  Singular Value Decomposition (SVD) is a powerful tool for multivariate
analysis. However, independent computation of the SVD for each sample taken
from a bandlimited matrix random process will result in singular value sample
paths whose tangled evolution is not consistent with the structure of the
underlying random process. The solution to this problem is developed as
follows: (i) a SVD with relaxed identification conditions is proposed, (ii) an
approach is formulated for computing the SVD's of two adjacent matrices in the
sample path with the objective of maximizing the correlation between
corresponding singular vectors of the two matrices, and (iii) an efficient
algorithm is given for untangling the singular value sample paths. The
algorithm gives a unique solution conditioned on the seed matrix's SVD. Its
effectiveness is demonstrated on bandlimited Gaussian random-matrix sample
paths. Results are shown to be consistent with those predicted by random-matrix
theory. A primary application of the algorithm is in multiple-antenna radio
systems. The benefit promised by using SVD untangling in these systems is that
the fading rate of the channel's SVD factors is greatly reduced so that the
performance of channel estimation, channel feedback and channel prediction can
be increased.
