We present our work to jointly optimize modulation waveforms and signal processing for long range vibration sensing using a heterodyne coherent laser radar in pulsed mode. The performance of various existing Instantaneous Frequency (IF) estimators is compared through simulation, taking into account Continuous Wave (CW) and pulse-pair waveforms, and for the first time poly-pulse waveforms. A new estimator, based on a pseudo time-frequency representation of the IF\'s likelihood function, was developed in response to the specific noise conditions encountered in laser radar. In agreement with theoretical calculations, our simulations show that, for pulsed mode, poly-pulse waveforms and our IF Likelihood (IFL) processing outperform the classical pulse-pair waveform in case of dominant speckle noise. With the same available laser power for the various operating modes, CW mode often demonstrates the best signal-to-noise ratio, given the strong speckle noise conditions and the vibration bandwidth considered here. Yet, pulsed mode with IFL processing proves to be more robust when the analysis bandwidth is increased and allows better demodulation, at low carrier-to-noise ratio.