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 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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".