Analysis for sparse channel representation based on dictionary learning in massive MIMO systems

Abstract The accuracy analysis of dictionary sparse representation for channels in massive MIMO systems is a relatively unexplored field. Existing research has primarily focused on investigating the accuracy of dictionary sparse representation using simulation in massive MIMO systems, but has not provided quantitative accuracy analysis. To address this gap, the correlation numerical proportional factor is proposed to represent the accuracy performance of non‐zero elements in the coefficient matrix. Additionally, a qualitative analytical formula for dictionary sparse representation accuracy is provided and an optimal upper bound for the correlation numerical proportional factor is established. Furthermore, the innovation indicates that the accuracy of dictionary sparse representation is mainly influenced by the cross‐correlation between the pilots matrix and the dictionary matrix, as well as sparsity. The author has also developed a method for minimizing the correlation numerical proportional factor. In order to obtain an optimal sparse representation coefficient matrix, a cross‐correlation matrix is constructed and an analytical expression is derived for it as well as its use as an optimal hard decision threshold is determined. Finally, a sparse representation coefficient optimization algorithm is proposed using this optimal threshold. Simulation results demonstrate that this algorithm can significantly improve channel sparse dictionary representation accuracy.