Grassmannian Signalling Achieves Tight Bounds on the Ergodic High-SNR Capacity of the Noncoherent MIMO Full-Duplex Relay Channel
Bibliographic record
Abstract
This paper considers the ergodic noncoherent capacity of a multiple-input multiple-output frequency-flat block Rayleigh fading full duplex relay channel at high signal-to-noise ratios (SNRs). It is shown that, for these SNRs, restricting the input distribution to be isotropic on a compact Grassmann manifold maximizes an upper bound on the cut-set bound. Furthermore, it is shown that, from a degrees of freedom point of view, no relaying is necessary and Grassmannian signalling at the source achieves the upper bound within an SNR-independent gap. When the source-relay channel is sufficiently stronger than the source-destination and relay-destination channels, it is shown that, with the number of relay transmit antennas appropriately chosen, a Grassmannian decode-and-forward scheme, which is devised herein, achieves the ergodic noncoherent capacity of the relay channel within an approximation gap that goes to zero as the SNR goes to infinity. Closed-form expressions for the optimal number of relay transmit antennas indicate that this number decreases monotonically with the source transmit power.
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How this classification was reachedexpand
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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".