Molecular signal modeling of a partially counting absorbing spherical receiver

To communicate at the nanoscale, researchers have proposed molecular communication as an energy-efficient solution. The drawback to this solution is that the histogram of the molecules' hitting times, which constitute the molecular signal at the receiver, has a heavy tail. Reducing the effects of this heavy tail, inter-symbol interference (ISI), has been the focus of most prior research. In this paper, a novel way of decreasing the ISI by defining a counting region on the spherical receiver's surface facing toward the transmitter node is proposed. The beneficial effect comes from the fact that the molecules received from the back lobe of the receiver are more likely to be coming through longer paths that contribute to ISI. In order to justify this idea, the joint distribution of the arrival molecules with respect to angle and time is derived. Using this distribution, the channel model function is approximated for the proposed system, i.e., the partially counting absorbing spherical receiver. After validating the channel model function, the characteristics of the molecular signal are investigated and improved performance is presented. Moreover, the optimal counting region in terms of bit error rate is found analytically.