On the capacity and energy efficiency of non‐coherent Rayleigh fading channels with additive Gaussian mixture noise
Bibliographic record
Abstract
This paper studies the capacity and energy efficiency of non‐coherent Rayleigh fading channels with Gaussian mixture noise where neither the transmitter nor the receiver has the knowledge of channel state information. The channel under consideration is suited for cellular networks having multi‐tier heterogeneous architectures in which the channel conditions change rapidly. In the first part of the paper, we characterize the structure of a capacity‐achieving input signal. Specifically, we establish an integrable upper bound on the integrand in the output entropy and demonstrate that there exists a unique optimal input. By formulating the Kuhn‐Tucker condition and establishing a diverging lower bound on it, we show that the optimal input is discrete having a finite number of mass points. Using this result, we investigate the capacity and energy efficiency of the considered channel in the second part of the paper. In particular, we first develop a numerical method to evaluate the optimal input and compute the capacity. The energy efficiency, which is related to the capacity and optimal input in low‐power regimes, is examined by calculating the minimum bit energy and wideband slope of the spectral‐efficiency curve. We also analytically show the optimality of an on‐off signal in this regime.
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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".