Low-Complexity Receivers and Energy-Efficient Constellations for SPAD VLC Systems

In radio frequency wireless communications with additive white Gaussian noise (AWGN), the commonly used bipolar pulse amplitude modulation (PAM) is considered to be the most energy-efficient 1-D constellation and admits a fast maximum likelihood (ML) receiver. For visible light communication (VLC) over AWGN channels, the unipolar PAM constellations are generated by adding proper direct currents to the bipolar PAM and have the same properties. However, for VLC systems with single-photon avalanche diode (SPAD VLC), the channel has additive Poisson noise (APN), and as a result, modified PAM over APN channels is not energy-efficient and its ML receiver has exponentially increasing complexity against average bit rate per symbol. In this letter, we first propose a low-complexity Anscombe root (AR) receiver by using AR transformation to approximately transform the APN channels into AWGN channels. Then, for SPAD VLC, with this proposed AR receiver, an energy-efficient constellation is designed by minimizing the average transmitted optical power for a fixed minimum Euclidean distance and shown to be the squared version of unipolar PAM constellations. Furthermore, for this constellation, an equally spaced threshold receiver is developed. Extensive simulations indicate that: 1) the proposed receiver and the ML receiver have almost the same error performance for PAM and our optimally designed constellation, respectively and 2) our designed constellations significantly outperform the unipolar PAM constellation for ML and our proposed receivers.