**4.1. Tuning of IFSQ parameters**

The parameters describing IFSQ approach can be divided into the ones inherited from the SQ method and the ones developed for the decoupling solution which correspond to three new IFSQ parameters that have to be set empirically (*r*, *δ*, *NVCPL*).

If the starting search space is too small, the search progress cannot move far from the starting point and the obtained solution results depend largely on the coupling strength. Under strong coupling the starting search space corresponding to *r*<sup>0</sup> = 10−<sup>5</sup> and *r*<sup>0</sup> = 10−<sup>4</sup> represents the selection of narrow starting search space. The obtained cost function precision is generally low, but as the reduction factor gets closer to one, it is increased in both cases. This is logical as if the small search space is additionally reduced at fast pace the algorithm is easily left

Simulated Quenching for Cancellation of Non-Linear Multi-Antennas Coupling 151

Consequently, two starting search spaces, in the middle of the image, built around *r*<sup>0</sup> = 0.001 and *r*<sup>0</sup> = 0.01 offer the adequate selection. In fact the best precision under strong coupling is reached with the following four pair of factors: (0.001, 0.99),(0.001, 0.999),(0.01, 0.90) and (0.01, 0.95) . The pairs are in accordance with the theoretical expectations as they ratify that in vicinity of adequate set of parameters smaller search space requires lower reduction factor to

**Figure 16.** IFSQ search based on different sets of (*r*, *δ*) factors under moderate coupling

made based on unreliable data which leads to poor cost function results.

The same analysis is repeated for system under moderate coupling of [13,-12,-10] dB in Figure 16. The behavior of algorithm is similar and the potentially adequate set of parameters is found in the central part of the image. However, in this case the best values are moved slightly to the left since the coupling strength is lower and the the ideal solution is located closer to the initial search point. Comparing the results obtained at two different coupling levels, the only pair of parameters appearing in both is *r*<sup>0</sup> = 0.001 and *δ* = 0.99 . Hence, these values are used as adequate parameters for IFSQ search adopted to nonlinear decoupling problem.

The number of visited candidates per temperature level defines the number of energy configurations analyzed between two temperature changes. If this number is large, the search space is analyzed in detail which produces stable results but consumes a lot of the processing time. Nevertheless, if the number of visited configurations is small, the search progress is

The performance of IFSQ search method based on different *NVCPL* number under strong coupling conditions of [-8,-6,-6] dB is depicted in Figure 17. As expected, when *NVCPL* number is small, like for *NVCPL* = 5 or *NVCPL* = 3, the search is easily drown into a blind ally.

without any new candidates and no progress can be made.

obtain the same precision level.

*4.1.2. Number of visited points per level*

The inherited SQ factors are set to the numerical values obtained in previous SQ analysis while three new IFSQ factors have to be set empirically (*r*, *δ*, *NVCPL*). When determining the correct level of the unknown parameters, the parameters that are still not analyzed are over-dimensioned which guarantees the correct functioning of IFSQ search at the cost of execution time. The first set of simulations focuses on adequate pair of parameters for maximum allowed displacement definition (*r*, *δ*). Afterwards, the obtained pair is used for analyzing the appropriate number of visited candidates per temperature level (*NVCPL*).
