Noisy feedback linear precoding: A Bayesian Cramér-Rao bound
Bibliographic record
Abstract
Transmitter precoding strategies in broadcast systems generally assume perfect knowledge of channel state information (CSI) at the transmitter. In this paper, we study linear precoding with arbitrary error in the CSI from an estimation theoretic point of view. We derive a Bayesian Cramer-Rao type bound on the sum mean squared error (SMSE) achievable at the receiver for any linear precoding scheme for arbitrary feedback noise and channel fading. We next specialize this result to power constrained precoders. It is shown that the regularity conditions of the bound may be significantly weakened for power constrained precoders. Interestingly, we obtain a bound whose validity depends on rather weak conditions of continuity and differentiability on the joint distribution of the channel and feedback. We demonstrate the bound by applying it to Gaussian, Nakagami-m and Weibull fading models, with the assumption of feedback corrupted by additive Gaussian noise.
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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 | 0.000 | 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 | 0.000 | 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.
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".