Signal Detection under Short-Interval Sampling of Continuous Waveforms for Optical Wireless Scattering Communication

In optical wireless scattering communication, received signal in each symbol interval is captured by a photomultiplier tube (PMT) and then sampled through very short but finite interval sampling. The resulting samples form a signal vector for symbol detection. The upper and lower bounds on transmission rate of such a processing system are studied. It is shown that the gap between two bounds approaches zero as the thermal noise and shot noise variances approach zero. The maximum a posteriori (MAP) signal detection is performed and a low computational complexity receiver is derived under piecewise polynomial approximation. Meanwhile, the threshold based signal detection is also studied, where two threshold selection rules are proposed based on the detection error probability and the Kullback-Leibler (KL) distance. For the latter, it is shown that the KL distance is not sensitive to the threshold selection for small shot and thermal noise variances, and thus the threshold can be selected among a wide range without significant loss from the optimal KL distance. The performances of the transmission rate bounds, the signal detection, and the threshold selection approaches are evaluated by the numerical results.