Amplitude and Phase Estimation for Absolute Calibration of Massive MIMO Front-Ends

Massive multiple-input multiple-output (MIMO) promises significantly higher performance relative to conventional multiuser systems. However, the promised gains of massive MIMO systems rely heavily on the accuracy of the absolute frontend calibration, as well as quality of channel estimates at the base station (BS). In this paper, we analyze user equipment-aided calibration mechanism to estimate the amplitude scaling and phase drift at each radio-frequency chain connected to the BS array. Assuming a uniform linear array at the BS and Ricean fading, we obtain the estimation parameters with moment-based (amplitude, phase) and maximum-likelihood (phase-only) estimation techniques. In stark contrast to previous works, we mathematically articulate the equivalence of the two approaches for phase estimation. Furthermore, we rigorously derive a Cramér-Rao lower bound to characterize the accuracy of the two estimators. Via numerical simulations, we evaluate the estimator performance with varying dominant line-of-sight powers, dominant angles-of-arrival, and signal-to-noise ratios.