The nature of molecular transmitter imposes some limitations on the molecule production process and its storage. As the molecules act the role of the information carriers, the limitations affect the transmission process and the system performance considerably. In this paper, we focus on the transmitter's limitations, in particular, the limited molecule production rate and the finite storage capacity. We consider a time-slotted communication where the transmitter opens its outlets and releases the stored molecules for a specific time duration to send bit "1" and remains silent to send bit "0". By changing the release duration, we propose an adaptive release duration modulation. The objective is to find the optimal transmission release duration to minimize the probability of error. We characterize the properties of the optimal release duration and use it to derive upper and lower bounds on the system performance. We see that the proposed modulation scheme improves the performance.Index Terms-Molecular transmitter, transmitter's limitations, production rate, storage capacity, release duration. 0. This contradicts (34) and completes the proof.
APPENDIX D PROOF OF LEMMA 3Consider the smallest optimal positive released molecule increment as ∆ * J . Remind that ∆ * j = 0 for j > J. We prove that ∆ * J ∈ [0, a J ]. We use contradiction. Suppose ∆ * J [0, a J ] i.e., ∆ * J > a J . This scheme is referred as scheme A. • Scheme A: Choose the smallest optimal positive ∆ J = ∆ * J