How much feedback is required in MIMO Broadcast Channels?
Bibliographic record
Abstract
In this paper, a downlink communication system, in which a base station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas is considered. We study the minimum required amount of feedback at the BS, in order to achieve the maximum sum-rate capacity. First, we define the amount of feedback as the average number of users who send information to the BS. In the asymptotic case of N rarr infin, we show that with finite amount of feedback, it is not possible to achieve the maximum sum-rate. Indeed, in order to reduce the gap between the achieve sum-rate and the optimum value to zero, a minimum feedback of ln ln ln N is asymptotically necessary. Then, we consider a practical scenario, in which the amount of feedback is defined as the average number of bits which is sent to the BS. We show that to achieve the maximum sum-rate, infinite amount of feedback is required. Moreover, the minimum amount of feedback, in order to reduce the gap to the optimum sum-rate to zero, scales as otimes(ln ln ln N), which is achievable by the random beam-forming scheme proposed in M. Sharif and B. Hassibi, (2005)
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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 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".