{"paper":{"title":"Fixed-rank Rayleigh Quotient Maximization by an $M$PSK Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"Anastasios Kyrillidis, George N. Karystinos","submitted_at":"2014-01-27T19:59:31Z","abstract_excerpt":"Certain optimization problems in communication systems, such as limited-feedback constant-envelope beamforming or noncoherent $M$-ary phase-shift keying ($M$PSK) sequence detection, result in the maximization of a fixed-rank positive semidefinite quadratic form over the $M$PSK alphabet. This form is a special case of the Rayleigh quotient of a matrix and, in general, its maximization by an $M$PSK sequence is $\\mathcal{NP}$-hard. However, if the rank of the matrix is not a function of its size, then the optimal solution can be computed with polynomial complexity in the matrix size. In this work"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6968","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"}