Distributed Collaborative Beamforming in the Presence of Angular Scattering
Bibliographic record
Abstract
In this paper, a collaborative beamformer (CB) is considered to achieve a dual-hop communication from a source to a receiver, through a wireless network comprised of K independent terminals. Whereas previous works neglect the scattering effect to assume a plane-wave single-ray propagation channel termed here as monochromatic (with reference to its angular distribution), a multi-ray channel termed as polychromatic due to the presence of scattering is considered, thereby broadening the range of applications in real-world environments. Taking into account the scattering effects, the weights of the so-called polychromatic CB (P-CB) are designed so as to minimize the received noise power while maintaining the desired power equal to unity. Unfortunately, their derivation in closed-form is analytically intractable due to the complex nature of polychromatic channels. However, when the angular spread (AS) is relatively small to moderate, it is proven that a polychromatic channel may be properly approximated by two rays and hence considered as bichromatic. Exploiting this fact, we introduce a new bichromatic CB (B-CB) whose weights can be derived in closed-form and, further, accurately approximate the P-CB's weights. Yet these weights, which turn out to be locally uncomputable at every terminal, are unsuitable for a distributed implementation. In order to circumvent this shortcoming, we exploit the asymptotic expression at large K of the B-CB whose weights could be locally computed at every terminal and, further, well-approximate their original counterparts. The performances of the so-obtained bichromatic distributed CB (B-DCB) and its advantages against the monochromatic DCB (M-DCB), which is designed without accounting for scattering, are analytically proved and further verified by simulations at practical values of K.
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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 | 0.000 | 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 | 0.000 |
| 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 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".