Efficient Receive Antenna Selection Algorithms and Framework for Transmit Zero-Forcing Beamforming
Bibliographic record
Abstract
MIMO wireless downlinks using transmit zero-forcing beamforming (TZFBF) with M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> transmit antennas can serve up to K = M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> receivers, each equipped with one antenna. To maximize the sum rate, waterfilling can be used. It is shown that unlike classical waterfilling, TZFBF waterfilling cannot simply drop the poorer spatial modes during optimization. Instead, receive antenna selection (RAS) must be incorporated and achieving the maximum sum rate requires an exhaustive search over ∑ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|s|</inf> ( <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Mr</inf> C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|s|</inf> ) = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MT</sup> −1 iterations to find the optimal subset S of active receivers where |s| = 1,..., M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> . In principle, a separate RAS algorithm can be used in conjunction with waterfilling to reduce the exponential complexity O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MT</sup> ) of the exhaustive search to linear complexity O(M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> ). We develop optimization algorithms that emulate classical waterfilling by progressively reducing the effects of poor spatial modes in M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> iterations. They do so by performing RAS jointly during the waterfilling process at little additional complexity. By avoiding a separate RAS process, complexity is thus further reduced. For the typical case where K>M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> , we propose a 2-phase framework that helps reduce the overall complexity while meeting the TZFBF dimensional constraints. Numerical results over different channel conditions are given.
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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".