Fundamental Relation Between Phased Array Radiation and Scattering Fields

In this article, the scattering mechanism of phased array antennas is systematically analyzed from the perspective of the scattering matrix representation. The scattering problem of an
$N$
-element phased array antenna is equivalent to an (
$N$
+ 1)-port microwave network described by an (
$N $
+ 1)
$\times $
(
$N$
+ 1) scattering matrix. The physical meanings of the coefficients in the matrix are analyzed, which imply different aspects of antenna properties like impedance matching and coupling, receiving, reradiation, and structural mode scattering. The coefficients associated with antenna receiving and reradiation are further studied to reveal the fundamental relation between phased array scattering and radiation fields. Eventually, the formulas to compute phased array scattering fields by radiation fields are deduced. Utilizing the formulas, phased array scattering under different element loads can be predicted precisely and rapidly by the precomputed data of an original phased array rather than repeating time-consuming full-wave computations. Furthermore, based on the fast scattering prediction approach, an efficient modified discrete particle swarm optimization algorithm is proposed to optimize the phased array element loads, and impressive improvement is made against the reported phased array scattering reduction approaches. The proposed scattering prediction and reduction approaches are well validated numerically and experimentally.