{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:W2DKRPYFZ7TMUPQ6CVMZVFUXBB","short_pith_number":"pith:W2DKRPYF","canonical_record":{"source":{"id":"1409.5886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-20T13:36:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cb0b8a980c95a88d10725d79fb6c2f3dd36cac60625a9755e2a271963e6c7281","abstract_canon_sha256":"d8952fe3c50b41adcdfc7f7ebf51a839fb138d68ae021a7050378f92377d9512"},"schema_version":"1.0"},"canonical_sha256":"b686a8bf05cfe6ca3e1e15599a96970840a3a0334e9ab300c334d0ecf33f71e2","source":{"kind":"arxiv","id":"1409.5886","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5886","created_at":"2026-05-18T00:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5886v1","created_at":"2026-05-18T00:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5886","created_at":"2026-05-18T00:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"W2DKRPYFZ7TM","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2DKRPYFZ7TMUPQ6","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2DKRPYF","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:W2DKRPYFZ7TMUPQ6CVMZVFUXBB","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-20T13:36:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cb0b8a980c95a88d10725d79fb6c2f3dd36cac60625a9755e2a271963e6c7281","abstract_canon_sha256":"d8952fe3c50b41adcdfc7f7ebf51a839fb138d68ae021a7050378f92377d9512"},"schema_version":"1.0"},"canonical_sha256":"b686a8bf05cfe6ca3e1e15599a96970840a3a0334e9ab300c334d0ecf33f71e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:02.555463Z","signature_b64":"gv9TRG1m2Glwcq5jrgcAVYhmO6FIsau7oou6pp1cDHxe5MM1ZksD5KKnzKD5/fk70QgnYgRyngLrntSAfJZuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b686a8bf05cfe6ca3e1e15599a96970840a3a0334e9ab300c334d0ecf33f71e2","last_reissued_at":"2026-05-18T00:59:02.554833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:02.554833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5886","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rgprJ08S5AF+R813tZUmRbN4zqQzTiOGUu4HJHNtqV+BpwFdt5F2G0poQvGuM21k8ngW2kHpoj/WSZwhf2yCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T13:26:45.066676Z"},"content_sha256":"7e8a10637bcc41e3b62ae555c2144b36c8833beabf2eadd6e9753de249f3935f","schema_version":"1.0","event_id":"sha256:7e8a10637bcc41e3b62ae555c2144b36c8833beabf2eadd6e9753de249f3935f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:W2DKRPYFZ7TMUPQ6CVMZVFUXBB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"AMMSE Optimization for Multiuser MISO Systems with Imperfect CSIT and Perfect CSIR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bruno Clerckx, Hamdi Joudeh","submitted_at":"2014-09-20T13:36:04Z","abstract_excerpt":"In this paper, we consider the design of robust linear precoders for MU-MISO systems where users have perfect Channel State Information (CSI) while the BS has partial CSI. In particular, the BS has access to imperfect estimates of the channel vectors, in addition to the covariance matrices of the estimation error vectors. A closed-form expression for the Average Minimum Mean Square Error (AMMSE) is obtained using the second order Taylor Expansion. This approximation is used to formulate two fairness-based robust design problems: a maximum AMMSE-constrained problem and a power-constrained probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5886","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Bm56g3cuJk71a8xtoFsnFiX+r3bmRkosruYrUhYAtJZL0dvg7mYhw31U3Ay9HSqXjJJqoDHXmQhLkh49t1TDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T13:26:45.067461Z"},"content_sha256":"13394f8e78a5b74315c9e5c081c7e34dafac94f5386b48c2aafcf79590d5dce1","schema_version":"1.0","event_id":"sha256:13394f8e78a5b74315c9e5c081c7e34dafac94f5386b48c2aafcf79590d5dce1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2DKRPYFZ7TMUPQ6CVMZVFUXBB/bundle.json","state_url":"https://pith.science/pith/W2DKRPYFZ7TMUPQ6CVMZVFUXBB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2DKRPYFZ7TMUPQ6CVMZVFUXBB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T13:26:45Z","links":{"resolver":"https://pith.science/pith/W2DKRPYFZ7TMUPQ6CVMZVFUXBB","bundle":"https://pith.science/pith/W2DKRPYFZ7TMUPQ6CVMZVFUXBB/bundle.json","state":"https://pith.science/pith/W2DKRPYFZ7TMUPQ6CVMZVFUXBB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2DKRPYFZ7TMUPQ6CVMZVFUXBB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W2DKRPYFZ7TMUPQ6CVMZVFUXBB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d8952fe3c50b41adcdfc7f7ebf51a839fb138d68ae021a7050378f92377d9512","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-20T13:36:04Z","title_canon_sha256":"cb0b8a980c95a88d10725d79fb6c2f3dd36cac60625a9755e2a271963e6c7281"},"schema_version":"1.0","source":{"id":"1409.5886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5886","created_at":"2026-05-18T00:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5886v1","created_at":"2026-05-18T00:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5886","created_at":"2026-05-18T00:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"W2DKRPYFZ7TM","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2DKRPYFZ7TMUPQ6","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2DKRPYF","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:13394f8e78a5b74315c9e5c081c7e34dafac94f5386b48c2aafcf79590d5dce1","target":"graph","created_at":"2026-05-18T00:59:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we consider the design of robust linear precoders for MU-MISO systems where users have perfect Channel State Information (CSI) while the BS has partial CSI. In particular, the BS has access to imperfect estimates of the channel vectors, in addition to the covariance matrices of the estimation error vectors. A closed-form expression for the Average Minimum Mean Square Error (AMMSE) is obtained using the second order Taylor Expansion. This approximation is used to formulate two fairness-based robust design problems: a maximum AMMSE-constrained problem and a power-constrained probl","authors_text":"Bruno Clerckx, Hamdi Joudeh","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-20T13:36:04Z","title":"AMMSE Optimization for Multiuser MISO Systems with Imperfect CSIT and Perfect CSIR"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5886","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7e8a10637bcc41e3b62ae555c2144b36c8833beabf2eadd6e9753de249f3935f","target":"record","created_at":"2026-05-18T00:59:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d8952fe3c50b41adcdfc7f7ebf51a839fb138d68ae021a7050378f92377d9512","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-20T13:36:04Z","title_canon_sha256":"cb0b8a980c95a88d10725d79fb6c2f3dd36cac60625a9755e2a271963e6c7281"},"schema_version":"1.0","source":{"id":"1409.5886","kind":"arxiv","version":1}},"canonical_sha256":"b686a8bf05cfe6ca3e1e15599a96970840a3a0334e9ab300c334d0ecf33f71e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b686a8bf05cfe6ca3e1e15599a96970840a3a0334e9ab300c334d0ecf33f71e2","first_computed_at":"2026-05-18T00:59:02.554833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:02.554833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gv9TRG1m2Glwcq5jrgcAVYhmO6FIsau7oou6pp1cDHxe5MM1ZksD5KKnzKD5/fk70QgnYgRyngLrntSAfJZuAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:02.555463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e8a10637bcc41e3b62ae555c2144b36c8833beabf2eadd6e9753de249f3935f","sha256:13394f8e78a5b74315c9e5c081c7e34dafac94f5386b48c2aafcf79590d5dce1"],"state_sha256":"b764c0d4e82bb4365bf2b009dff6639fc6b0614a313298783145bbbdd8d4c6c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8PuJbosGee++w8EM0yO0ZFZJ7TvPLIZUJsyCr4uGjbwgCJRsRAyRmIK2q77pBlQVlhoqpg2DhfQiJNcAt/mBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T13:26:45.071459Z","bundle_sha256":"61115bfc59987ecc267423752a556b8a1580fa3421a8749d6ccae26839923266"}}