Low-Complexity CSI Feedback for FDD Massive MIMO Systems via Learning to Optimize

In frequency-division duplex (FDD) massive multiple-input multiple-output (MIMO) systems, the growing number of base station antennas leads to prohibitive feedback overhead for downlink channel state information (CSI). To address this challenge, state-of-the-art (SOTA) fully data-driven deep learning (DL)-based CSI feedback schemes have been proposed. However, the high computational complexity and memory requirements of these methods hinder their practical deployment on resource-constrained devices like mobile phones. To solve the problem, we propose a model-driven DL-based CSI feedback approach by integrating the wisdom of compressive sensing and learning to optimize (L2O). Specifically, only a linear learnable projection is adopted at the encoder side to compress the CSI matrix, thereby significantly cutting down the user-side complexity and memory expenditure. On the other hand, the decoder incorporates two specially designed components, i.e., a learnable sparse transformation and an element-wise L2O reconstruction module. The former is developed to learn a sparse basis for CSI within the angular domain, which explores channel sparsity effectively. The latter shares the same long short term memory (LSTM) network across all elements of the optimization variable, eliminating the retraining cost when problem scale changes. Simulation results show that the proposed method achieves a comparable performance with the SOTA CSI feedback scheme but with much-reduced complexity, and enables multiple-rate feedback.