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.