Given an array of antennae with a given specific layout, compute the complex coefficients with which to multiply each individual signal before adding them together so that the combined signal has unit gain in a specific direction, the so-called look direction, and the smallest average gain possible outside a certain neighborhood of the look direction.
The specific problem whose solution is shown above involved a hexagonally shaped hexagonal lattice, a look direction that is 40 degrees off bore sight (which is straight up), and the requirement to minimize the response at all angles 20 degrees or more away from the look direction. The large lobe is aligned along the look direction. The plot is in decibels vs direction. The peak of the main lobe corresponds to 0 dB. Each color band (green, blue, red, etc.) corresponds to a 10 dB reduction in signal strength. To see the AMPL file that was used to generate the surface shown above, click here.
LOQO was used to compute the response surface shown above. To get a better feel for the surface, set it in motion by dragging and releasing the globe. The problem is described in detail in: J. O. Coleman and R. J. Vanderbei, `` Random-Process Formulation of Computationally Efficient Performance Measures for Wideband Arrays in the Far Field,'' Proc. 1999 Midwest Symp. on Circuits and Systems, Las Cruces, NM, August 1999.