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Phase alignment is critical to have compact order decomposition.
The algorithm provides compact order matrices as an approximation of polynomial matrix decomposition for an arbitrary polynomial order.
We set up a nonlinear quadratic minimization for phase alignment of decomposition at each frequency sample, which leads to a compact order approximation of decomposed matrices.
Compact order approximation of decomposed matrices makes it suitable in filterbank and multiple-input multiple-output (MIMO) precoding applications or any application dealing with realization of polynomial matrices as transfer function of MIMO systems.
However, we will show later in this article that in order to have compact order decomposition, phase alignment of decomposed constant matrices in DFT domain results in polynomial matrices with considerably lower order.
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