When does vectored Multiple Access Channels (MAC) optimal power allocation converge to an FDMA solution?

Vectored Multiple Access Channels (MAC) have attracted a lot of interest during the past few years. The optimal structure of vectored MAC in the uplink is based on the Successive Interference Canceller-Minimum Mean Square Error (SIC-MMSE). For equal weights and zero Signal to Noise Ratio (SNR) gap, the optimal transmit covariance matrices are found by iterative waterfilling. However, practical scenarios include nonzero SNR gap required to achieve the target probability of error at the desired data rate. With non-zero SNR gap, it is possible to achieve a weighted rate sum higher than iterative waterfilling by means of MAC-Optimal Spectrum Balancing (MAC-OSB). Moreover, it has been shown in the literature that the optimal power allocation for single-carrier flat scalar MAC with nonzero SNR gap is given by a Frequency Division Multiple Access (FDMA) type solution. In this paper, we investigate the problem of optimal power allocation for multi-carrier vectored MAC with non-zero SNR gap. Simulation results are given for VDSL2 channels and wireless channels. We confirm by simulations that FDMA is indeed the optimal power allocation in multi-carrier scalar MAC systems. When extending to multi-carrier vectored MAC systems, the optimal power allocation will tend towards a shared spectrum solution or a FDMA type solution depending on the level of crosstalk, the SNR, the SNR gap and the power constraints.