The density field reconstruction technique has been widely used for recovering the Baryon Acoustic Oscillation (BAO) feature in galaxy surveys that has been degraded due to nonlinearities. In this paper, we investigate the performance of iterative reconstruction on the BAO and the broadband, focusing on the iterative implementation based on citet{Seo:2010} and citet{Schmittfull:2017}. We include redshift-space distortions, halo bias, and shot noise and inspect the components of the reconstructed field in Fourier space and in configuration space using both density field-based reconstruction and displacement field-based reconstruction. We find that the displacement field reconstruction becomes quickly challenging in the presence of non-negligible shot noise and therefore present surrogate methods that can be practically applied to a much more sparse field such as galaxies. For a galaxy field, implementing a debiasing step to remove the Lagrangian bias appears crucial for the displacement field reconstruction. We show that the iterative reconstruction does not substantially improve the BAO feature beyond an optimized standard reconstruction; however, we find that such aggressive optimization of the standard reconstruction with a small smoothing kernel is achieved at the cost of degradation on large scales while taking iterative steps allows us to use a small smoothing kernel `stably, i.e., without causing a substantial deviation from the linear theory model on large scales.
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