In the ecological literature, there is broad consensus that the diversity profile is a useful tool for diversity evaluation. Since the diversity profile is a positive, decreasing, and convex curve, it is possible to cast the problem of its estimation into a constrained functional context. In this work, a functional design-based estimation of diversity profiles is considered by taking into account the constrained nature of the profile. Indeed, a naive direct application of the functional data analysis methodology can be misleading, both theoretically and practically. To tackle this issue, the constrained estimation problem is redefined into an unconstrained one by defining the diversity profile in terms of a differential equation. An approximation of the bias and the variance of the estimator is derived using the delta method.