2.2.3 Updating the weight matrix

After obtaining the original weight vector <sup>w</sup> <sup>¼</sup> ½ � <sup>w</sup>1; <sup>w</sup>2; … <sup>T</sup>, the weight matrix <sup>Q</sup> is updated as <sup>Q</sup> <sup>¼</sup> diag wð Þ j j <sup>1</sup> <sup>þ</sup> <sup>δ</sup> �<sup>p</sup> ; ð Þ j j <sup>w</sup><sup>2</sup> <sup>þ</sup> <sup>δ</sup> �<sup>p</sup> ð Þ ½ � ; … (usually, <sup>p</sup> is an integer greater than 1; it was demonstrated experimentally that p ¼ 2 is a better choice for our APS problem). To ensure that the weight matrix is effectively updated when a zero-valued component in w, we introduce a parameter δ>0. It is empirically demonstrated that δ should be set slightly smaller than the expected nonzero magnitudes of w.

#### 2.2.4 Forming the nonuniform array

The sparse weight vector w<sup>s</sup> is obtained by pruning the original weight vector, and then the antenna elements corresponding to nonzero-valued indices of w<sup>s</sup> are retained to form a nonuniform array with fewer elements.

The above steps (A, B, C) are repeated until the final synthesized array performance is satisfactory or the specified maximum number of iterations is attained.
