The Diversity-Multiplexing Tradeoff of Lognormal Channels as a Function of the dB Spread
Bibliographic record
Abstract
In this paper, we investigate the dependency of the diversity-multiplexing tradeoff (DMT) of lognormal channels on their dB spread for both single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) channels. We tackle both the finite and the asymptotically high signal-to-noise ratio (SNR) regimes. The finite SNR DMT for a SISO lognormal channel is shown to be strongly dependent on the dB spread, [10/ln(10)]σx, where σxis the shaping parameter of the lognormal distribution. For different values of σx, the outage probability versus SNR curves on a log-log scale have different slopes and significant flooring for high values of σx. In order to capture the DMT dependency on the dB spread, the SNR gap between the outage curves of lognormal channels with different σxis derived. Moreover, the relative slopes of the outage probability curves are derived. Given that in the limiting-case of high SNR, the DMT for MIMO channels are dictated by the tail behaviour of their probability density function [1] and based on the similarities between the tail behavior of lognormal and normal random variables for very small σx≪1 dB, and lognormal and Gamma random variables for small to medium σx≤ 1.5 dB, we analyze the dependency of the high-SNR DMT for MIMO lognormal channels on σx. We show that for σx≪ 1, the lognormal fading channel behaves like a Gaussian one where the power control techniques are sufficient, whereas for medium to high values of σx, the lognormal channels act like regular multipath fading channels, and thus, diversity techniques should be utilized to improve communication reliability over such 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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".