On the Eigenvalue Distribution of Ricean MIMO Channels by Character Expansion of Groups
Bibliographic record
Abstract
Joint eigenvalue distribution of the noncentral complex Wishart matrix, i.e. HH* where H is the nonzero-mean complex Gaussian random channel matrix of a multiple-input multiple-output (MIMO) system, is required for the analysis of Ricean MIMO channels from different aspects, including the average of mutual information between the transmitter and the receiver (ergodic capacity), when the channel gains are known to the receiver only. Previous works rely on the available results in mathematics for the joint eigenvalue distribution, obtained by integration over unitary matrices using classic integration methods. In this paper, we present a powerful integration method over unitary matrices which exploits the representation theory and characters of groups. The method was originally proposed for square matrices. We modify the approach from square matrices to rectangular matrices to solve a more general integral over unitary matrices and obtain the joint eigenvalue distribution of the noncentral Wishart matrix. Our result is the generalization of the previous classical integral over unitary matrices so that the result is not restricted to diagonal and/or real matrices, particularly.
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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".