Sparsified Calibration: Ensuring Channel Sparsity in Massive MIMO Systems

Channel sparsity in the angular domain is a fundamental assumption in many applications in massive multiple-input multiple-output (MIMO) systems, such as channel estimation and pilot decontamination. This sparsity is crucial for supporting a higher number of data streams in future massive MIMO systems. However, in practical scenarios, channel sparsity cannot always be guaranteed due to various non-ideal factors, including radio-frequency (RF) gain mismatches, mutual coupling effects, inaccuracies in antenna location or near-field approximations, and non-ideal base station (BS) surroundings. To tackle this problem, this paper proposes a novel calibration scheme, termed sparsified calibration, which aims to ensure channel sparsity in massive MIMO systems. Different from traditional relative and absolute calibration methods, the proposed sparsified calibration focuses on calibrating the BS to ensure channel sparsity in massive MIMO systems with non-ideal conditions. To implement this calibration, general sparsified calibration (GSC) algorithms are developed based on dictionary learning theory. Additionally, when the dictionary matrix has specific structures, we propose tailored structured sparse calibration (SSC) algorithms that exploit these structures to enhance performance. Finally, numerical results are provided to demonstrate the effectiveness of the proposed methods, confirming that the sparsified calibration scheme can significantly enhance the sparsity of the channel and improve the overall performance of massive MIMO systems.