We introduce CQnet, a neural network with origins in the CQ algorithm for solving convex split-feasibility problems and forward-backward splitting. CQnet's trajectories are interpretable as particles that are tracking a changing constraint set via its point-to-set distance function while being elements of another constraint set at every layer. More than just a convex-geometric interpretation, CQnet accommodates learned and deterministic constraints that may be sample or data-specific and are satisfied by every layer and the output. Furthermore, the states in CQnet progress toward another constraint set at every layer. We provide proof of stability/nonexpansiveness with minimal assumptions. The combination of constraint handling and stability put forward CQnet as a candidate for various tasks where prior knowledge exists on the network states or output.

The Massive Multiple Input Multiple Output (MIMO) system is a core technology of the next generation communication. With the growing complexity of CSI in massive MIMO system, traditional compressive sensing based CSI feedback has become a bottleneck problem that is limited in piratical. Recently, numerous deep learning based CSI feedback approaches demonstrate the efficiency and potential. However, the existing methods lack a reasonable interpretation of the deep learning model and the accuracy of the model decreases significantly as the CSI compression rate increases. In this paper, from the intrinsic properties of CSI data itself, we devised the corresponding deep learning building blocks to compose a novel neural network CQNet and experiment result shows CQNet outperform the state-of-the-art method with less computational overhead by achieving an average performance improvement of 8.07% in both outdoor and indoor scenarios. In addition, this paper also investigates the reasons for the decrease in model accuracy at large compression rates and proposes a strategy to embed a quantization layer to achieve effective compression, by which the original accuracy loss of 67.19% on average is reduced to 21.96% on average, and the compression rate is increased by 8 times on the original benchmark. The massive multiple-input multiple-output (MIMO) technology is considered one of the core technologies of the next generation communication system, e.g., 5G. By equipping large number of antennas, base station (BS) can sufficiently utilize spatial diversity to improve channel capacity.