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Discover LudwigExact(3)
where l∈{1,⋯,4}, N is the number of observations, E is the average symbol energy of the modulation constellation before the shift, and β is the portion of E that is allocated to the shift.
The result in (16) links the closed-form lower bound of the estimation error to the average energy of the modulation constellation before the shift and the portion of this average energy allocated to the shift.
For the sake of numerically investigating the problem of smallest possible shift energy, we define β as the portion of the average energy per symbol that is allocated to the shift and use the real constant (striangleq sqrt {beta E}), where 0<β<1 to shift the symmetric modulation constellation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com