Minimax mean-square-error transmit Wiener filter

A minimax solution of the transmit Wiener filter (TxWF) allocating identical mean-square-errors (MSEs) to all users is derived for multi-user multiple-input single-output (MU-MISO) systems with transmit processing. The conventional TxWF minimizes the sum MSE of all users and features the possibility to allocate different MSEs to the individual users depending on the given channel realization. In contrast, the modified minimax version is characterized by an equal user treatment resulting from a minimization of the maximum single-user MSE. Although this fairness can also be achieved by a transmit zero-forcing filter (TxZF), the minimax TxWF meets this equality with a reduced sum MSE since no other constraint is active than the fairness. Simulation results reveal, that our new approach features a decreased outage probability compared to the conventional TxWF and the TxZF, i.e., bit-error-rates (BERs) exceeding a certain threshold become less likely. Moreover, the new criterion (equal single-user MSEs) translates itself into nearly identical BERs to all users for every channel realization.