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The concept of massive spatial modulation aided multiple-input multiple-output (SM-MIMO) systems, where the base station (BS) is equipped with a large number of antennas and simultaneously serves several multi-antenna users that employ SM for their uplink transmission, has recently attracted substantial research interest. In this paper, we investigate the uplink bandwidth efficiency (BE) of single-cell massive SM-MIMO systems, and derive a new BE lower bound when the BS employs maximum ratio combining for uplink user detection. The proposed BE bound takes into account the impact of spatial correlations at the transmitter, of imperfect channel estimation, and of non-uniform power allocation among each user's antennas (i.e., different antennas are allocated with different levels of transmit power). These bounds are shown to be tight even when a moderate number of antennas is used by the BS. Based on this bound, a gradient ascent method-based optimization is carried out to find the optimal power allocation among the transmit antennas (TAs) of each user, so that the uplink BE can be maximized. More specifically, the optimal power allocation is found to be typically dependent both on the TAs' spatial correlation and on the large-scale attenuation of each user. Aided by this new power allocation scheme, a substantial BE gain can be achieved over the conventional uniform power allocation schemes, which is substantiated by our simulation results.

Bandwidth Efficiency Maximization for Single-Cell Massive Spatial Modulation MIMO: An Adaptive Power Allocation Perspective