Rate-Optimal Power Allocation for MIMO Channels Under Joint Total and Per-Group Power Constraints
Bibliographic record
Abstract
We consider a multiple-input multiple-output (MIMO) channel, in which the transmit antennas are partitioned into groups, each with a per-group power constraint (PGPC) and a total power constraint (TPC). We considered two cases: (i) right unitary-invariant, including Rayleigh, fading MIMO channels with perfect channel state information at the receiver (CSI-R), and (ii) massive MIMO channels with perfect CSI at the transmitter and the receiver (CSI-TR). For both cases, we show that the rate-optimal input covariance matrix is diagonal, implying reduced design complexity and independent signaling on each antenna. We derive closed-form expressions for the diagonal entries, i.e., the powers allocated to each antenna. For CSI-R channels, we derive a criterion to identify groups with active PGPCs. Majorization theory and Schur-concavity are used to obtain the optimal power allocations. For CSI-TR channels, we use the Karush-Kuhn-Tucker conditions to show that the PGPCs result in a ceiling profile, causing the rate-optimal power allocations to deviate from standard water-filling. Compared to numerical algorithms, our closed-form expressions are significantly more efficient to compute and guarantee globally optimality. Our analytical findings are validated via numerical experiments.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 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".