Randomized Resource Allocation in Decentralized Wireless Networks
Bibliographic record
Abstract
In this paper, we consider a decentralized wireless communication network with a fixed numberuof frequency subbands to be shared amongNtransmitter-receiver pairs. It is assumed that the number of active users is a realization of a random variable with a given probability mass function. Moreover, users are unaware of each other's codebooks and hence, no multiuser detection is possible. We propose a randomized frequency hopping (FH) scheme in which each transmitter randomly hops over a subset ofusubbands from transmission slot to transmission slot. Assuming all users transmit Gaussian signals, the distribution of the noise plus interference is mixed Gaussian, which makes calculation of the mutual information between the transmitted and received signals of each user intractable. We derive lower and upper bounds on the mutual information of each user and demonstrate that, for large signal-to-noise ratio (SNR) values, the two bounds coincide. This observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity. We compare the performance of the FH system to that of the frequency division (FD) system in terms of the following performance measures: average sum multiplexing gain (η(1)) and average minimum multiplexing gain per user (η(2)). We show that (depending on the probability mass function of the number of active users) the FH system can offer a significant improvement in terms of η(1)and η(2)(implying a more efficient usage of the spectrum). In the sequel, we consider a scenario where the transmitters are unaware of the number of active users in the network as well as the channel gains. Developing a new upper bound on the differential entropy of a mixed Gaussian random vector and using entropy power inequality, we obtain lower bounds on the maximum transmission rate per user to ensure a specified outage probability at a given SNR level. We demonstrate that the so-called outage capacity can be considerably higher in the FH scheme than in the FD scenario for reasonable distributions on the number of active users. This guarantees a higher spectral efficiency in FH compared to FD.
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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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".