Uniform Approximations for Wireless Performance in Fading Channels
Bibliographic record
Abstract
We derive uniform approximations (UAs) for typical performance measures such as error probability, outage probability and capacity of wireless transmissions over flat fading channels impaired by noise. Uniform refers to the fact that these approximations are accurate over the whole range (low to high) of signal-to-noise ratio (SNR) values. First, the high-SNR results of Wang and Giannakis are generalized and unified for an arbitrary performance measure. Second, we develop a Mellin-transform-based procedure to construct low- and high-SNR asymptotics of error probability or outage. Specifically, these asymptotics are related to the left- and right-sided poles of a Mellin product with respect to its fundamental strip. Third, by using multiple low-SNR terms and a single high-SNR term, UAs for the error probability of coherent modulation are constructed for Rayleigh fading, maximal-ratio-combining (MRC), selection-combining (SC), dual hop relaying, and co-channel interference. UAs are also developed for the error probability of single- and multi-channel differential modulation, the product of two Q functions, and the miss probability of energy detection. By using a single low-SNR term and multiple high-SNR terms, the outage probability UA is also developed. Finally, since the capacity measure is not an exponentially decaying function, we derive a UA for an intermediate function which is based on the moment-generating function (MGF) and ultimately, the resulting approximation for the capacity.
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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 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 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".