Performance Tradeoffs Offered by Beamforming in Cognitive Radio Systems: An Analytic Approach
Bibliographic record
Abstract
This paper studies the design of beamforming weights for a multi-antenna secondary transmitter in an underlay cognitive setting that simultaneously maximizes the secondary received-power while limiting the primary interference to some threshold ∈. With perfect channel state information (CSI), a closed-form expression for the maximum secondary received-power is found. Under imperfect CSI and when the beamforming weights are computed using the channel estimates, the actual secondary received-power, G, and the actual primary interference-power, I, are derived. We show that the mean E[G] has a term that grows linearly with the number of secondary antennas, N, and additional terms dependent on ∈. Consequently, we obtain tradeoffs between E[G] and c. Under perfect CSI, we show that small increases in c from zero lead to moderate enhancements in E[G] for small N. However, increasing N reduces the enhancements. Under imperfect CSI, the gain in E[G] is less compared to the perfect CSI case. Furthermore, we show that the dominant parts of E[I] are independent of N. Thus, we conclude that there is no significant loss for the secondary to perform null-steering beamforming instead. Moreover, it can employ additional antennas to improve E[G] without generating significant extra interference on the primary.
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".