**5. Conclusion**

24 Will-be-set-by-IN-TECH

**Figure 19.** The precision of IFSQ search after 1500 iterations

**Figure 20.** Performance of IFSQ based decoupling module under moderate coupling

the theoretical transmission curve as close as is the SQ approach.

The reduction of permitted number of iterations to 1500 is verified in Figure 20 where the performance of IFSQ decoupling module under moderate coupling conditions is presented. The first curve on the image presents the behavior of system without the decoupling module under coupling of [-10,-12,-10] dB. The lowest curve shows the theoretical system performance with only AWGN. Two curves in the middle present two decoupling module instances based on IFSQ approach stopped after 1500 iterations. Actually, the coefficients used for generating this two curves correspond to the seventh and tenth IFSQ execution depicted in Figure 19. Regardless of the numerical difference of cost functions, the performance of both decoupling modules is very similar. Since the search is abandoned when cost function reaches sufficient *Q* value defined with *Qsuf f* = 0.005 the performance of decoupling module does not follow The effect of coupling are minimized with the software module positioned at the output of analog-to-digital converter and before any further digital signal processing. Inside the module, signal reconstruction based on the approximation of inverse nonlinear coupling is achieved. The generation of inverse coupling function is based on fitting surface approach which can be divided into two steps: calibration process and point-to-point real-time decoupling. Inside calibration process inverse nonlinear coupling surface is build based on function formed with 20 degrees of freedom. Inspired by SA class of approaches, two SQ algorithms are proposed for locating the optimal inverse function parameters.

Even though classical SQ method can not be used under real time conditions it provides the upper limit of the decoupling precision module and is used for tuning the required system parameters like for example calibration data size. It is intended only for proof of concept and precision reference to other two decoupling search approaches. Eventually actually confirms the adequate selection of the surface model and proves the concept of decoupling software module. The performance of decoupling module based on the SQ search method shows stable behavior and excellent decoupling results.

The proposed Improved Fast SQ search method is included in decoupling module as the fast version of the previously developed SQ search. It follows the same search logic as the SQ algorithm with the difference in the annealing schedule which is much steeper, the initial search space is wider and the probability of uphill movement is higher at the beginning. This way the search is carried out more thoroughly in the initial stage, allowing stepper search progress sooner than in the original SQ approach. Furthermore, since the search space is reduced according to the exponential function, the maximum allowed displacement is reduced with temperature, and as consequence the search concentrates more on small space around the global minimum area. The performance of IFSQ decoupling module, based on 1500 iterations, shows good decoupling results, with slightly lower BER level when compared to the standard SQ search. Nevertheless, the required number of iterations is reduced by more than 90% which justifies the precision loss. The approach requires less processing power than SQ, and as such might be used in mobile phones inside the decoupling module.

With the introduction of normalization, the search domain is well defined between �−1, 1�, and the search depth is easily controlled with symbol resolution factor. This proposal allows the adaptation of implemented search methods to general decoupling problem offering at the same time constant precision and efficient optimization of search process with no restrictions on the physical coupling source nor signal constellation.
