Performance bounds of estimators in molecular communications under structural constraints

Parameter estimation is a key task in many aspects of communication systems including molecular communications (MC). The performance of parameter estimators involved in MC has been so far assessed using the Cramer-Rao lower bound (CRLB). However, for the discrete-amplitude parameters associated with the released "information molecules" in MC, pertinent regularity conditions do not hold, and consequently the CRLB does not exist. In this context, the present paper advocates the more general Hammersley-Chapman-Robinson lower bound (HCRLB), for MC parameter estimation. As a special case of practical importance, estimation of the number of released molecules, N, is investigated. A simple yet tight approximation of the HCRLB is developed by solving a non-convex optimization problem. A more accurate lower bound is also derived after accounting for the structural constraints inherent to the model under consideration. The resultant approach does not require the aforementioned regularity conditions to be satisfied.