Molecular Communication (MC) is an important nanoscale communication paradigm, which is employed for the interconnection of the nanomachines (NMs) to form nanonetworks. A transmitter NM (TN) sends the information symbols by emitting molecules into the transmission medium and a receiver NM (RN) receives the information symbols by sensing the molecule concentration. In this paper, a model of how a RN measures and reconstructs the molecular signal is proposed. The signal around the RN is assumed to be a Gaussian random process instead of deterministic approach in a more realistic way. After the reconstructed signal is derived as a Doubly Stochastic Poisson Process (DSPP), the distortion between the signal around the RN and the reconstructed signal is derived as a new performance parameter in MC systems. The derived distortion which is a function of system parameters such as RN radius, sampling period and the diffusion coefficient of the channel, is shown to be valid by employing random walk simulations. Then, it is shown that the original signal can be satisfactorily reconstructed with a sufficiently low-level of distortion. Finally, optimum RN design parameters, namely RN radius, sampling period and sampling frequency, are derived by minimizing the signal distortion. The simulation results reveal that there is a trade-off among the RN design parameters which can be jointly set for a desired signal distortion.