Hellinger-Distance-Optimal Space Constellations

In this letter, we consider the space constellation design for a multi-input-multi-output optical wireless communication (MIMO-OWC) system equipped with a single photon avalanche diode receiver array (SPAD MIMO-OWC) in presence of log-normal fading. For conventional intensity modulated direct detection (IM/DD) MIMO-OWC with Gaussian noise, repetition code (RC), which transmits the same pulse amplitude modulation symbols, has been proved to be the diversity-optimal space-only constellation. However, different from IM/DD MIMO-OWC with Gaussian noise, the output of SPAD MIMO-OWC is Poisson distributed due to the photon-counting nature of SPADs. For such a system, the maximum likelihood function is difficult to provide a useful insight into energy-efficient signal designs. In this letter, we develop a vector-version Anscombe root transform-based receiver, for which the minimum Hellinger distance of transmitted constellation dominates the error performance. Then, an energy-efficient space constellation is attained by maximizing the worst case minimum Hellinger distance for a fixed average transmitted optical power within the non-negative orthants of a multidimensional space. Comprehensive simulations indicate that our proposed space constellation significantly outperforms RC, which is the best space constellation currently available for this system.