Compensation for missing array elements by direct beam synthesis

A theoretical formulation allowing optimization of phased-array beam patterns in the presence of missing elements is described. The approach specifies the desired beam pattern at a set of control points (directions) in the focal plane covering both the main beam and sidelobes. Complex element weights (for either transmit or receive) are found as the vector with minimum norm (i.e. minimum energy) minimizing the square error between the realized and the specified beam patterns at the control points. The method lends itself to a robust efficient numerical calculation permitting online implementation