Closed-Form Expressions for the BER/SER of OFDM Systems With an Integer Time Offset
Bibliographic record
Abstract
This paper provides a detailed mathematical analysis of the impact of integer time offsets on the performance of OFDM systems. Although a number of approximate expressions for the probability of error in OFDM systems with integer time offset can be found in the literature, to the best of our knowledge, this work is the first that provides exact expressions. In particular, we derive exact closed-form expressions for the bit error rate (BER) and the symbol error rate (SER) of BPSK, QPSK, and 16-QAM modulation for transmission over both AWGN and Rayleigh fading channels. The effect of the fractional carrier frequency offset (CFO) is taken into consideration in the derivations. This makes the derived expressions more useful in evaluating the probability of error for OFDM systems with CFO only, especially in cases like 16-QAM modulation for transmission over Rayleigh fading channels where exact closed-form expressions are not available. For OFDM systems with a large number of subcarriers, an approximate method for evaluating the BER/SER is given. Finally, numerical results are included to demonstrate the exactness of the derived expressions and the accuracy of the approximate method.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".