Bit Allocation Laws for Multi-Antenna Channel Quantization: Multi-User Case
Bibliographic record
Abstract
This paper addresses the optimal design of limitedfeedback multi-user spatial multiplexing systems. A base station with M antennas is considered serving M single-antenna users, which share a common feedback link with a total rate of B bits per fading block. The optimization problem is cast in form of minimizing the average transmission power at the base station subject to users’ outage probability constraints. Our goal is to optimize the bit allocations among users and the corresponding channel magnitude and direction quantization codebooks in the asymptotic regime where B tends to infinity. In order to achieve a tractable formulation, we first fix the quantization codebooks and study the optimal power control problem. This leads to an upper bound for the average transmission sum power, which is then used to optimize the quantization codebooks and to derive the bit allocation laws. The paper shows that for channels in the real space, the number of channel direction quantization bits should be (M−1) times the number of channel magnitude quantization bits. It is further shown that users with higher requested QoS (lower target outage probabilities) and higher requested downlink rates (higher target SINR’s) should receive larger shares of the feedback rate. The paper also shows that, for the target QoS parameters to be feasible, the total feedback bandwidth should scale logarithmically with γ, the geometric mean of the target SINR values, and 1/q, the geometric mean of the inverse target outage probabilities. Moreover, the minimum required feedback rate increases if the users’ target parameters deviate from the average parameters γ and q. Finally, we show that, as B increases, the limited-feedback system performance approaches the performance of the perfect channel state information system as 2 B M2 .
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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".