Hutt Systems together with IBE Systems Corporation, has applied non-linear search methods - both direct-search and gradient based methods - to the optimization of antenna arrays. Specifically, we have focused on using a novel algorithm termed Empirical Optimization to develop methods to optimize an array in a specific environment.

Publications

• S.J. Blank and M.F. Hutt, "Transmitter Illumination Taper as a Design Parameter for Wireless Power Transmission Systems", IEEE International Microwave Symposium 2012, Montreal, Canada, June 18, 201.
• S.J. Blank and M.F. Hutt, "Antenna Array Synthesis Using Derivative, Non-Derivative and Random Search Optimization", Sarnoff Symposium, Princeton, N.J., April 2008.
• S.J. Blank and M.F. Hutt, "On the Empirical Optimization of Antenna Arrays", IEEE Antennas and Propagation Magazine, 47, 2, April 2005, pp. 58-67
• Overview of Empirical Optimization

EmpOp^TM

Empop^TM is an application for the optimum synthesis of antenna arrays accounting for the effects of mutual coupling and scattering between the elements of the array and the nearby environment. It can also be used for the analysis of an array in a specified environment. The empirical optimization method employed by Empop^TM can find both the optimum set of array element locations (non-uniform spacing) as well as the optimum set of element excitations. This provides added degrees of freedom in achieving optimum array performance and in compensating for coupling effects, as compared to traditional analytical design methods. Non-uniform spacing offers special advantages in suppressing grating lobes in thinned arrays and in wide angle scan and broad frequency bandwidth array operation.

Features:

• Linear and Planar Array Optimization
• Optimum pattern synthesis, i.e. extraction of element excitations used to create a specified array pattern, based on the physical array dimensions
• Optimum synthesis to minimize sidelobe levels
• Optimum synthesis to minimize the power in the sidelobes
• Optimum synthesis of sum/diff patterns
• Optimization of complex valued element excitations and/or spacing
• Optimization can incorporate measured 'in-situ' element pattern data
• Optimization can incorporate element pattern data provided by advanced computational software such as NEC.

EmpOp^TM accounts for coupling between the elements of the array and nearby structure by using either measured or calculated element pattern data. The calculated element pattern data is obtained either by the induced emf method or by method of moments, e.g.,NEC.

Platform Support:

• 32 Bit Linux
• 64 Bit Linux
• Mac OSX 10.4

EmpOp^TM README file.

EmpopLite

EmpopLite Screen Shots

Empoplite is suitable for classroom use, to illustrate the effects of mutual coupling on antenna arrays and the benefits of optimization. Available for Windows only, it is restricted to thin wire elements of fixed length and radius.

The EmpopLite Eval is restricted to 8 elements. Unrestricted licenses are available. Please contact us for pricing.

Nelder-Mead Simplex Method

We have implemented several versions of the Nelder-Mead Simplex Method. It was originally written it in C, crosen.c, and then ported to FORTRAN 77, frosen.f and FORTRAN 90, frosen.90. The C and FORTRAN 77 versions compile with gcc and g77 respectively. The FORTRAN 90 version compiles with ELF90.

The programs have all been tested with Rosenbrock's function starting at -1.2,1.0 and converge after 54 iterations and 107 function evaluations. In each case the initial simplex is constructed as a regular simplex, as opposed to taking a particular step in the n coordinate directions from the starting point.

Creating the initial simplex in this way means that it will typically have to be scaled. However, we've found that we get better results, at least in our applications - Impedance matching, Optimization of antenna arrays.

nmlatest.c contains the Nelder-Mead algorithm as specified in Margaret H. Wright's paper on Direct Search Methods. It was tested with Rosenbrock's function, as before, with a starting point of -1.2,1.0 and converged after 53 iterations and 105 function evaluations.