A Multi-Agent Complex-Valued LSTM Framework for mmWave Coordinated Beamforming in Interference Networks via Sub-6 GHz CSI

In this study, we explore the mmWave coordinated beamforming (CBF) for multi-cell multi-user interference networks. Given the challenges in obtaining accurate timely mmWave channels of mobile users, we leverage historical sub-6 GHz channel state information (CSI) to predict mmWave CBF vectors. Notably, there is a similarity between sub-6 GHz and mmWave channels when their transceivers are co-located, as observed in non-standalone (NSA) dual-connectivity networks. Consequently, we construct a deep neural network (DNN) to map historical multi-link sub-6 GHz CSI to mmWave CBF vectors. However, traditional DNNs and related data processing are designed for real-valued data, which may cause distortion when applied to complex-valued CSI. To address this, we adopt a complex-valued long-short term memory (CVLSTM) model capable of capturing temporal correlations in multi-link CSI. Moreover, we propose complex-valued feature and layer normalization to standardize the distribution of input and intermediate features, respectively. Furthermore, we propose a multi-agent self-supervised learning framework for centrally training the CVLSTM model and deploying it locally for each link to reduce control and communication overhead.We set the sum-rate objective and the CVLSTM as the critic and actor, respectively, thereby enabling self-supervised learning aimed at maximizing the sum-rate. As for the local execution, the CVLSTM requires only the interference, interfered, and own CSI of a single link to predict its beamforming vector. Simulation results verify the effectiveness and superiority of our proposed CVLSTM-based CBF framework compared with iterative optimization algorithm and other beamforming algorithms that also leverage sub-6 GHz channels. Besides, our results highlight the robustness and low complexity of the CVLSTM model.