Golden Angle Modulation aided Fractional Spatial Modulation: System Design and Performance Optimization

A specific limitation of spatial modulation (SM) is that the number of transmit antennas must be a power of two, otherwise it will cause a fractional bits problem. To solve this problem, this paper proposes a novel transmission scheme, called golden angle modulation aided fractional spatial modulation (GAM-FSM), which exploits the property of golden angle modulation (GAM), i.e., it can have an arbitrary number of constellation points or the modulation order of GAM can be any positive integer. In addition, the average bit error probability (ABEP) and mutual information (MI) of our proposed GAMFSM scheme are derived. To further enhance the system performance, geometric and probabilistic constellation shaping aided GAM-FSM schemes are investigated and optimized under three optimization criteria, maximization of the minimum Euclidean distance (MMED), minimization of the the bit error rate (MBER) and maximization of the MI (MMI). Simulation results reveals the superiority of our proposed GAM-FSM over the conventional fractional spatial modulation (FSM) systems. Besides, simulation results also show that our proposed constellation shaping aided GAM-FSM schemes exhibit significant system performance improvements compared to the one without constellation shaping.