**2.2. Coupling cancellation module**

The coupling cancellation is performed with nonlinear software decoupling module located at the output of analog-to-digital (AD) converter as shown in Fig. 3. The advantage of this position is that it deals directly with sampled physical data avoiding any dependency on specific signal type. Inside the module, cancellation is achieved by determining the inverse coupling function.

**Figure 3.** Coupling cancellation module positioned at the output of AD converters

Taking into account that the signals at the output of decoupling module, *x*ˆ1 and *x*ˆ2, should theoretically be equal to *x*<sup>1</sup> and *x*2, the inverse functions take the form of:

$$\begin{aligned} \pounds\_1 &= y\_1 - c\_{11}\pounds\_2 - c\_{12}\pounds\_2^2 - c\_{13}\pounds\_2^3\\ \pounds\_2 &= y\_2 - c\_{21}\pounds\_1 - c\_{22}\pounds\_1^2 - c\_{23}\pounds\_1^3 \end{aligned} \tag{3}$$

Assuming that all distortion parameters *cij* are a priori known, a problem of two nonlinear equations with two unknown variables is presented. By extracting *x*ˆ2 the problem is reduced to single variable and can be described as a nonlinear problem of the ninth order:

$$\sum\_{i=0}^{i=9} k\_i \mathfrak{X}\_1^i = 0 \tag{4}$$

reference surface. This reference surface is then used as basis for building the approximated

Simulated Quenching for Cancellation of Non-Linear Multi-Antennas Coupling 135

With the introduction of the fitting surface approach the solution to the inverse coupling problem can be divided into two steps: calibration process and point-to-point real-time decoupling. Once all decoupling surface design parameters are defined, the decoupling, based on eq. 9, is implemented inside coupling cancellation module on all incoming pair

In order to develop a surface fitting algorithm four important parameters should be defined,

The calibration process includes the transmission of the calibration data used for the reference surface construction and the search for the inverse surface based on some search optimized algorithm. The calibration data should be well defined covering the whole direct function domain. For discrete signal coupling systems, the calibration points would correspond to the constellation specific points of the two antennas. In other words the whole domain of two 16 QAM constellations is covered with at least 256 (16 × 16) data points, while 64 QAM constellation requires a minimum of 4096 (64 × 64) points as the influence of all point combinations should be analyzed. The required number of calibration points is analyzed in detail in [1]. All the results presented in this chapter correspond to 2000 calibration symbols.

Low-order polynomials tend to be smooth and high order polynomial curves like the one of the ninth degree, tend to be "lumpy" with several local minimum and maximums making the surface approximation severe. Having in mind that complex curves can be formed without higher order multiplications, a model based on a sum of two independent higher order

> *j*≤*N*<sup>2</sup> ∑ *j*=1 *bjy j*

where *N*<sup>1</sup> and *N*<sup>2</sup> represent the degrees of freedom of variables *y*<sup>1</sup> and *y*<sup>2</sup> respectively, while variables *ai*, *bj*, *k*1, *k*<sup>2</sup> are the decoupling coefficients that are to be found with surface

This surface function is simple and offers a unique solution to each input pair. The ranks of polynomials, controlled with (*N*1, *N*<sup>2</sup> ), are determined as a trade off between the acceptable system performance and the required computational power. In [2], the approximation with 20 coefficients for the coupling cancellation fitting surface is proven to be accurate enough.

<sup>2</sup> + *k*1*y*1*y*<sup>2</sup> + *k*<sup>2</sup> (6)

polynomials with one simple linear multiplication is proposed in [3]:

*i*≤*N*<sup>1</sup> ∑ *i*=1

*aiy<sup>i</sup>* <sup>1</sup> +

*x*ˆ1 =

of signals achieving signal enhancement with very low processing demands.

inverse surface.

namely:

• calibration data

• cost function

*2.2.1. Calibration data*

• mathematical surface model

• parameter search algorithm

*2.2.2. Mathematical surface model*

approximation search.

with:

$$k\_0 = y\_1 - c\_{11}y\_2 - c\_{12}y\_2^2 - c\_{13}y\_2^3$$

$$k\_1 = c\_{11}c\_{21} + 2c\_{12}c\_{21}y\_2 + 3c\_{13}c\_{21}y\_2^2 - 1$$

$$k\_2 = c\_{11}c\_{22} - c\_{12}c\_{21}^2 + 2c\_{12}c\_{22}y\_2 - 3c\_{13}c\_{21}^2y\_2 + 3c\_{13}c\_{22}y\_2^2$$

$$k\_3 = c\_{11}c\_{23} - 2c\_{12}c\_{21}c\_{22} + 2c\_{12}c\_{23}y\_2 + c\_{13}c\_{21}^3 - 6c\_{13}c\_{21}c\_{22}y\_2 + 3c\_{13}c\_{23}y\_2^2 \tag{5}$$

$$k\_4 = -2c\_{12}c\_{21}c\_{23} - c\_{12}c\_{22}^2 + 3c\_{13}c\_{21}^2c\_{22} - 3c\_{13}c\_{22}^2y\_2 - 6c\_{12}c\_{23}c\_{13}y\_2$$

$$k\_5 = -2c\_{12}c\_{22}c\_{23} + 3c\_{13}c\_{21}c\_{22}^2 + 3c\_{13}c\_{21}^2c\_{23} - 6c\_{13}c\_{22}c\_{23}y\_2$$

$$k\_6 = -c\_{12}c\_{23}^2 + 6c\_{13}c\_{21}c\_{22}c\_{33} + 3c\_{13}^2c\_{23}^2 - 3c\_{13}c\_{23}^2y\_2$$

$$k\_7 = 3c\_{13}c\_{21}c\_{23}^2 + 3c\_{13}c\_{22}^2c\_{23} \qquad k\_8 = 3c\_{13}c\_{22}c\_{23}^2 \qquad k\_9 = c\_{13}c\_{23}^3$$

It is shown in [1] that the existence of one analytically expressed inverse function supporting the range of all input pairs (*x*1, *x*2) is extremely low and depends on all involved parameters (*x*1, *x*2, *c*11, *c*12, *c*13, *c*21, *c*22, *c*23), together with the signal constellation definition which determines the root space. Consequently mathematical surface approximation in combination with calibration process is proposed.This approach is based on finding a surface that matches a series of constraints by minimizing the distance between reference and re-constructed or inverse surface. In other words, a set of predefined points, denominated calibration data, are available to the observed process (in our case coupling) forming the reference surface. This reference surface is then used as basis for building the approximated inverse surface.

With the introduction of the fitting surface approach the solution to the inverse coupling problem can be divided into two steps: calibration process and point-to-point real-time decoupling. Once all decoupling surface design parameters are defined, the decoupling, based on eq. 9, is implemented inside coupling cancellation module on all incoming pair of signals achieving signal enhancement with very low processing demands.

In order to develop a surface fitting algorithm four important parameters should be defined, namely:

• calibration data

4 Will-be-set-by-IN-TECH

Taking into account that the signals at the output of decoupling module, *x*ˆ1 and *x*ˆ2, should

Assuming that all distortion parameters *cij* are a priori known, a problem of two nonlinear equations with two unknown variables is presented. By extracting *x*ˆ2 the problem is reduced

2 <sup>2</sup> − *c*13*x*ˆ 3 2

2 <sup>1</sup> − *c*23*x*ˆ 3 1

<sup>2</sup> <sup>−</sup> *<sup>c</sup>*13*y*<sup>3</sup> 2

<sup>21</sup>*c*<sup>22</sup> <sup>−</sup> <sup>3</sup>*c*13*c*<sup>2</sup>

<sup>22</sup> <sup>+</sup> <sup>3</sup>*c*13*c*<sup>2</sup>

<sup>22</sup>*c*<sup>23</sup> *<sup>k</sup>*<sup>8</sup> <sup>=</sup> <sup>3</sup>*c*13*c*22*c*<sup>2</sup>

<sup>2</sup> − 1

<sup>21</sup>*y*<sup>2</sup> <sup>+</sup> <sup>3</sup>*c*13*c*22*y*<sup>2</sup>

<sup>21</sup>*c*<sup>23</sup> − 6*c*13*c*22*c*23*y*<sup>2</sup>

<sup>22</sup> <sup>−</sup> <sup>3</sup>*c*13*c*<sup>2</sup>

<sup>21</sup> <sup>−</sup> <sup>6</sup>*c*13*c*21*c*22*y*<sup>2</sup> <sup>+</sup> <sup>3</sup>*c*13*c*23*y*<sup>2</sup>

<sup>22</sup>*y*<sup>2</sup> − 6*c*21*c*23*c*13*y*<sup>2</sup>

<sup>23</sup>*y*<sup>2</sup>

<sup>23</sup> *<sup>k</sup>*<sup>9</sup> <sup>=</sup> *<sup>c</sup>*13*c*<sup>3</sup>

2

2

23

<sup>1</sup> = 0 (4)

*x*ˆ1 = *y*<sup>1</sup> − *c*11*x*ˆ2 − *c*12*x*ˆ

*x*ˆ2 = *y*<sup>2</sup> − *c*21*x*ˆ1 − *c*22*x*ˆ

to single variable and can be described as a nonlinear problem of the ninth order:

*i*=9 ∑ *i*=0 *kix*ˆ *i*

*<sup>k</sup>*<sup>0</sup> <sup>=</sup> *<sup>y</sup>*<sup>1</sup> <sup>−</sup> *<sup>c</sup>*11*y*<sup>2</sup> <sup>−</sup> *<sup>c</sup>*12*y*<sup>2</sup>

*<sup>k</sup>*<sup>2</sup> <sup>=</sup> *<sup>c</sup>*11*c*<sup>22</sup> <sup>−</sup> *<sup>c</sup>*12*c*<sup>2</sup>

*<sup>k</sup>*<sup>4</sup> <sup>=</sup> <sup>−</sup>2*c*12*c*21*c*<sup>23</sup> <sup>−</sup> *<sup>c</sup>*12*c*<sup>2</sup>

*<sup>k</sup>*<sup>6</sup> <sup>=</sup> <sup>−</sup>*c*12*c*<sup>2</sup>

*k*<sup>7</sup> = 3*c*13*c*21*c*<sup>2</sup>

*<sup>k</sup>*<sup>3</sup> <sup>=</sup> *<sup>c</sup>*11*c*<sup>23</sup> <sup>−</sup> <sup>2</sup>*c*12*c*21*c*<sup>22</sup> <sup>+</sup> <sup>2</sup>*c*12*c*23*y*<sup>2</sup> <sup>+</sup> *<sup>c</sup>*13*c*<sup>3</sup>

*<sup>k</sup>*<sup>5</sup> <sup>=</sup> <sup>−</sup>2*c*12*c*22*c*<sup>23</sup> <sup>+</sup> <sup>3</sup>*c*13*c*21*c*<sup>2</sup>

<sup>23</sup> <sup>+</sup> <sup>3</sup>*c*13*c*<sup>2</sup>

*k*<sup>1</sup> = *c*11*c*<sup>21</sup> + 2*c*12*c*21*y*<sup>2</sup> + 3*c*13*c*21*y*<sup>2</sup>

<sup>22</sup> <sup>+</sup> <sup>3</sup>*c*13*c*<sup>2</sup>

<sup>23</sup> <sup>+</sup> <sup>6</sup>*c*13*c*21*c*22*c*<sup>23</sup> <sup>+</sup> *<sup>c</sup>*13*c*<sup>3</sup>

It is shown in [1] that the existence of one analytically expressed inverse function supporting the range of all input pairs (*x*1, *x*2) is extremely low and depends on all involved parameters (*x*1, *x*2, *c*11, *c*12, *c*13, *c*21, *c*22, *c*23), together with the signal constellation definition which determines the root space. Consequently mathematical surface approximation in combination with calibration process is proposed.This approach is based on finding a surface that matches a series of constraints by minimizing the distance between reference and re-constructed or inverse surface. In other words, a set of predefined points, denominated calibration data, are available to the observed process (in our case coupling) forming the

<sup>21</sup> <sup>+</sup> <sup>2</sup>*c*12*c*22*y*<sup>2</sup> <sup>−</sup> <sup>3</sup>*c*13*c*<sup>2</sup>

**Figure 3.** Coupling cancellation module positioned at the output of AD converters

theoretically be equal to *x*<sup>1</sup> and *x*2, the inverse functions take the form of:

with:


(3)

(5)

• parameter search algorithm

#### *2.2.1. Calibration data*

The calibration process includes the transmission of the calibration data used for the reference surface construction and the search for the inverse surface based on some search optimized algorithm. The calibration data should be well defined covering the whole direct function domain. For discrete signal coupling systems, the calibration points would correspond to the constellation specific points of the two antennas. In other words the whole domain of two 16 QAM constellations is covered with at least 256 (16 × 16) data points, while 64 QAM constellation requires a minimum of 4096 (64 × 64) points as the influence of all point combinations should be analyzed. The required number of calibration points is analyzed in detail in [1]. All the results presented in this chapter correspond to 2000 calibration symbols.

#### *2.2.2. Mathematical surface model*

Low-order polynomials tend to be smooth and high order polynomial curves like the one of the ninth degree, tend to be "lumpy" with several local minimum and maximums making the surface approximation severe. Having in mind that complex curves can be formed without higher order multiplications, a model based on a sum of two independent higher order polynomials with one simple linear multiplication is proposed in [3]:

$$\mathfrak{X}\_1 = \sum\_{i=1}^{i \le N\_1} a\_i y\_1^i + \sum\_{j=1}^{j \le N\_2} b\_j y\_2^j + k\_1 y\_1 y\_2 + k\_2 \tag{6}$$

where *N*<sup>1</sup> and *N*<sup>2</sup> represent the degrees of freedom of variables *y*<sup>1</sup> and *y*<sup>2</sup> respectively, while variables *ai*, *bj*, *k*1, *k*<sup>2</sup> are the decoupling coefficients that are to be found with surface approximation search.

This surface function is simple and offers a unique solution to each input pair. The ranks of polynomials, controlled with (*N*1, *N*<sup>2</sup> ), are determined as a trade off between the acceptable system performance and the required computational power. In [2], the approximation with 20 coefficients for the coupling cancellation fitting surface is proven to be accurate enough.

#### 6 Will-be-set-by-IN-TECH 136 Simulated Annealing – Single and Multiple Objective Problems Simulated Quenching for Cancellation of Non-Linear Multi-Antennas Coupling <sup>7</sup>

Hence, (*N*1, *N*2)=(9, 9) is selected for describing the mathematical surface model. In order to be able to adopt the surface search method to general decoupling problem, the data, on which the search is carried out, is restrained to �−1, 1�. This is achieved by implementing the normalization according to the maximum received symbol level taking into account all calibration symbols on both antennas, as shown in the following equation:

$$\begin{array}{c} y\_{1k}^{N} = \frac{y\_{1k}}{\max(|y\_{1k}|, |y\_{2k}|)}\\ y\_{12k}^{N} = \frac{y\_{12k}}{\max(|y\_{1k}|, |y\_{2k}|)} \end{array} k = 1..N\tag{7}$$

the nature of the metal which is heated and than cooled slowly in order to reach its absolute

Simulated Quenching for Cancellation of Non-Linear Multi-Antennas Coupling 137

During the last few decades a number of variations of original SA algorithm have been published. The comparison of different SA algorithms, with other mostly heuristic algorithms can be find in [4, 6–10, 13, 18]. Regardless of different variations, any algorithm based on physical SA has proven to be an effective global optimization method because of several

• it can process the cost functions with arbitrary degrees of nonlinearities and

The basic assumption of the SA class of approaches is that sometimes, in order to avoid the trap of local minimum, intermediate points that lead to worse minimum solution are accepted. The fact is that classical SA search is very slow when compared to other heuristic methods and is often avoided as more importance is given to speed than to precision. Hence, the original SA algorithm is rarely used, but it is worth mentioning some of the known SA enhancements like Quantum Annealing (QA), Simulated Quenching (SQ), Mean Field Annealing (MFA), Fast Simulated Annealing (FSA), Parallel Recombinative Simulated Annealing (PRSA) or Adaptive Simulated Annealing (ASA) that have been proposed in numerous articles [5, 7, 14–16]. In contrast to the original SA approach these methods have been characterized as fast search algorithms. Eventually, inspired by SA algorithms two SQ approaches, which do not follow physical analogy, are put forward for parameter search algorithms. The first one offers high precision but requires large number of iterations to reach it, while inside the second one the search progress is accelerated on the cost of the decoupling precision. Still, the decoupling results are kept at high level which make the precision loss acceptable compared to the speed

**3. Simulated quenching applied to nonlinear decoupling problem**

into initialization and the simulated annealing part as presented in Figure 4.

The functioning of the classical SQ method can be described using the pseudo code, divided

Inside the first section the temperature factor *T* is set to the initial temperature (*T*0). The temporary minimum of the cost function (*Qmin*) is calculated for the initial set of decoupling coefficients (*Coef*0). These values are then appointed to actual state configuration. Afterwards, the algorithm enters the search loop until allowed processing time measured in number of iterations is exceeded (*Iter* > *IMAX*). The selection of new coefficients (neighbors) is done inside the *New\_Candidate* function, and then the cost function for the set of selected coefficients is calculated (*Qnew*). If the cost function (*Cost*) of the new neighbor presents lower value than temporary minimum cost function (*Qmin* ), the perturbation is accepted. The new cost function value (*Qnew*) becomes the new minimum and the corresponding set of the coefficients is stored in *Coefmin*. In case of higher cost function value the perturbation is accepted only if the randomly selected number between zero and one is smaller than the *Trans\_Prob* function of the actual temperature *T*. However, in this case only the actual position is updated and the global minimum cost configuration is left unchanged. The search at one temperature level is limited

discontinuities, as no restriction on the form of the cost function exists

• it can be implemented easily when convergence speed is not relevant

• it can statistically guarantee finding an optimal solution

minimum energy state.

important features:

gain.

where *y<sup>N</sup>* <sup>1</sup>*<sup>k</sup>* and *<sup>y</sup><sup>N</sup>* <sup>2</sup>*<sup>k</sup>* are the *k*-th normalized received symbols on the corresponding antennas, *Max*(|*y*1*k*|, |*y*2*k*|) is the maximum received absolute value level, and *N* is the number of calibration signals. Eventually, since the approximation surface is constructed based on the normalized levels, the true value of reconstructed symbol is obtained by expanding the reconstructed normalized symbol *x*ˆ*<sup>N</sup>* <sup>1</sup>*<sup>k</sup>* to the received dynamic range:

$$\pounds\_{1k} = \pounds\_{1k}^{N} \text{Max}(|y\_{1k}|\_{\prime}|y\_{2k}|) \tag{8}$$

Hence, the decoupling approximation surface is defined as:

$$\mathfrak{X}\_{1k} = \text{Max}(|y\_{1k}|\_{\prime}|y\_{2k}|) \left\{ \sum\_{i=1}^{i \le N\_1} a\_i \left( y\_{1k}^N \right)^i + \sum\_{j=1}^{j \le N\_2} b\_j \left( y\_{2k}^N \right)^j + k\_1 y\_{1k}^N y\_{2k}^N + k\_2 \right\} \tag{9}$$

This way, the processing load of the decoupling process is basically concentrated on the approximation fitting surface parameter search.

#### *2.2.3. Cost function*

The objective of surface search consists in finding the decoupling coefficients that minimize the cost function. The calculation of cost function has to be carried out for each new candidate and presents the most demanding part of the decoupling processing load. The cost function typically implemented for the search of approximate inverse function is root mean square, also known as the quadratic mean:

$$Q\_j = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} \left(\mathbf{x}\_{ji} - \mathbf{f}\_{ji}\right)^2} \tag{10}$$

where *N* is the number of symbols used, *xji* is the sent *i th* calibration symbol on *j th* antenna, and *x*ˆ*ji* its corresponding value calculated using the coefficients of new surface candidate according to eq. 9. The set of decoupling coefficients displaying minimum *Qj* value are then used in decoupling module as the inverse coupling surface function.

#### *2.2.4. Parameter search algorithm*

SA methods are chosen as starting point since this approach can statistically guarantee finding an optimal solution, although no estimate can be made on the number of trials needed to reach it. The name and inspiration come from the annealing in metallurgy, as the technique mimics the nature of the metal which is heated and than cooled slowly in order to reach its absolute minimum energy state.

During the last few decades a number of variations of original SA algorithm have been published. The comparison of different SA algorithms, with other mostly heuristic algorithms can be find in [4, 6–10, 13, 18]. Regardless of different variations, any algorithm based on physical SA has proven to be an effective global optimization method because of several important features:


6 Will-be-set-by-IN-TECH

Hence, (*N*1, *N*2)=(9, 9) is selected for describing the mathematical surface model. In order to be able to adopt the surface search method to general decoupling problem, the data, on which the search is carried out, is restrained to �−1, 1�. This is achieved by implementing the normalization according to the maximum received symbol level taking into account all

*Max*(|*y*1*<sup>k</sup>* |,|*y*2*<sup>k</sup>* |)

*k* = 1..*N* (7)

<sup>1</sup>*kMax*(|*y*1*k*|, |*y*2*k*|) (8)

+ *k*1*y<sup>N</sup>* 1*ky<sup>N</sup>* <sup>2</sup>*<sup>k</sup>* + *k*<sup>2</sup>

*th* calibration symbol on *j*

⎫ ⎬ ⎭

(9)

(10)

*th* antenna,

*Max*(|*y*1*<sup>k</sup>* |,|*y*2*<sup>k</sup>* |)

*Max*(|*y*1*k*|, |*y*2*k*|) is the maximum received absolute value level, and *N* is the number of calibration signals. Eventually, since the approximation surface is constructed based on the normalized levels, the true value of reconstructed symbol is obtained by expanding the

This way, the processing load of the decoupling process is basically concentrated on the

The objective of surface search consists in finding the decoupling coefficients that minimize the cost function. The calculation of cost function has to be carried out for each new candidate and presents the most demanding part of the decoupling processing load. The cost function typically implemented for the search of approximate inverse function is root mean square,

> *N* ∑ *i*=1 �

and *x*ˆ*ji* its corresponding value calculated using the coefficients of new surface candidate according to eq. 9. The set of decoupling coefficients displaying minimum *Qj* value are then

SA methods are chosen as starting point since this approach can statistically guarantee finding an optimal solution, although no estimate can be made on the number of trials needed to reach it. The name and inspiration come from the annealing in metallurgy, as the technique mimics

*xji* − *x*ˆ*ji*

�2

<sup>2</sup>*<sup>k</sup>* are the *k*-th normalized received symbols on the corresponding antennas,

<sup>1</sup>*<sup>k</sup>* to the received dynamic range:

calibration symbols on both antennas, as shown in the following equation:

<sup>1</sup>*<sup>k</sup>* <sup>=</sup> *<sup>y</sup>*1*<sup>k</sup>*

<sup>12</sup>*<sup>k</sup>* <sup>=</sup> *<sup>y</sup>*12*<sup>k</sup>*

*x*ˆ1*<sup>k</sup>* = *x*ˆ*<sup>N</sup>*

*i*≤*N*<sup>1</sup> ∑ *i*=1 *ai* � *yN* 1*k* �*i* + *j*≤*N*<sup>2</sup> ∑ *j*=1 *bj* � *yN* 2*k* �*j*

*Qj* = ���� 1 *N*

used in decoupling module as the inverse coupling surface function.

where *N* is the number of symbols used, *xji* is the sent *i*

⎧ ⎨ ⎩

*yN*

*yN*

Hence, the decoupling approximation surface is defined as:

where *y<sup>N</sup>*

<sup>1</sup>*<sup>k</sup>* and *<sup>y</sup><sup>N</sup>*

*2.2.3. Cost function*

reconstructed normalized symbol *x*ˆ*<sup>N</sup>*

*x*ˆ1*<sup>k</sup>* = *Max*(|*y*1*k*|, |*y*2*k*|)

also known as the quadratic mean:

*2.2.4. Parameter search algorithm*

approximation fitting surface parameter search.

• it can be implemented easily when convergence speed is not relevant

The basic assumption of the SA class of approaches is that sometimes, in order to avoid the trap of local minimum, intermediate points that lead to worse minimum solution are accepted. The fact is that classical SA search is very slow when compared to other heuristic methods and is often avoided as more importance is given to speed than to precision. Hence, the original SA algorithm is rarely used, but it is worth mentioning some of the known SA enhancements like Quantum Annealing (QA), Simulated Quenching (SQ), Mean Field Annealing (MFA), Fast Simulated Annealing (FSA), Parallel Recombinative Simulated Annealing (PRSA) or Adaptive Simulated Annealing (ASA) that have been proposed in numerous articles [5, 7, 14–16]. In contrast to the original SA approach these methods have been characterized as fast search algorithms. Eventually, inspired by SA algorithms two SQ approaches, which do not follow physical analogy, are put forward for parameter search algorithms. The first one offers high precision but requires large number of iterations to reach it, while inside the second one the search progress is accelerated on the cost of the decoupling precision. Still, the decoupling results are kept at high level which make the precision loss acceptable compared to the speed gain.
