming , 1996, SIAM J. Optim..

[17]  A. Massa,et al.  Bayesian Compressive Sampling for Pattern Synthesis With Maximally Sparse Non-Uniform Linear Arrays , 2011, IEEE Transactions on Antennas and Propagation.

[18]  Sanjay Mehrotra,et al.  On the Implementation of a Primal-Dual Interior Point Method , 1992, SIAM J. Optim..

[19]  A. Trucco,et al.  Thinning and weighting of large planar arrays by simulated annealing , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[20]  Hong Zhou,et al.  Synthesis of extreme sparse array for real-time 3D acoustic imaging , 2015 .

[21]  Ke-song Chen,et al.  Sparse Planar Array Synthesis Using Matrix Enhancement and Matrix Pencil , 2013 .

[22]  Shahriar Negahdaripour,et al.  Stereovision imaging on submersible platforms for 3-D mapping of benthic habitats and sea-floor structures , 2003 .

[23]  Andrea Trucco,et al.  Devising an Affordable Sonar System for Underwater 3-D Vision , 2008, IEEE Transactions on Instrumentation and Measurement.

[24]  B. Fuchs.  Synthesis of Sparse Arrays With Focused or Shaped Beampattern via Sequential Convex Optimizations , 2012, IEEE Transactions on Antennas and Propagation.

[25]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[26]  Michael J. Todd,et al.  Self-Scaled Barriers and Interior-Point Methods for Convex Programming , 1997, Math. Oper. Res..

[27]  Marco Donald Migliore,et al.  An Effective Compressed-Sensing Inspired Deterministic Algorithm for Sparse Array Synthesis , 2018, IEEE Transactions on Antennas and Propagation.

[28]  N. Wachowski,et al.  A New Synthetic Aperture Sonar Processing Method Using Coherence Analysis , 2011, IEEE Journal of Oceanic Engineering.

[29]  A. Massa,et al.  Complex-Weight Sparse Linear Array Synthesis by Bayesian Compressive Sampling , 2012, IEEE Transactions on Antennas and Propagation.

[30]  Randy L. Haupt,et al.  Thinned arrays using genetic algorithms , 1993, Proceedings of IEEE Antennas and Propagation Society International Symposium.

[31]  Fan Zhou,et al.  Distributed Convex Optimization Compressed Sensing Method for Sparse Planar Array Synthesis in 3-D Imaging Sonar Systems , 2020, IEEE Journal of Oceanic Engineering.

[32]  Y. Higashi,et al.  Measurement of seabed topography by multibeam sonar using CFFT , 1986 .

[33]  E. Rajo-Iglesias,et al.  Ant Colony Optimization in Thinned Array Synthesis With Minimum Sidelobe Level , 2006, IEEE Antennas and Wireless Propagation Letters.

[34]  Marco Donald Migliore,et al.  Synthesis of Large Sparse Arrays Using IDEA (Inflating-Deflating Exploration Algorithm) , 2018, IEEE Transactions on Antennas and Propagation.

[35]  M. J. Wilson,et al.  Sparse-periodic hybrid array beamformer , 2007 .

[36]  T. L. Henderson,et al.  Seafloor profiling by a wideband sonar: simulation, frequency-response optimization, and results of a brief sea test , 1989 .

[37]  Min Gao,et al.  Synthesis of Pattern Reconfigurable Sparse Arrays With Multiple Measurement Vectors FOCUSS Method , 2017, IEEE Transactions on Antennas and Propagation.

[38]  Z. Yu,et al.  Beampattern Synthesis for Linear and Planar Arrays With Antenna Selection by Convex Optimization , 2010, IEEE Transactions on Antennas and Propagation.