Bussgang decomposition-based sparse channel estimation in wideband hybrid millimeter wave MIMO systems with finite-bit ADCs

Both the hybrid architecture and low precision analog-to-digital converters (ADCs) are considered to alleviate the burden of high power cost and hardware implementation of millimeter wave (mmWave) communication system. Accordingly, the channel estimation issue in wideband mmWave system with finite-bit ADCs becomes even challenging. To address this issue, the non-linear mmWave channel estimation problem is reformulated into a linear sparse signal recovery problem by utilizing the Bussgang decomposition. Then, based on the equivalent linear sparse model, a Bussgang decomposition-based OMP (BD-OMP) algorithm is proposed to both exploit the inherent sparsity of wideband mmWave channel and alleviate the quantization error. Furthermore, we analyze that the actual noise of linear sparse model consists of combined noise and distortion noise, which is related to the number of quantization bits, antennas, and received signal power in a large scale regime. In addition, the terminal condition of BD-OMP algorithm is derived based on the residual difference of two consecutive iterations, where the expectation of residual difference is the variance of the actual noise. Simulation results demonstrate that the proposed approach can significantly reduce the training overhead for estimating wideband mmWave channel with finite-bit ADCs at the receiver.