Feedback requirements in MIMO broadcast channels: An asymptotic analysis
Bibliographic record
Abstract
In this paper, we consider a downlink communication system in which a base station (BS) equipped with M antennas and power constraint P communicates with N users each equipped with K receive antennas. It is assumed that the receivers have perfect channel state information (CSI), while the BS only knows the partial CSI, provided by the receivers via feedback. We study the minimum amount of feedback required at the BS, to achieve the maximum sum-rate capacity in the asymptotic case of N rarr infin, considering various signal to noise ratio (SNR) regimes. The amount of feedback is defined as the total average number of binits sent to the BS from the users. It is shown in the paper that i) In the low and fixed SNR regimes, it is not possible to achieve the maximum sum-rate with finite amount of feedback. Moreover, in order to get arbitrarily close to the sum-rate capacity in the fixed SNR regime, the amount of feedback must grow logarithmically with the sum-rate capacity. It is also established that random beam-forming scheme, proposed in, is feedback optimal in these regimes. ii) In the high SNR regime, the minimum required amount of feedback to achieve the sum-rate capacity depends on the number of receive antennas; in the case of K < M and large enough SNR, the minimum amount of feedback grows linearly with the sum-rate capacity and in the case of K ges M, it grows at most logarithmically with the sum-rate capacity. Furthermore, the amount of feedback does not need to grow with SNR in the case of K ges M.
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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 | 0.003 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".