Once computationally impractical, wideband digital antenna arrays are now a reality thanks to the continued evolution of computing power. Whereas formerly wideband arrays required switched analog delay elements and attenuators, now the (nonadaptive) array-pattern synthesis can be performed by digital filtering of data sampled at the antenna, with the usual gains in precision and flexibility. A conventional approach to digital pattern synthesis is to simply approximate the analog hardware with digital filters. This has the same drawback as the analog system it replaces--it places artificial restrictions on the resulting array pattern. In most cases even ideal time-delay steering results in a suboptimal array response. It seems appropriate to rethink the problem of array pattern design from first principles taking an optimization viewpoint, since the tools now exist [1,2,3,4,5] to solve large problems posed as convex programs.
We first present a quick review of the far-field equations for narrowband and wideband antenna arrays, along with the classic time-delay approach to wideband pattern synthesis. We then show through a progression of examples how direct optimization of the array response pattern itself with respect to frequency and angle offers greater flexibility and performance than the time-delay approach.