{"paper":{"title":"Closed-Form Directivity Expression for Arbitrary Volumetric Antenna Arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Bruno Felipe Costa, Taufik Abrao","submitted_at":"2018-10-01T17:57:27Z","abstract_excerpt":"It is proposed a closed-form expression of directivity for an arbitrary volumetric antenna arrays using a general element pattern expression of type $\\sin^u{(\\theta)}\\cos^v{(\\theta)}$, with $v > -\\frac{1}{2}$ and $u > -1$, and $u, v \\in \\mathbb{Z}$. Variations of this expression for different values of $v$ and $u$ are analyzed from the analytical and numerical perspectives. The parameters found in the closed-form expression are related to the order $v$ and $u$ of the element patterns, the rectangular spatial coordinate of each antenna element, the magnitude and phase excitation coefficients (c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01487","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}