We report on our ongoing effort to measure the Boltzmann constant, , using the Doppler broadening technique on ammonia. This paper presents some of the improvements made to the mid-infrared spectrometer including the use of a phase-stabilized quantum cascade laser, a lineshape analysis based on a refined physical model and an improved fitting program increasing the confidence in our estimates of the relevant molecular parameters, and a first evaluation of the saturation parameter and its impact on the measurement of . A summary of the systematic effects contributing to the measurement is given and the optimal experimental conditions for mitigating those effects in order to reach a competitive measurement of at a part per million accuracy level are outlined.