A pilot sequence design method for ultra-massive MIMO-OTFS

Abstract

The application belongs to the field of wireless communication, and particularly relates to a pilot sequence design method of super large scale MIMO-OTFS, aiming at a near-field high mobility environment, a communication system based on spherical waves is established, an optimization function is established in the communication system with a minimum average mutual interference between pilots as a target, and a genetic algorithm is used to obtain an optimal pilot sequence. The system model based on spherical waves has a significant performance advantage compared with a traditional plane wave model in the near-field high mobility environment, and the pilot sequence optimization design based on the genetic algorithm has a superior channel estimation performance compared with other pilot designs due to its strong adaptive search capability.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication, and specifically relates to a pilot sequence design method for ultra-large-scale MIMO-OTFS. Background Technology

[0002] XL-MIMO technology, as a key enabling technology for future 6G, can achieve higher channel capacity and signal processing performance by utilizing the spatial degrees of freedom and channel state information among a large number of antennas. However, the use of extremely large aperture arrays leads to non-negligible near-field spherical wave characteristics, rendering traditional channel and system models based on plane wave assumptions inaccurate, and causing a certain degree of performance degradation in existing pilot channel estimation schemes. Furthermore, with the increasing prevalence of high-mobility scenarios, signal transmission is affected by multipath fading, Doppler fading, and noise interference, resulting in dual-selective channel characteristics. In this situation, the signal processing performance of traditional modulation techniques deteriorates sharply, especially in very large-scale antenna arrays, which is unacceptable for real-time communication systems with high reliability requirements. Orthogonal Time Frequency Space (OTFS) is a promising modulation technique to address these challenges. In OTFS, all information symbols are mapped to a two-dimensional delay-Doppler (DD) domain, and the wireless channel is also represented in the DD domain to combat the dynamic changes of time-varying multipath channels. Combining XL-MIMO and OTFS can not only enhance channel capacity and improve signal transmission efficiency through spatial multiplexing, but also introduce spherical waveguide vectors to accurately characterize near-field high-mobility wireless channels in the DD domain, thereby increasing the reliability of signal transmission.

[0003] Currently, the system frameworks and pilot design schemes proposed by scholars both domestically and internationally for near-field high mobility communication scenarios have certain limitations. Existing low-pilot-overhead, high-accuracy channel estimation algorithms heavily rely on the classical far-field plane assumption. However, the non-negligible near-field spherical wavefront characteristics in XL-MIMO render existing system model construction inaccurate and severely damage channel estimation schemes. Most studies make relatively simple scenario assumptions, focusing on channel modeling while neglecting integration with modulation techniques and pilot design, and lacking closed-form derivations of end-to-end input-output relationships that consider near-field characteristics. Furthermore, in XL-MIMO systems, reasonable pilot pattern and pilot sequence design can effectively utilize spectrum and time resources, reduce channel bandwidth and transmission time occupied by pilots, thereby improving the system's spectral efficiency and energy efficiency, and saving system resource overhead. However, existing pilot designs for OTFS focus on the design of the pilot pattern and pilot sequence itself, neglecting the possibility of optimizing the pilot sequence itself. Summary of the Invention

[0004] To improve spectrum utilization efficiency and achieve accurate channel estimation in near-field high mobility scenarios, this invention proposes a pilot sequence design method for ultra-large-scale MIMO-OTFS, which includes: establishing a spherical wave-based communication system for near-field high mobility environments; establishing an optimization function in the communication system with the objective of minimizing the average non-interference metric between pilots; and solving for the optimal pilot sequence.

[0005] Furthermore, in a spherical wave-based communication system, a coded bit sequence is mapped to the time-delay-Doppler domain, then modulated and transformed to the time domain by OTFS, and transmitted through a uniform linear antenna array at the base station; at the receiving end, after receiving the signal through a single antenna, the received signal is demodulated by OTFS and converted to the time-delay-Doppler domain.

[0006] Furthermore, the optimization function established with the objective of minimizing the average non-interference metric between pilots is expressed as:

[0007]

[0008] Constraint: max(abs(X) DDS ))≤D

[0009] Among them, X DDS Represents the pilot matrix; μ avg This represents the average non-interference measure between pilots; abs(·) is the function for finding the absolute value; max(·) is the function for finding the maximum value; D represents the maximum power threshold.

[0010] Furthermore, the average non-interference measure μ between pilots avg Represented as:

[0011]

[0012] Where Q represents the number of coherent operations; L represents the total number of possible time-delay-Doppler offset pairs, expressed as L = (l m +1)(2k m +1), l m k is the maximum value of the index of Doppler frequency offset. m N represents the maximum value of the delay offset index. t α represents the number of antennas at the base station. i To measure the i-th column vector in the matrix, α j Let be the vector in the j-th column of the measurement matrix; <,> means to calculate the dot product of two vectors; |·| means modulo operation; ||·||2 means 2-norm operation.

[0013] Furthermore, a genetic algorithm is used to solve the optimization function to obtain the optimal pilot sequence, specifically including the following steps:

[0014] 100. Select M items that meet the criteria max(abs(x)). DDS Pilot sequence x ≤ D DDS As individuals in the initial population, the initial crossover and mutation probabilities of the genetic algorithm are changed, and the expected value of the fitness is set;

[0015] 101. Calculate whether the fitness of any individual has reached the expected value. If so, end the process and output the individual that meets the expected value as the optimal pilot sequence.

[0016] 102. Calculate the probability of an individual being selected based on fitness, and select from M individuals sequentially using a gambler's selection method, arranging them in the order of selection to obtain the population sequence X'={x1',…x M '};

[0017] 103. Using crossover probability p c From the population sequence X'={x1',…x M Select M·p in '} c Each pilot sequence individual performs a crossover operation;

[0018] 104. Perform fitness assessment on individuals, calculate whether any individual's fitness has reached the expected value. If so, end the process and output the individual that meets the expected value as the optimal pilot sequence; otherwise, perform mutation operation.

[0019] 105. Choose any pilot sequence and, based on the mutation probability p m Specify a mutation point, perform the mutation operation, and return to step 101.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] 1. Based on the near-field spherical wave characteristics brought by the ultra-large scale array, this invention constructs an XL-MIMO OTFS system suitable for near-field high mobility scenarios, and then combines the embedded pilot frame structure design to derive and analyze the input-output relationship;

[0022] 2. To improve the accuracy of near-field channel estimation, a pilot sequence optimization design based on genetic algorithm is proposed.

[0023] In summary, the system model based on spherical waves constructed in this invention has significant performance advantages over traditional plane wave models in near-field high mobility environments. The proposed pilot sequence optimization design based on genetic algorithm achieves superior channel estimation performance compared to other pilot designs due to its powerful adaptive search capability. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the XL-MIMO OTFS system framework of the present invention;

[0025] Figure 2 This is a schematic diagram of the pilot, protection, and data symbol design for the transmit antenna of the XL-MIMO OTFS system of the present invention;

[0026] Figure 3 This is the pilot design flow for the XL-MIMO OTFS system of the present invention;

[0027] Figure 4 This is a schematic diagram comparing the channel estimation performance of far-field and near-field models in a near-field environment according to the present invention.

[0028] Figure 5 This is a comparative diagram showing how the correlation of the pilot matrix changes with the number of iterations in this invention;

[0029] Figure 6 A schematic diagram comparing the NMSE performance of different pilot symbols in this invention. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] This invention proposes a pilot sequence design method for ultra-large-scale MIMO-OTFS, which includes: establishing a spherical wave-based communication system for near-field high mobility environments; establishing an optimization function in the communication system with the objective of minimizing the average non-interference metric between pilots; and solving for the optimal pilot sequence.

[0032] like Figure 1 As shown, consider constructing an XL-MIMO OTFS system that takes into account the near-field spherical wavefront characteristics. Assume that N is equipped at the base station (BS). t U antennas form a uniform linear array (ULA) to provide services to U single-antenna user terminals. In the near-field environment, the point target model can be described by two main parameters: distance and angle. Consider that both the base station array antennas and the users are located in a two-dimensional plane, with the antenna spacing being half a wavelength. λ c Let be the wavelength. Assume the nth... t The coordinates of the antennas are in This represents the distance from the array center (i.e., the reference antenna) to the u-th user or the last hop scatterer via the l-th path. Indicates the nth t The distance from the l-th antenna to the u-th user or the last hop scatterer. This represents the angle between the array center and the last hop scatterer or the user. For ease of representation, this embodiment defines... Since the downlink channel estimation is the same for U users, this embodiment only needs to focus on one user. The user's index is omitted without loss of generality. Based on geometric relationships, it can be deduced that:

[0033]

[0034] Where, θ l ∈[-1,1] represents the spatial angle of the l-th path. Therefore, the spherical waveguide vector in the near-field environment can be characterized as:

[0035]

[0036] in 1×N t A time-frequency dual-selective channel of dimension 1 can be modeled as:

[0037]

[0038] in,(·) H This represents the conjugate transpose operation, where P represents the number of scattering paths, and h... i Let v represent the complex gain of the i-th path. i τ represents the Doppler frequency shift of the i-th path. i Let b(θ) represent the time delay of the i-th path. i ,r i ) H The spherical waveguide vector at the transmitting end, r i This represents the distance to the user or the last hop scatterer via the i-th path.

[0039] Following the standard derivation of the OTFS input-output relationship, a sequence of encoded bits is mapped into the Delay-Doppler (DD) domain to obtain {x}. d[k,l],k=[0,N-1],l=[0,M-1]}, where k represents the Doppler frequency shift index, l represents the time delay index, N is the number of indices for the Doppler frequency shift index, and M is the number of indices for the time delay index. This is transformed to the time-frequency (TF) domain using an inverse symplectic fast Fourier transform (ISFFT) to obtain the time-frequency domain signal.

[0040]

[0041] Where n∈[0,N-1],m∈[0,M-1].

[0042] Then, the continuous time-domain waveform s(t) of the transmitter is obtained through the Heisenberg transform, that is:

[0043]

[0044] Where T represents the symbol duration, Δf represents the subcarrier spacing, and g tx (·) represents the shaped pulse transmitted. After propagation through the channel defined by equation (3), the noise-removed continuous-time-domain received signal can be expressed as:

[0045]

[0046] Define the cross-fuzzy function as follows It measures the accuracy of radar's perception of speed and time delay, v * (·) denotes finding the conjugate of v(·). At the receiving end, the received signal r(t) passes through a function C that calculates the cross-ambiguity. grx,r Matched filter for (τ,v):

[0047]

[0048] After sampling t = nT, f = mΔf, and applying the substitution method and cross-fuzzy function to rearrange, the time-frequency domain input-output relationship is obtained as follows:

[0049]

[0050] Where H n,m [n',m'] represents the equivalent TF-domain channel, i.e.:

[0051]

[0052] The received signal in the DD domain can be obtained using the Symptotic Fast Fourier Transform (SFFT):

[0053]

[0054] in Defined by the following formula:

[0055]

[0056] definition And taking into account the presence of noise, To represent matrix multiplication, the input-output relationship in the DD field can be expressed in the following matrix-vector form:

[0057]

[0058] in, Represents a two-dimensional equivalent DD domain channel. Represents all N t Transmit pilot signals in the DD domain at the root transmitting antenna. This represents additive white Gaussian noise.

[0059] Considering the use of rectangular waves as pulse shaping filters at both the transmitter and receiver, the above equation can be further expressed as follows:

[0060]

[0061] Where w[k,l] represents noise, [·] N To represent modulo N operation, [] M Represents the modulo-M operation, α i (k,l) represents the additive phase shift caused by the imperfect biorthogonality of the rectangular waveform, which can be expressed as:

[0062]

[0063] Where, k i Let l represent the integer Doppler offset corresponding to the i-th path in the DD domain. i This represents the delay offset index corresponding to the i-th path in the DD domain.

[0064] In an XL-MIMO OTFS system, each transmit antenna arranges pilot, guard, and data symbols on a time-delay-Doppler grid for transmission. The symbols from the transmit antennas must be carefully designed to facilitate channel estimation and data detection at the receive antennas; such an arrangement is described below. Considering the scenario assumptions and system framework described above, this embodiment is the nth...t root transmitting antenna n t =1,...,N t The following symbol arrangement was proposed.

[0065]

[0066] Figure 2 Given the pilot pattern in the DD domain for any antenna, this invention considers that the pilot structure in the DD domain is the same for each transmitting antenna. Different antennas can place different pilot and data symbols in the same structure, where k p Indicates the initial position of the pilot symbol along the Doppler dimension, l p This indicates the initial position of the pilot symbol along the time delay dimension, with a length of l. m and k m The guard interval is placed at the beginning and end of the pilot signal to eliminate interference between the pilot and data symbols.

[0067] The time-delay-Doppler-antenna domain channel has finite support [0,τ] in both the time delay and Doppler dimensions. max ] and [-v max ,v max The guard interval must be set to be greater than or equal to the maximum time delay offset and the maximum Doppler frequency offset, i.e.:

[0068]

[0069] Therefore, the indices k' and l' of the time delay offset and Doppler frequency offset in the channel description are restricted to [0, l], respectively. m ] and [-k m ,k m [Within]. Considering the above frame structure design, this embodiment further represents the input-output relationship of the XL-MIMO OTFS system in the DD domain as follows:

[0070]

[0071] Where, k∈[k p ,k p +N p -1],l∈[l p ,l p +M p -1] indicates The time-delay-Doppler-antenna domain channel, additive phase shift is represented as:

[0072]

[0073] The input-output relationship of the XL-MIMO OTFS system in the DD domain is further organized into a matrix-vector representation:

[0074] y DDS =(X DDS ⊙Φ)h DDS +w=Ah DDS +w

[0075] in, The pilot matrix is ​​L = (l m +1)(2k m +1); This is the channel vector; For receiving signals, the channel estimation problem of the XL-MIMO OTFS system is transformed into a sparse signal reconstruction problem.

[0076] In the CS algorithm, the main factors affecting the accuracy of channel estimation are h DDS The sparsity and whether the measurement matrix A satisfies the Restricted Isometry Property (RIP) condition are investigated. However, directly proving the RIP of a measurement matrix is ​​quite complex, being a non-deterministic polynomial hard (NP-hard) problem with polynomial complexity. Therefore, the Mutual Incoherence Property (MIP) principle, which has relatively relaxed conditions and lower computational cost, is used to optimize the measurement matrix. The maximum column correlation is expressed as:

[0077]

[0078] Where, α i and α j For any two columns in the measurement matrix, the higher the value of μ, the better the recovery performance of the CS algorithm. However, the above only considers the maximum absolute value of the normalized inner product between each column, and the overall correlation of the entire measurement matrix cannot be measured. Therefore, the average MIP criterion can be used:

[0079]

[0080] Where Q represents the number of coherent operations. Based on the aforementioned formula, this invention constructs the following pilot sequence optimization problem:

[0081] (P1)

[0082] stmax(abs(x DDS ))≤D

[0083] Where D represents the maximum power threshold.

[0084] Since problem (P1) is a non-convex problem, traditional mathematical optimization methods are prone to getting trapped in local optima, making it difficult to find the global optimum. Therefore, this invention considers using a stochastic, highly parallel, and adaptive search method that draws on the mechanisms of natural selection and natural inheritance in the biological world, namely, a genetic algorithm.

[0085] First, randomly generate a set of X values ​​that satisfy the constraints in the optimization problem. DDS ,Right now As the initial population, each individual Let X represent an initial solution to problem (P1), and M represent the population size. Calculate the total population size X. DDS Fitness of each individual To conduct the evaluation, since the probability of an individual being selected for reproduction is proportional to its fitness, we can assume p i It is the probability that the i-th individual is selected, that is:

[0086]

[0087] Using the betting odds selection method, select M times to form X'={x1',…x M '}; then with crossover probability p c Randomly select M·p from X' c Each pilot matrix is ​​an individual entity, and every two adjacent pilot matrices x i '、x j Crossover and recombination are performed on ξ, ξ' ∈ M, and each crossover randomly generates ξ, ξ' ∈ U(1, LN). t The pilot sequences between two cut points are swapped using sort(ξ,ξ') to generate the next generation of superior individuals. The fitness of the new population is evaluated; if the conditions for elimination are not met, a mutation operation is performed, randomly selecting a pilot matrix and applying it with probability p. m Specify a mutation point and replace the pilot sequence at that point with a Gaussian sequence or Bernoulli sequence that satisfies the constraints; repeat this process iteratively until the maximum number of iterations is reached or the fitness of the entire population converges. Finally, select the minimum fitness f(x) among all the population. i DDS The corresponding pilot matrix is ​​used as the optimized output. The overall computational complexity of this invention mainly depends on the individual evaluation complexity, population operation complexity, and number of iterations, i.e., O(TM(LN)). t ) 2 Since this solution can run offline, its complexity is negligible in a real system.

[0088] like Figure 3This invention constructs a pilot sequence optimization problem in the time-delay Doppler domain based on the average mutual uncorrelation criterion, and solves it using a genetic algorithm. The algorithm mainly includes steps such as fitness evaluation, selection, crossover, and mutation. Utilizing its random, highly parallel, and adaptive search characteristics, it can find the global optimum more accurately and efficiently, obtaining the optimized pilot sequence, thereby achieving more accurate channel estimation. This invention provides a specific implementation process for solving the optimization problem using a genetic algorithm, specifically including the following steps:

[0089] 100. Select M items that meet the criteria max(abs(x)). DDS Pilot sequence x ≤ D DDS As individuals in the initial population, the initial crossover and mutation probabilities of the genetic algorithm are changed, and the expected value of the fitness is set;

[0090] 101. Calculate whether the fitness of any individual has reached the expected value. If so, end the process and output the individual that meets the expected value as the optimal pilot sequence.

[0091] 102. Calculate the probability of an individual being selected based on fitness, and select from M individuals sequentially using a gambler's selection method, arranging them in the order of selection to obtain the population sequence X'={x1',…x M '};

[0092] 103. Using crossover probability p c From the population sequence X'={x1',…x M Select M·p in '} c Each pilot sequence individual performs a crossover operation;

[0093] 104. Perform fitness assessment on individuals, calculate whether any individual's fitness has reached the expected value. If so, end the process and output the individual that meets the expected value as the optimal pilot sequence; otherwise, perform mutation operation.

[0094] 105. Choose any pilot sequence and, based on the mutation probability p m Specify a mutation point, perform the mutation operation, and return to step 101.

[0095] like Figure 4As shown, this paper compares the channel estimation performance of the traditional far-field model and the near-field model proposed in this invention in a near-field environment. In this embodiment, the number of transmitting antennas is set to 256 and the spacing between antennas is half a wavelength distance of 32.5 mm. The Rayleigh distance can be calculated to be approximately 2457 m. In this embodiment, the subcarrier spacing Δf = 150 kHz is taken, and other parameters remain unchanged. At this time, the distance between the mobile terminal and the array is 2 km, which is less than the Rayleigh distance and belongs to the near-field range. Subsequently, the OMP algorithm is used to estimate the channel of the far-field model based on the traditional plane wave assumption and the near-field model based on the spherical wave assumption. The simulation results show that the near-field XL-MIMO OTFS framework proposed in this invention can more accurately describe the near-field high mobility scenario and achieve better channel estimation performance than the traditional far-field model.

[0096] like Figure 5 The figure shows the curve of the pilot matrix correlation changing with the number of iterations. Since the transmit pilots of each antenna are the same and the correlation of the matrix is ​​mainly affected by the correlation between the columns representing the transmit pilots at different antennas, this embodiment focuses on optimizing this part during the simulation. The average power of the pilot symbols is set to 30 dBW, the population size of the genetic algorithm is 50, the crossover probability is 0.8, the mutation probability is 0.1, and the fitness function throw threshold is 10. -5 The maximum number of iterations is 2.5 × 10. 4 This allows for thorough iterative optimization. Figure 5 It can be seen that the correlation between the columns of the measurement matrix is ​​approximately 2 × 10⁻⁶. 4 After several iterations, the correlation coefficient tends to converge, and the average correlation coefficient is optimized from the original 0.2937 to 0.1815. To more clearly demonstrate the optimization effect, the correlation coefficient is expressed as a sum, which is 1.91 × 10⁻⁶. 4 Optimized to 1.084×10 4 .

[0097] like Figure 6As shown, the NMSE performance of random pilot sequences, Gaussian pilot sequences, Bernoulli sequences, Toeplitz sequences, and the pilot sequence optimized by the genetic algorithm proposed in this invention is illustrated. Bernoulli sequences are simple to generate and can fully utilize spectrum resources; however, the resulting binary sequences have weak autocorrelation, and due to the presence of zero-power pilot symbols, their performance is poor in high-noise environments. Toeplitz sequences have structured autocorrelation and perform well in scenarios with similar channel characteristics; however, due to the complexity of multipath propagation and significant changes in the channel environment in near-field high-mobility scenarios, their non-random structure limits the performance of channel estimation. Gaussian sequences have good robustness to noise due to their randomness and good autocorrelation; however, generating this sequence in practical applications is relatively complex. Simulation results show that the NMSE performance of the pilot sequence optimization scheme based on the genetic algorithm is superior to other comparative algorithms at any SNR, and can reach 10 when the SNR reaches 30dB. -1 This scheme can be iteratively optimized based on randomly generated pilot sequences, adapting to complex channel environments in near-field high-mobility scenarios and achieving good channel estimation performance.

[0098] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A pilot sequence design method for ultra-large-scale MIMO-OTFS, characterized in that, For near-field high mobility environments, the propagation characteristics of spherical waves are introduced into channel modeling and combined with the OTFS modulation and demodulation mechanism to establish a communication system based on spherical waves. In the communication system, an optimization function is established with the goal of minimizing the average non-interference metric between pilots. The optimal pilot sequence is obtained by solving the problem through the random parallel search mechanism of the genetic algorithm. The optimization function established with the objective of minimizing the average non-interference metric between pilots is expressed as: Constraints: in, Represents the pilot matrix; It represents the average non-interference measure between pilot signals; A function for finding the absolute value; The function to find the maximum value; D represents the maximum power threshold; Average non-interference measure between pilots Represented as: Where Q represents the number of coherent operations; L represents the total number of possible time-delay-Doppler offset pairs, denoted as... , l m k is the maximum value of the index of Doppler frequency offset. m N represents the maximum value of the delay offset index. t This refers to the number of antennas at the base station; To measure the vector in the i-th column of the matrix, Let j be the vector in the measurement matrix; This indicates finding the dot product of two vectors; This represents the modulo operation; This indicates the 2-norm operation.

2. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 1, characterized in that, In a spherical wave-based communication system, a coded bit sequence is mapped to the time-delay-Doppler domain, then modulated to the time domain using OTFS, and transmitted through a uniform linear antenna array at the base station. At the receiving end, the signal is received by a single antenna and then demodulated using OTFS to convert the received signal to the time-delay-Doppler domain.

3. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 1 or 2, characterized in that, The optimal pilot sequence is obtained by solving the optimization function using a genetic algorithm, specifically including the following steps:

100. Select M matching items. pilot sequence As individuals in the initial population, the initial crossover and mutation probabilities of the genetic algorithm are changed, and the expected value of the fitness is set; 101. Calculate whether the fitness of any individual has reached the expected value. If so, end the process and output the individual that meets the expected value as the optimal pilot sequence.

102. Calculate the probability of an individual being selected based on fitness, and select from M individuals sequentially using the gambler selection method, arranging them in the order of selection to obtain the population sequence. ; 103. Using crossover probability From population sequence Select Each pilot sequence individual performs a crossover operation; 104. Perform fitness assessment on individuals, calculate whether any individual's fitness has reached the expected value. If so, end the process and output the individual that meets the expected value as the optimal pilot sequence; otherwise, perform mutation operation.

105. Choose any pilot sequence and, based on the mutation probability... Specify a mutation point, perform the mutation operation, and return to step 101.

4. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 3, characterized in that, The probability of an individual being selected is expressed as: in, This represents the probability that individual i is selected; Represents the i-th pilot sequence The fitness value.

5. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 3, characterized in that, The fitness of an individual is a measure of the average non-interference among the pilots in the pilot sequence.

6. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 3, characterized in that, The process of performing a crossover operation on a selected individual includes: randomly selecting two tangent points between the selected individual and its neighboring individuals, and exchanging the pilot symbols at the two tangent points to complete the crossover operation.

7. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 3, characterized in that, The process of performing a crossover operation on the selected individuals includes replacing the pilot symbols at the mutation points with elements from a Gaussian or Bernoulli sequence that satisfy the constraints of the optimization function.

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