  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.
