Interference modulation anti-interference communication method based on modulation gain optimization

Abstract

The invention discloses an interference modulation anti-interference communication method based on modulation gain optimization, and belongs to the technical field of wireless communication anti-interference. The problem that the communication anti-interference performance of an existing AAJ scheme is limited is solved. According to the method, firstly, an interference modulation anti-interference system model is established, a sending end modulates and forwards interference signals by means of a programmable gain amplifier, and transmission information is borne by configuring different gain modes of the programmable gain amplifier; secondly, establishing an optimization problem by taking minimization of a system bit error rate as an optimization target, decoupling the optimization problem, and deducing an optimal judgment threshold of a receiving end detector; and finally, a modulation gain optimization method based on BER approximate expression is designed according to the channel state, so that on the premise of ensuring the bit error rate performance, the calculation complexity is remarkably reduced, the communication anti-interference performance is improved, and reliable and efficient communication is realized. The method can be applied to the field of interference modulation anti-interference communication.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication anti-interference technology, specifically relating to an interference modulation anti-interference communication method based on modulation gain optimization. Background Technology

[0002] Wireless communication, relying on the open electromagnetic space, is often threatened by malicious interference, which compromises its reliability and effectiveness. In suppression-type interference scenarios, the power of strong interference signals often far exceeds that of the useful signal, overwhelming the received signal and leading to demodulation failure and communication link interruption. Furthermore, the time-varying fading characteristics of channels in complex electromagnetic environments, along with the unknown and non-cooperative nature of the interference source's channel state, further exacerbate the degradation of communication performance. Therefore, improving the robustness of the system under suppression-type interference environments has become a critical and urgent technical requirement.

[0003] In recent years, to address the need for reliable communication transmission in environments with strong non-cooperative signals, the use of interference signals to assist communication has received widespread attention. Among these approaches, an active anti-jamming (AAJ) scheme based on a programmable gain amplifier (PGA) has been proposed. PGAs offer advantages such as flexible gain control and low gain error, playing a crucial role in anti-jamming communication. Existing research has achieved a good trade-off between high gain range, low gain error, and low power consumption through cascaded unit structure design of PGAs. In this AAJ scheme, the transmitter controls the PGA to amplify or zero the radio frequency signal based on the information bits to be transmitted, thereby performing secondary modulation on the received interference signal, i.e., "interference modulation"; the receiver detects the interference by identifying differences in signal energy levels. Compared with traditional anti-jamming methods, this scheme does not rely on prior knowledge such as channel state information and interference type, demonstrating certain advantages in resisting suppression interference. However, existing AAJ schemes only use a simple amplification / zeroing modulation method and do not systematically design the PGA gain from the perspective of bit error rate (BER) performance optimization. Especially in the region of high jamming to noise ratio (JNR), its BER curve has obvious flatness, which restricts further improvement of communication performance.

[0004] In summary, optimizing the modulation gain through PGA to address the limited anti-interference performance of existing AAJ schemes and achieve highly reliable communication under suppression interference is a pressing issue that needs to be addressed. Summary of the Invention

[0005] This invention addresses the problem that existing AAJ schemes have fixed modulation forms and cannot optimize modulation gain according to channel conditions, resulting in limited communication anti-interference performance. Therefore, it proposes an interference modulation anti-interference communication method based on modulation gain optimization.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is: an interference modulation anti-interference communication method based on modulation gain optimization, the method specifically including the following steps:

[0007] Step 1: Establish an optimization problem based on minimizing the bit error rate to solve for the energy detection decision threshold and interference modulation gain;

[0008] Step 2: Decouple the optimization problem established in Step 1 into two sub-problems, namely the sub-problem of the optimal energy detection decision threshold and the sub-problem of the optimal interference modulation gain of the PGA.

[0009] Step 3: Solve the subproblems of the optimal energy detection decision threshold and the optimal interference modulation gain of the PGA to obtain the optimal energy detection decision threshold and the optimal interference modulation gain of the PGA.

[0010] Step 4: The transmitter modulates the bit stream information to be transmitted according to the obtained PGA optimal interference modulation gain, and the receiver makes a decision based on the optimal energy detection decision threshold to recover the bit stream information.

[0011] The beneficial effects of this invention are:

[0012] The present invention first establishes a system model for interference modulation anti-interference, in which the transmitting end modulates and forwards the interference signal using a programmable gain amplifier, and carries the transmitted information by configuring different gain modes of the programmable gain amplifier; then, an optimization problem is established with the goal of minimizing the system bit error rate, and the optimization problem is decoupled to derive the optimal decision threshold of the receiver detector; finally, a modulation gain optimization method based on BER approximation is designed according to the channel state, which significantly reduces the computational complexity and improves the anti-interference performance of communication while ensuring bit error rate performance, thus achieving reliable and efficient communication. Attached Figure Description

[0013] Figure 1 This is a flowchart of an interference modulation anti-interference communication method based on modulation gain optimization according to the present invention;

[0014] Figure 2 This is a comparison chart of BER (Burst Error) for different anti-interference methods when the signal-to-noise ratio (SNR) is 10dB and N=8.

[0015] In the traditional AAJ method, PGA uses an on / off mode to send information bits '1' and '0';

[0016] Figure 3 This is a comparison chart of BER under different SNR conditions. Detailed Implementation

[0017] This invention first establishes a jamming modulation anti-jamming system model based on PGA: a malicious jammer continuously transmits jamming signals to attempt to suppress legitimate communication between the transmitter and receiver. Under jamming suppression conditions, the transmitter determines the jamming modulation gain of the PGA based on the bit stream, and then forwards the remodulated jammed transmitted signal to the receiver. The receiver recovers the information bits by demodulating a specific pattern in the received signal, thus achieving jamming-modulated anti-jamming communication. The channel coefficients for jammer-to-transmitter (JT), jammer-to-receiver (JR), and transmitter-to-receiver (TR) are respectively represented by... This indicates that the channel coefficient remains constant during the channel coherence time, but may vary independently within different coherence intervals. The communicating parties employ a full-duplex transceiver, allowing simultaneous reception and transmission of signals within the same time slot, with directional signal transmission achieved through a duplexer. At the transmitter, the bit stream to be transmitted is input to the RF terminal via symbol mapping, and a mapped PGA (Programmable Gate Array) interference modulation gain is generated based on different information bits. The PGA modulates the received interference signal through precise gain control. At the receiver, the filtered and sampled received signal undergoes energy detection to demodulate the interference, and then decoding is achieved through symbol demapping.

[0018] The method of the present invention will be described in detail below with reference to the established system model.

[0019] Specific Implementation Method 1: The interference modulation anti-interference communication method based on modulation gain optimization described in this implementation method specifically includes the following steps:

[0020] Step 1: Establish an optimization problem based on minimizing the bit error rate to solve for the energy detection decision threshold and interference modulation gain;

[0021] Step 2: Decouple the optimization problem established in Step 1 into two sub-problems, namely the sub-problem of the optimal energy detection decision threshold and the sub-problem of the optimal interference modulation gain of the PGA.

[0022] Step 3: Solve the subproblems of the optimal energy detection decision threshold and the optimal interference modulation gain of the PGA to obtain the optimal energy detection decision threshold and the optimal interference modulation gain of the PGA.

[0023] Step 4: The transmitter modulates the bit stream information to be transmitted according to the obtained PGA optimal interference modulation gain, and the receiver makes a decision based on the optimal energy detection decision threshold to recover the bit stream information.

[0024] Specifically, step four involves steps one and two. The receiver calculates the average power of the sampled sequence and then makes a decision based on formula (6).

[0025] It should be noted that the method of this invention is illustrated using binary source transmission information as an example. When it is necessary to transmit K-state information bits and When the value is greater than 2, the receiving end needs to... Verdict threshold Make a decision to divide the signal decision space into Each part.

[0026] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the specific process of step one is as follows:

[0027] Step 11: In a PGA-based interference modulation anti-jamming system, under the action of the jammer, the transmitted signal at the transmitting end is:

[0028] (1)

[0029] in, Let's represent the interference signal. Assume the jammer sends a complex Gaussian distributed interference signal, satisfying... And the average power of the interference signal is , Indicates the interference modulation gain. This represents the channel coefficient from the jammer to the transmitter;

[0030] For binary information sources, i.e., sending binary information bits:

[0031] (2)

[0032] in, This represents the interference modulation gain when transmitting 0. This represents the interference modulation gain when transmitting 1;

[0033] The signal received by the receiver's omnidirectional receiving antenna is a superposition of the JR link interference signal and the TR link interference modulation signal, that is:

[0034] (3)

[0035] in, This indicates the signal received by the omnidirectional receiving antenna. This represents the channel coefficient from the transmitter to the receiver. This represents the channel coefficients from the jammer to the receiver. JR link indicates the link between the jammer and the receiver, and TR link indicates the link between the transmitter and the receiver. This indicates the delay in the arrival of JR link signals and TR link signals at the receiving end. This represents a noise signal, which is composed of PGA noise and Additive White Gaussian Noise (AWGN). Follows a pattern with a mean of zero and a variance of . The complex Gaussian distribution, i.e. , This represents the average power of the noise.

[0036] The signal received by the omnidirectional receiving antenna Sampling is performed to obtain the received signal sampling sample sequence. :

[0037] (4)

[0038] in, This represents the number of samples taken, i.e., the number of samples taken within each symbol period. Next, the superscript T indicates transpose. These represent the sampling number 1 and 2 respectively. One sample;

[0039] (5)

[0040] in, Indicates the sampling number One sample, Indicates the first [unclear] of the interference signal One sample, Indicates the first [unclear] of the interference signal One sample, Represents the first... One sample, Indicates the first The interference modulation gain corresponding to the sampling sample, and the first sampled sample The data transmitted at the time corresponding to each sample is related to the data transmitted at that moment. If the data transmitted by the binary source at that time is 0, then... If the data sent by the binary source at this time is 1, then ;

[0041] Steps one and two: It should be noted that the value of N directly affects the accuracy of the estimation of the signal's true power. When When the value is much smaller than the symbol period, it can be ignored. The influence of the sampling sequence is then calculated. average power According to average power The decision-making process is modeled as a binary hypothesis testing problem. :

[0042] (6)

[0043] in, This is the energy detection decision threshold, when the state is satisfied. When, it indicates that the transmitter is sending 0, and when the state is satisfied. When, it indicates that the transmitter is sending a 1;

[0044] Step 13: Calculate the bit error rate

[0045] Will status and Under the given conditions, the average power (test statistic) of the sampled sequence is denoted as follows: and The distributions of the test statistics are as follows:

[0046] (7)

[0047] in, This represents the signal variance of the sampled sequence at the receiver when the transmitter sends 0; This represents the signal variance of the sampled sequence when the transmitter sends a 1; Describing the degrees of freedom as The chi-square distribution means that the test statistic follows a chi-square distribution.

[0048] According to equation (5):

[0049] (8)

[0050] in, This indicates the calculation of the modulus. This represents the average power of the interference signal. Indicates the average noise power;

[0051] According to the decision criterion of equation (6), we get:

[0052] (9)

[0053] in, Indicates bit error rate, This represents the probability of firing 0. This represents the probability of firing 1, and is usually set to... , express The probability density function (PDF). express The probability density function, Represents the integral variable. The base of the natural logarithm. The Gamma function is defined as follows: , Represents the integral variable;

[0054] Step 14: Establish the optimization problem

[0055] Let the average transmit power of the PGA be If the test statistic for sending 0 is smaller than that for sending 1, then the bit error rate will be minimized. The optimization problem is modeled as follows:

[0056] (10)

[0057] in, This represents the energy detection decision threshold that minimizes the value of equation (10). and This represents the interference modulation gain that minimizes the value of equation (10).

[0058] The other steps and parameters are the same as in Specific Implementation Method 1.

[0059] It should be noted that the average transmit power of the PGA .

[0060] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the sampled sample sequence... average power for:

[0061] (11)

[0062] in, Represents the sample sequence The average power.

[0063] Other steps and parameters are the same as in specific implementation method one or two.

[0064] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the sub-problem of the optimal energy detection decision threshold is:

[0065] (12)

[0066] in, This represents the optimal energy detection decision threshold obtained by solving the problem.

[0067] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0068] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the solution method for the subproblem of the optimal energy detection decision threshold is as follows:

[0069] Step S1: Differentiate equation (9) to obtain the partial derivative function:

[0070] (13)

[0071] make That is, when At that time, the optimal detection decision threshold is obtained. :

[0072] (14)

[0073] Therefore, in order to solve the optimal detection decision threshold Requires known variables and However, in actual transmission, these variables cannot be directly obtained. This invention utilizes the prior length of the data from both the sender and receiver. Furthermore, a pilot sequence containing only 0s and 1s is used to estimate the decision threshold of the receiver energy detector, so as to ensure the feasibility of the interference modulation anti-interference communication method in actual transmission.

[0074] Step S2: Calculate the average received power of each pilot symbol in the pilot sequence, and then... The average received power of each pilot symbol is denoted as . ;

[0075] Step S3, Calculation Estimated value;

[0076] Step S4, Calculation Estimated value;

[0077] Step S5, and Substituting into formula (14), we obtain the optimal detection decision threshold. .

[0078] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0079] The algorithm flow corresponding to this implementation is shown in Table 1. Wherein, This represents the set of indices of '0' in the pilot sequence. Represents a set The number of elements in express The estimated value.

[0080] Table 1

[0081]

[0082] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the specific process of step S2 is as follows:

[0083]

[0084] in, Indicates the received number A sequence of sampling points for each pilot symbol. , Represents the sequence of sampling points The first in One sampling point.

[0085] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0086] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One to Six in that the specific process of step S3 is as follows:

[0087] (15)

[0088] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0089] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the specific process of step S4 is as follows:

[0090] (16)

[0091] in, This represents the set of indices of '1' in the pilot sequence. Represents a set The number of elements in express The estimated value.

[0092] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0093] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the sub-problem of the optimal interference modulation gain of the PGA is:

[0094] (17)

[0095] in, and This represents the optimal interference modulation gain of the PGA obtained by solving.

[0096] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0097] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One through Nine in that the solution method for the subproblem of optimal interference modulation gain of the PGA is as follows:

[0098] Step 1: Set the weighting factor in the offset mode Initial variance ratio Initialize the weighting factor in the offset mode ;

[0099] Step 2: Initialize the number of iterations ;

[0100] Step 3, according to Calculate the interference modulation gain:

[0101] (18)

[0102] in, This represents the cancellation coefficient based on pilot estimation;

[0103] (19)

[0104] in, and Let these represent the Gaussian white noise at the transmitter and receiver, respectively, which obey the following rules: and ;

[0105] Then calculate according to formula (8) and And then according to and calculate :

[0106] (20)

[0107] like Greater than Then update , Then proceed to step 4;

[0108] like Not greater than If so, proceed directly to step 4;

[0109] Step 4: Determine if the condition is met. :

[0110] If not satisfied Then let Continue to step 5;

[0111] If satisfied Then, based on the weighting factor obtained from the last update during the iteration process under the offsetting mode... Calculate the optimal interference modulation gain (i.e., according to formula (18));

[0112] Step 5, let Return to step 3.

[0113] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0114] This implementation optimizes interference modulation gain based on variance ratio, which can significantly improve the speed of modulation gain optimization. Specifically, the method of this invention (LC-JMGC method) iteratively searches for the maximum variance ratio. To determine the weighting factors, each iteration requires only one complex multiplication, with a complexity of O(n log n). In contrast, if the minimum is searched in each iteration... The corresponding optimal weighting factor (called the O-JMGC method, where the computational complexity of each iteration mainly comes from the calculation of PDF integrals of two chi-square distributions), if an M-point numerical integration method is used to solve the integral (e.g., using the trapezoidal rule), the complexity of a single iteration is O(n). Clearly, the method of this invention significantly reduces the computational overhead of iteratively searching for weight factors.

[0115] Simulation results

[0116] Define the signal-to-noise ratio at the receiver as Assume the jammer emits random jamming signals that follow a complex Gaussian distribution. Assume that the Ricean fading model is used in each channel, i.e., the channel model is expressed as... ,in, Rice factor, and ( The ) represent the channel responses of the line-of-sight path and the non-line-of-sight path in the link, respectively. The AWGNs received by the transceiver satisfy the independent and identically distributed (i.e., ...) The simulation parameter settings are shown in Table 2.

[0117] Table 2 Simulation Parameters

[0118]

[0119] Figure 2 The BER variation curves of the method of this invention and the traditional AAJ method under Ricean channel are presented. In the simulation, the comparison methods are all based on step values. Search weighting factors. (By...) Figure 2 As can be seen, the BER performance of the method of this invention is superior to that of the traditional AAJ method, and the BER performance advantage increases significantly with increasing JNR. This is due to the gain of the method of this invention on PGA interference modulation. Fine-grained control was implemented, which effectively improved transmission reliability.

[0120] Figure 3 The BER performance of the traditional AAJ method and the method of this invention was compared under different SNR and N values. In the simulation, JNR was set to 5 dB. Figure 3 As can be seen, the BER of both methods decreases significantly with increasing N. Therefore, communication reliability can be enhanced not only by improving SNR but also by increasing the N value. However, for specific BER performance requirements, the method of this invention has advantages over the AAJ method in both SNR and N. That is, at the same SNR, the method of this invention can meet the requirements with a lower SNR or a smaller N value.

[0121] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An interference modulation anti-interference communication method based on modulation gain optimization, characterized in that, The method specifically includes the following steps: Step 1: Establish an optimization problem based on minimizing the bit error rate to solve for the energy detection decision threshold and interference modulation gain; Step 2: Decouple the optimization problem established in Step 1 into two sub-problems, namely the sub-problem of the optimal energy detection decision threshold and the sub-problem of the optimal interference modulation gain of the PGA. Step 3: Solve the subproblems of the optimal energy detection decision threshold and the optimal interference modulation gain of the PGA to obtain the optimal energy detection decision threshold and the optimal interference modulation gain of the PGA. Step 4: The transmitter modulates the bit stream information to be transmitted according to the obtained PGA optimal interference modulation gain, and the receiver makes a decision based on the optimal energy detection decision threshold to recover the bit stream information.

2. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 1, characterized in that, The specific process of step one is as follows: Step 11: Under the action of the jammer, the transmitted signal from the transmitter is: (1) in, Indicates interference signal. Indicates the interference modulation gain. This represents the channel coefficient from the jammer to the transmitter; For binary information sources: (2) in, This represents the interference modulation gain when transmitting 0. This represents the interference modulation gain when transmitting 1; The signal received by the receiver's omnidirectional receiving antenna is a superposition of the JR link interference signal and the TR link interference modulation signal, that is: (3) in, This indicates the signal received by the omnidirectional receiving antenna. This represents the channel coefficient from the transmitter to the receiver. This represents the channel coefficients from the jammer to the receiver. JR link indicates the link between the jammer and the receiver, and TR link indicates the link between the transmitter and the receiver. This indicates the delay in the arrival of JR link signals and TR link signals at the receiving end. Indicates a noise signal; The signal received by the omnidirectional receiving antenna Sampling is performed to obtain the received signal sampling sample sequence. : (4) in, This indicates the number of samples taken, and the superscript T indicates transpose. These represent the sampling number 1 and 2 respectively. One sample; (5) in, Indicates the sampling number One sample, Indicates the first [unclear] of the interference signal One sample, Indicates the first [unclear] of the interference signal One sample, Represents the first... One sample, Indicates the first The interference modulation gain corresponding to each sampled sample; Steps 1 and 2: Calculate the sample sequence again. average power According to average power The decision-making process is modeled as a binary hypothesis testing problem. : (6) in, This is the energy detection decision threshold, when the state is satisfied. When, it indicates that the transmitter is sending 0, and when the state is satisfied. When, it indicates that the transmitter is sending a 1; Step 13: Calculate the bit error rate Will status and Under the given conditions, the average power of the sampled sequence is denoted as follows: and The distributions of the test statistics are as follows: (7) in, This represents the signal variance of the sampled sequence at the receiver when the transmitter sends 0; This represents the signal variance of the sampled sequence when the transmitter sends a 1; Describing the degrees of freedom as The chi-square distribution; According to equation (5): (8) in, This indicates the calculation of the modulus. This represents the average power of the interference signal. Indicates the average noise power; According to the decision criterion of equation (6), we get: (9) in, Indicates bit error rate, This represents the probability of firing 0. This represents the probability of firing a 1. express The probability density function, express The probability density function, Represents the integral variable. The base of the natural logarithm. The Gamma function is defined as follows: , Represents the integral variable; Step 14: Establish the optimization problem Let the average transmit power of the PGA be This will minimize the bit error rate. The optimization problem is modeled as follows: (10) in, This represents the energy detection decision threshold that minimizes the value of equation (10). and This represents the interference modulation gain that minimizes the value of equation (10).

3. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 2, characterized in that, The sample sequence average power for: (11) in, Represents the sample sequence The average power.

4. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 3, characterized in that, The subproblem of the optimal energy detection decision threshold is: (12) in, This represents the optimal energy detection decision threshold obtained by solving the problem.

5. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 4, characterized in that, The solution method for the subproblem of the optimal energy detection decision threshold is as follows: Step S1: Differentiate equation (9) to obtain the partial derivative function: (13) make That is, when At that time, the optimal detection decision threshold is obtained. : (14) Step S2: Calculate the average received power of each pilot symbol in the pilot sequence, and then... The average received power of each pilot symbol is denoted as . ; Step S3, Calculation Estimated value; Step S4, Calculation Estimated value; Step S5, and Substituting into formula (14), we obtain the optimal detection decision threshold. .

6. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 5, characterized in that, The specific process of step S2 is as follows: in, Indicates the received number A sequence of sampling points for each pilot symbol. , Represents the sequence of sampling points The first in One sampling point.

7. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 6, characterized in that, The specific process of step S3 is as follows: (15) in, This represents the set of indices of '0' in the pilot sequence. Represents a set The number of elements in express The estimated value.

8. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 7, characterized in that, The specific process of step S4 is as follows: (16) in, This represents the set of indices of '1' in the pilot sequence. Represents a set The number of elements in express The estimated value.

9. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 8, characterized in that, The subproblem of the optimal interference modulation gain of the PGA is: (17) in, and This represents the optimal interference modulation gain of the PGA obtained by solving.

10. The interference modulation anti-interference communication method based on modulation gain optimization according to claim 9, characterized in that, The solution method for the subproblem of optimal interference modulation gain of PGA is as follows: Step 1: Set the weighting factor in the offset mode Initial variance ratio Initialize the weighting factor in the offset mode ; Step 2: Initialize the number of iterations ; Step 3, according to Calculate the interference modulation gain: (18) in, This represents the cancellation coefficient based on pilot estimation; (19) in, and These represent the Gaussian white noise at the transmitter and receiver, respectively. Then calculate according to formula (8) and And then according to and calculate : (20) like Greater than Then update , Then proceed to step 4; like Not greater than If so, proceed directly to step 4; Step 4: Determine if the condition is met. : If not satisfied Then let Continue to step 5; If satisfied Then, based on the weighting factor obtained from the last update during the iteration process under the offsetting mode... Calculate the optimal interference modulation gain; Step 5, let Return to step 3.

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