I think you refer to this paper:
The paper don't show any measurements results, only theory vs simulation results.
From my experience with array feeding networks I have doubts that this approach will work well in real life.
Especially vs frequency, because most of the arrays are not narrowband.
Grating lobes occur when the spacing between array antenna elements are large enough to permit in-phase addition of radiated fields in more than one direction.
Here are few proven approaches how to reduce the array grating lobes.
- Making the element spacing equal (or less) than λ/2 will ensure low grating lobes for any scan angle.
- Grating lobes may be reduced by applying an amplitude taper over the array (drive the outer elements with lower amplitude power).
- The antenna pattern of an antenna element (which forms the array) may reduce the grating lobes of the array to acceptable levels.
Most of the array designers do not spend much time on optimizing the performance of a single antenna element, part of the array. You could be better mathematician than Chebyshev, but if the performance of the antenna elements (each of them) is poor, the performances of the entire array will be poor.