Cramer-Rao Lower Bounds of DOA Estimates from Square QAM-Modulated Signals
Bibliographic record
Abstract
In this paper, we derive for the first time analytical expressions for the inphase/quadrature (I/Q) non-data-aided (NDA) Cramér-Rao lower bounds (I/Q NDA CRLBs) of the direction of arrival (DOA) estimates from square quadrature amplitude (QAM)-modulated signals corrupted by additive white circular complex Gaussian noise (AWCCGN) with any antenna configuration. Yet the main contribution embodied by this paper consists in deriving for the first time analytical expressions for the NDA Fisher information matrix (FIM) and then for the stochastic CRLB of the NDA DOA estimates in the case of square QAM-modulated signals. It will be shown that in the presence of any unknown phase offset (i.e., non-coherent estimation), the ultimate achievable performance on the NDA DOA estimates holds almost the same irrespectively of the modulation order. However, the NDA CRLBs obtained in the absence of the phase offset (i.e., coherent estimation) vary, in the high SNR region, from one modulation order to another.
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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 | 0.005 | 0.045 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".