Pattern synthesis of an array antenna with maximum directivity and nulls at specified directions

In order to solve a problem of maximizing a directivity of a transmitting array antenna with nulls at specified directions, we intended to utilize an adaptive antenna algorithm which enables the SNR to be maximum under the incidence of interferences. However, we encountered the discrepancy between transmitting antenna patterns and receiving ones. We investigated why this discrepancy arises, although a reciprocity theorem is effective between the transmitting pattern and the receiving one. Through these investigations, we derived the equation which determines the matched load impedances of the array elements and solved it numerically up to five elements. We also derived an equation to evaluate output voltages which are summed up into an output of the array and confirmed the coincidence between the transmitting pattern and the receiving one.