Pattern Synthesis With Multipoint Accurate Array Response Control

In this paper, the problem of pattern synthesis with antenna arrays is addressed, and new approaches based on the recently developed accurate array response control (<inline-formula> <tex-math notation="LaTeX">$ {\textrm {A}}^{2}\textrm {RC} $ </tex-math></inline-formula>) algorithm are presented. It is shown that the array weight vector obtained by the <inline-formula> <tex-math notation="LaTeX">$ {\textrm {A}}^{2}\textrm {RC} $ </tex-math></inline-formula> algorithm to control the normalized response at a single direction in each step belongs to a specific set. Thus, an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses. This results in the so-called multipoint accurate array response control (<inline-formula> <tex-math notation="LaTeX">$ {\textrm {MA}}^{2}\textrm {RC} $ </tex-math></inline-formula>) algorithm. Moreover, in order to avoid possible beam axis shift in pattern synthesis, a modified <inline-formula> <tex-math notation="LaTeX">$ {\textrm {MA}}^{2}\textrm {RC} $ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$ {\textrm {M}}^{2}{\textrm {A}}^{2}\textrm {RC} $ </tex-math></inline-formula>) algorithm is proposed by imposing a derivative constraint on the direction of beam axis. Representative numerical examples are provided to demonstrate the effectiveness of the proposed <inline-formula> <tex-math notation="LaTeX">$ {\textrm {MA}}^{2}\textrm {RC} $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$ {\textrm {M}}^{2}{\textrm {A}}^{2}\textrm {RC} $ </tex-math></inline-formula> algorithms for multipoint responses control and pattern synthesis.

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