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b Successful estimation probability.

Then, the proposed method enabled successful ordinal regression, i.e., successful estimation of prediction error degrees.

b Successful estimation probability Fig. 5 Estimation performances versus SNR for coherent wideband LFM signals (small angle interval).

Note that for realizing the successful estimation of the HR frame in this approach, the following approach becomes necessary.

Furthermore, we introduce the following novel points into this approach to realize successful estimation of prediction error degrees.

The estimated probability is defined by the formula EP = count Mon, where count is the number of successful estimation.

For each noise level we do 20 Monte Carlo trials and then we calculate the percentage of successful estimations obtained after three multigrid levels.

We can see that the proposed algorithm reconstruct exactly the signal with a rate upper than 80% for an SNR1 more than 6 dB; and the rate of success is 100% with an SNR1 upper than 15 dB. Figure 8 Rate of successful estimations with different noise levels of SNR 1.

In this study, the estimation without permutation was empirically adopted as the first approximation, based on the successful estimations of the relationships in our previous studies [ 10, 11].

Indeed, the number of successful estimations by GA in our method was less than that of the standard method in Model 1.

In the case of successful channel estimation, q can be 5, which means that the lowest complexity is achieved.