Angular-Domain Channel Estimation for One-Bit Massive MIMO Systems: Performance Bounds and Algorithms

We consider angular-domain channel estimation in massive MIMO systems using one-bit analog-to-digital converters (ADCs) with various thresholding schemes at the receivers. We first derive the performance bounds for estimating angular-domain channel parameters, including the angles-of-arrival (AoA), angles-of-departure (AoD) and the associated path gains. Specifically, we derive 1) the deterministic Cramér-Rao bound (CRB) when all of the angular-domain channel parameters are treated as deterministic unknowns; 2) the hybrid CRB when some parameters have known prior probability density functions (pdfs) while the rest are assumed to be deterministic unknowns; 3) the Bayesian CRB when all of them have known prior pdfs. We also consider using the maximum likelihood (ML) method for channel estimation and a computationally efficient relaxation based cyclic algorithm (referred to as 1bRELAX) to obtain the ML estimates. When the prior information is available, the maximum a posteriori (MAP) and joint ML-MAP (JML-MAP) estimators are derived. We also use the one-bit Bayesian information criterion (1bBIC) to determine the number of scattering paths. Numerical examples are provided to verify the derived performance bounds with different thresholding schemes and demonstrate the performance of the proposed channel estimation algorithms.