Abstract:

We study the temporal evolution of the singular value decomposition of vehicular 4 X 4 MIMO channel measurements H(t)in the 5.2 GHz band for a selected single OFDM sub-carrier. First, we estimate the number of relevant singular values p(t), 0 less-than p(t) less-than 4 for each sampling time t by applying the minimum descriptive length (MDL) criterion. The MDL criterion is used here as an estimate for the time-variant dimension p(t) of the dominant "signal" subspace. Then we characterize the dynamics of the estimated dominant singular subspaces by the principal angles between the corresponding subspaces at times t and t + delta where delta is the channel sounder's MIMO channel acquisition period which defines the resolution in the Doppler domain. These principle angles are closely related to covariances and measures of dependency. When principal angles are evaluated for pairs of column spaces of matrices, the principal angles describe canonical correlations of a matrix pair. Ultimately, we wish to describe the evolution of the dominant singular vectors as trajectories in the (complex) Stiefel manifold Vp(t),4 and the corresponding evolution of the dominanant subspaces as trajectories in the (complex) Grassmann manifold Gp(t),4.