Hardware Impairments-Aware Design of noncoherent Grassmannian Constellations

In this paper, we propose a robust algorithm for designing unstructured Grassmannian constellations for noncoherent MIMO communications that accounts for the effect of hardware impairments (HWIs) such as I/Q imbalance (IQI) and carrier frequency offset (CFO). The algorithm uses the minimum diversity product as a cost function to ensure full-diversity constellations. The constellation points in the Grassmannian are optimized to be robust against any value of the HWIs belonging to a given uncertainty set, the values of which are determined by the characteristics of the hardware used. The cost function is optimized by means of a gradient ascent algorithm on the Grassmann manifold. Simulation results suggest that the constellations designed with the robust algorithm show a significant improvement in symbol-error-rate (SER) performance over the HWI-unaware algorithm optimized for ideal devices.