Operating a wireless MIMO system to determine forward and reverse channel reciprocity matrices relating a first wireless MIMO device and a second wireless MIMO device of the wireless MIMO system includes, during each of a plurality of time intervals, determining a forward composite channel estimates and a reverse composite channel estimates between the first wireless MIMO device and the second wireless MIMO device to yield a plurality of forward composite channel estimates and a plurality of reverse composite channel estimates. Operation continues with creating a mathematical relationship between the plurality of forward composite channel estimates and the plurality of reverse composite channel estimates and the forward and reverse channel reciprocity matrices. Operation concludes with finding a solution to the mathematical relationship between the plurality of forward composite channel estimates and the plurality of reverse composite channel estimates to yield the forward reciprocity matrix and the reverse channel reciprocity matrix.