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.
The definition of a stopping stage avoids the problem of convergence.
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.
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.
Once the stopping stage of the channel assignment is reached, nodes accordingly tune their radio interfaces permanently used for data communication, to the channels dictated by ZAP.
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.
Obviously, as the weighting factor gets smaller (i.e., β = 2) the residual error decreases slower as well and therefore needs more stages to satisfy the Morozov discrepancy rule and hence the average stopping stage index increases with decreasing values of ω as depicted in Figure 12. Figure 12 Average stopping stage index versus the number of Morozov-LPIC stages in AWGN channel.
Figure 8 Histogram of the stopping stage index for SNR = (a) 1 dB, (b) 10 dB, (c) 20 dB, and (d) 30 dB. Figure 9 Histogram of the stopping stage index for SNR = (a) 1 dB, (b) 10 dB, (c) 20 dB, and (d) 30 dB.
Similar to Figure 14, the average stopping stage index increases with the SNR and the rate of increase becomes larger for decreasing values of β. Figure 17 Average stopping stage index versus SNR of the Morozov-LPIC detector in Rayleigh fading channel.
This is a very important result as it allows avoiding the calculation of the stopping stage for every OFDM symbol and thus renders this scheme very efficient in terms of computational complexity.
