With the rapid development of mobile Internet, the demand for multicast is growing rapidly, such as content pushing and video streaming. The multicast service is usually offered to users without interrupting their on-going unicast transmission, and thus the multicast and unicast beamformers needs to be jointly designed, which generally requires perfect channel state information (CSI). However, perfect CSI is usually unavailable due to the channel estimation error. In this paper, we propose a learning based approach to jointly design the multicast and unicast beamformers with imperfect CSI. To learn the beamforming strategy, a new graph neural network (GNN) based architecture named unicast-multicast GNN (UMGNN) is proposed, which only requires the estimated channel. UMGNN can guarantee the permutation invariance/equivalence and model the special property in the multicast transmission, i.e., the multicast rate is determined by the worst user. Moreover, by sharing the parameters across different users, UMGNN exhibits a pretty good scalability to different number of users. Numerical results show that UMGNN outperforms a fully connected neural network and a widely used sampling-based algorithm. To highlight its performance in the multicast transmission, we also show that UMGNN can find the correct worst user that determines the multicast rate.

We consider a class of non-convex complex modulus constrained problems (CMCPs), which has many important applications in signal processing for wireless communications, including multicast beamforming and multi-input multi-output detection. Due to the non-convex constraints, traditional optimization-based algorithms either obtain sub-optimal solutions or take exponential complexity to reach the optimum. In this paper, we propose a learning based branch-and-bound (LBB) algorithm for solving the considered CMCPs. LBB regards the search procedure of the global optimal argument-cut based branch-and-bound (AC-BB) algorithm as a sequential decision problem in a binary tree and learns the optimal pruning policy via supervised learning. We first propose to apply ensemble learning to train multiple classifiers and then combine them to achieve better performance. To tackle the imbalanced issue, we propose an undersampling-supervised learning method to sample several balanced subsets and train a classifier on each of them. We also show that the computational complexity of LBB is determined by the depth of the binary tree and give its expression in the worst case. Finally, we validate the proposed LBB with two classic problems in wireless communications, i.e., multicast beamforming and MIMO detection. Numerical results show that LBB runs significantly faster than AC-BB while achieving nearly the same optimal performance.

Consider the single-group multicast beamforming problem in wireless systems, where a multi-antenna transmitter has a common message intended to a group of users. The problem is known be non-convex and NP-hard except in very few special cases. Traditional optimization-based algorithms either obtain sub-optimal solutions or take exponential complexity to reach the optimum. In this paper, we propose a learning based branch-and-bound (LBB) algorithm to find a near-optimal solution of the quality-of-service (QoS)-constrained multicast beamforming problem with affordable computational complexity. LBB regards the search procedure of the argument-cut based branch-and-bound (AC-BB) algorithm as a sequential decision problem in a binary tree and learns the optimal pruning policy via supervised learning. We propose to apply ensemble learning to train multiple classifiers and then combine them to achieve better performance. To tackle the imbalanced issue, we propose an undersampling-supervised learning method to sample several balanced subsets and train a classifier on each of them. We also show that the computational complexity of LBB is determined by the depth of the binary tree and give its expression in the worst case. Numerical results show that LBB runs significantly faster than AC-BB while achieving nearly the same optimal performance.

Coded caching is effective in leveraging the accumulated storage size in wireless networks by distributing different coded segments of each file in multiple cache nodes. This paper aims to find a wireless coded caching policy to minimize the total discounted network cost, which involves both transmission delay and cache replacement cost, using tools from deep learning. The problem is known to be challenging due to the unknown, time-variant content popularity as well as the continuous, high-dimensional action space. We first propose a clustering based long short-term memory (C-LTSM) approach to predict the number of content requests using historical request information. This approach exploits the correlation of the historical request information between different files through clustering. Based on the predicted results, we then propose a supervised deep deterministic policy gradient (SDDPG) approach. This approach, on one hand, can learn the caching policy in continuous action space by using the actor-critic architecture. On the other hand, it accelerates the learning process by pre-training the actor network based on the solution of an approximate problem that minimizes the per-slot cost. Real-world trace-based numerical results show that the proposed prediction and caching policy using deep learning outperform the considered existing methods.