Channel Estimation and Data Detection in MIMO channels with 1-bit ADC using Probit Regression

We address in this article the uplink transmission in a multiple-input multiple-output channel employing 1-bit analog-to-digital converters at the base station, assuming no a priori channel state information. In particular, we investigate under the original "probit" statistical model, the problems of channel estimation and data detection by first formulating them as binary classification procedures based on the cross-entropy loss. Under perfect CSI, the proposed data detection scheme relaxes the exhaustive search requirement to a convex problem with a box boundary constraint that can be solved using gradient descent methods. Achievable mismatched rates of proposed metrics are evaluated with the generalized mutual information and symbol error rates are presented. Simulation results show that the proposed channel estimation scheme under the probit model does not exhibit any instability with imperfect CSI in comparison with the Bussgang linear minimum mean square error estimator.