Maximizing data rate-sum over vector multiple access channel

We discuss multiuser loading algorithms for maximum data rate-sum through a vector multiple access channel (MAC) with additive white Gaussian noise (AWGN). We prove that the maximum rate-sum can be obtained with very limited, if any, sharing of frequency and space dimensions of the channel between users, which significantly simplifies the optimal transmission technique and detection in case of two users. For arbitrarily narrow frequency subchannels, the maximum rate-sum in a two-user problem can always be achieved without having more than one user in each space-frequency channel dimension. The results apply, e.g., to single-input and multi-input multi-output (MIMO) wireless MAC channels with a small spread factor. The transmission efficiency is significantly improved in comparison with frequency-division multiple access (FDMA), the optimal transmission scheme for a scalar MAC