A pilot optimization method based on genetic algorithm combined with random search algorithm for OTFS system

Abstract

The application discloses a pilot optimization method based on a combination of a genetic algorithm and a random search algorithm for an OTFS system, and the method comprises the following steps: initializing a population; calculating the fitness value of each individual in the population; entering a breeding cycle iteration; performing a cross-recombination operation on offspring; performing a mutation operation on the offspring; performing a reinsertion operation on the offspring; selecting excellent individuals and performing a random search algorithm on the excellent individuals; aiming at a pilot optimization problem in channel estimation of an orthogonal time frequency space (OTFS) system based on compressed sensing, taking minimization of a cross-correlation value of a recovery matrix as a target, and taking the minimum cross-correlation value as a criterion for selecting the best pilot. The method has the advantages of the genetic algorithm, and a part of the population is randomly searched to avoid falling into a local optimum problem. Compared with a conventional genetic algorithm, the method has better effect, and a pilot obtained by using the method can obtain a lower channel estimation mean square error when applied to channel estimation.

Description

Technical Field

[0001] This invention relates to a pilot optimization method based on a combination of genetic algorithm and random search algorithm for use in OTFS systems. It belongs to the field of channel estimation and pilot optimization technology for pilot-assisted communication systems, and particularly relates to the pilot optimization problem in channel estimation of Orthogonal Time Frequency Space (OTFS) systems. Background Technology

[0002] Compressed sensing (CS) is a technique that utilizes the sparsity of signals to recover them. It reconstructs the entire signal using fewer observations and has proven highly valuable in fields such as image processing, biomedicine, and wireless communication. CS theory states that as long as the signal possesses sparsity, even with a sampling frequency lower than the Nyquist rate, the original signal can still be accurately reconstructed using optimized algorithms. The Time-Delay-Doppler Grid-Synchronization (OTFS) system modulates and processes signals in the time-delay-Doppler domain. In real-world communication environments, signal transmission only experiences a limited number of multipath propagation paths and Doppler shifts, which occupy only a few points in the time-delay-Doppler domain. Therefore, the channel response at most time-delay-Doppler grid points is close to zero, resulting in channel sparsity. This sparsity allows the OTFS system to effectively perform channel estimation and signal reconstruction using compressed sensing technology. Meanwhile, CS can reconstruct high-dimensional signals using a small number of observations. Therefore, sparse channel estimation based on compressed sensing can have less pilot overhead than traditional least squares (LS) and minimum mean square error (MMSE) algorithms.

[0003] Pilot-assisted channel estimation based on CS (Coordinated Scattering) has been extensively studied, and many sparse signal recovery algorithms have been applied to channel estimation, such as Orthogonal Matching Pursuit (OMP), Simultaneous Orthogonal Matching Pursuit, and Sparsity Adaptive Matching Pursuit. Another research focus in channel estimation is pilot design. The design of pilot positions and symbol values ​​significantly affects the performance of CS-based sparse channel estimation. With the rapid development of mobile communication systems towards fifth-generation (5G) and higher versions, the demands for new transmission technologies and system architectures are constantly increasing. Among these, Orthogonal Time-Frequency-Spacetime (OTFS) modulation technology has attracted widespread attention due to its significant performance advantages in high-speed mobile environments. OTFS systems can effectively handle the Doppler effect and provide more stable signal transmission in time-varying channels; therefore, research on channel estimation in OTFS systems is essential. Genetic Algorithms (GAs) are heuristic search algorithms well-suited for solving optimization and search problems. They can perform global searches and find effective solutions for various types of problems (including nonlinear, multimodal, and discrete problems). However, they also have some limitations. For example, they require appropriate selection of parameters such as crossover, mutation rate, and population size, which often rely on experience or multiple trials. Furthermore, using GAs solely for pilot optimization can easily lead to getting stuck in local optima, resulting in suboptimal pilot optimization performance, especially in highly complex search spaces. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings and deficiencies of the existing technology by proposing a pilot optimization method based on a combination of genetic algorithm and random search algorithm for use in OTFS systems. By using better pilots for channel estimation, better estimation performance is obtained, that is, the channel estimation has a lower mean square error (MSE), and a recovery matrix with the smallest possible cross-correlation value is obtained.

[0005] The technical solution adopted by this invention to solve its technical problem is: a pilot optimization method based on a combination of genetic algorithm and random search algorithm for OTFS system, the method comprising the following steps:

[0006] Step 1: Initialize the population: In this algorithm, the different sets of pilot symbols represent each individual in the genetic algorithm. The genes in an individual correspond to the values ​​of each pilot symbol in the pilot symbol set. Set the number of individuals to NIND, with a value of 100. The length of each individual is INDLENGTH (determined by the number of pilot symbols in the pilot symbol set used by the system). At this point, the initial population size is (NIND, INDLENGTH). The maximum number of generations MAXGEN and the generation gap between offspring and parents are defined as GGAP. Select a gene value of +1 or -1 for each individual, and set the generation counter gen = 0.

[0007] Step 2: Calculate the fitness value of each individual in the population. Select a fitness value FitnV that is equal to the reciprocal of the cross-correlation value μ of the recovery matrix corresponding to the pilot symbol set, and calculate the fitness value FitnV(i) for each individual in the population, i = 1, 2, ..., NIND;

[0008] Step 3: Enter the breeding cycle iteration. First, the offspring selection operation is performed. Offspring are selected based on fitness values ​​and implemented by roulette wheel. Individuals with high fitness values ​​are selected to generate the offspring population SelCh. The probability of an offspring being selected is GGAP. Therefore, the dimension of the offspring population SelCh is (NIND*GGAP,INDLENGTH).

[0009] Step 4: Perform crossover and recombination operations on the offspring, and select a crossover probability P for each individual in the offspring population. r Perform discrete recombination, P r The value is 0.8, meaning that a multi-point intersection method is selected at the intersection point with probability P. r Select multiple individuals from the population, group them in pairs in sequence, and exchange certain positions of the genes of the two individuals (the positions are randomly generated) to produce two new individuals;

[0010] Step 5: Perform mutation operation on the offspring and select an appropriate mutation probability P. m And set a mutation constraint FieldDR. Since the gene value range is +1 or -1 in step 1 above, the FieldDR value is also +1 or -1, that is, with probability P. m Multiple genes are randomly selected from individuals, and the values ​​of these genes are changed within the range of FieldDR, thereby increasing the diversity of the population.

[0011] Step 6: Perform the re-insertion operation on offspring. After steps 3 to 5 above, the new offspring population size is NIND*GGAP. Recalculate its fitness value FitnVSel(i), where i represents the i-th offspring individual. Use the re-insertion strategy to replace the NIND*GGAP individuals with the lowest fitness values ​​in the original population with the new offspring population to obtain a new population.

[0012] Step 7: Select excellent individuals, sort the fitness values ​​of the new population obtained after re-insertion in descending order, find the top 10% of individuals with the highest fitness values ​​and save them to obtain the individual set Chrom_ten, and record the position of these individuals in the original population as Index.

[0013] Step 8: For each individual in the Chrom_ten set selected above, use the following random search algorithm: starting from the first gene of the individual, take the negative of each gene and recalculate the fitness value of the current individual. Determine whether the current fitness value is greater than the fitness value before the change. If it is greater, replace the original individual with the individual with the modified gene. If it is less than or equal to, keep the original individual unchanged. Then perform the same operation on the next gene. After all gene positions of the current individual have been operated on, jump to the next individual and repeat the above operation until every individual in the Chrom_ten set has been traversed.

[0014] Step 9: Re-insert the new individuals obtained after processing with the random search algorithm into the population according to the Index position in Step 7 above, thereby obtaining a new population, and use this new population as the initial population for the next generation of reproduction.

[0015] Step 10: Increment the generation counter gen by one, and record the reciprocal of the maximum objective function value of the current generation, which is the minimum cross-correlation value of the recovery matrix corresponding to the pilot symbol set. Determine whether gen is greater than the maximum number of generations MAXGEN. If it is, proceed to the next step; otherwise, jump to step 3 above.

[0016] Step 11: Output the results. Select the individual with the largest fitness value in the last generation of the population. This is the final optimized pilot symbol set pilotFinal. At this point, it is a column vector. After dimensional transformation, it is converted into a two-dimensional pilot symbol set, which is the final pilot.

[0017] Further, step 1 includes: initializing the population size NIND to 100 and the maximum generation number MAXGEN to 600.

[0018] Furthermore, in step 1, the generation gap (GGAP) between the offspring and the parent generation is set to 0.98.

[0019] Furthermore, in step 4, the crossover probability P r The value is 0.8.

[0020] Furthermore, in step 5, the mutation probability P m The value is 0.6.

[0021] Furthermore, the method also includes determining pilot optimization criteria for compressed sensing-based OTFS channel estimation, considering an OTFS system where the transmitted signal belongs to the time-delay Doppler domain, denoted as x. d [k,l],k∈[0,N-1],l∈[0,M-1], where N represents the Doppler dimension and M represents the time delay dimension. The placement pattern of the pilot symbol set is further optimized when performing channel estimation in the OTFS system. There is no guard band on the right side of the pilot and data symbols. This is because the data symbols on the right side will not interfere with the pilot symbols, which can improve the data utilization efficiency. Therefore, we focus on the pilot symbol optimization design under this mode.

[0022] The transmitted signal x[k,l] is represented as:

[0023]

[0024] Where k p ,l p k represents the center position of the pilot symbol. m and l m The pilot symbols represent the maximum Doppler tap and maximum delay tap of the channel, with a dimension of L. p =(2N) p +1)×M p ;

[0025] During channel estimation, the pilot symbol x p When inserted together with the data symbols in the DD field, the received pilot signal in the DD field at the receiver is represented as follows:

[0026]

[0027] in H represents phase compensation. k',l' It is the channel matrix in the DD domain;

[0028] To correspond with the compressed sensing signal reconstruction model, Equation 2 is simplified into vector form, which rearranges the two-dimensional data y[k,l] into a vector. And the ((k+N)th p M p +ll p The elements of ) are equal to y[k,l], and the channel matrix H in the DD domain is also set. k',l'Arranged into column vectors Where L = (l m +1)(2k m +1), and the (l'(2k)th m +1)+k'+k m The element of ) is equal to H k',l' ;

[0029] Therefore, Equation 2 can be expressed in vector form as follows:

[0030]

[0031] in It represents the Hadamah accumulation. It is the additional phase matrix, where the ((k+N)th phase matrix is... p M p +ll p ,l'(2k m +1)+k'+k m The elements of ) represent α k',l-l' , It is derived from x[k,l], and its ((k+N)th p M p +ll p ,l'(2k m +1)+k'+k m The elements of ) represent x[k-k',l-l'], and will Defined as a recovery matrix, it is written as:

[0032] y p =Ah+w Formula 4

[0033] Here, h contains only P non-zero elements, meaning h is a sparse vector. In the recovery matrix A, considering the placement pattern of the proposed pilot symbol set, X p From the pilot symbol x in Equation 1 p It consists of the pilot symbol set and the guard band symbol set, and it has a certain relationship with the guard band symbol set. The specific relationship is expressed as follows:

[0034]

[0035] Where x p,g The symbol set consists of the pilot symbol set and the guard band symbol set. Therefore, channel estimation is regarded as a sparse signal recovery problem.

[0036] Research progress in CS indicates that if the recovery matrix A satisfies the restricted isometry property (RIP), then using y pThe sparse matrix h is reconstructed using the recovery matrix A. However, due to the complexity of the RIP criterion, its practical application for pilot optimization is limited. Therefore, the less complex Minimum Cross-Correlation Criterion (MIP) is used as the standard for the recovery matrix. MIP is defined as the maximum absolute value of the normalized inner product between any two columns of A. The MIP condition is stronger than RIP because MIP implies RIP, but the converse is not true. Furthermore, MIP is more intuitive and practical than RIP. Therefore, MIP is considered the design criterion for the recovery matrix A, thereby solving the pilot design problem. The cross-correlation value of the matrix is ​​defined as the maximum absolute correlation value between two different columns, expressed as:

[0037]

[0038] Where α i Let μ represent the i-th column of the restoration matrix A, and max(·) means taking the maximum value, that is, the research objective can be transformed into designing the restoration matrix A to have the minimum μ.

[0039] In CS-based channel estimation, the pilot symbol set determines the recovery matrix. Therefore, the pilot symbol set is determined based on the design of the recovery matrix, and the optimal pilot symbol set is found to minimize the μ value of the recovery matrix.

[0040] Beneficial effects:

[0041] 1. The research on CS in this invention has proven that the smaller the cross-correlation value of the recovery matrix, the higher the reconstruction quality of the sparse signal. Minimizing the cross-correlation value is used as the criterion for selecting the best pilot. In channel estimation based on compressed sensing, the recovery matrix is ​​determined by the value of the pilot symbol.

[0042] 2. This invention can find a smaller cross-correlation value while avoiding getting trapped in local optima, and use better pilots for channel estimation to obtain better estimation performance, that is, the channel estimation has a lower mean square error (MSE), and obtains a recovery matrix with the smallest possible cross-correlation value. Attached Figure Description

[0043] Figure 1 This is a diagram showing the placement pattern of the pilot symbol set in the OTFS system of this invention.

[0044] Figure 2 This is a comparison of the cross-correlation value decrease curves corresponding to different pilot optimization algorithms used in this invention.

[0045] Figure 3 This is a comparison chart of the MSE of different pilot optimization algorithms under the 7×12 pilot dimension in the OTFS system of this invention.

[0046] Figure 4This is a comparison chart of the MSE of different pilot optimization algorithms under the 7×13 pilot dimension in the OTFS system of this invention. Detailed Implementation

[0047] The invention will now be described in further detail with reference to the accompanying drawings.

[0048] This invention proposes a pilot optimization method for OTFS systems based on a combination of genetic algorithms and random search algorithms. It mainly addresses two key technical issues: first, determining pilot optimization criteria for compressed sensing-based OTFS channel estimation; and second, proposing a new algorithm combining genetic and random search algorithms to solve for an optimized pilot symbol set, which is then applied to the channel to complete channel estimation. The specific implementation methods for these two parts are described below, and simulations demonstrate that this pilot symbol set design method can effectively improve the performance of OTFS sparse channel estimation.

[0049] (I) Determination of Pilot Optimization Criteria

[0050] Consider an OTFS system where the transmitted signal belongs to the time-delay Doppler domain, denoted as x. d [k,l], k∈[0,N-1], l∈[0,M-1], where N represents the Doppler dimension and M represents the time delay dimension. In the traditional OTFS signal structure, to ensure the accuracy of channel estimation, a large number of guard symbols are placed around the pilot symbols to avoid interference from data symbols, thus leading to degradation of spectral effectiveness. To solve this problem, research shows that the placement pattern of the pilot symbol set during channel estimation in the OTFS system can be further optimized, such as... Figure 2 As shown, there is no guard band to the right of the pilot and data symbols. This is because the data symbols on the right do not interfere with the pilot symbols, thus improving data utilization efficiency. Therefore, we focus on the optimized design of pilot symbols in this mode.

[0051] according to Figure 2 It can be seen that the transmitted signal x[k,l] can be represented as

[0052]

[0053] Where, k p ,l p k represents the center position of the pilot symbol. m and l m The pilot symbols represent the maximum Doppler tap and maximum delay tap of the channel, with a dimension of L. p =(2N) p +1)×M p .

[0054] During channel estimation, the pilot symbol x p When inserted together with the data symbols in the DD field, the received pilot signal in the DD field at the receiver can be expressed as:

[0055]

[0056] in, H represents phase compensation. k',l' It is the channel matrix in the DD domain.

[0057] To correspond with the compressed sensing signal reconstruction model, we simplify Equation 2 into vector form, which rearranges the two-dimensional data y[k,l] into a vector. And the ((k+N)th p M p +ll p The elements of ) are equal to y[k,l], and we also set the channel matrix H in the DD domain. k',l' Arranged into column vectors Where L = (l m +1)(2k m +1), and the (l'(2k)th m +1)+k'+k m The element of ) is equal to H k',l' ;

[0058] Therefore, equation 2 can be expressed in vector form as:

[0059]

[0060] in, It represents the Hadamah accumulation. It is the additional phase matrix, where the ((k+N)th phase matrix is... p M p +ll p ,l'(2k m +1)+k'+k m The elements of ) represent α k',l-l' , It is derived from x[k,l], and its ((k+N)th p M p +ll p ,l'(2k m +1)+k'+k m The elements of ) represent x[k-k',l-l'], and will Defined as a recovery matrix, it can be written as:

[0061] y p =Ah+w Formula 4

[0062] Here, h contains only P non-zero elements, meaning h is a sparse vector. In the recovery matrix A, considering the placement pattern of the proposed pilot symbol set, X p From the pilot symbol x in formula (1) p It consists of the pilot symbol set and the guard band symbol set, and it has a certain relationship with the guard band symbol set. The specific relationship is expressed as follows:

[0063]

[0064] Where, x p,g Representative pilot symbol set and guard band symbol basis Figure 1 The channel consists of a set of symbols, therefore, channel estimation can be viewed as a sparse signal recovery problem.

[0065] By observing Equations 3 and 4, the OTFS system transmission model is very similar to the problem described by compressed sensing. Therefore, the channel estimation problem can be transformed into a compressed sensing problem to be solved. Since the pilot design determines the recovery matrix, the pilot optimization problem can be solved according to the design principles of the recovery matrix in compressed sensing.

[0066] Research progress in CS indicates that if the recovery matrix A satisfies the restricted isometry property (RIP), then y can be used. p The sparse matrix h is reconstructed using the recovery matrix A. However, due to the complexity of the RIP criterion, its practical application for pilot optimization is limited. Therefore, the less complex Minimum Cross-Correlation Criterion (MIP) is used as the criterion for the recovery matrix. MIP is defined as the maximum absolute value of the normalized inner product between any two columns of A. The MIP condition is stronger than RIP because MIP implies RIP, but the converse is not true. Furthermore, MIP is more intuitive and practical than RIP. Therefore, in this invention, we consider MIP as the design criterion for the recovery matrix A, thereby solving the pilot design problem. The cross-correlation value of the matrix is ​​defined as the maximum absolute correlation value between two different columns, expressed as:

[0067]

[0068] Where, α i Let represent the i-th column of the recovery matrix A, and max(λ) represent taking the maximum value. That is, our research objective can be transformed into designing the recovery matrix A to have the minimum μ.

[0069] In CS-based channel estimation, as shown in Equation 5, the pilot symbol set determines the recovery matrix. Therefore, the pilot symbol set can be determined based on the design of the recovery matrix. Our task is to find the optimal pilot symbol set that minimizes the μ value of the recovery matrix.

[0070] (II) Obtaining the optimal pilot symbol set using a new algorithm combining genetic algorithm and random search algorithm.

[0071] Since genetic algorithms can perform global searches and find effective solutions for various types of problems, but are prone to getting trapped in local optima and thus fail to obtain the optimal solution for the global problem, we use a random search algorithm to continue searching for better solutions on some of the better individuals after reinserting offspring in the genetic algorithm.

[0072] When using a genetic algorithm, the population size should be set to an appropriate value. To obtain the optimal solution as much as possible and avoid getting trapped in local optima, population diversity should be maintained. Therefore, we try to choose a relatively large number of generations and select higher crossover and mutation probabilities when performing crossover and mutation operations to increase population diversity. Since the genetic algorithm selects the individual with the largest fitness value, we can define the fitness value as the reciprocal of the restoration matrix μ, so that the higher the fitness value, the smaller the restoration matrix μ value. Furthermore, after re-insertion of offspring, a random search algorithm is used to obtain even larger fitness values ​​for some individuals with large fitness values. After continuous iteration, the individual with the minimum cross-correlation value is finally selected. The specific implementation algorithm includes the following steps:

[0073] Step 1: Initialize the population: In this algorithm, the different sets of pilot symbols represent each individual in the genetic algorithm. The genes in an individual correspond to the values ​​of each pilot symbol in the pilot symbol set. Set the number of individuals to NIND, which is 100, and the length of each individual to INDLENGTH (determined by the number of pilot symbols in the pilot symbol set used by the system). The initial population size is (NIND, INDLENGTH). Also, define the maximum number of generations MAXGEN and the generation gap between offspring and parents as GGAP, with MAXGEN set to 600 and GGAP set to 0.98. Select a gene value of +1 or -1 for each individual, and set the generation counter gen = 0.

[0074] Step 2: Calculate the fitness value of each individual in the population. Select a fitness value FitnV that is equal to the reciprocal of the cross-correlation value μ of the recovery matrix corresponding to the pilot symbol set, and calculate the fitness value FitnV(i) for each individual in the population, i = 1, 2, ..., NIND;

[0075] Step 3: Enter the breeding cycle iteration. First, the offspring selection operation is performed. Offspring are selected based on fitness values ​​and implemented by roulette wheel. Individuals with high fitness values ​​are selected to generate the offspring population SelCh. The probability of an offspring being selected is GGAP. Therefore, the dimension of the offspring population SelCh is (NIND*GGAP,INDLENGTH).

[0076] Step 4: Perform crossover and recombination operations on the offspring, and select a crossover probability P for each individual in the offspring population. r Perform discrete recombination, P r The value is 0.8, meaning that a multi-point intersection method is selected at the intersection point with probability P. r Select multiple individuals from the population, group them in pairs in sequence, and exchange certain positions of the genes of the two individuals (the positions are randomly generated) to produce two new individuals;

[0077] Step 5: Perform mutation operation on the offspring and select an appropriate mutation probability P. m And set the mutation limit FieldDR, P m The value is 0.6. Since the gene value range is +1 or -1 during the population initialization step, the value of FieldDR is also +1 or -1, i.e., with probability P. m Multiple genes are randomly selected from individuals, and the values ​​of these genes are changed within the range of FieldDR, thereby increasing the diversity of the population.

[0078] Step 6: Perform the re-insertion operation on offspring. After steps 3 to 5 above, the new offspring population size is NIND*GGAP. Recalculate its fitness value FitnVSel(i), where i represents the i-th offspring individual. Use the re-insertion strategy to replace the NIND*GGAP individuals with the lowest fitness values ​​in the original population with the new offspring population to obtain a new population.

[0079] Step 7: Select excellent individuals, sort the fitness values ​​of the new population obtained after re-insertion in descending order, find the top 10% of individuals with the highest fitness values ​​and save them to obtain the individual set Chrom_ten, and record the position of these individuals in the original population as Index.

[0080] Step 8: For each individual in the Chrom_ten set selected above, use the following random search algorithm: starting from the first gene of the individual, take the negative of each gene and recalculate the fitness value of the current individual. Determine whether the current fitness value is greater than the fitness value before the change. If it is greater, replace the original individual with the individual with the modified gene. If it is less than or equal to, keep the original individual unchanged. Then perform the same operation on the next gene. After all gene positions of the current individual have been operated on, jump to the next individual and repeat the above operation until every individual in the Chrom_ten set has been traversed.

[0081] Step 9: Re-insert the new individuals obtained after processing with the random search algorithm into the population according to the Index position in Step 7 above, thereby obtaining a new population, and use this new population as the initial population for the next generation of reproduction.

[0082] Step 10: Increment the generation counter gen by one, and record the reciprocal of the maximum objective function value of the current generation, which is the minimum cross-correlation value of the recovery matrix corresponding to the pilot symbol set. Determine whether gen is greater than the maximum number of generations MAXGEN. If it is, proceed to the next step; otherwise, jump to step 3 above.

[0083] Step 11: Output the results. Select the individual with the largest fitness value in the last generation of the population. This is the final optimized pilot symbol set pilotFinal. At this point, it is a column vector. After dimensional transformation, it is converted into a two-dimensional pilot symbol set, which is the final pilot.

[0084] The following simulation will demonstrate that, compared to the pilot symbol set obtained by the simple GA algorithm, the pilot symbol set obtained by using this algorithm, which is obtained by randomly selecting pilot symbols, can achieve a smaller mean square error in OTFS sparse channel estimation.

[0085] (III) Simulation Experiments and Results of the Invention

[0086] Below, we will illustrate the performance of the proposed pilot optimization method through simulation. Pilot symbols generated by three methods proposed in this invention—the algorithm combining genetic algorithm and random search algorithm, the simple GA algorithm, and the random generation of pilot symbol sets—are applied to channel estimation, and their channel estimation performance is compared. Specific simulation parameters are set as follows: the carrier frequency is set to 3 GHz, and the subcarrier spacing is 7.5 kHz. The size of an OTFS frame in the DD domain is set to N = 32 and M = 128, respectively. All data symbols are modulated using quadrature phase shift keying (QPS). The maximum delay tap and maximum Doppler tap of the channel model are set to 1. m =10 and k m =5, which corresponds to a high-speed scenario of 120km / h. Furthermore, to obtain accurate channel estimation results, the pilot signal magnitude needs to cover the maximum time delay and Doppler spread, i.e., 2N. p +1≥k m M p ≥l m Therefore, we set 2N respectively. p +1 = 7, M p =13 and M p=12. To verify the effectiveness of the optimized pilot for sparse channel estimation, the classic OMP algorithm was used as the channel estimation algorithm. The performance evaluation was carried out in the following ways: 1. The minimum cross-correlation value that the two algorithms can obtain through optimization for the same initial pilot symbol set; 2. The normalized signal estimation MSE.

[0087] Figure 2 The curves showing the decrease in μ during the iteration process when using the simple GA algorithm and the GA+SSS algorithm proposed in this invention with a specific number of random population individuals are presented. It can be seen from the figure that the μ value of both algorithms shows a decreasing trend, but the μ value of the GA+SSS algorithm proposed in this invention decreases faster at the first iteration and can obtain a smaller μ value after all iterations.

[0088] Figure 3 Comparison of pilot dimensions of 7x12 (2N) p +1 = 7, M p =12) When the pilot symbol sets optimized by different algorithms are applied to the system, the mean square error (MSE) curves of channel estimation are shown. The CS reconstruction algorithm we use here is the OMP algorithm. As can be seen from the figure, the pilot symbol set optimized by our proposed scheme is significantly better than the randomly generated pilot symbol set and the pilot symbol set optimized by simply using the GA algorithm. Moreover, the difference in channel estimation performance is more obvious at high signal-to-noise ratio.

[0089] Figure 4 We compared the mean square error (MSE) curves of channel estimation when pilot symbol sets optimized by different algorithms were applied to the system with a pilot dimension of 7x13. The CS reconstruction algorithm used was still the OMP algorithm. As can be seen from the figure, the pilot symbol set optimized by our proposed scheme is significantly better than the randomly generated pilot symbol set and the pilot symbol set optimized by simply using the GA algorithm. Moreover, the performance difference is more obvious at high signal-to-noise ratio.

[0090] The specific implementation schemes described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific implementation schemes of the present invention and are not intended to limit the scope of the present invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the present invention should fall within the scope of protection of the present invention.

Claims

1. A pilot optimization method for OTFS systems based on a combination of genetic algorithm and random search algorithm, characterized in that, The method includes the following steps: Step 1: Initialize the population: In this algorithm, the different sets of pilot symbols are each individual in the genetic algorithm. The genes in an individual correspond to the values ​​of each pilot symbol in the set of pilot symbols. Set the number of individuals to NIND and the length of each individual to INDLENGTH, which is determined by the number of pilot symbols in the set of pilot symbols used by the system. At this time, the initial population size is (NIND, INDLENGTH). At the same time, the maximum number of generations MAXGEN and the generation gap between offspring and parents are defined as GGAP. Select the gene value of each individual as +1 or -1, and set the generation counter gen=0. Step 2: Calculate the fitness value of each individual in the population. Select the fitness value FitnV as the reciprocal of the cross-correlation value μ of the recovery matrix corresponding to the pilot symbol set, and calculate the fitness value FitnV(i) for each individual in the population, i=1,2,…,NIND; Step 3: Enter the breeding cycle iteration. First, the offspring selection operation is performed. Offspring are selected based on fitness values ​​and implemented by roulette wheel. Individuals with high fitness values ​​are selected to generate the offspring population SelCh. The probability of an offspring being selected is GGAP. The dimension of the offspring population Se1Ch is (NIND*GGAP, NDLENGTH). Step 4: Perform crossover and recombination operations on the offspring, and select a crossover probability P for each individual in the offspring population. r Discrete recombination is performed, that is, selecting multiple intersection points at the intersection points with probability P. r Select multiple individuals from the population, group them in pairs, and swap certain positions of the genes of the two individuals. The positions are randomly generated to produce two new individuals. Step 5: Perform mutation operation on the offspring and select an appropriate mutation probability P. m A mutation constraint, FieldDR, is set, and the value of FieldDR is either +1 or -1, i.e., with probability P. m Multiple genes are randomly selected from individuals, and the values ​​of these genes are changed within the range of FieldDR to increase population diversity. Step 6: Perform the re-insertion operation of offspring. After steps 3 to 5 above, the new offspring population size is NIND*GGAP. Recalculate its fitness value FitnVSel(i), where i represents the i-th offspring individual. Use the re-insertion strategy to replace the NIND*GGAP individuals with the lowest fitness value in the original population with the new offspring population to obtain a new population. Step 7: Select excellent individuals, sort the fitness values ​​of the new population obtained after re-insertion in descending order, find the top 10% of individuals with the highest fitness values ​​and save them to obtain the individual set Chrom_ten, and record the position of these individuals in the original population as Index. Step 8: For each individual in the selected set Chrom_ten, use a random search algorithm. Starting from the first gene of the individual, take the negative of each gene and recalculate the fitness value of the current individual. Determine whether the current fitness value is greater than the fitness value before the change. If it is greater, replace the original individual with the individual with the modified gene. If it is less than or equal to, keep the original individual unchanged. Then perform the same operation on the next gene. After all gene positions of the current individual have been operated on, jump to the next individual and repeat the above operation until every individual in the set Chrom_ten has been traversed. Step 9: Re-insert the new individuals obtained after processing with the random search algorithm into the population according to the Index position in Step 7 above to obtain a new population, and use this new population as the initial population for the next generation of reproduction. Step 10: Increment the generation counter gen by one, and record the reciprocal of the maximum objective function value of the current generation, which is the minimum cross-correlation value of the recovery matrix corresponding to the pilot symbol set. Determine whether gen is greater than the maximum number of generations MAXGEN. If it is, proceed to the next step; otherwise, jump to step 3 above. Step 11: Output the results. Select the individual with the largest fitness value in the last generation of the population. This is the final optimized pilot symbol set pilotFinal. At this point, it is a column vector. Then, transform it into a two-dimensional pilot symbol set through dimensional transformation, which is the final pilot. The method further includes determining pilot optimization criteria for compressed sensing-based OTFS channel estimation, considering an OTFS system where the transmitted signal belongs to the time-delay Doppler domain, represented as... x d [ k,l ], k ∈[0, N -1], l ∈[0, M -1], where N Indicates the Doppler dimension. M In terms of time delay dimension, the placement pattern of the pilot symbol set is further optimized when performing channel estimation in the OTFS system, and there is no guard band on the right side of the pilot and data symbols; Send signal x [ k,l ] is represented as: Formula 1 in k p , l p This represents the center position of the pilot symbol. k m and l m Representing the channel's maximum Doppler tap and maximum delay tap, the pilot symbol dimension is... L p =(2 N p +1)× M p ; Pilot symbols during channel estimation x p When inserted together with the data symbols in the DD field, the received pilot signal in the DD field at the receiver is represented as follows: Formula 2 in Represents phase compensation. H k’,l’ It is the channel matrix in the DD domain; To correspond with the compressed sensing signal reconstruction model, Equation 2 is simplified into vector form, which represents the two-dimensional data. y [ k, l Rearrange into vectors And the (( k + N p ) M p + l - l p The elements of ) are equal to y [ k,1 ], and simultaneously the channel matrix in the DD domain H k’,l’ Arranged into column vectors, ,in L =( l m +1)(2 k m +1), and the ( 1’ (2 k m +1)+ k' + k m The element of ) is equal to H k’,l’ ; Therefore, Equation 2 can be expressed in vector form as follows: Formula 3 Where ∘ represents the Hadamard product, It is the additional phase matrix, where the (( k + N p ) M p + l - l p , l’ (2 k m +1)+ k’ + k m The element represented by ) is , It is by x [ k,l ] It is obtained, its first (( k + N p ) M p + l - l p , l’ (2 k m +1)+ k’ + k m The elements represent x [ k-k',ll' ],Will Defined as a recovery matrix, it is written as: Formula 4 Here, h contains only P non-zero elements, meaning h is a sparse vector. In the recovery matrix A, considering the proposed placement pattern of the pilot symbol set, X... p From the pilot symbol in Equation 1 x p It consists of the pilot symbol set and the guard band symbol set, and it has a certain relationship with the guard band symbol set. The specific relationship is expressed as follows: Formula 5 in x p,g The symbol set consists of the pilot symbol set and the guard band symbol set. Therefore, channel estimation is regarded as a sparse signal recovery problem. The minimum cross-correlation criterion, which has lower complexity, is used as the standard for the recovery matrix. Here, MIP is defined as the maximum absolute value of the normalized inner product between any two columns of A, and the cross-correlation value of the matrix is ​​defined as the maximum absolute correlation value between two different columns, expressed as: Formula 6 Where α i Let μ represent the i-th column of the restoration matrix A, and max(·) means taking the maximum value, that is, the research objective can be transformed into designing the restoration matrix A to have the minimum μ. In CS-based channel estimation, the pilot symbol set determines the recovery matrix. Therefore, the pilot symbol set is determined based on the design of the recovery matrix, and the optimal pilot symbol set is found to minimize the μ value of the recovery matrix.

2. The pilot optimization method based on a combination of genetic algorithm and random search algorithm for OTFS system according to claim 1, characterized in that, Step 1 includes: initializing the population size NIND to 100 and the maximum generation number MAXGEN to 600.

3. The pilot optimization method based on a combination of genetic algorithm and random search algorithm for OTFS system according to claim 1, characterized in that, In step 1, the generation gap (GGAP) between offspring and parents is set to 0.

98.

4. The pilot optimization method based on a combination of genetic algorithm and random search algorithm for OTFS system according to claim 1, characterized in that, In step 4, the crossover probability P r The value is 0.

8.

5. The pilot optimization method based on a combination of genetic algorithm and random search algorithm for OTFS system according to claim 1, characterized in that, In step 5, the mutation probability P m The value is 0.6.

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