MMSE Beamforming for SC-FDMA Transmission over MIMO ISI Channels
Bibliographic record
Abstract
We consider transmit beamforming for single-carrier frequency-division multiple access (SC-FDMA) transmission over frequency-selective multiple-input multiple-output (MIMO) channels. The beamforming filters are optimized for minimization of the sum of the mean-squared errors (MSEs) of the transmitted data streams after MIMO minimum mean-squared error linear equalization (MMSE-LE), and for minimization of the product of the MSEs after MIMO MMSE decision-feedback equalization (MMSE-DFE), respectively. We prove that for SC-FDMA transmission in both cases eigenbeamforming, diagonalizing the overall channel, together with a nonuniform power distribution is the optimum beamforming strategy. The optimum power allocation derived for MMSE-LE is similar in spirit to classical results for the optimum continuous-time transmit filter for linear modulation formats obtained by Berger/Tufts and Yang/Roy, whereas for MMSE-DFE the capacity achieving waterfilling strategy well known from conventional single-carrier transmission schemes is obtained. Moreover, we present a modification of the beamformer design to mitigate an increase of the peak-to-average power ratio (PAPR) which is in general associated with beamforming. Simulation results demonstrate the high performance of the proposed beamforming algorithms.
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How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".