Broadcast in MIMO Systems Based on a Generalized QR Decomposition: Signaling and Performance Analysis
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Bibliographic record
Abstract
A simple signaling method for broadcast channels with multiple-transmit multiple-receive antennas is proposed. In this method, for each user, the direction in which the user has the maximum gain is determined. The best user in terms of the largest gain is selected. The corresponding direction is used as the modulation vector (MV) for the data stream transmitted to the selected user. The algorithm proceeds in a recursive manner where in each step, the search for the best direction is performed in the null space of the previously selected MVs. It is demonstrated that with the proposed method, each selected MV has no interference on the previously selected MVs. Dirty-paper coding is used to cancel the remaining interference. For the case that each receiver has one antenna, the presented scheme coincides with the known scheme based on Gram-Schmidt orthogonalization (QR decomposition). To analyze the performance of the scheme, an upper bound on the cumulative distribution function (CDF) of each subchannel is derived which is used to establish the diversity order and the asymptotic sum-rate of the scheme. It is shown that using fixed rate codebooks, the diversity order of the jth data stream, 1 les j les M, is equal to N(M - j + 1)(K - j + 1), where M, N, and K indicate the number of transmit antennas, the number of receive antennas, and the number of users, respectively. Furthermore, it is proven that the throughput of this scheme scales as M log log(K) and asymptotically (K rarr infin) tends to the sum-capacity of the multiple-input multiple-output (MIMO) broadcast channel. The simulation results indicate that the achieved sum-rate is close to the sum-capacity of the underlying broadcast channel.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it