  Explicit channel state information at the transmitter side is helpful to
improve downlink precoding performance for multi-user MIMO systems. In order to
reduce feedback signalling overhead, compression of Channel State Information
(CSI) is essential. In this work different low complexity compressed sensing
algorithms are compared in the context of an explicit CSI feedback scheme for
5G new radio. A neural network approach, based on learned approximate message
passing for the computation of row-sparse solutions to matrix-valued compressed
sensing problems is introduced. Due to extensive weight sharing, it shares the
low memory footprint and fast evaluation of the forward pass with few
iterations of a first order iterative algorithm. Furthermore it can be trained
on purely synthetic data prior to deployment. Its performance in the explicit
CSI feedback application is evaluated, and its key benefits in terms of
computational complexity savings are discussed.
