Dh. Werner et al., Closed-form representation for directivity of nonuniformly spaced linear arrays with arbitrary element patterns, ELECTR LETT, 35(25), 1999, pp. 2155-2157
A closed-form expression involving lambda functions is derived for the dire
ctivity of nonuniformly spaced symmetrical linear arrays which is valid for
a wide variety of commonly used antenna elements. It is shown that this ge
neral expression for directivity reduces to the well-known classical result
for a uniformly excited broadside array of isotropic sources with elements
spaced a half-wavelength apart.