Generalized bussgang LMMSE channel estimator for one-bit massive MIMO systems

We consider the problem of channel estimation for uplink massive multiple-input multiple-output systems, where one-bit analog-to-digital converters (ADCs) are used at the base station (BS) to quantize the received signal. In this paper, we study the problem of one-bit quantizer design when a Bussgang linear minimum mean square error (BLMMSE) estimator is used for channel estimation. We first extend the conventional Bussgang LMMSE estimator cite{LiTao17} to the general nonzero threshold case. We then analyze the estimation performance of the generalized Bussgang LMMSE estimator and investigate the design of quantization thresholds. A gradient descent scheme is developed to search for optimal quantization thresholds. Simulation results show that, with carefully devised quantization thresholds, the generalized Bussgang LMMSE estimator can achieve a substantial performance improvement over the conventional Bussgang LMMSE estimator.