Sparse representation for massive MIMO satellite channel based on joint dictionary learning

A constrained joint dictionary learning (CJDL) algorithm for high-precision channel representation in massive multiple input multiple output (MIMO) satellite systems is proposed. Furthermore, taking into account the angular reciprocity of massive MIMO satellite systems, joint dictionary learning can establish a common support basis for both uplink and downlink. Previous deterministic dictionary has utilized deterministic basis, such as discrete Fourier transform (DFT) or orthogonal DFT (ODFT) basis, which tend to represent noise interference as part of channel characteristics. Furthermore, this deterministic dictionary is not able to adapt to dynamic communication environments. However, dictionary learning has shown the potential to significantly improve the accuracy of channel representation. Nevertheless, current research on training dictionary lacks analysis regarding constraints and boundary requirements, resulting in a suboptimal basis. To address this issue, conditional constraints associated with joint dictionary for channel representation are analysed. To screen for optimal basis, the joint dictionary is subject to constraints, including uplink and downlink constraints. Furthermore, the authors aim to quantify the maximum boundary of joint dictionary learning. Additionally, a joint dictionary updating method with singular value decomposition under constraint boundary conditions is proposed. Simulation results demonstrate that the proposed CJDL algorithm provides a more accurate and robust channel representation.