Closed-form impulse response model of non-line-of-sight single-scatter propagation

For optical scattering communication, a closed-form expression of channel impulse response (CIR) is favorable for further system design and channel capacity analysis. Combining the mean value theorem of integrals and L'Hôpital's rule, the exact non-line-of-sight (NLOS) single-scatter propagation model is simplified to a closed-form CIR model for a laser source with a narrow beam. Based on this model, by joint geometrical and empirical approaches, a piecewise CIR expression is presented under certain system NLOS geometries. Through numerical results on CIR for various NLOS geometries, the proposed model is verified with the exact NLOS single-scatter propagation model and the previous Gamma fitting model, showing that our model agrees better with the former than the latter.