{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:4TNKKDLVZ5OHDN3AKCN2MBWJTV","short_pith_number":"pith:4TNKKDLV","schema_version":"1.0","canonical_sha256":"e4daa50d75cf5c71b760509ba606c99d42eae8e7069dc2ac08076b9813db7926","source":{"kind":"arxiv","id":"0710.5758","version":1},"attestation_state":"computed","paper":{"title":"Grassmannian Beamforming for MIMO Amplify-and-Forward Relaying","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Behrouz Khoshnevis, Raviraj Adve, Wei Yu","submitted_at":"2007-10-30T21:08:55Z","abstract_excerpt":"In this paper, we derive the optimal transmitter/ receiver beamforming vectors and relay weighting matrix for the multiple-input multiple-output amplify-and-forward relay channel. The analysis is accomplished in two steps. In the first step, the direct link between the transmitter (Tx) and receiver (Rx) is ignored and we show that the transmitter and the relay should map their signals to the strongest right singular vectors of the Tx-relay and relay-Rx channels. Based on the distributions of these vectors for independent identically distributed (i.i.d.) Rayleigh channels, the Grassmannian code"},"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":"0710.5758","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2007-10-30T21:08:55Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8c55f18d1e2040a4d8d671947855e57234ac34f7ca6b5c8d7657eef4a0ade884","abstract_canon_sha256":"80931eaca3133885449d28ec866a4be52680765214c05d9f9ae31787fe8b64dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:48.808128Z","signature_b64":"QLxV0J6hY2n8UOFeBC1szI/C4x+LaHkq9aHFBKnobhZudlPMYr8dDYA+9S+tBqFe1jG8xKH5SuvANweg4XBdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4daa50d75cf5c71b760509ba606c99d42eae8e7069dc2ac08076b9813db7926","last_reissued_at":"2026-05-18T00:58:48.807656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:48.807656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Grassmannian Beamforming for MIMO Amplify-and-Forward Relaying","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Behrouz Khoshnevis, Raviraj Adve, Wei Yu","submitted_at":"2007-10-30T21:08:55Z","abstract_excerpt":"In this paper, we derive the optimal transmitter/ receiver beamforming vectors and relay weighting matrix for the multiple-input multiple-output amplify-and-forward relay channel. The analysis is accomplished in two steps. In the first step, the direct link between the transmitter (Tx) and receiver (Rx) is ignored and we show that the transmitter and the relay should map their signals to the strongest right singular vectors of the Tx-relay and relay-Rx channels. Based on the distributions of these vectors for independent identically distributed (i.i.d.) Rayleigh channels, the Grassmannian code"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5758","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":"0710.5758","created_at":"2026-05-18T00:58:48.807726+00:00"},{"alias_kind":"arxiv_version","alias_value":"0710.5758v1","created_at":"2026-05-18T00:58:48.807726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5758","created_at":"2026-05-18T00:58:48.807726+00:00"},{"alias_kind":"pith_short_12","alias_value":"4TNKKDLVZ5OH","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"4TNKKDLVZ5OHDN3A","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"4TNKKDLV","created_at":"2026-05-18T12:25:55.427421+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/4TNKKDLVZ5OHDN3AKCN2MBWJTV","json":"https://pith.science/pith/4TNKKDLVZ5OHDN3AKCN2MBWJTV.json","graph_json":"https://pith.science/api/pith-number/4TNKKDLVZ5OHDN3AKCN2MBWJTV/graph.json","events_json":"https://pith.science/api/pith-number/4TNKKDLVZ5OHDN3AKCN2MBWJTV/events.json","paper":"https://pith.science/paper/4TNKKDLV"},"agent_actions":{"view_html":"https://pith.science/pith/4TNKKDLVZ5OHDN3AKCN2MBWJTV","download_json":"https://pith.science/pith/4TNKKDLVZ5OHDN3AKCN2MBWJTV.json","view_paper":"https://pith.science/paper/4TNKKDLV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0710.5758&json=true","fetch_graph":"https://pith.science/api/pith-number/4TNKKDLVZ5OHDN3AKCN2MBWJTV/graph.json","fetch_events":"https://pith.science/api/pith-number/4TNKKDLVZ5OHDN3AKCN2MBWJTV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4TNKKDLVZ5OHDN3AKCN2MBWJTV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4TNKKDLVZ5OHDN3AKCN2MBWJTV/action/storage_attestation","attest_author":"https://pith.science/pith/4TNKKDLVZ5OHDN3AKCN2MBWJTV/action/author_attestation","sign_citation":"https://pith.science/pith/4TNKKDLVZ5OHDN3AKCN2MBWJTV/action/citation_signature","submit_replication":"https://pith.science/pith/4TNKKDLVZ5OHDN3AKCN2MBWJTV/action/replication_record"}},"created_at":"2026-05-18T00:58:48.807726+00:00","updated_at":"2026-05-18T00:58:48.807726+00:00"}