Table 2 Spectrum balancing algorithm

M_k = U^T (V^TS_k V) U, $M_k^{-}=0\left(k=0,...,K-1\right)$ and $M=\left[M_0,...,M_{K-1}\right],M^{-}=\left[M_0^{-},...,M_{K-1}^{-}\right]$

- Iterations:

while || M - M^- || ≥ ε, (ε ≪ 1)

   $M_k^{-}=M_k,\left(k=0,...,K-1\right)$

   loop a = 1 → L - 1

      loop b = a + 1 → L

         $\theta =\frac{1}{4}arctan\left(\frac{2{\sum }_{k=0}^{K-1}\left(M_{ab}^k+M_{ba}^k\right)\left(M_{aa}^k-M_{bb}^k\right)}{{\sum }_{k=0}^{K-1}{\left(M_{ab}^k+M_{ba}^k\right)}^2}\right)$

         M _k = R^(a,b)(θ) M _k R^(a,b)(-θ), (k = 0,..., K - 1)

         U = U R^(a,b), (-θ)

      end loop b

   and loop a

end while

W = VU