A progressive optimization method for a fluid antenna assisted symbiotic communication system

Abstract

This invention discloses an incremental optimization method for a fluid antenna-assisted co-occurrence communication system, comprising: deploying a base station, users, and a backscattering device; and installing fluid antennas on the base station and the backscattering device to assist transmission. After receiving the uplink transmitted signal, the base station derives the corresponding weighted sum rate optimization objective. Through an incremental optimization framework, the weighted sum rate optimization problem is transformed into three sub-problems. For sub-problems one and two, a second-order Taylor expansion combined with a successive convex approximation method is used for solution. For sub-problem three, a positive semi-definite matrix transformation is used to solve the problem, thereby obtaining the final result. This invention can effectively reduce the computational complexity of the system while improving power efficiency and spectral efficiency. Through fluid antenna position optimization and receiver combining vector optimization, this invention can effectively improve diversity gain, power efficiency, and spectral efficiency.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and particularly relates to a progressive optimization method for a fluid antenna-assisted symbiotic communication system. Background Technology

[0002] Symbiotic communication is a promising technology that incorporates backscattering devices to assist transmission. These backscattering devices modulate information onto a continuous wave signal generated by a dedicated carrier transmitter, significantly reducing the communication power required for transmission. Furthermore, backscattering devices lack active transmitter components, thus reducing equipment cost and energy consumption. However, backscattering devices are typically small, carrying only a single antenna, and often have weak diversity gain, greatly impacting system performance and reducing power and spectral efficiency.

[0003] To address this, a novel technique called fluidic antennas has been proposed. These represent any software-controlled fluid, conductive, or dielectric structure capable of dynamically changing its shape and position to reconfigure fundamental radio frequency characteristics. This allows small-sized communication devices to overcome spatial limitations and achieve good diversity. Therefore, fluidic antenna-assisted co-occurrence communication systems hold great potential. However, current fluidic antenna-assisted co-occurrence communication systems still face several challenges. One typical problem is the need for simultaneous optimization of the fluidic antenna position and receiver combining vector optimization. Traditional optimization schemes are highly complex, necessitating a low-complexity optimization approach. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide an incremental optimization method for a fluid antenna-assisted symbiotic communication system, which improves diversity gain, system power efficiency and spectral efficiency. By decomposing the original problem through an incremental optimization framework, the complexity of algorithm implementation can be greatly reduced and the consumption of computing resources can be significantly reduced.

[0005] Technical solution: The present invention provides a progressive optimization method for a fluid antenna-assisted symbiotic communication system, comprising the following steps:

[0006] Step 1: Deploy base stations, users, and backscattering devices in the fluid antenna-assisted symbiotic communication system, and install fluid antennas on the base stations and backscattering devices respectively;

[0007] Step 2: During the uplink signal transmission phase, the user sends a signal to the base station, and at the same time, the backscatter device sends a signal to the base station. After receiving the signal, the base station obtains the rates of the direct link and the backscatter link, and then obtains the weighted sum rate optimization target. The weighted sum rate optimization target is subject to the minimum rate constraint of the direct link, the minimum rate constraint of the backscatter link, the mobility range constraint of the flow antenna, and the receiver combining vector normalization constraint.

[0008] Step 3: Construct an incremental optimization framework, transforming the weighted sum rate optimization problem into three sub-problems: the direct link channel gain maximization problem, the backscatter link channel gain maximization problem, and the receiver combining vector design problem for weighted sum rate maximization.

[0009] Step 4: For the channel gain maximization problem of direct link and backscatter link, the solution is obtained by second-order Taylor expansion combined with successive convex approximation method.

[0010] Step 5: For the receiver combining vector design problem of weighted sum maximization, the solution is obtained by transformation using a positive semi-definite matrix, thus achieving the optimization of the symbiotic communication system.

[0011] Furthermore, step 1 specifically involves: the channel between the base station and the user is a direct link channel, and the channel between the base station, the backscattering device, and the user is a backscattering link channel; a streaming antenna is installed on both the backscattering device and the user; the direct link channel is represented as:

[0012]

[0013] in, Represents the local coordinates of the user-mounted fluidic antenna. This represents the conjugate transpose of the corresponding matrix from the base station to the user's transmission field. This represents the path response vector from the base station to the user.

[0014] The backscatter link channel is represented as:

[0015]

[0016] in, Represents the local coordinates of the fluid antenna mounted on the backscattering device. This represents the conjugate transpose of the received field response matrix from the user to the base station. This represents the path response vector from the base station to the backscattering device and then to the user.

[0017] Furthermore, step 2 specifically involves: during the uplink signal transmission phase, the user sends a signal to the base station, and simultaneously, the backscattering device sends a signal to the base station. The signal received by the base station is:

[0018]

[0019] in, The conjugate transpose of the normalized receiver combining vector, simultaneously satisfying , The information symbols sent to the user simultaneously satisfy , For mathematical expectation, The power of the signal sent to the user. The modulation coefficient of the backscattering device, The information symbols sent by the backscattering device simultaneously satisfy , The noise received by the base station has a mean of 0 and a variance of . The normal distribution, and Noise power;

[0020] After receiving the signal, the base station first decodes the signal from the user, and the resulting direct link rate is:

[0021]

[0022] After decoding the signal from the user, the base station uses serial interference cancellation technology to remove the decoded signal. The remaining signal after removal is:

[0023]

[0024] Then, the base station will decode the signal from the backscattering device, and the resulting backscattering link rate is:

[0025]

[0026] in, Given the signal period of the backscattering device, the optimization objective is set as the weighted sum rate of the direct link and the backscattering link, expressed as:

[0027]

[0028] in, The weighting coefficients represent the total sum rate. The optimization problem is represented as:

[0029]

[0030] in, and These represent the sets of location coordinates of the user and the fluid antenna mounted on the backscattering device, respectively.

[0031] Furthermore, step 3 specifically involves: using an incremental optimization framework, transforming the weighted sum rate optimization problem into three sub-problems: the direct link channel gain maximization problem, the backscatter link channel gain maximization problem, and the receiver combining vector design problem for weighted sum rate maximization; sub-problem one is maximizing the direct link channel gain by optimizing the position of the user-mounted flowing antenna, expressed as:

[0032]

[0033] Subproblem two is to maximize the backscatter link channel gain by optimizing the position of the fluid antenna mounted on the backscatter device, expressed as:

[0034]

[0035] Subproblem 3, after solving subproblems 1 and 2, involves maximizing the sum rate by optimizing the receiver combining vector, given the locations of the user and the backscattering device. This can be expressed as:

[0036]

[0037] Furthermore, step 4 specifically involves the following: Subproblems one and two have the same form and are independent of each other, therefore they are solved using the same method. For subproblem one, the objective function is first established:

[0038]

[0039] Where tr() represents the trace of the matrix, A TR (z1) represents the transmission field response matrix from the base station to the user. Since the objective function is a positive definite matrix and is non-convex, relaxation is achieved through a continuous convex approximation. This is done using a first-order Taylor expansion:

[0040]

[0041] Where Re{} denotes the real part of the complex number, A TR (z1) i ) indicates the first The transmission field response matrix from the base station to the user in this iteration; A TR (z1) i ) H Indicates the first The received field response matrix from the user to the base station in the next iteration; constant1 represents the remainder term of the first-order Taylor expansion;

[0042] Because the objective function after the first-order Taylor expansion It is non-convex, and we can obtain the following using a second-order Taylor expansion:

[0043]

[0044] Among them, superscript Represents the transpose of a matrix. and Representing the gradient vector and The Hessian matrix; Represent real numbers, Let be a positive number, where For vectors The row number, constant2 represents the remainder term in the second-order Taylor expansion. express The OK;

[0045] Based on the above transformation, in the... After several iterations of continuous convex approximation, the optimization problem can be expressed as:

[0046]

[0047] in This represents the objective function after second-order Taylor expansion. Since this function has been transformed into a convex function, it is solved using the CVX toolbox in Matlab. The solution method for subproblem two is the same.

[0048] Furthermore, step 5 specifically involves optimizing the receiver combining vector to maximize the sum rate for sub-problem 3. First, a positive semi-definite matrix is ​​introduced to transform the objective function:

[0049]

[0050] in, , , Therefore, subproblem three is transformed into:

[0051]

[0052] Solve using the CVX toolbox in Matlab software.

[0053] Furthermore, the specific steps of using the CVX toolbox in Matlab software to solve the problem are as follows: without setting any constraints, the CVX toolbox is used to find the optimal solution V* for V; if the rank of V* is 1, it is the optimal solution; otherwise, a randomization-based method is used to derive an approximate suboptimal solution using singular value decomposition to solve the target problem.

[0054] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method of the present invention.

[0055] The present invention also discloses a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the method of the present invention.

[0056] The present invention also discloses a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the method of the present invention.

[0057] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0058] 1. This invention can effectively improve diversity gain, power efficiency and spectral efficiency of the system by optimizing the position of the fluid antenna and the receiver combining vector, and is especially suitable for large-scale multi-user communication scenarios in complex channel environments;

[0059] 2. To address the problem of exponentially increasing computational complexity in traditional global optimization algorithms, this invention decomposes the original problem through an incremental optimization framework, which can significantly reduce the algorithm implementation complexity and substantially reduce computational resource consumption.

[0060] 3. This invention decomposes the original problem into three sub-problems, of which sub-problem one and sub-problem two can be calculated simultaneously. This not only significantly improves the system response speed, but also ensures the compatibility and overall optimality of the solutions to each sub-problem through global coupling constraints, laying the foundation for the rapid deployment and flexible expansion of complex communication systems. Attached Figure Description

[0061] Figure 1 A flowchart illustrating a progressive optimization framework for a fluid antenna-assisted symbiotic communication system according to an embodiment of the present invention;

[0062] Figure 2 This is a schematic diagram of a network architecture for a symbiotic communication system assisted by a fluid antenna, according to an embodiment of the present invention.

[0063] Figure 3 This is a simulation comparison diagram of the technical solution of the present invention and the optimization results of existing solutions. Detailed Implementation

[0064] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the scope of protection of the present invention. The embodiments described in this invention are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0065] 1. An incremental optimization method for symbiotic communication systems assisted by fluid antennas

[0066] This invention provides a progressive optimization method for a coexistence communication system assisted by a fluid antenna, such as... Figure 1As shown, it includes the following steps:

[0067] Step 101: The symbiotic communication system assisted by the fluid antenna is deployed with one base station, one user and one backscattering device. Fluid antennas are installed on the base station and the backscattering device to assist transmission.

[0068] Step 102: During the uplink signal transmission phase, the user sends a signal to the base station. At the same time, the backscattering device also sends a signal to the base station. After receiving the signal, the corresponding rates of the direct link and backscattering link are obtained, and the weighted sum rate optimization target is derived accordingly. It is subject to the minimum rate constraint of the direct link, the minimum rate constraint of the backscattering link, the mobility range constraint of the flow antenna, and the receiver combining vector normalization constraint.

[0069] Step 103: Using an incremental optimization method, the weighted sum rate optimization problem is transformed into three sub-problems: the direct link channel gain maximization problem, the backscatter link channel gain maximization problem, and the receiver combining vector design problem for weighted sum rate maximization.

[0070] Step 104: The channel gain maximization problem for direct links and backscattered links can be solved by second-order Taylor expansion combined with successive convex approximation method.

[0071] Step 105: For the receiver combining vector design problem of weighted sum rate maximization, a semi-positive definite matrix can be used for transformation to obtain the final result.

[0072] 2. Network architecture of a symbiotic communication system assisted by a fluidic antenna

[0073] The network architecture of the symbiotic communication system assisted by the fluidic antenna in this embodiment is as follows: Figure 2 As shown, the illustrated scenario includes one base station, one backscattering device, and one user. Both the backscattering device and the user are equipped with a fluid antenna. The entire system consists of modules 201, 202, 203, and 204. Module 201 is the base station, primarily responsible for transmitting and receiving data; module 202 is the backscattering device, primarily responsible for modulating and transmitting the received signal; module 203 is the user, primarily responsible for transmitting signal data; and module 204 is the fluid antenna, primarily responsible for changing its position to obtain more diversity gain.

[0074] 3. Simulation experimental data

[0075] Simulation data of the progressive optimization method for the fluid antenna-assisted symbiotic communication system in this embodiment are as follows: Figure 3As shown, the curves in the figure include the system and rate of using the joint optimization method, the system and rate of using the incremental optimization method, and the baseline system and rate. It can be seen that the incremental optimization method disclosed in this invention can provide a similar sum rate to the joint optimization method with lower complexity, while significantly outperforming the baseline system and rate.

[0076] 4. Uplink transmission

[0077] The channel between the base station and the user is called the direct link channel, and the channel between the base station, the backscattering device, and the user is called the backscattering link channel. A streaming antenna is installed on both the backscattering device and the user, and it can move within a certain range to construct a better channel environment. The direct link channel can be represented as:

[0078]

[0079] in Represents the local coordinates of the user-mounted fluidic antenna. This represents the conjugate transpose of the corresponding matrix from the base station to the user's transmission field. This represents the path response vector from the base station to the user.

[0080] The backscatter link channel can be represented as:

[0081]

[0082] in Represents the local coordinates of the fluid antenna mounted on the backscattering device. This represents the conjugate transpose of the received field response matrix from the user to the base station. This represents the path response vector from the base station to the backscattering device and then to the user. During the uplink signal transmission phase, the user sends a signal to the base station, and simultaneously, the backscattering device also sends a signal to the base station. The signal received by the base station is:

[0083]

[0084] in, The conjugate transpose of the normalized receiver combining vector, simultaneously satisfying , The information symbols sent to the user simultaneously satisfy , For mathematical expectation, The power of the signal sent to the user. The modulation coefficient of the backscattering device, The information symbols sent by the backscattering device simultaneously satisfy , The noise received by the base station has a mean of 0 and a variance of . The normal distribution, and This represents noise power.

[0085] After receiving the signal, the base station first decodes the signal from the user, and the resulting direct link rate is:

[0086]

[0087] After decoding the signal from the user, the base station uses serial interference cancellation technology to remove the decoded signal. The remaining signal after removal is:

[0088]

[0089] Then, the base station will decode the signal from the backscattering device, and the resulting backscattering link rate is:

[0090]

[0091] in, Let be the signal period of the backscattering device. The optimization objective is set as the weighted sum rate of the direct link and the backscattering link; therefore, the optimization objective can be expressed as:

[0092]

[0093] in, where are the weighting coefficients. Ultimately, the overall optimization problem can be expressed as:

[0094]

[0095] in, and These represent the sets of possible location coordinates for the user and the fluidic antenna mounted on the backscattering device, respectively.

[0096] 5. Optimize target transformation

[0097] Since the above optimization problem is difficult to solve, the weighted sum rate optimization problem can be transformed into three sub-problems using an asymptotic optimization method: the direct link channel gain maximization problem, the backscatter link channel gain maximization problem, and the receiver combining vector design problem for weighted sum rate maximization. Specifically, sub-problem one is to maximize the direct link channel gain by optimizing the position of the user-mounted flowing antenna, which can be expressed as:

[0098]

[0099] Subproblem two is to maximize the backscatter link channel gain by optimizing the position of the fluid antenna mounted on the backscatter device, which can be expressed as:

[0100]

[0101] Subproblem 3, after solving subproblems 1 and 2 and given the locations of the user and the backscattering device, aims to maximize the sum rate by optimizing the receiver combining vector, and can be expressed as:

[0102]

[0103] 6. Solving subproblems one and two

[0104] Since subproblems one and two are similar in form and independent of each other, they can be solved using the same method. Taking subproblem one as an example, we first establish the objective function:

[0105]

[0106] Where tr() represents the trace of the matrix, A TR (z1) represents the transmission field response matrix from the base station to the user. Since the objective function is a positive definite matrix and is non-convex, relaxation will be performed using a continuous convex approximation. This is achieved through a first-order Taylor expansion:

[0107]

[0108] Where Re{} denotes the real part of the complex number, A TR (z1) i ) indicates the first The transmission field response matrix from the base station to the user in this iteration; A TR (z1) i ) H Indicates the first The received field response matrix from the user to the base station in this iteration. consiant1 represents the remainder term of the first-order Taylor expansion;

[0109] because It remains non-convex, and further using a second-order Taylor expansion, we obtain:

[0110]

[0111] Among them, superscript Represents the transpose of a matrix. and Representing the gradient vector and The Hessian matrix, Represent real numbers, Let be a positive number, where For vectors The row number, constant2 represents the remainder term in the second-order Taylor expansion. express The OK.

[0112] Based on the above transformation, in the... After several iterations of continuous convex approximation, the optimization problem can be expressed as:

[0113]

[0114] in This represents the objective function after second-order Taylor expansion. Since this function has been transformed into a convex function, it can be solved directly using the CVX toolbox in Matlab. Subproblem two can also be solved using similar steps.

[0115] 7. Solving Subproblem Three

[0116] After solving subproblems one and two, for subproblem three, the receiver combining vector can be optimized to maximize the sum rate. To this end, a positive semi-definite matrix is ​​first introduced to transform the objective function:

[0117]

[0118] in , , Therefore, subproblem three can be transformed into:

[0119]

[0120] As can be seen, the above function is concave, therefore it can be solved using the CVX toolbox in Matlab. The specific process is as follows: First, without setting any constraints, use the CVX toolbox to find the optimal solution V* for V. If the rank of V* is 1, then it is the optimal solution. Otherwise, a randomization-based method can be used to derive an approximate suboptimal solution using singular value decomposition. Thus, the target problem is solved.

[0121] In summary, this invention can effectively improve diversity gain, power efficiency and spectral efficiency, while having low signal processing complexity and reducing the requirements for system hardware.

Claims

1. A progressive optimization method for a fluid antenna-assisted symbiotic communication system, characterized in that, Includes the following steps: Step 1: Deploy base stations, users, and backscattering devices in the fluid antenna-assisted symbiotic communication system, and install fluid antennas on the base stations and backscattering devices respectively; Step 2: During the uplink signal transmission phase, the user sends a signal to the base station, and at the same time, the backscatter device sends a signal to the base station. After receiving the signal, the base station obtains the rates of the direct link and the backscatter link, and then obtains the weighted sum rate optimization target. The weighted sum rate optimization target is subject to the minimum rate constraint of the direct link, the minimum rate constraint of the backscatter link, the mobility range constraint of the flow antenna, and the receiver combining vector normalization constraint. Step 3: Construct an incremental optimization framework, transforming the weighted sum rate optimization problem into three sub-problems: the direct link channel gain maximization problem, the backscatter link channel gain maximization problem, and the receiver combining vector design problem for weighted sum rate maximization. Step 4: For the channel gain maximization problem of direct link and backscatter link, the solution is obtained by second-order Taylor expansion combined with successive convex approximation method. Step 5: For the receiver combining vector design problem of weighted sum maximization, the solution is obtained by transformation using a positive semi-definite matrix, thus achieving the optimization of the symbiotic communication system.

2. The incremental optimization method for a fluid antenna-assisted symbiotic communication system according to claim 1, characterized in that, Step 1 specifically involves: the channel between the base station and the user is a direct link channel, and the channel between the base station, the backscattering device, and the user is a backscattering link channel; a streaming antenna is installed on both the backscattering device and the user; the direct link channel is represented as: ； in, Represents the local coordinates of the user-mounted fluidic antenna. This represents the conjugate transpose of the corresponding matrix from the base station to the user's transmission field. This represents the path response vector from the base station to the user. The backscatter link channel is represented as: ； in, Represents the local coordinates of the fluid antenna mounted on the backscattering device. This represents the conjugate transpose of the received field response matrix from the user to the base station. This represents the path response vector from the base station to the backscattering device and then to the user.

3. The incremental optimization method for a fluid antenna-assisted symbiotic communication system according to claim 2, characterized in that, Step 2 specifically involves the following: During the uplink signal transmission phase, the user sends a signal to the base station, and simultaneously, the backscattering device sends a signal to the base station. The signal received by the base station is: ； in, The conjugate transpose of the normalized receiver combining vector, simultaneously satisfying , The information symbols sent to the user simultaneously satisfy , For mathematical expectation, The power of the signal sent to the user. The modulation coefficient of the backscattering device, The information symbols sent by the backscattering device simultaneously satisfy , The noise received by the base station has a mean of 0 and a variance of . The normal distribution, and Noise power; After receiving the signal, the base station first decodes the signal from the user, and the resulting direct link rate is: ； After decoding the signal from the user, the base station uses serial interference cancellation technology to remove the decoded signal. The remaining signal after removal is: ； Then, the base station will decode the signal from the backscattering device, and the resulting backscattering link rate is: ； in, Given the signal period of the backscattering device, the optimization objective is set as the weighted sum rate of the direct link and the backscattering link, expressed as: ； in, The weighting coefficients represent the total sum rate. The optimization problem is represented as: ； in, and These represent the sets of location coordinates of the user and the fluid antenna mounted on the backscattering device, respectively.

4. The incremental optimization method for a fluid antenna-assisted symbiotic communication system according to claim 3, characterized in that, Step 3 specifically involves: using an incremental optimization framework, transforming the weighted sum rate optimization problem into three sub-problems: maximizing the direct link channel gain, maximizing the backscatter link channel gain, and designing a receiver combining vector to maximize the weighted sum rate. Sub-problem one involves maximizing the direct link channel gain by optimizing the location of the user-mounted streaming antennas, expressed as: ； Subproblem two is to maximize the backscatter link channel gain by optimizing the position of the fluid antenna mounted on the backscatter device, expressed as: ； Subproblem 3, after solving subproblems 1 and 2, involves maximizing the sum rate by optimizing the receiver combining vector, given the locations of the user and the backscattering device. This can be expressed as: 。 5. The incremental optimization method for a fluid antenna-assisted symbiotic communication system according to claim 4, characterized in that, Step 4 specifically involves the following: Subproblems one and two have the same form and are independent of each other, therefore they are solved using the same method. For subproblem one, the objective function is first established: ； Where tr() represents the trace of the matrix, A TR (z1) represents the transmission field response matrix from the base station to the user. Since the objective function is a positive definite matrix, relaxation is achieved through a continuous convex approximation, given that the objective function is non-convex. This is done using a first-order Taylor expansion: ； Where Re{} denotes the real part of the complex number, A TR (z1) i ) indicates the first The transmission field response matrix from the base station to the user in this iteration; A TR (z1) i ) H Indicates the first The received field response matrix from the user to the base station in the next iteration; constant1 represents the remainder term of the first-order Taylor expansion; Because the objective function after the first-order Taylor expansion It is non-convex, and we can obtain the following using a second-order Taylor expansion: ； Among them, superscript Represents the transpose of a matrix. and Representing the gradient vector and The Hessian matrix; Represent real numbers, Let be a positive number, where For vectors The row number, constant2 represents the remainder term in the second-order Taylor expansion. express The OK; In the After several iterations of continuous convex approximation, the optimization problem can be expressed as: ； in This indicates that the objective function is obtained by applying the second-order Taylor expansion and is solved using the CVX toolbox in Matlab software. The solution method for subproblem two is the same.

6. The incremental optimization method for a fluid antenna-assisted symbiotic communication system according to claim 5, characterized in that, Step 5 specifically involves optimizing the receiver combining vector to maximize the sum rate for subproblem 3. First, a positive semi-definite matrix is ​​introduced to transform the objective function: ； in, , , Therefore, subproblem three is transformed into: ； Solve using the CVX toolbox in Matlab software.

7. A progressive optimization method for a fluid antenna-assisted symbiotic communication system according to claim 5 or 6, characterized in that, The specific steps of using the CVX toolbox in Matlab software to solve the problem are as follows: without setting any constraints, the CVX toolbox is used to find the optimal solution V* for V; if the rank of V* is 1, it is the optimal solution; otherwise, a randomization-based method is used to derive an approximate suboptimal solution using singular value decomposition to solve the target problem.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method of claim 1.

9. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method of claim 1.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method of claim 1.

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