Riemannian-Optimization-Based Hybrid Precoder for Spatial Modulation Aided Millimeter Wave MIMO

The millimeter wave (mmWave) technology is considered as the potential candidate for high speed telecommunications service in 5G wireless communication, as it offers a ten times larger spectrum than existing cellular systems. The generalized spatial modulation (GenSM) aided millimeter wave multiple input multiple-output (mm-wave MIMO) concept have attracted substantial research interest, as it could lead to significant performance enhancement of mm-wave MIMO while maintaining the antennas with reduced number of active chains. However, current solvers either get stuck in a local minimum or have much computational complexity of GenSM-aided mm-wave MIMO schemes because the non-convex nature of the hybrid precoding design incurs significant performance degradation. To address this problem, we employ the Riemannian Optimization (RO) algorithms for the design of a hybrid precoder for GenSM-aided mm-wave MIMOs in order to enhance the spectral efficiency (SE). That is, we first re-design the hybrid precoding structures, i.e., by integrating the RF chain power constraints into the objective function; this allows the original optimized problem with constraints to be transformed into an unconstrained optimization problem on a nonlinear search space. Next, by considering the characteristics of a digital precoder, we are able to construct a proper manifold, in which we could effectively apply the RO iterative gradient descent method for computing a better solution. Our simulation results show that the proposed RO-based hybrid precoder is able to (a) outperform traditional GenSM-aided mm-wave MIMOs schemes, and (b) achieve comparable SE performance, when compared with modern mm-wave MIMO schemes.