Embedded Patterns and Extended Array Admittance Matrix

Sparse arrays of antennas can sometimes be modeled without accounting for the mutual coupling. In that case, the array radiation pattern can be expressed as the product of two factors: the isolated antenna radiation pattern and the array factor. Using the array impedance matrix, this formalism can be extended to account for the mutual coupling when the array is made of single-mode antennas. In this letter, we propose an extension of that formalism to the case of multimode antennas. We show that, contrary to the single-mode case, the array impedance matrix and isolated element patterns are not sufficient to rigorously account for mutual coupling. Building on these concepts, we propose a new quantity, the extended array admittance matrix. Combined with a modal decomposition of the currents on the antennas, it can be used to rigorously account for mutual coupling between multimode antennas in an array. The proposed formalism is illustrated by numerical examples.