An Effective Compressed-Sensing Inspired Deterministic Algorithm for Sparse Array Synthesis

The aim of this paper is to discuss a novel technique for sparse array synthesis. The synthesis strategy is based on a sparse-forcing algorithm using an improvement of the reweighted <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> minimization proposed in the framework of the compressed-sensing literature, specifically modified in order to tailor both linear and conformal array synthesis problems. The numerical examples show that the proposed algorithm improves the results provided by concurrent techniques, reducing the number of radiating elements and/or the computational effort.

[1]  A. Massa,et al.  Peak sidelobe level reduction with a hybrid approach based on GAs and difference sets , 2004, IEEE Transactions on Antennas and Propagation.

[2]  Marco Donald Migliore,et al.  Array Diagnosis From Far-Field Data Using the Theory of Random Partial Fourier Matrices , 2013, IEEE Antennas and Wireless Propagation Letters.

[3]  Douglas H. Werner,et al.  Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning , 2002 .

[4]  Stefano Perna,et al.  Synthesis of Isophoric Sparse Arrays Allowing Zoomable Beams and Arbitrary Coverage in Satellite Communications , 2015, IEEE Transactions on Antennas and Propagation.

[5]  Marco Donald Migliore,et al.  Fast Antenna Array Diagnosis from a Small Number of Far-Field Measurements , 2016, IEEE Transactions on Antennas and Propagation.

[6]  M. Migliore On the Sampling of the Electromagnetic Field Radiated by Sparse Sources , 2015, IEEE Transactions on Antennas and Propagation.

[7]  D. Caratelli,et al.  A Novel Deterministic Synthesis Technique for Constrained Sparse Array Design Problems , 2011, IEEE Transactions on Antennas and Propagation.

[8]  Marco Donald Migliore A simple introduction to compressed sensing/sparse recovery with applications in antenna measurements , 2014, IEEE Antennas and Propagation Magazine.

[9]  Paolo Rocca,et al.  Compressive Sensing in Electromagnetics - A Review , 2015, IEEE Antennas and Propagation Magazine.

[10]  Zhaoshui He,et al.  A modified real GA for the sparse linear array synthesis with multiple constraints , 2006 .

[11]  Marco Donald Migliore,et al.  Plane-Wave Generators: Design Guidelines, Achievable Performances and Effective Synthesis , 2013, IEEE Transactions on Antennas and Propagation.

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

[13]  Wee Ser,et al.  Linear Sparse Array Synthesis With Minimum Number of Sensors , 2010, IEEE Transactions on Antennas and Propagation.

[14]  Fang Li,et al.  Reducing the Number of Elements in Linear and Planar Antenna Arrays With Sparseness Constrained Optimization , 2011, IEEE Transactions on Antennas and Propagation.

[15]  Marco Donald Migliore,et al.  Compressed sensing in electromagnetics: Theory, applications and perspectives , 2011, Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP).

[16]  T. Isernia,et al.  Solving Some Array Synthesis Problems by Means of an Effective Hybrid Approach , 2007, IEEE Transactions on Antennas and Propagation.

[17]  D. Pinchera,et al.  A Generalized Hybrid Approach for the Synthesis of Uniform Amplitude Pencil Beam Ring-Arrays , 2012, IEEE Transactions on Antennas and Propagation.

[18]  Tommaso Isernia,et al.  Isophoric Sparse Arrays Ensuring Global Coverage in Satellite Communications , 2014, IEEE Transactions on Antennas and Propagation.

[19]  W. Keizer Linear Array Thinning Using Iterative FFT Techniques , 2008, IEEE Transactions on Antennas and Propagation.

[20]  Marco Donald Migliore,et al.  A Virtual Subarray Architecture for Imaging Radar , 2014, IEEE Transactions on Antennas and Propagation.

[21]  D. Pozar The active element pattern , 1994 .

[22]  M. D'Urso,et al.  Maximally Sparse Arrays Via Sequential Convex Optimizations , 2012, IEEE Antennas and Wireless Propagation Letters.

[23]  Stefano Perna,et al.  Interleaved Isophoric Sparse Arrays for the Radiation of Steerable and Switchable Beams in Satellite Communications , 2017, IEEE Transactions on Antennas and Propagation.

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

[25]  D. Pinchera,et al.  Advances in the Deterministic Synthesis of Uniform Amplitude Pencil Beam Concentric Ring Arrays , 2012, IEEE Transactions on Antennas and Propagation.

[26]  Z. Yu,et al.  Linear Aperiodic Array Synthesis Using an Improved Genetic Algorithm , 2012, IEEE Transactions on Antennas and Propagation.

[27]  Marco Donald Migliore,et al.  A Sparse Recovery Approach for Pattern Correction of Active Arrays in Presence of Element Failures , 2015, IEEE Antennas and Wireless Propagation Letters.

[28]  T. Isernia,et al.  A hybrid approach for the optimal synthesis of pencil beams through array antennas , 2004, IEEE Transactions on Antennas and Propagation.

[29]  E. Pike,et al.  Element positioning for linear arrays using generalized Gaussian quadrature , 2003 .

[30]  V. Murino,et al.  Stochastic optimization of linear sparse arrays , 1999 .

[31]  Giuseppe Di Massa,et al.  Radar Array Diagnosis from Undersampled Data Using a Compressed Sensing/Sparse Recovery Technique , 2013, J. Electr. Comput. Eng..

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

[33]  Fenggan Zhang,et al.  Linear Aperiodic Array Synthesis Using Differential Evolution Algorithm , 2013, IEEE Antennas and Wireless Propagation Letters.

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

[35]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[36]  Z. Nie,et al.  Reducing the Number of Elements in a Linear Antenna Array by the Matrix Pencil Method , 2008, IEEE Transactions on Antennas and Propagation.

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

[38]  A. Massa,et al.  Linear Array Thinning Exploiting Almost Difference Sets , 2009, IEEE Transactions on Antennas and Propagation.

[39]  Marco Donald Migliore,et al.  Comparison Guidelines and Benchmark Procedure for Sparse Array Synthesis , 2016 .

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

[41]  J. A. Araque Quijano,et al.  Sparse 2-D Array Placement for Arbitrary Pattern Mask and With Excitation Constraints: A Simple Deterministic Approach , 2014, IEEE Transactions on Antennas and Propagation.

[42]  J. N. Sahalos,et al.  Sparse Linear Array Synthesis With Multiple Constraints Using Differential Evolution With Strategy Adaptation , 2011, IEEE Antennas and Wireless Propagation Letters.

[43]  Marco Donald Migliore,et al.  A Compressive-Sensing Inspired Alternate Projection Algorithm for Sparse Array Synthesis , 2016 .

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

[45]  Paolo Rocca,et al.  Robust mask-constrained linear array synthesis through an interval-based particle swarm optimisation , 2013 .

[46]  R. Leahy,et al.  On the design of maximally sparse beamforming arrays , 1991 .