Robust mask-constrained linear array synthesis through an interval-based particle swarm optimisation

An innovative strategy for the robust design of linear antenna arrays is presented. Being the array elements characterised by tolerance errors, the synthesis is aimed at determining the intervals of values fitting the user-defined mask constraints on the radiated power pattern. With reference to the upper and lower bounds of the power pattern analytically determined for given tolerances through interval analysis, the nominal excitations of the array elements are then optimised by means of a global stochastic optimiser suitably customised to deal with interval numbers. A set of numerical examples is reported to show the behaviour of the proposed method as well as to assess its potentials in dealing with the robust synthesis of pencil and shaped beams.

[1]  Giuseppe D'Elia,et al.  Antenna pattern synthesis: a new general approach , 1994, Proc. IEEE.

[2]  Randy L. Haupt,et al.  Phase-only adaptive nulling with a genetic algorithm , 1997 .

[3]  Tommaso Isernia,et al.  Deterministic Synthesis of Uniform Amplitude Sparse Arrays via New Density Taper Techniques , 2010, IEEE Transactions on Antennas and Propagation.

[4]  P. Rocca,et al.  Design of Subarrayed Linear and Planar Array Antennas With SLL Control Based on an Excitation Matching Approach , 2009, IEEE Transactions on Antennas and Propagation.

[5]  P. Rocca,et al.  Evolutionary optimization as applied to inverse scattering problems , 2009 .

[6]  Shiwen Yang,et al.  Design of a uniform amplitude time modulated linear array with optimized time sequences , 2005 .

[7]  Ju-Hong Lee,et al.  Robust adaptive array beamforming under steering vector errors , 1997 .

[8]  P. Rocca,et al.  An Innovative Approach Based on a Tree-Searching Algorithm for the Optimal Matching of Independently Optimum Sum and Difference Excitations , 2008, IEEE Transactions on Antennas and Propagation.

[9]  M D Gregory,et al.  Fast Optimization of Electromagnetic Design Problems Using the Covariance Matrix Adaptation Evolutionary Strategy , 2011, IEEE Transactions on Antennas and Propagation.

[10]  P. Rocca,et al.  An Improved Excitation Matching Method Based on an Ant Colony Optimization for Suboptimal-Free Clustering in Sum-Difference Compromise Synthesis , 2009, IEEE Transactions on Antennas and Propagation.

[11]  A. Neumaier.  Interval iteration for zeros of systems of equations , 1985 .

[12]  D. A. Lowther,et al.  The use of interval mathematics in electromagnetic design , 2001 .

[13]  Paolo Rocca,et al.  Imaging weak scatterers by means of an innovative inverse scattering technique based on the Interval Analysis , 2012, 2012 6th European Conference on Antennas and Propagation (EUCAP).

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

[15]  H.S.C. Wang.  Performance of phased array antennas with mechanical errors , 1990 .

[16]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[17]  L. L. Bailin,et al.  Factors Affiecting the Performance of Linear Arrays , 1952, Proceedings of the IRE.

[18]  R. Elliott,et al.  Mechanical and electrical tolerances for two-dimensional scanning antenna arrays , 1958 .

[19]  D. Cheng,et al.  Optimum spatial processing in a noisy environment for arbitrary antenna arrays subject to random errors , 1968 .

[20]  P. Rocca,et al.  Interval Analysis as applied to inverse scattering , 2012, Proceedings of the 2012 IEEE International Symposium on Antennas and Propagation.

[21]  J. Ruze,et al.  The effect of aperture errors on the antenna radiation pattern , 1952 .

[22]  J. K. Hsiao,et al.  Design of error tolerance of a phased array , 1985 .

[23]  Sensitivity of complex response zeros of linear power inversion arrays in the presence of random amp , 1993 .

[24]  A. Adams,et al.  Random Effects in Planar Arrays of Thin-Wire Dipoles , 1978, IEEE Transactions on Electromagnetic Compatibility.

[25]  R. Q. Lee,et al.  Measured mutual coupling between linearly tapered slot antennas , 1997 .

[26]  K. Madsen,et al.  Synthesis of nonuniformly spaced arrays using a general nonlinear minimax optimisation method , 1976 .

[27]  E. Hansen.  Global optimization using interval analysis — the multi-dimensional case , 1980 .

[28]  Ju-Hong Lee,et al.  Adaptive array beamforming with robust capabilities under random phase perturbations , 2005, IEEE Trans. Signal Process..

[29]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[30]  A. Zaghloul.  Statistical analysis of EIRP degradation in antenna arrays , 1985 .

[31]  D.H. Werner,et al.  Particle swarm optimization versus genetic algorithms for phased array synthesis , 2004, IEEE Transactions on Antennas and Propagation.

[32]  E. Hansen.  On solving systems of equations using interval arithmetic , 1968 .

[33]  Yuen Lo,et al.  Antenna pattern synthesis based on optimization in a probabilistic sense , 1975 .

[34]  T. Samaras,et al.  Self-Adaptive Differential Evolution Applied to Real-Valued Antenna and Microwave Design Problems , 2011, IEEE Transactions on Antennas and Propagation.

[35]  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.

[36]  P. Rocca,et al.  Handling Sideband Radiations in Time-Modulated Arrays Through Particle Swarm Optimization , 2010, IEEE Transactions on Antennas and Propagation.

[37]  A. Massa,et al.  ADS-Based Guidelines for Thinned Planar Arrays , 2010, IEEE Transactions on Antennas and Propagation.

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

[39]  R. Haupt,et al.  Low Sidelobe Arrays via Dipole Rotation , 2009, IEEE Transactions on Antennas and Propagation.

[40]  R. Haupt,et al.  Optimized Weighting of Uniform Subarrays of Unequal Sizes , 2007, IEEE Transactions on Antennas and Propagation.

[41]  P. Rocca,et al.  Analysis of the Pattern Tolerances in Linear Arrays With Arbitrary Amplitude Errors , 2013, IEEE Antennas and Wireless Propagation Letters.

[42]  L. Godara,et al.  The effect of phase-shifter errors on the performance of an antenna-array beamformer , 1985 .

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

[44]  D. Ashmead.  Optimum design of linear arrays in the presence of random errors , 1952 .

[45]  G.L. Soares,et al.  An Interval-Based Target Tracking Approach for Range-Only Multistatic Radar , 2008, IEEE Transactions on Magnetics.

[46]  A Massa,et al.  Hybrid ADS-Based Techniques for Radio Astronomy Array Design , 2011, IEEE Transactions on Antennas and Propagation.

[47]  T. Isernia,et al.  An Effective Deterministic Procedure for the Synthesis of Shaped Beams by Means of Uniform-Amplitude Linear Sparse Arrays , 2013, IEEE Transactions on Antennas and Propagation.

[48]  Jeongheum Lee,et al.  Decision of error tolerance in array element by the Monte Carlo method , 2005, IEEE Transactions on Antennas and Propagation.

[49]  Y. Rahmat-Samii,et al.  Particle swarm optimization in electromagnetics , 2004, IEEE Transactions on Antennas and Propagation.

[50]  Shiwen Yang,et al.  Design of a Low Sidelobe Time Modulated Linear Array With Uniform Amplitude and Sub-Sectional Optimized Time Steps , 2012, IEEE Transactions on Antennas and Propagation.

[51]  E. Jacobs,et al.  Phase error effects on gain and sidelobe level of a space-fed array , 1980 .

[52]  Harry L. Van Trees,et al.  Optimum Array Processing , 2002 .

[53]  R. Elliott.  Antenna Theory and Design , 2003 .

[54]  Ju-Hong Lee,et al.  Adaptive array beamforming with robust capabilities under random sensor position errors , 2005 .

[55]  G. Spagnuolo,et al.  Robust Design of Electromagnetic Systems Based on Interval Taylor Extension Applied to a Multiquadric Performance Function , 2008, IEEE Transactions on Magnetics.

[56]  Tommaso Isernia,et al.  Shaped Beam Antenna Synthesis Problems: Feasibility Criteria and New Strategies , 1998 .