On the Optimal Performance in Asymmetric Gaussian Wireless Sensor Networks With Fading
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Bibliographic record
Abstract
We study the estimation of a Gaussian source by a Gaussian wireless sensor network (WSN) where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> distributed sensors transmit noisy observations of the source through a fading Gaussian multiple access channel to a fusion center. In a recent work Gastpar, [¿Uncoded transmission is exactly optimal for a Simple Gaussian Sensor Network¿, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IEEE Trans. Inf. Theory</i> , vol. 54, no. 11, pp. 5247-5251, Nov. 2008] showed that for a symmetric Gaussian WSN with no fading, uncoded (analog) transmission achieves the optimal performance theoretically attainable (OPTA). In this correspondence, we consider an asymmetric fading WSN in which the sensors have differing noise and transmission powers. We first present lower and upper bounds on the system's OPTA under random fading. We next focus on asymmetric networks with deterministic fading. By comparing the obtained lower and upper OPTA bounds under deterministic fading, we provide a sufficient condition for the optimality of the uncoded transmission scheme for a given power tuple \mbi <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> =( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,..., <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PL</i> ) . Then, allowing the sensor powers to vary under a weighted sum constraint (this includes the sum-power constraint as a special case), we obtain a sufficient condition for the optimality of uncoded transmission and provide the system's corresponding OPTA.
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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 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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