Improved Orchard-Elliott pattern synthesis algorithm by pseudo-inverse and LMS

This paper describes a procedure to improve the Orchard-Elliott algorithm for shaped radiation pattern synthesis. By far, this algorithm results in the best performance for shaping radiation patterns. However, its iterative procedure occasionally suffers from singularity problems throughout the matrix inversion embedded in the algorithm for large number of array elements and small ripple in the shaped radiation pattern region. This deficiency that restricts the maximum number of elements for which the algorithm still converges, can be resolved by using a pseudo-inverse technique. Further improvement is gained by choosing better initial values, which are found through a simple LMS (least mean square) procedure. The proposed algorithm converges faster, can handle much higher number of array elements and enables to obtain very small ripple in the shaped region. The algorithm performance is demonstrated on the synthesis of a linear array with a symmetric flat-topped radiation pattern