Broadband Multiple Cone-Beam 3-D IIR Digital Filters Applied to Planar Dense Aperture Arrays

A digital beamformer that can synthesize array factors (AFs) with multiple, ultrawideband (UWB), frequency-independent beams at lower computational complexity is proposed. The beamformer is based on a novel 3-D infinite impulse response (IIR) transfer function <formula formulatype="inline"><tex Notation="TeX">$H_{\rm MC}\left({\bf z}\right)$</tex></formula> having multiple cone-shaped passbands in the 3-D spatio–temporal (ST) frequency-domain <formula formulatype="inline"><tex Notation="TeX">$\mmb{\omega}\in\BBR^{3}$</tex></formula>. The magnitude frequency response and the AF of <formula formulatype="inline"> <tex Notation="TeX">$H_{\rm MC}\left({\bf z}\right)$</tex></formula> are simulated for dual- and single-passband cases. An element pattern of a broadband Vivaldi antenna is simulated at 1.4 GHz and is used to obtain the total array pattern. Computational complexity of <formula formulatype="inline"><tex Notation="TeX">$H_{\rm MC}\left({\bf z}\right)$</tex></formula> for single-passband (1Cone) case and that of the conventional phased array (PA) beamformer are derived. The magnitude frequency response of the proposed beamformer for 1Cone case and that of the PA beamformer are compared using the mean square error (MSE). For the given selectivity specified by the half cone angle <formula formulatype="inline"><tex Notation="TeX">$\epsilon={\hbox {5}}^{\circ}$</tex></formula>, proposed beamformer provides around 60% lower MSE for the same complexity and around 90% lower complexity for the same MSE compared with the PA beamformer.

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