Pilot frequency sequence design method of super-large scale MIMO-OTFS

Abstract

The invention belongs to the field of wireless communication, and particularly relates to a pilot frequency sequence design method for a super-large-scale MIMO-OTFS (Multiple Input Multiple Output-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 by taking an average non-interference measurement between minimization pilots as a target, and the pilot frequency sequence is optimized. And solving by adopting a genetic algorithm to obtain an optimal pilot frequency sequence. Compared with a traditional plane wave model, the system model based on the spherical wave has remarkable performance advantages in a near-field high-mobility environment, and the pilot frequency sequence optimization design based on the genetic algorithm obtains more superior channel estimation performance than other pilot frequency designs through the powerful self-adaptive search capability.

Description

Technical Field

[0001] The invention belongs to the field of wireless communications, and in particular relates to a pilot sequence design method for ultra-large-scale MIMO-OTFS. Background Art

[0002] As a key enabling technology for future 6G, XL-MIMO technology can utilize the spatial degrees of freedom and channel state information between a large number of antennas to achieve higher channel capacity and signal processing performance. However, the use of extremely large aperture arrays will lead to non-negligible near-field spherical wave characteristics, and the traditional channel and system models based on the plane wave assumption will no longer be accurate, which will cause the existing pilot channel estimation scheme to have a certain degree of performance degradation. In addition, with the increasing popularity of high mobility scenarios, signal transmission is affected by multiple factors such as multipath fading, Doppler fading and noise interference, resulting in the channel showing a dual selection characteristic. In this case, the signal processing performance of traditional modulation technology drops sharply, especially in ultra-large-scale antenna arrays, which is unbearable for real-time communication systems with high reliability requirements. Orthogonal Time Frequency Space (OTFS) is a promising modulation technology to solve the above challenges. In OTFS, all information symbols are mapped to the 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 effectiveness through spatial multiplexing, but also introduce spherical waveguide vectors to accurately characterize near-field high-mobility wireless channels in the DD domain and increase the reliability of signal transmission.

[0003] At present, for near-field high-mobility communication scenarios, the system frameworks and pilot design schemes proposed by domestic and foreign scholars have certain limitations. The existing low pilot overhead and high-accuracy channel estimation algorithms rely heavily on the classic far-field plane assumption, while the non-negligible near-field spherical wavefront characteristics in XL-MIMO make the existing system model construction no longer accurate and the channel estimation scheme suffers serious losses. Most of the scenarios in the research are relatively simple, focusing on channel modeling while ignoring the combination with modulation technology and pilot design, and lacking the closed-form derivation of the end-to-end input-output relationship considering the near-field characteristics; in addition, in the XL-MIMO system, reasonable pilot pattern and pilot sequence design can effectively utilize spectrum and time resources, reduce the channel bandwidth and transmission time occupied by the pilot, thereby improving the spectrum efficiency and energy efficiency of the system and saving system resource overhead. However, the existing pilot design for OTFS focuses on the design of the pilot pattern and pilot sequence itself, while ignoring the possibility of optimizing the pilot sequence itself. Summary of the invention

[0004] In order to improve spectrum utilization efficiency and achieve accurate channel estimation in near-field high mobility scenarios, the present invention proposes a pilot sequence design method for ultra-large-scale MIMO-OTFS, including: for near-field high mobility environments, establishing a communication system based on spherical waves, establishing an optimization function in the communication system with the goal of minimizing the average non-interference metric between pilots, and solving the optimal pilot sequence.

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

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

[0007]

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

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

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

[0011]

[0012] Where Q is the number of coherent operations; L is the number of all possible delay-Doppler shift pairs, expressed as L = (l m +1)(2k m +1), l m is the maximum value of the Doppler frequency shift index, k m is the maximum value of the delay offset index; N t is the number of antennas at the base station; α i is the i-th column vector in the measurement matrix, α j is the j-th column vector in the measurement matrix; <,> means the scalar 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, which specifically includes the following steps:

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

[0015] 101. Calculate whether the fitness of any individual reaches the expected value. If yes, terminate the process and output the individual that meets the expected value as the optimal pilot sequence.

[0016] 102. Calculate the probability of individual selection based on fitness, select from M individuals in sequence based on the roulette selection method, and arrange them in the order of selection to obtain the population sequence X'={x1',...x M '};

[0017] 103. With crossover probability p c From the population sequence X'={x1',…x M '}Select M·p c The pilot sequence individuals perform crossover operation;

[0018] 104. Evaluate the fitness of the individuals to calculate whether the fitness of any individual reaches the expected value. If so, terminate the process and output the individual that meets the expected value as the optimal pilot sequence. Otherwise, perform a mutation operation.

[0019] 105. Choose any pilot sequence and calculate 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, the present invention constructs an XL-MIMO OTFS system suitable for near-field high mobility scenarios, and then derives and analyzes the input-output relationship in combination with the embedded pilot frame structure design;

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

[0023] In summary, the spherical wave-based system model constructed in the present invention has significant performance advantages over the traditional plane wave model in a near-field high-mobility environment. The proposed genetic algorithm-based pilot sequence optimization design achieves better channel estimation performance than other pilot designs due to its powerful adaptive search capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 Schematic diagram of the XL-MIMO OTFS system framework of the present invention;

[0025] Figure 2 It is a schematic diagram of the design of pilot, protection and data symbols at the transmitting antenna end of the XL-MIMO OTFS system of the present invention;

[0026] Figure 3 The pilot design process of the XL-MIMO OTFS system of the present invention is provided;

[0027] Figure 4 It is a schematic diagram of the comparison of channel estimation performance based on far-field and near-field models in the near-field environment of the present invention;

[0028] Figure 5 It is a comparative schematic diagram of the change of the correlation of the pilot matrix with the number of iterations of the present invention;

[0029] Figure 6 A schematic diagram of NMSE performance comparison of different pilot symbols in the present invention. DETAILED DESCRIPTION

[0030] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0031] The present invention proposes a pilot sequence design method for ultra-large-scale MIMO-OTFS, comprising: aiming at a near-field high mobility environment, establishing a communication system based on spherical waves, establishing an optimization function in the communication system with the goal of minimizing the average mutual non-interference metric between pilots, and solving to obtain an optimal pilot sequence.

[0032] like Figure 1 As shown in Figure 2, we consider building an XL-MIMO OTFS system that takes into account the near-field spherical wavefront characteristics. Assume that the base station (BS) is equipped with N t antennas form a uniform linear array (ULA) to serve 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 the base station array antenna and the user are located in a two-dimensional plane, and the antenna spacing is half a wavelength. λ c is the wavelength. Assume that the nth t The coordinates of the antennas are in It represents the distance from the center of the array (i.e., the reference antenna) to the uth user or the last scatterer via the lth path. Indicates the nth t The distance from the first antenna to the uth user or the last scatterer via the lth path. Indicates the angle between the array center and the last scatterer or user. For convenience 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 and omits the user's subscript without loss of generality, that is, According to the geometric relationship, it can be deduced that:

[0033]

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

[0035]

[0036] in 1×N t The dimensional time-frequency dual-selective channel can be modeled as:

[0037]

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

[0039] Following the standard derivation of the OTFS input-output relationship, a coded bit sequence 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 delay index, N is the number of Doppler frequency shift index indexes, and M is the number of delay index indexes. The signal is converted to the time-frequency (TF) domain by inverse symplectic fast Fourier transform (ISFFT) to obtain the time-frequency domain signal:

[0040]

[0041] Among them, n∈[0,N-1],m∈[0,M-1].

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

[0043]

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

[0045]

[0046] The cross fuzzy function is defined as It measures the radar's perception accuracy of speed and delay, v * (·) represents the conjugate of v(·). At the receiving end, the received signal r(t) is subjected to a cross-ambiguity function C grx,r Matched filter for (τ,v):

[0047]

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

[0049]

[0050] Among them, H n,m [n',m'] is the equivalent TF domain channel, that is:

[0051]

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

[0053]

[0054] in Defined by:

[0055]

[0056] definition Considering the presence of noise, Represents matrix multiplication. The DD domain input-output relationship can be expressed as the following matrix-vector form:

[0057]

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

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

[0060]

[0061] where w[k,l] represents noise, [·] N Represents modulo N operation, [] M represents the modulo M operation, α i (k,l) represents the additive phase shift due to the imperfect biorthogonality of the rectangular waveform and can be expressed as:

[0062]

[0063] Among them, k i represents the integer Doppler shift corresponding to the i-th path in the DD domain, l i Indicates the delay offset index corresponding to the i-th path in the DD domain.

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

[0065]

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

[0067] The delay-Doppler-antenna domain channel has finite support [0,τ max ] and [-v max ,v max ]. The setting of the guard interval is required to be greater than or equal to the maximum delay offset and the maximum Doppler frequency deviation, that is:

[0068]

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

[0070]

[0071] Among them, k∈[k p ,k p +N p -1],l∈[l p ,l p +M p -1], indicating For the delay-Doppler-antenna domain channel, the additive phase shift is expressed as:

[0072]

[0073] The input and 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, is the pilot matrix and L=(l m +1)(2k m +1); is the channel vector; To receive the signal, 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 that affect the accuracy of channel estimation are h DDS Sparsity and whether the measurement matrix A satisfies the restricted isometry property (RIP) condition. However, it is quite complicated to directly prove the RIP of a measurement matrix. It is a non-deterministic polynomial hard (NP-hard) problem of polynomial complexity. Therefore, the mutual incoherence property (MIP) principle with relatively loose conditions and relatively low computational cost is used to optimize the measurement matrix. The maximum column correlation is expressed as:

[0077]

[0078] Among them, α i and α j are 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 columns, and the total correlation of the entire measurement matrix cannot be measured. Therefore, the average MIP criterion can be used:

[0079]

[0080] Wherein, Q is the number of coherent operations. According to the above formula, the present invention constructs the following pilot sequence optimization problem:

[0081] (P1)

[0082] stmax(abs(x DDS ))≤D

[0083] Wherein, D represents the maximum power threshold.

[0084] Since problem (P1) is a non-convex problem, it is easy to fall into the local optimal solution when solving it using traditional mathematical optimization methods, and it is difficult to find the global optimal solution. Therefore, the present invention considers using a random, highly parallel, and adaptive search method that draws on the natural selection and natural genetic mechanism of the biological world, namely a genetic algorithm.

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

[0086]

[0087] Select M components X'={x1',...x M '}; then with crossover probability p c Randomly select M·p from X' c pilot matrix individuals, each adjacent pair of pilot matrices x i ', x j ',i,j∈M for crossover recombination, and each crossover randomly generates ξ,ξ'∈U(1,LN t ), sort(ξ,ξ') as the tangent point position, exchange the pilot sequence between the two tangent points, so as to produce the next generation of excellent individuals; evaluate the fitness of the new population, if it does not meet the throw-out condition, perform mutation operation, select a pilot matrix, according to the probability p m Specify a mutation point and replace the pilot sequence at that point with a Gaussian sequence or Bernoulli sequence that meets the constraints. Repeat this cycle until the number of iterations reaches the maximum or the fitness of the entire population converges. Finally, select the population with the minimum fitness min f(x i DDS ) is used as the optimized output. The overall computational complexity of the present invention mainly depends on the complexity of individual evaluation, the complexity of population operation, and the number of iterations, namely O(TM(LN t ) 2 ), since the scheme can be run offline, its complexity can be ignored in the actual system.

[0088] like Figure 3The present invention constructs a pilot sequence optimization problem in the delay-Doppler domain based on the average mutual uncorrelation criterion, and adopts a genetic algorithm to solve it, which mainly includes the steps of fitness evaluation, selection, crossover, mutation, etc. By utilizing its random, highly parallel, and adaptive search characteristics, it can more accurately and efficiently find the global optimal solution and obtain the optimized pilot sequence, thereby achieving more accurate channel estimation. The present invention provides a specific implementation process for solving the optimization problem according to the genetic algorithm, which specifically includes the following steps:

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

[0090] 101. Calculate whether the fitness of any individual reaches the expected value. If yes, terminate the process and output the individual that meets the expected value as the optimal pilot sequence.

[0091] 102. Calculate the probability of individual selection based on fitness, select from M individuals in sequence based on the roulette selection method, and arrange them in the order of selection to obtain the population sequence X'={x1',...x M '};

[0092] 103. With crossover probability p c From the population sequence X'={x1',…x M '}Select M·p c The pilot sequence individuals perform crossover operation;

[0093] 104. Evaluate the fitness of the individuals to calculate whether the fitness of any individual reaches the expected value. If so, terminate the process and output the individual that meets the expected value as the optimal pilot sequence. Otherwise, perform a mutation operation.

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

[0095] like Figure 4As shown, a comparison of the channel estimation performance based on the traditional far-field model and the near-field model proposed in the present invention in a near-field environment is demonstrated. In this embodiment, the number of transmitting antennas is set to 256 and the spacing between antennas is 32.5 mm, a half-wavelength distance. It can be calculated that the Rayleigh distance is 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 is within the near-field range. Subsequently, the OMP algorithm is used to perform channel estimation on the far-field model based on the traditional plane wave assumption and the near-field model based on the spherical wave. The simulation results show that the near-field XL-MIMO OTFS framework proposed in the present 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 As shown in FIG. 1 , a graph showing the correlation of the pilot matrix with the number of iterations is shown. Since the transmission pilots of each antenna are the same and the correlation of the matrix is ​​mainly affected by the correlation between the columns representing the transmission pilots at different antennas, this embodiment focuses on optimizing this part during the simulation process, setting the average power of the pilot symbol to 30 dBW, the population size of the genetic algorithm to 50, the crossover probability to 0.8, the mutation probability to 0.1, and the fitness function throw threshold to 10 -5 The maximum number of iterations is 2.5×10 4 , so that it can be fully iterated and optimized. Figure 5 It can be seen that the correlation between the columns of the measurement matrix is ​​about 2×10 4 After iterations, it converges and the average correlation coefficient is optimized from the original 0.2937 to 0.1815. In order to more clearly show the effect of optimization, the correlation coefficient and are expressed as 1.91×10 4 Optimized to 1.084×10 4 .

[0097] like Figure 6As shown, the NMSE performance of random pilot sequence, Gaussian pilot sequence, Bernoulli sequence, Toeplitz sequence and the pilot sequence optimized based on genetic algorithm proposed in the present invention is demonstrated. The Bernoulli sequence is simple to generate and can make full use of spectrum resources. However, the autocorrelation of the binary sequence it generates is weak, and due to the existence of zero-power pilot symbols, its performance is poor in high-noise environments; the Toeplitz sequence has structured autocorrelation and can perform well in scenarios with similar channel characteristics. However, due to the complex multipath propagation and large changes in channel environment in near-field high-mobility scenarios, its non-random structure limits the performance of channel estimation; the randomness and good autocorrelation of the Gauss sequence make it robust to noise, but it is more complicated to generate the sequence in practical applications. The simulation results show that the NMSE performance of the pilot sequence optimization scheme based on the genetic algorithm is better than other comparison algorithms at any SNR, and can reach 10 when the SNR reaches 30dB. -1 This scheme can perform iterative optimization based on randomly generated pilot sequences, adapt to complex channel environments in near-field high-mobility scenarios, and achieve better channel estimation performance.

[0098] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention 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: Aiming at the near-field high mobility environment, a communication system based on spherical waves is established. In the communication system, an optimization function is established with the goal of minimizing the average non-interference metric between pilots, and the optimal pilot sequence is obtained by solving it.

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 delay-Doppler domain, then transformed to the time domain through OTFS modulation and sent through the uniform linear antenna array of the base station; after the signal is received by a single antenna at the receiving end, the received signal is converted to the delay-Doppler domain through OTFS demodulation.

3. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 2, characterized in that: The optimization function established with the goal of minimizing the average non-interference measure between pilots is expressed as: Constraints: max(abs(X DDS ))≤D Among them, X DDS represents the pilot matrix; μ avg represents the average non-interference measure between pilots; abs(·) is a function for finding the absolute value; max(·) is a function for finding the maximum value; D represents the maximum power threshold.

4. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 3, characterized in that: The average non-interference measure μ between pilots avg It is expressed as: Where Q is the number of coherent operations; L is the number of all possible delay-Doppler shift pairs, expressed as L = (l m +1)(2k m +1), l m is the maximum value of the Doppler frequency deviation index, k m is the maximum value of the delay offset index; N t is the number of antennas at the base station; α i is the i-th column vector in the measurement matrix, α j is the j-th column vector in the measurement matrix; <,> means the scalar product of two vectors; |·| means modulo operation; ||·||2 means 2-norm operation.

5. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 2, 3 or 4, characterized in that: The genetic algorithm is used to solve the optimization function to obtain the optimal pilot sequence, which specifically includes the following steps:

100. Select M items that meet max(abs(x DDS ))≤D pilot sequence x DDS As individuals in the initial population, the crossover probability and mutation probability of the genetic algorithm are initially changed, and the expected value of fitness is set; 101. Calculate whether the fitness of any individual reaches the expected value. If yes, terminate the process and output the individual that meets the expected value as the optimal pilot sequence.

102. Calculate the probability of individual selection based on fitness, select from M individuals in sequence based on the roulette selection method, and arrange them in the order of selection to obtain the population sequence X'={x1',...x M '}; 103. With crossover probability p c From the population sequence X'={x1',…x M '}Select M·p c The pilot sequence individuals perform crossover operation; 104. Evaluate the fitness of the individuals to calculate whether the fitness of any individual reaches the expected value. If so, terminate the process and output the individual that meets the expected value as the optimal pilot sequence. Otherwise, perform a mutation operation.

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

6. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 5, characterized in that: The probability of an individual being selected is expressed as: Among them, p i represents the probability of individual i being selected; represents the i-th pilot sequence The fitness value of .

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

8. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 5, characterized in that: The process of performing the crossover operation on the selected individual includes: randomly selecting two tangent points between the individual selected for the crossover operation and its neighbor individuals, and exchanging pilot symbols at the two tangent points to complete the crossover operation.

9. The pilot sequence design method for ultra-large-scale MIMO-OTFS according to claim 5, characterized in that: The process of performing the crossover operation on the selected individuals includes: replacing the pilot symbols at the variation points with elements in a Gaussian sequence or a Bernoulli sequence that meets the constraints of the optimization function.

Images