CTH07-4: Singular Value Decomposition of Correlated MIMO Channels

The singular value decomposition (SVD) is a important tool for MIMO radio communications. However, independent computation of the SVD for each matrix in a MIMO channel sample path places an ordering condition on the singular values that results in singular value sample paths whose evolution is not consistent with the structure of the underlying random process. This problem is addressed as follows: (i) a generic SVD with relaxed identification conditions is proposed, (ii) an optimization problem is formulated for computing the SVD´s of two adjacent matrices in the sample path with the objective of maximizing the correlation between the two matrices´ singular vectors, and (iii) an efficient algorithm is given for untangling the singular value sample paths. The algorithm produces a unique solution conditioned on the seed matrix´s SVD. The algorithm´s effectiveness is demonstrate on spatially correlated and spatially white MIMO channnels. A primary application of the algorithm is in closed loop MIMO communications and MIMO channel estimation in general.