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We investigate weighted sum-rate maximization and rate-balancing problems for spectrum-sharing multiple-input-multiple-output orthogonal frequency-division-multiplexing (MIMO OFDM) based broadcast channels. The problem is solved by converting the MIMO OFDM channel into a block-diagonal form and applying the principle of multiple-access channel-broadcast channel (MAC-BC) duality. The algorithm in its dual form is solved using subgradient methods. The simulation results demonstrate the convergence of the algorithms.