Generalized Bussgang LMMSE Channel Estimation for One-Bit Massive MIMO Systems

In this paper, we consider the problem of channel estimation for uplink multiuser massive MIMO systems, where, in order to significantly reduce the hardware cost and power consumption, one-bit analog-to-digital converters (ADCs) are used at the base station (BS) to quantize the received signal. We first extend the conventional Bussgang linear minimum mean square error (BLMMSE) estimator to the general nonzero threshold case. We then study the problem of one-bit quantization design, aiming at minimizing the mean squared error of the generalized BLMMSE estimator. A set partition scheme is proposed to devise the quantization thresholds. The rationale behind the proposed scheme is to divide each antenna's received samples into a number of disjoint subsets according to their pairwise correlation and assign diverse thresholds to those highly correlated data samples. In addition to the set partition scheme, a gradient descent scheme is developed to search for optimal quantization thresholds. The proposed schemes only require the statistical information of the received signals to devise the quantization thresholds, which can be calculated in advance before the training process begins. Simulation results show that the generalized BLMMSE estimator can achieve a significant performance improvement over the conventional Bussgang LMMSE estimator.