Deep Unfolding Basis Pursuit: Improving Sparse Channel Reconstruction via Data-Driven Measurement Matrices

TL;DR

This paper introduces a data-driven approach to design measurement matrices for sparse channel estimation in massive MIMO systems, significantly improving reconstruction accuracy and reducing measurement requirements compared to traditional random matrices.

Contribution

It proposes a novel hybrid data-driven method using autoencoders to optimize measurement matrices, enhancing sparse channel reconstruction performance.

Findings

Data-driven measurement matrices outperform random matrices in accuracy.

Fewer measurements are needed for reliable channel estimation.

The hybrid approach surpasses pure deep learning methods in accuracy.

Abstract

For massive multiple-input multiple-output (MIMO) systems operating in frequency-division duplex mode, downlink channel state information (CSI) acquisition will incur large overhead. This overhead is substantially reduced when sparse channel estimation techniques are employed, owing to the channel sparsity in the angular domain. When a sparse channel estimation method is implemented, the measurement matrix, which is related to the pilot matrix, is essential to the channel estimation performance. Existing sparse channel estimation schemes widely adopt random measurement matrices, which have been criticized for their suboptimal reconstruction performance. This paper proposes novel data-driven solutions to design the measurement matrix. Model-based autoencoders are customized to optimize the measurement matrix by unfolding the classical basis pursuit algorithm. The obtained data-driven measurement matrices are applied to existing sparse reconstruction algorithms, leading to flexible hybrid data-driven implementations for sparse channel estimation. Numerical results show that the proposed data-driven measurement matrices can achieve more accurate reconstructions and use fewer measurements than the existing random matrices, thereby leading to a higher achievable rate for CSI acquisition. Moreover, compared with existing pure deep learning-based sparse reconstruction methods, the proposed hybrid data-driven scheme, which uses the novel data-driven measurement matrices with conventional sparse reconstruction algorithms, can achieve higher reconstruction accuracy.