Non-Coherent Detection for Diffusive Molecular Communication Systems

We study non-coherent detection schemes for molecular communication (MC) systems with negligible inter-symbol interference that do not require knowledge of the channel state information (CSI). In particular, we first derive the optimal maximum likelihood (ML) multiple-symbol (MS) detector for MC systems. As a special case of the optimal MS detector, we show that the optimal ML symbol-by-symbol (SS) detector can be equivalently written in the form of a threshold-based detector, where the optimal decision threshold is constant and depends only on the statistics of the MC channel. The main challenge of the MS detector is the complexity associated with the calculation of the optimal detection metric. To overcome this issue, we propose an approximate MS detection metric that can be expressed in closed form. In addition, we develop a non-coherent decision-feedback detector, which introduces a lower detection delay compared with the optimal MS detector, and a suboptimal blind detector, which has a significantly lower complexity than the optimal MS detector. Finally, we derive analytical expressions for the bit error rate (BER) of the optimal SS detector, as well as upper and lower bounds for the BER of the optimal MS detector. Simulation results confirm the analysis and reveal the effectiveness of the proposed optimal and suboptimal detection schemes compared with the benchmark scheme that assumes perfect CSI knowledge, particularly, when the number of observations used for detection is sufficiently large. Simulation results are also presented that show the performance of the proposed detectors, when inter-symbol interference is non-negligible.