Beamforming is an effective means to improve the quality of the received signals in multiuser multiple-input-single-output (MISO) systems. Traditionally, finding the optimal beamforming solution relies on iterative algorithms, which introduces high computational delay and is thus not suitable for real-time implementation. In this paper, we propose a deep learning framework for the optimization of downlink beamforming. In particular, the solution is obtained based on convolutional neural networks and exploitation of expert knowledge, such as the uplink-downlink duality and the known structure of optimal solutions. Using this framework, we construct three beamforming neural networks (BNNs) for three typical optimization problems, i.e., the signal-to-interference-plus-noise ratio (SINR) balancing problem, the power minimization problem, and the sum rate maximization problem. For the former two problems the BNNs adopt the supervised learning approach, while for the sum rate maximization problem a hybrid method of supervised and unsupervised learning is employed. Simulation results show that the BNNs can achieve near-optimal solutions to the SINR balancing and power minimization problems, and a performance close to that of the weighted minimum mean squared error algorithm for the sum rate maximization problem, while in all cases enjoy significantly reduced computational complexity. In summary, this work paves the way for fast realization of optimal beamforming in multiuser MISO systems.

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用于优化 MISO 下行链路波束成形的深度学习框架

波束成形是提高多用户多输入单输出 (MISO) 系统中接收信号质量的有效手段。传统上，寻找最佳波束成形解决方案依赖于迭代算法，这会引入高计算延迟，因此不适合实时实现。在本文中，我们提出了一个用于优化下行链路波束成形的深度学习框架。特别是，该解决方案是基于卷积神经网络和专家知识的利用获得的，例如上下行链路对偶性和最优解的已知结构。使用这个框架，我们为三个典型的优化问题构建了三个波束形成神经网络 (BNN)，即信号干扰加噪声比 (SINR) 平衡问题、功率最小化问题、和总速率最大化问题。对于前两个问题，BNN 采用监督学习方法，而对于和率最大化问题，则采用监督学习和无监督学习的混合方法。仿真结果表明，BNN 可以实现 SINR 平衡和功率最小化问题的近乎最优解，性能接近加权最小均方误差算法的和速率最大化问题，同时在所有情况下都显着减少了计算量复杂。总之，这项工作为在多用户 MISO 系统中快速实现最佳波束成形铺平了道路。而对于总速率最大化问题，则采用了监督和无监督学习的混合方法。仿真结果表明，BNN 可以实现 SINR 平衡和功率最小化问题的近乎最优解，性能接近加权最小均方误差算法的和速率最大化问题，同时在所有情况下都显着减少了计算量复杂。总之，这项工作为在多用户 MISO 系统中快速实现最佳波束成形铺平了道路。而对于总速率最大化问题，则采用了监督和无监督学习的混合方法。仿真结果表明，BNN 可以实现 SINR 平衡和功率最小化问题的近乎最优解，性能接近加权最小均方误差算法的和速率最大化问题，同时在所有情况下都显着减少了计算量复杂。总之，这项工作为在多用户 MISO 系统中快速实现最佳波束成形铺平了道路。而在所有情况下都享受显着降低的计算复杂度。总之，这项工作为在多用户 MISO 系统中快速实现最佳波束成形铺平了道路。而在所有情况下都享受显着降低的计算复杂度。总之，这项工作为在多用户 MISO 系统中快速实现最佳波束成形铺平了道路。