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Table 1 FAWC optimization

From: Compressive sampling-based CFO-estimation with exploited features

Objective: Measurement matrix optimization with
given dictionary D, i.e.,
\({\boldsymbol {\Phi }} =\mathop {\arg \min }\limits _{\boldsymbol {\Phi }} \left \{ {\frac {1}{2}\eta + \left ({1 - \alpha } \right)\mu _{NC}^{t} + \alpha {\mu _{C}^{t}}} \right \}.\)
Initialization:Set n=0, and calculate the
eigenvalue decomposition of D D H, i.e.,
D D H=U Λ U H.
Then, we calculate the initial value of Φ
according to
\({{\boldsymbol {\Phi }}^{\left (0 \right)}} = \left [ {\begin {array}{cccc} {{{\mathbf {I}}_{M}}}&0 \end {array}} \right ]{{\boldsymbol {\Lambda }}^{- \frac {1}{2}}}{{\mathbf {U}}^{H}}.\)
a). Update G (n) according to Φ (n):
G (n)=(Φ (n) D)H Φ (n) D.
b). Calculate h t (G (n)) according to the
forthcoming Eq. (24), and form the matrix
\( {\boldsymbol {\Upsilon }=} {{\boldsymbol {\Lambda }}^{- \frac {1}{2}}}{{\mathbf {U}}^{H}}{\mathbf {D}}{h_{t}}\left ({{{\mathbf {G}}^{\left (n \right)}}} \right){\mathbf {U}}{{\mathbf {D}}^{H}}{{\boldsymbol {\Lambda }}^{- \frac {1}{2}}}.\)
c). Calculate the eigenvalue decomposition of Υ,
and find its M top eigenvalues Δ M and the
corresponding eigenvectors V M of Υ.
d). Update measurement matrix according to
\({{\boldsymbol {\Phi }}^{\left ({n+1} \right)}} = {\boldsymbol {\Delta }}_{M}^{\frac {1}{2}}{\mathbf {V}}_{M}^{H}{{\boldsymbol {\Lambda }}^{- \frac {1}{2}}}{{\mathbf {U}}^{H}}.\)
e). n=n+1.
Until: Convergence criterion is satisfied.