A direction-controlled weighting factor of crossed-loop element radiation pattern is derived

which shows that under weighting condition the principle of pattern multiplication can be applied to phased circular arrays of arbitrarily-oriented crossed-loop elements. Up till now

the techniques for optimization are considered appropriate for an array of similarly-oriented identical directive elements. Such techniques are expressed by the ratio of two Hermitian forms. The paper holds that such techniques can be applied to phased circular arrays of arbitrarily-oriented crossed-loop elements.The paper proposes a formula of far-zone radiation field for phased circular arrays of arbitrarily-oriented crossed-loop elements

derives an expression of far-zone field for phased circular arrays of crossed-loop elements under the weighting condition

and the optimization formula by adjusting either complex excitation or phase.