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 N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3/2</sup> as the number of the levels N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> tends 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 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".