Optimal rotations for quasi-orthogonal STBC with two-dimensional constellations
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Bibliographic record
Abstract
Quasi-orthogonal space-time block codes (QSTBC) achieve full diversity by constellation rotations. Several authors have introduced optimal rotation angles, found either by computer search or by analytical derivation. However, existing analytical methods do not seem general enough to analyze optimal rotations for arbitrary constellations, and some previous results seem to conflict. We present a novel method to exactly derive the coding gain of QSTBC as a function of the rotation angle and the minimum Euclidean distance of two-dimensional constellations such as the ones carved from lattices of squares and triangles, and phase-shift keying (PSK) constellations. The upper bound of coding gain for amplitude PSK (APSK) is also obtained. We find the whole range of optimal rotations for maximizing the coding gain of QSTBC. Simulation results confirm the theoretical analysis.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it