Integer Linear Programming Roundoff Method for Arbitrary Planar Phased-Array Scanning

In this paper, an approximate linear formula of the relationship between element errors and beam pointing errors in an arbitrary planar array is derived. Based on the formula, a phase feeding method is proposed. The proposed method, referred to as integer linear programming (ILP) roundoff, significantly reduces beam pointing errors by controlling the state of the digital phase shifters through ILP. Examples are given showing that a 10 × 10 element planar array with 5 bit digital phase shifters using this method can reduce beam pointing errors to less than 1% compared with other methods.