Enhanced receive spatial modulation based on power allocation

In this paper, we investigate the benefits of power allocation (PA) for multiple-input multiple-output (MIMO) receive spatial modulation (RSM) with both a total transmit power constraint (TTPC) and a per-antenna power constraint (PAPC). First, we derive optimal PA closed-form solutions that maximize the minimum distance d(min) between the received signal points for (N-t x 2)-element RSM with arbitrary phase-shift keying schemes (where N-t is the number of transmit antennas) subject to a TTPC. Based on the derived solutions and the error vector reduction (EVR) method, we propose a low-complexity iterative algorithm to identify PA parameters for high numbers of receive antennas (N-r >= 2). Specifically, the EVR-based PA (EVR-PA) algorithm resembles its traditional exhaustive-search-based counterpart, but only exploits the receive distances of a few dominant error vectors to iteratively optimize the PA matrix. Then, a more strict yet practical PAPC is considered for PA in RSM-MIMO systems, and a well-designed approximate convex optimization (ACO)-based iterative PA algorithm is proposed. Compared to EVR-PA, the ACO-based PA (ACO-PA) algorithm first formulates the PA problems with the PAPC in RSM into constrained quadratic program problems and then utilizes the powerful augmented Lagrangian multiplier to find their optimal solutions. Our simulation results show that the proposed EVR-PA- and ACO-PA-aided RSM schemes outperform the equal-power-allocated RSM- and PA-aided spatial multiplexing schemes