Antenna pattern synthesis with multiple discrete and continuous nulls

Antenna pattern synthesis with a set of prescribed discrete nulls can be formulated as a least squares problem where the modified weight is in the null space of the antenna response matrix of the null region and the modified pattern is closest to the quiescent pattern. The solution involves determining the null space using the singular value decomposition (SVD) of the antenna response matrix of the null region. Here we are concerned with an antenna pattern synthesis problem in forming multiple nulls that include those that are continuously specified across intervals of prescribed widths. A conventional approach may involve discretizing the continuous nulls over the constraint width. An exact approach involves a quasi-matrix formulation of the antenna response or forming the correlation matrix over the continuous intervals. This paper uses quasiand mixed-matrix techniques to obtain the minimal set of basis vectors that best define nulls that may be continuously specified across intervals of prescribed widths; it then presents an efficient practical implementation procedure for inserting single as well as multiple extended and/or discrete nulls.