Abstract
In this letter we consider beamforming (BF) with per user Quality of Service (QoS) requirements for a single-carrier frequency-division multiple-access (SC-FDMA) transmission employing a linear equalizer at the receiver. A virtual multiple-input multiple-output (V-MIMO) uplink transmission with user pairing is studied. The problem of finding the optimum BF filter coefficients that minimize the transmit power is addressed. It is shown that the optimum solution for a given data rate requirement can be analytically determined for zero-forcing (ZF) equalization, which results in an expression related to the solution available for optimum transmitter-receiver design assuming conventional linear modulation. The transmit power savings of BF compared to constant power allocation (CPA) for all subcarriers are analyzed for user pairing in the uplink of LTE. Additionally, BF for minimum mean-squared error (MMSE) equalization is investigated, for which it turns out that a numerical search algorithm has to be used for coefficient optimization. Numerical results show that the transmit power can be significantly reduced with the proposed BF scheme.
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