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A major challenge to implement the compressed sensing method for channelstate information (CSI) acquisition lies in the design of a well-performedmeasurement matrix to reduce the dimension of sparse channel vectors. Thewidely adopted randomized measurement matrices drawn from Gaussian or Bernoullidistribution are not optimal. To tackle this problem, we propose a fullydata-driven approach to optimize the measurement matrix for beamspace channelcompression, and this method trains a mathematically interpretable autoencoderconstructed according to the iterative solution of sparse recovery. Theobtained measurement matrix can achieve near perfect CSI recovery with fewermeasurements, thus the feedback overhead can be substantially reduced.

Compressed CSI Feedback With Learned Measurement Matrix for mmWave Massive MIMO