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In addition, the L-curve technique is used over 5,000 consecutive OFDM symbols and the histogram of the stage indices of the RNSD-LPIC and CGLS-LPIC detectors are plotted in Figures 8 and 9, respectively.
In Figure 14, the average stopping stage index for each SNR is obtained simply by summing up the stopping stage indices determined by the Morozov discrepancy rule for M OFDM symbols and then dividing by M. The averaged stopping stage index is plotted versus the SNR. Figure 14 Average stopping stage index versus SNR of the Morozov-LPIC detector in AWGN channel.
In Figure 12, the average stopping stage index for each Morozov-LPIC stage is obtained simply by summing up the stopping stage indices determined by the Morozov discrepancy rule for M OFDM symbols and then dividing by M. The average stopping stage index is plotted versus the number of Morozov-LPIC stages.
The L-curve method is somewhat sensitive to the size of the system matrix determined by the number of subcarriers N. To illustrate this fact, we plot the histogram of the stage indices determined by the L-curve method over 5,000 OFDM symbols for two values of the subcarriers N, that is N = 8 and N = 32, respectively.
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In addition, we have seen previously from Figures 8 and 9 that for N = 128, the most dominant stage index is six stages which indicates that the most dominant stage index increases with the number of subcarriers N. Figure 10 Histogram of the stopping stage index for N = 8. Figure 11 Histogram of the stopping stage index for N = 32.
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Therefore, we introduce the index, lacunarity, as second stage index to characterize different spatial patterns that have the same FD value, since lacunarity has been verified to solve the problem effectively.
In Figure 17, the average stopping stage index is plotted versus the SNR.
We can see from Figures 10 and 11 that the most dominant stage index for N = 8 is four stages while the most dominant stage index for N = 32 is five stages.
Consequently, it is sufficient to evaluate the stopping stage index for a few OFDM symbols (say 100 OFDM symbol) and then get the average stopping stage index and use it for the subsequent OFDM symbols.
The resulting exponentially fitted curve is used instead in computing the maximum curvature and hence the optimal stage index.
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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