An efficient generalized sphere decoder for rank-deficient MIMO systems
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Bibliographic record
Abstract
We derive a generalized sphere decoder (GSD) for rank-deficient multiple input multiple output (MIMO) systems using N transmit antennas and M receive antennas. This problem arises when N>M or when the channel gains are strongly correlated. The upper triangular factorization of the Grammian yields an under-determined system and the standard sphere decoding (SD) fails. For constant modulus constellations, we modify the maximum likelihood (ML) cost metric so that the equivalent Grammian is rank N. The resulting GSD algorithm has significantly lower complexity than previous algorithms. A method to handle nonconstant modulus constellations is also developed.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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.
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