Downlink-Uplink Collaborative Channel Estimation for TDD Massive MIMO Communications

Channel estimation (CE) is a crucial component in massive multiple-input multiple-output (MIMO) communication systems, while existing CE methods require a large training overhead and suffer from limited estimation accuracy due to the excessively high number of antennas. In this paper, we focus on the CE problem for time-division duplex (TDD) massive MIMO systems, where downlink (DL) and uplink (UL) channels exhibit strong reciprocity. To fully exploit the channel reciprocity, we design a DL-UL collaborative channel sounding scheme that employs a limited number of transmit antennas on both sides to save training overhead. By integrating DL and UL channel measurements with different signal-to-noise ratios into two data-fitting terms, we formulate the CE problem as a downlink-uplink collaborative atomic norm minimization (DUCANM) problem and provide theoretical analysis to select the hyperparameters involved. A partially decoupled atomic norm minimization formulation is proposed to solve the DUCANM problem effectively. To further accelerate the computation of DUCANM, we propose a fast algorithm based on the alternating direction method of multipliers. Numerical simulations are provided that demonstrate the superiority of our proposed method in terms of CE accuracy, training overhead, and running time.