Massive MIMO uplink and downlink joint representation based on couple dictionary learning

The challenge of jointly representing both the uplink (UL) and downlink (DL) in massive multiple input multiple output (MIMO) systems have been tackled. Considering the angular reciprocity, a couple dictionary learning (CDL) support to enhance performance and address high complexity has been introduced. This approach minimizes the number of pilots and improves accuracy. Currently, accuracy analysis of UL/DL representation primarily relies on simulation. To bridge this gap, a proportion factor (PF) operator is proposed for CDL to assess accuracy. Specifically, a qualitative analysis formula is provided for accuracy and an optimal upper bound is established. Through theoretical proof, it is demonstrated that the accuracy of CDL for representation is mainly influenced by the cross-correlation between the pilot matrix and the dictionary matrix. Inspired by PF operator, an optimal couple dictionary learning (OCDL) algorithm using singular value decomposition (SVD) is introduced to obtain dictionary updating, aiming at high-precision representation. By establishing normalized mean squared error (NMSE), successful representation ratio, bit error rate (BER), and constellation performance, an OCDL algorithm that outperforms existing methods is showcased and channel representation accuracy is enhanced significantly.