A Novel Gridless Uplink/Downlink Channel Estimation Method for Millimeter Wave MIMO-OFDM Systems

Traditional grid-based compressed sensing algorithms usually suffer from the base mismatch effect in channel estimation problems. To address this, we propose a novel gridless uplink/downlink (UL/DL) channel estimation strategy for millimeter wave (mmWave) massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. By exploiting inherent sparsity in the angle-delay domain of the mmWave channel, we first formulate the UL channel estimation problem as a joint sparse signal recovery problem. Then, we introduce the reweighted atomic norm for enhancing angular resolution of the mmWave channel on continuous Fourier dictionaries; we suggest a novel reweighted atomic norm minimization (NRAM) algorithm to solve the channel estimation problem by leveraging the Hankel-Toeplitz block model with multiple measurement vectors (MMVs), and the original NRAM problem is approximated by the solution of a semi-definite programming (SDP) problem with structured sparsity, which is efficiently solved by a low-complexity alternating direction multiplier method (ADMM). Subsequently, in the frequency division duplex (FDD) system, we design a simplified DL channel estimation scheme by leveraging the angle-delay reciprocity of UL and DL channels. This scheme reconstructs the DL channel matrix using the angle and path delay estimated from the UL channel, along with the channel gain obtained through least squares (LS). Finally, simulation results validate that our proposed approach achieves superior channel estimation accuracy and reduces pilot overhead compared to conventional UL/DL channel estimation techniques.