Linear receivers for optical wireless scattering communication with multiple photon detectors

We propose linear minimum mean square error (LMMSE) receivers for optical wireless scattering communications with single transmitter and multiple receivers, namely the single-input multiple-output (SIMO) system, where the received signals exhibit the characteristics of discrete photons. We first propose an LMMSE receiver scheme based on photon counting detection, and then generalize to other type of receivers with amplification gains such as photomultiplier tube (PMT) and avalanche photodetector (APD). The proposed LMMSE receiver is designed for both on-off key (OOK) modulation and pulse-position modulation (PPM). Simulation results are provided to show the the bit estimation performance of the proposed LMMSE receivers. It is concluded that OOK incurs a larger estimation error at smaller required bandwidth, while M-PPM with M > 4 leads to a smaller estimation error with more bandwidth requirements.