Optimal Algorithms and CRB for Reciprocity Calibration in Massive Mimo

Abstract

Gains from Massive MIMO are crucially dependent on the availability of channel state information at the transmitter which is far too costly if it has to estimated directly. Hence, for a time division duplexing system, this is derived from the uplink channel estimates using the concept of channel reciprocity. However, while the propagation channel is reciprocal, the overall digital channel in the downlink also involves the radio frequency chain which is non-reciprocal. This calls for calibration of the uplink channel with reciprocity calibration parameters to derive the downlink channel estimates. Initial approaches towards estimation of the reciprocity calibration parameters [1], [2] were all based on least squares. An ML estimator and a CRB for the estimators was introduced in [3]. This paper presents a more elegant and accurate CRB expression for a general reciprocity calibration framework. An optimal algorithm based on Variational Bayes is presented and it is compared with existing algorithms.