On the Eigenvalue Distribution of Correlated MIMO Channels by Character Expansion of Groups
Bibliographic record
Abstract
Multiple-input multiple-output (MIMO) channels have been studied from various aspects including the average of the mutual information between the transmitter and receiver (ergodic capacity) when the channel gains are known to the receiver only. A common approach for capacity analysis is to find the moment generating function (MGF) of the mutual information and by direct differentiation, the mean of the mutual information (capacity) is calculated. Recently, character expansions of groups have been used for integration over unitary matrices to obtain the joint eigenvalue distribution of the correlated Wishart matrix i.e. HH* where H is the zero mean full correlated complex Gaussian random MIMO channel matrix. In this paper, we show that the previous attempt for capacity analysis of full correlated MIMO channels is correct for square channel matrices only. We modify the approach from square matrices to rectangular matrices to obtain the correct joint eigenvalue distribution of the correlated Wishart matrix. The result can be used to obtain the MGF and the capacity of full correlated MIMO channels.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 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".