High resolution quantization codebook design for multiple-antenna fading channels
Bibliographic record
Abstract
This paper investigates the asymptotic structure of the channel vector quantization codebook for limited-feedback multiple-input single-output fading channels. The design criteria is to minimize the average transmission power subject to a target outage probability. First, we consider the design of scalar channel magnitude quantization codebook and prove that the asymptotically optimal quantization levels are uniformly spaced in dB scale. Such optimality does not depend on the the channel magnitude distribution, as long as some regularity conditions are satisfied. It is shown that the gradient of the objective function (the average transmission power) with respect to such quantization levels diminishes as Np-3/2as the number of the levels Nptends to infinity. We then form a product channel vector quantization codebook comprising a uniform (in dB) channel magnitude quantization codebook and a spatially uniform channel direction quantization codebook and derive the optimal bitsharing law between the two codebooks. It is shown that the asymptotically optimal number of direction quantization bits is M-1 times the number of channel magnitude quantization bits, where M is the number of base station antennas. The paper also shows that as the target outage probability decreases, more bits should be allocated to magnitude quantization.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".