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The estimates are updated by the SISO decoders in every iteration, using the most recent channel estimate.
where c1 = t i - tsp1 is the time interval starting from the most recent channel switch point tsp1 to the i th SU transmission.
The lower right corner element of V is then the variance of a causal filter estimating the most recent channel coefficient, h n.
where s is the residual time of the PU's OFF state, c 2 = t j ′ - t sp 2 is the time interval between the most recent channel switch point tsp2 and the j th transmission of Stage II.
The interference cancellation is operating separately on each subcarrier and OFDM symbol, and makes use of the most recent channel estimate H ^ [ m ], and soft symbol estimates x ̃ [ m, s ] from the SISO decoders.
Given a set of observations, Y n =[y 1,…,y n ], we are interested in deriving the distribution, in particular the variance, of the resulting estimate, (hat {h}_{n}), of the most recent channel coefficient, h n.
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This is a result of the fact that a pilot signal in the infinite past carries as much information about the current channel as the most recent pilot signal, in the ideal example of a constant channel.
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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