Pre-Scaling Optimization for Space Shift Keying Based on Semidefinite Relaxation

The performance of space shift keying (SSK) is known to be dominated by the minimum Euclidean distance (MED) in the received SSK constellation. In this paper, we propose a method of enhancing the MED in the received SSK constellation and improving both the attainable performance and the power efficiency by means of symbol scaling at the transmitter. To this aim, we formulate a pair of optimization problems, one for maximizing the MED subject to a specific transmit power constraint and one for minimizing the transmit power subject to a MED threshold. As these problems are NP-hard, we re-formulate their optimization using semidefinite relaxations, which results in convex problem formulations that can be efficiently solved using standard approaches. Moreover, we design pre-scaling techniques for imperfect channel state information at the transmitter, where the existing approaches are inapplicable. Our results show that the proposed schemes substantially improve the power efficiency of SSK systems with respect to state-of-the-art techniques by offering an improved performance for specific transmit power requirements or, equivalently, a transmit power reduction for a given MED threshold.