Modal dispersion characterization of multimode optical fibers can be performed using the recently-proposed mode-dependent signal delay method. This method consists of sending optical pulses using different combinations of modes though the multimode optical fiber and measuring the mode group delay at the fiber output. From these measurements, it is possible to estimate the modal dispersion vector, the principal modes, and their corresponding differential mode group delays. In this paper, we revise and extend the theoretical framework of the mode-dependent signal delay method to include the impact of receiver noise and mode-dependent loss. We compute optimal launch modes, minimizing the noise error in the estimation of the fiber modal dispersion vector. We show that, for a 40-mode fiber, the electronic signal-to-noise ratio (SNR) is improved asymptotically by almost 6 dB compared to conventional mode combinations.