The problem of single-group multicast beamforming (SMBF) is well-known NP-hard. It motivates the pursuit of computationally efficient near-optimal solutions. Due to multicasting, the multicast group is bottlenecked by the user(s) with the minimum received signal-to-noise ratio (SNR). This paper provides an in-depth interpretation of the SMBF problem from the multicasting point of view and proposes to solve it in two steps: i) select the bottlenecking users by a machine learning approach based on determinantal point process (DPP), and ii) design the beamformer for the selected users. The DPP model jointly considers the magnitudes and directions of users’ channel vectors, and thus enables an efficient selection of the bottlenecking users. Moreover, for a specific channel model, the DPP model is only associated with network size and each takes a one-off training cost, thus can be used as a codebook. The proposed DPP-based subset selection is incorporated adaptively into two fast beamforming algorithms, i.e., the QR decomposition algorithm and the successive beamforming (SB) algorithm. They specifically design the beamformers for the selected users by leveraging channel orthogonalization therein. Numerical results demonstrate the superiority of the proposed QR-DPP and SB-DPP algorithms in terms of the performance-complexity compromise and their robustness to different scenarios.

中文翻译：

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基于行列式点过程的高效组播波束形成学习方法


单组多播波束成形（SMBF）问题是众所周知的 NP 难题。它激励人们追求计算效率接近最优的解决方案。由于多播，多播组受到具有最小接收信噪比（SNR）的用户的瓶颈。本文从多播的角度对SMBF问题进行了深入解释，并提出分两步解决：i）通过基于行列式点过程（DPP）的机器学习方法选择瓶颈用户，ii）为选定的用户设计波束形成器。 DPP模型联合考虑用户信道向量的大小和方向，从而能够有效地选择瓶颈用户。而且，对于特定的信道模型，DPP模型仅与网络规模相关，并且每个模型都需要一次性的训练成本，因此可以用作码本。所提出的基于DPP的子集选择被自适应地结合到两种快速波束形成算法中，即QR分解算法和连续波束形成（SB）算法。他们通过利用其中的信道正交化专门为选定的用户设计波束形成器。数值结果证明了所提出的 QR-DPP 和 SB-DPP 算法在性能复杂性折衷及其对不同场景的鲁棒性方面的优越性。