LAUSR

Although there has been a wide investigation on channel estimation in frequency-division duplex (FDD) massive multiple-input–multiple-output (MIMO) systems, the effect of imperfect radio frequency (RF) chains have been largely ignored. In this paper, we consider a downlink massive MIMO system with in-phase/quadrature imbalance (IQI) at the base station (BS). Focusing on the joint estimation for channel and IQI, we model the joint estimation problem as a two-timescale non-convex optimization based on maximum a posteriori (MAP) estimate, where the IQI parameter is treated as the long-term variable and the sparse channel vector is short-term. We propose a batch algorithm and a two-timescale online joint sparse estimation (TOJSE) algorithm to solve the problem. The proposed batch algorithm utilizes all the previously received signals to update the current long-term variable, which can achieve better performance but with increasing computational complexity over time. In contrast, the TOJSE algorithm solves the short-term problem related to the current system state and constructs a recursive convex approximation to update the long-term variable in each iteration. Thus, the memory requirements and computational complexity of the TOJSE are remarkably reduced. Moreover, for the low mobility regime, a dynamic TOJSE algorithm is further presented to exploit the temporal correlation of channel support. Finally, the simulations show that our proposed algorithms can achieve significant gain over various baselines.