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Simultaneous Diagonalization Using Baseband Beamforming in mmWave MU-MIMO Systems

We consider the problem of simultaneous diagonalization of Hermitian matrices for the desired and co-channel interference terms of millimeter-wave (mmWave) multi-user multiple-input multiple-output systems. The joint unitary eigenvectors and the corresponding eigenvalues are known to assist in the mathematical tractability of key performance metrics, such as outage probability, ergodic capacity, and spectral efficiency. We formulate the signal-to-interference-plus-noise ratio in a canonical quadratic form and subsume the digital baseband beamforming vectors in the weight matrices of channels at the transmitter side. Next, a real scalar objective function is defined, which quantifies the correlation loss due to joint-diagonalization. The objective function is then maximized using baseband beamforming under the hardware constraints of the mmWave system. Through simulations, the proposed beamforming algorithm is evaluated by employing several non-linear optimization sub-routines, and it is shown that the “active-set” approach results in improved summary statistics both for the correlation metric and for the time complexity. We also reflect on the effect of optimization on the channel scatterers in mmWave systems.