Channel Estimation in One-Bit Massive MIMO Systems: Angular Versus Unstructured Models

Millimeter wave (mmWave) massive MIMO cellular systems will be characterized by increased bandwidths and the ability to handle a large number of users. To cope with the power consumption problem due to an increased number of receive antennas, the idea of equipping one-bit ADCs at the base station has been proposed. The goal of this paper is to establish performance bounds on the channel estimation of one-bit mmWave massive MIMO receivers for different types of channel models. The Cramér-Rao bound (CRB) is a lower bound on the performance of unbiased estimators and sets a benchmark for the design of channel estimators. We consider both a structured channel model for a single user where the channel is composed of a superposition of multipaths characterized by path delays and directions-of-arrival (DOAs), and an unstructured channel model where the channel is a generic FIR filter. The Fisher information matrix (FIM) for these channel models are derived in closed form. The CRB is also extended to a dictionary-based channel model, where the path delays and DOAs are selected from small perturbations on a discrete grid, and a sparsity constraint applies to the vector of path loss components. We also derive the Bayesian CRB when the array response is imperfectly known and is affected by perturbations in the sensor pattern or position. The CRBs are evaluated numerically and the effects of various system parameters on the CRB are studied. The dependencies between channel parameters and the effect of array perturbations are also investigated.