Using a new structured joint congruence (STJOCO) transformation of Hermitian matrices for precoding in multi-user MIMO systems

In this paper, we propose a new algorithm for jointly processing a set of Hermitian matrices. It is called structured joint congruence (STJOCO) transformation. Instead of simultaneously diagonalizing a set of matrices, the STJOCO transformation finds a non-singular matrix which jointly minimizes the squared magnitude of the off-diagonal elements in the ith row and the ith column of the ith matrix in the set. The STJOCO transformation is proposed for real-valued as well as complex-valued matrices and the corresponding new scaling-invariant cost function is introduced. Numerical simulations demonstrate the efficiency of the algorithm. As an example application for the STJOCO transformation we present coordinated beamforming (CBF), where the system has a smaller number of transmit antennas than the aggregate number of receive antennas. In the literature, the transmit-receive beamforming weights of CBF are obtained via iterative algorithms, where the convergence of these iterative algorithms cannot be guaranteed. We show that the STJOCO transformation represents an elegant closed-form solution for the transmit-receive beamforming weights of CBF and can achieve the same sum rate performance as existing iterative algorithms.