The advantages of holographic displays over stereoscopic displays are that they provide both real motion parallax and solve the vergence-accommodation conflict without varifocal lenses and gaze tracking. For large holographic displays, pupil tracking and beam steering are required to ensure that the pupil is within the so-called viewing window or eye box between the diffraction maxima in the Fourier plane of the display system. We present a simulation study of the possibilities when the pupil is precisely tracked and can be considered in an iterative optimization process for hologram computation. Our study focuses on different initial phases and the resulting speckle noise.