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 ($K \leq M$), is considered. 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. The minimum amount of feedback required at the BS, to achieve the maximum sum-rate capacity in the asymptotic case of $N \to \infty$ and different ranges of SNR is studied. In the fixed and low SNR regimes, it is demonstrated that to achieve the maximum sum-rate, an infinite amount of feedback is required. Moreover, in order to reduce the gap to the optimum sum-rate to zero, in the fixed SNR regime, the minimum amount of feedback scales as $θ(\ln \ln \ln N)$, which is achievable by the Random Beam-Forming scheme proposed in [14]. In the high SNR regime, two cases are considered; in the case of $K < M$, it is proved that the minimum amount of feedback bits to reduce the gap between the achievable sum-rate and the maximum sum-rate to zero grows logaritmically with SNR, which is achievable by the "Generalized Random Beam-Forming" scheme, proposed in [18]. In the case of $K = M$, it is shown that by using the Random Beam-Forming scheme and the total amount of feedback not growing with SNR, the maximum sum-rate capacity is achieved.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 | 0.001 |
| 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".