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For sake of notation, in the following subsections we shall denote CRM1 and CRM2 as the CRM for PPH and the CRM for PPH-UD, respectively.
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Constraint (3) defines the aggregate average interference power constraint ( I th PU assumed identical for all PUs for the sake of notation simplicity) for each sub-channel k at each PU receiver l using that channel and denoted by ℒ k.
For the sake of notation, the factor matrices for r = 1,..., R are represented by A(r), and it can be written as a function of as follows (34).
For the sake of notation let us denote (A=M+1).
Thus for the sake of notation clarity, we omit it hereafter when no confusion arises.
For the sake of notation simplicity, we define an arbitrary link - between two nodes and.
For the sake of notation, we will identify with a generic any of the subcarriers assigned to terminal k.
where the second equality comes from the Rayleigh fading assumption, and has been defined as for the sake of notation simplicity.
For the sake of notation, we term the sensor active, if it has some sensed data to transmit, or inactive otherwise.
For the sake of notation, let us define the mapping (phi :{mathcal {K}} rightarrow {mathcal {Q}}) to univocally associate each user (k in {mathcal {K}}) to the relevant BS (q in {mathcal {Q}}), so that ϕ k), with ϕ k)=q, identifies the link between user k and its BS q.
For the sake of notation simplicity, we are not denoting external inputs with a different symbol.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com