In this paper we propose a general framework for transmit waveform design for parameter estimation based on the Cramér-Rao lower bound. Our framework focuses on optimizing the transmit waveform in a one-dimensional space, in contrast to the extensively studied two-dimensional optimization (e.g. space and time). We relax the problem into a semi-definite program. The success of finding a solution to the original problem based on the relaxed solution heavily relies on the rank of the relaxed solution. We therefore derive an upper bound on the rank of the solution, enabling us to analyze the requirements that a model must fulfill to facilitate the successful design of a transmit waveform. The working of the framework is demonstrated using an illustrative example.