Estimate-and-Forward Relaying in Diffusion-Based Molecular Communication Networks: Performance Evaluation and Threshold Optimization

In this paper, we propose and investigate an estimate-and-forward (EF) relaying scheme with half-duplex transmission protocol in a two-hop diffusion-based molecular communication (DMC) system under the influence of both residual and counting noises. The proposed relaying scheme forwards an estimate of the transmitted number of molecules, which is derived using maximum likelihood principle. Based on this estimate, we assess the performance of EF relaying in terms of molecular throughput and end-to-end error probability. Further, we calculate energy consumption in synthesizing the information molecules at the relay nanomachine. Thereafter, we optimize the detection threshold by solving the convex optimization problem using logarithmic barrier followed by modified Karush-Kuhn-Tucker conditions, Newton Raphson method, and finally rounding the solution to the nearest integer value. Numerical and simulation results show the improvement in molecular throughput when EF relaying scheme is employed in contrast to the baseline direct communication scheme. The systematic comparisons reveal the scenarios where EF scheme can be beneficial over the existing amplify-and-forward and decodeand-forward relaying schemes. Moreover, we examine the effect of various parameters on error performance of the considered DMC system. Eventually, we demonstrate the effectiveness of our optimization solution in terms of accuracy and convergence time.