The Polynomial EVD (PEVD) was developed to achieve broadband subspace decomposition as a part of two-stage convolutive Blind Source Separation (BSS) algorithm. It has the ability to accomplish strong (total) decorrelation and spectral majorization on convolutive signals. We explore different algorithms for constructing FIR paraunitary (PU) matrices with the aim of performing broadband subspace decomposition. We adopt a set of new iterative PEVD algorithms for this task: a) Sequential matrix diagonalization (SMD) b) Maximum element sequential matrix diagonalization (ME-SMD). We also present a procedure to find out the total number of source signals in the convolved data, without having prior knowledge, based on the energy of individual polynomial eigen values. This helps us to find out exact signal and noise subspaces. To measure the performance of PEVD for broadband subspace decomposition, we use the diagonalization performance measure and subspace estimation measure. We present the results both for simulated data and for actual convolved speech data in the presence of noisy environment to show the effectiveness of the adopted algorithms over existing SBR2/SBR2C algorithms in the literature. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.