Optimization with controlled null placement in antenna array pattern synthesis

The optimal solution to the problem of minimizing the complex weight vector norm subject to a "look direction" and null constraints in array pattern synthesis is given. It is also shown that several constrained optimization problems in pattern synthesis, viz, constrained maximization of signal-to-noise ratio (SNR), constrained pattern gain maximization, and constrained least squares pattern synthesis are, in fact, equivalent. Reduction of the maximum gain in the look direction and the occurrence of main-lobe angular shifts which are inherent in constrained pattern synthesis are also investigated.