Uplink-Downlink Duality in Normalized MSE or SINR Under Imperfect Channel Knowledge
Bibliographic record
Abstract
Duality between the multi-antenna multi-user uplink and the downlink has been discovered in terms of sum rate, capacity region, signal-to-interference-plus-noise-ratio (SINR) region or normalized mean-squared error (MSE) region. Previous work on duality has assumed perfect channel knowledge. However, channel estimation is never perfect in practice. In this paper, channel estimation error as well as antenna correlation at the base station (BS) is taken into account. A multi-user system with multiple antennas at the BS and with single-antenna users is studied. Joint detection and transmission are used in the uplink and the downlink, respectively. It is analytically shown that with imperfect channel state information (CSI), under the same sum power constraint, the achievable SINR regions or the normalized MSE regions in both links are the same, as in the case with perfect CSI. Monte Carlo simulation results and discussions are also provided to complement the analysis.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".