Methods for formation of antenna array using asymmetry

An antenna system, comprising:

• a plurality of antenna elements arranged asymmetrically in an antenna array, each antenna element comprising:
• one or more first terminals that receive a vertically polarized wireless signal;
• and
• one or more second terminals that receive horizontally a polarized wireless signal;
• and
• a processing circuit that combines the vertically polarized signal and the horizontally polarized signal using a combiner after applying a 90-degree phase shift to the vertically polarized signal or the horizontally polarized signal to obtain a left-hand circularly polarized (LHCP) signal or a right-hand circularly polarized (RHCP) signal,
• wherein the antenna system is configured to steer a beam of the antenna array to a best antenna pattern,
• wherein the plurality of antenna elements are asymmetrically positioned and asymmetrically oriented in the antenna array to provide tunability to each antenna element, and
• wherein the antenna system is configured to steer the beam of the antenna array to the best antenna pattern by:
• positioning and orienting the plurality of antenna elements asymmetrically to form a geometrical structure in the antenna array;
• characterizing the geometrical structure of the antenna array in terms of multiple parameters;
• optimizing the multiple parameters off-line in conjunction with a plurality of quantized phase shift values to shape an antenna pattern;
• saving results of a plurality of off-line computations in a lookup table within the terminals;
• and
• indexing the lookup table by an input vector comprising multiple variables to determine selection of the best antenna pattern.