On the effect of the SLL-floor on the directivity of thinned arrays

This work explores the fundamental properties of the radiation pattern of an irregular array with a specified side lobe level (SLL) floor. We develop an analytical formulation that provides an accurate expression for the directivity and highlights an inherent trade-off between the SLL and the beam width of thinned arrays. By combining our proposed mathematical model with the ceiling on directivity imposed by the SLL floor, we derive a limit on the achievable degree of sparsity for the array. The developed theory is validated through numerical results. Finally, we discuss how we can incorporate directivity into the synthesis problem to mitigate the effects of the SLL floor.