Unambiguous Manifold Analysis of Spatially Spread Dual-Polarized Dipole Array

In this article, the comprehensive analysis of the spatially spread dual-polarized dipole array (SSDDA) manifold ambiguity is conducted, and the sufficient conditions for the unambiguous array manifold geometries of the linear SSDDA (LSSDDA) and planar SSDDA (PSSDDA) are derived. Consequently, if one of the two linear horizontal dipole configurations is involved in the LSSDDA, i.e., the configuration owning adjacent horizontal dipoles and the configuration owning coprime horizontal dipoles’ spacings, the unambiguous 1-D direction-of-arrival (DOA) and polarization estimations can be achieved apart from vertically polarized signals. Similarly, if one of the two linear vertical dipole configurations is involved in the LSSDDA, i.e., the configuration owning adjacent vertical dipoles and the configuration owning coprime vertical dipoles’ spacings, the unambiguous 1-D DOA and polarization estimations can be achieved apart from horizontally polarized signals. Furthermore, it is also confirmed that when one of the two planar horizontal dipole configurations is integrated in the PSSDDA, i.e., the configuration owning adjacent horizontal dipoles along <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i>- and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i>-axes and the configuration owning coprime horizontal dipoles’ spacings along <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i>- and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i>-axes, the unambiguous 2-D DOA and polarization estimations are available except for the condition <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${p_{ph}}({\theta },{\varphi },{\gamma },{\eta }) = 0$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${p_{pv}}({\theta },{\varphi },{\gamma },{\eta }) \ne 0$</tex-math></inline-formula>. Meanwhile, when one of the two planar vertical dipole configurations is integrated in the PSSDDA, i.e., the configuration owning adjacent vertical dipoles along <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i>- and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i>-axes and the configuration owning coprime vertical dipoles’ spacings along <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i>- and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i>-axes, the unambiguous 2-D DOA and polarization estimations are available except for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${p_{ph}}({\theta },{\varphi },{\gamma },{\eta }) \ne 0$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${p_{pv}}({\theta },{\varphi },{\gamma },{\eta }) = 0$</tex-math></inline-formula>. Numerical simulations are performed to verify the proof of unambiguous LSSDDA and PSSDDA manifold geometries.