Description
Squared Generalized Cosine Similarity (SGCS) is a metric defined in 3GPP NR specifications to evaluate the alignment or similarity between two complex vectors, often representing beamforming weights or channel state information. Mathematically, for vectors **a** and **b**, SGCS is computed as |**a**^H **b**|^2 / (||**a**||^2 ||**b**||^2), where ^H denotes the conjugate transpose. This yields a value between 0 and 1, indicating orthogonality (0) or perfect alignment (1). In NR, SGCS is applied primarily in beam management procedures to assess how similar candidate beams are, which informs decisions on beam switching, combining, or refinement.
Architecturally, SGCS is utilized within the gNB and UE physical layer algorithms, as detailed in specifications like 38.212 (multiplexing and channel coding) and 38.214 (physical layer procedures). It operates on beamforming vectors derived from channel measurements, such as those obtained via Channel State Information Reference Signals (CSI-RS) or Synchronization Signal Blocks (SSBs). The gNB may calculate SGCS between different beam pairs to identify redundant beams or to optimize multi-beam transmissions, reducing interference and improving spectral efficiency.
How it works: During beam management, the UE reports measurements like Reference Signal Received Power (RSRP) for multiple beams. The gNB can compute SGCS between the reported beams' spatial characteristics to determine if they are sufficiently distinct. For instance, in a multi-panel UE scenario, SGCS helps decide whether to use multiple simultaneous beams (spatial multiplexing) or switch to a single beam, based on similarity thresholds. This is critical for massive MIMO systems where numerous beams are available, and efficient selection is key to maintaining high throughput and coverage.
Key components include the beamforming codebook, from which vectors are selected, and the channel estimation module that provides the input vectors. SGCS is also referenced in 38.843 for non-terrestrial networks, where beam similarity assessment must account for dynamic satellite movements. By quantifying beam correlation, SGCS enables advanced features like beam failure recovery and coordinated multi-point transmission, ensuring robust performance in diverse deployment scenarios.
Purpose & Motivation
SGCS was introduced to address the complexity of beam management in NR, especially with massive MIMO and high-frequency bands (e.g., mmWave). Prior approaches relied heavily on RSRP-based beam selection, which could lead to suboptimal choices when beams have similar power but different spatial properties, causing interference or missed multiplexing opportunities. SGCS provides a standardized metric to evaluate beam similarity, enabling more intelligent beam coordination and resource allocation.
Historically, beam management in LTE was simpler due to limited MIMO layers. With NR's support for hundreds of antenna elements and flexible beamforming, a quantitative similarity measure became necessary to handle beam correlation and avoid redundant transmissions. SGCS, specified from Release 18, fills this gap by offering a mathematical foundation for comparing beam vectors, directly supporting features like multi-beam operation and enhanced mobility.
The motivation stems from the need to improve spectral efficiency and reduce overhead in dense beam environments. By using SGCS, networks can identify orthogonal beams for simultaneous transmission, enhance beam refinement accuracy, and adapt to rapid channel changes. This is particularly crucial for non-terrestrial networks in 38.843, where beam alignment must be dynamically adjusted due to satellite motion. Ultimately, SGCS contributes to higher data rates, better coverage, and reliable connectivity in advanced NR deployments.
Detected Changes Across Releases
from 3GPP Change RequestsSpecific changes extracted from the „Change history“ tables of 3GPP specifications (31 CRs across 5 releases). Complements the general historical overview above with the evidence-based evolution of this function.
In Release 15, the SGCS function was newly introduced to calculate the bitwidth for Channel State Information (CSI) fields, including PMI, RI, and CRI, for codebookType=typeI-SinglePanel reporting. It specifically defined procedures for determining payload sizes based on the number of configured CSI-RS resources within a resource set or a CSI-ReportSubConfig. The function also provided the methodology for mapping rank indicator field values and for handling differential reporting between two CSI-RS resources in a resource pair.
In Release 16, the SGCS function was enhanced to support more complex CSI reporting configurations involving multiple CSI-RS resources and resource pairs, as detailed in the updated bitwidth calculations for CRI, RI, and PMI fields. Specifically, new procedures were introduced for handling the number of CSI-RS resources (\(K_{s}^{CSI-RS}\)) within a resource set and for determining rank indicator values across single and multi-TRP scenarios. These updates also included corrections and clarifications for aperiodic CSI-RS triggering with specific beam switching timing values and for cross-carrier scheduling operations.
- Aperiodic CSI-RS Triggering for UE reporting beamSwitchTiming values of 224 and 336 TS 38.214CR0060
- Correction on aperiodic CSI-RS triggering with beam switching timing of 224 and 336 and on CSI reporting TS 38.214CR0107
- Correction on aperiodic CSI-RS triggering with beam switching timing of 224 and 336 TS 38.214CR0121
- Corrections for default TCI state of AP CSI-RS in multi-TRP TS 38.214CR0131
- Correction on increased number of CSI-RS for mobility per MO TS 38.214CR0133
- Active time duration of NZP CSI-RS resource TS 38.214CR0177
+ 5 more changes
In Release 17, the SGCS function was enhanced with corrections and clarifications for multi-TRP (mTRP) and multi-PDSCH operations. Specifically, this included corrections to the CSI-RS port restriction for mTRP CSI and the slot offsets for CSI-RS resource pairs used in MTRP. Furthermore, refinements were made to the handling of ZP CSI-RS for rate-matching in multi-PDSCH scheduling and to the aperiodic CSI-RS timing for configurations with mixed numerologies.
- CR for CSI-RS power for inter-cell mTRP TS 38.214CR0313
- CR on default QCL for unified TCI state for PDSCH and A-CSI-RS TS 38.214CR0314
- Correction on CSI-RS port restriction for mTRP CSI TS 38.214CR0319
- Correction on slot offsets of CSI-RS resource pairs for MTRP TS 38.214CR0320
- Correction on aperiodic CSI-RS for tracking for fast SCell activation TS 38.214CR0321
- Correction on frequency resource for CSI-RS for tracking in TS 38.214 TS 38.214CR0351
+ 3 more changes
In Release 18, the SGCS function was updated with clarifications and corrections for CSI reporting procedures, specifically addressing the bitwidth determination for PMI and RI fields when configured with a single CSI-RS port. The release also introduced handling for scenarios involving CSI-ReportSubConfig and corrected the reporting mechanism for 'ssb-Index-RSRP' to prevent erroneous dropping when CSI-RS is absent.
- Correction on threshold for A-CSI-RS reception for Rel-18 TCI framework TS 38.214CR0613
- Correction on CSI reporting for 1 CSI-RS port TS 38.212CR0160
- CR on clarification of CSI-RS transmission occasion for NCJT CSI TS 38.214CR0475
- ssb-index-RSRP/SINR CSI report dropping due to absence of CSI-RS TS 38.214CR0521
In Release 19, the SGCS function was updated to refine the counting of CSI-RS resources for simultaneous CSI reporting settings, specifically addressing configurations within CSI-ReportSubConfig. The changes clarified the determination of the bitwidth for fields like CRI and PMI by more precisely defining how the value \(K_{s}^{CSI - RS}\), representing the number of configured CSI-RS resources, is used in these calculations. Additionally, corrections were introduced for semi-persistent CSI procedures and the association between NZP CSI-RS and CSI-IM resources.
- TEI19 Counting of CSI-RS resource referred by N CSI reporting settings [SimCSI_count] TS 38.214CR0681
- TEI19 Simultaneous NZP-CSI-RS resource counting with NES [SimCSI_countNES] TS 38.214CR0689
- Correction on Semi-persistent CSI/Semi-persistent CSI-RS for LTM TS 38.214CR0733
- Correction on association between NZP CSI-RS and CSI-IM TS 38.214CR0744
Explore further
Broader topics and technologies where SGCS plays a role.
Defining Specifications
3GPP specifications that define or reference SGCS, with the latest known release. Sourced from the 3GPP document catalog — see methodology.
| Specification | Title | Release |
|---|---|---|
| TS 38.212 vj10 | NR Multiplexing and Channel Coding | Rel-19 |
| TS 38.214 vj10 | NR Physical Layer Procedures for Data | Rel-19 |
| TS 38.843 vj00 | Study on AI/ML for NR Air Interface | Rel-19 |