{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TGSFC4XQRAF5KEDAG7GAI6YR2A","short_pith_number":"pith:TGSFC4XQ","schema_version":"1.0","canonical_sha256":"99a45172f0880bd5106037cc047b11d021f5410d1b27f68a6dd1b1ad85c1e062","source":{"kind":"arxiv","id":"1502.04860","version":1},"attestation_state":"computed","paper":{"title":"Low-Complexity QL-QR Decomposition Based Beamforming Design for Two-Way MIMO Relay Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Moon Ho Lee, Wei Duan, Wei Song","submitted_at":"2015-02-17T11:04:50Z","abstract_excerpt":"In this paper, we investigate the optimization problem of joint source and relay beamforming matrices for a twoway amplify-and-forward (AF) multi-input multi-output (MIMO) relay system. The system consisting of two source nodes and two relay nodes is considered and the linear minimum meansquare- error (MMSE) is employed at both receivers. We assume individual relay power constraints and study an important design problem, a so-called determinant maximization (DM) problem. Since this DM problem is nonconvex, we consider an efficient iterative algorithm by using an MSE balancing result to obtain "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.04860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-17T11:04:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9c37a72245026b32bea8fe1243b6c4e644d5c27c49eb9bceccf8eceeb0ad1942","abstract_canon_sha256":"af2cbd44484560c1301b92c4fdd7445f23cfd683a14a688223194eb45b1798ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:53.671465Z","signature_b64":"4n4HBgT2/9Z7kIg1+/OtbYIUr5TOBCtmnFbm6lS78EvVkIIZqSX285qC/IWG2Nj7AIixpztcTOnJgmqPn5SxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99a45172f0880bd5106037cc047b11d021f5410d1b27f68a6dd1b1ad85c1e062","last_reissued_at":"2026-05-18T02:26:53.670870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:53.670870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low-Complexity QL-QR Decomposition Based Beamforming Design for Two-Way MIMO Relay Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Moon Ho Lee, Wei Duan, Wei Song","submitted_at":"2015-02-17T11:04:50Z","abstract_excerpt":"In this paper, we investigate the optimization problem of joint source and relay beamforming matrices for a twoway amplify-and-forward (AF) multi-input multi-output (MIMO) relay system. The system consisting of two source nodes and two relay nodes is considered and the linear minimum meansquare- error (MMSE) is employed at both receivers. We assume individual relay power constraints and study an important design problem, a so-called determinant maximization (DM) problem. Since this DM problem is nonconvex, we consider an efficient iterative algorithm by using an MSE balancing result to obtain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04860","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.04860","created_at":"2026-05-18T02:26:53.670962+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04860v1","created_at":"2026-05-18T02:26:53.670962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04860","created_at":"2026-05-18T02:26:53.670962+00:00"},{"alias_kind":"pith_short_12","alias_value":"TGSFC4XQRAF5","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TGSFC4XQRAF5KEDA","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TGSFC4XQ","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A","json":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A.json","graph_json":"https://pith.science/api/pith-number/TGSFC4XQRAF5KEDAG7GAI6YR2A/graph.json","events_json":"https://pith.science/api/pith-number/TGSFC4XQRAF5KEDAG7GAI6YR2A/events.json","paper":"https://pith.science/paper/TGSFC4XQ"},"agent_actions":{"view_html":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A","download_json":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A.json","view_paper":"https://pith.science/paper/TGSFC4XQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04860&json=true","fetch_graph":"https://pith.science/api/pith-number/TGSFC4XQRAF5KEDAG7GAI6YR2A/graph.json","fetch_events":"https://pith.science/api/pith-number/TGSFC4XQRAF5KEDAG7GAI6YR2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A/action/storage_attestation","attest_author":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A/action/author_attestation","sign_citation":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A/action/citation_signature","submit_replication":"https://pith.science/pith/TGSFC4XQRAF5KEDAG7GAI6YR2A/action/replication_record"}},"created_at":"2026-05-18T02:26:53.670962+00:00","updated_at":"2026-05-18T02:26:53.670962+00:00"}