Pilot symbols for channel estimation in OFDM systems
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Bibliographic record
Abstract
We consider superimposing pilot symbols on to data symbols for channel estimation for orthogonal frequency division multiplexing (OFDM) systems. We first derive maximum-likelihood (ML) and minimum-mean square error (MMSE) iterative channel estimators. Modeling the time domain signal as Gaussian, we derive an ML channel estimator by averaging the likelihood function for both data and channel impulse response (CIR) over the resulting Gaussian vector. Two data detectors are also proposed by eliminating the CIR from the likelihood function. The resulting integer least squares problem can be efficiently solved using a sphere decoder (SD). Furthermore, the Cramer-Rao bound (CRB) for the superimposed channel and data estimation is derived. The equispaced pilot placement is optimal in superimposed training. The ideal performance benchmarks are reached by our proposed estimators. Their performance is comparable to that of a separated training scheme, but they offer a higher data rate.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 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 it