Maximum Likelihood Estimation of Carrier Frequency Offset in Correlated MIMO OFDM Systems
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Bibliographic record
Abstract
This paper discusses maximum likelihood (ML) carrier frequency offset (CFO) estimation based on virtual subcarriers for multiple-input multiple-output (MIMO) systems employing orthogonal frequency division multiplexing (OFDM) over Rayleigh fading channels. In our ML approach, the channel and data are treated as random variables, unlike existing ML approaches in which the channel and data are treated as unknown constants. This in turn enables us to incorporate the spatial correlation and transmit data correlation into the analysis. In particular, we derive closed-form cost functions which can be used to accurately estimate the CFO. We also derive the Cram r-Rao lower bounds (CRLBs) for these estimators. We show that the presence of these correlations does not impact the CFO estimation significantly, especially at high signal-to-noise ratio. We present several examples to support the analysis
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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 | 0.001 | 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 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