GFDM waveform design method for jungle communication system

Abstract

The invention belongs to the technical field of wireless communication systems, and particularly relates to a GFDM waveform design method for a jungle communication system. The method mainly comprises two parts of performance test and waveform design, and in the GFDM jungle communication system, a receiving end tests the bit error rate and the symbol transmission rate of the GFDM jungle communication system according to a known pilot signal sent by a sending end; a utility function is confirmed, and waveform design parameters including a cyclic prefix and a roll-off coefficient are optimized step by step by applying a genetic algorithm; through careful construction and parameter optimization of each part, the invention aims to improve the overall performance of the jungle communication system, can give full play to the potential of the GFDM technology, and meets the diversified requirements of jungle communication.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication system technology, and specifically relates to a GFDM waveform design method for jungle communication systems. Background Technology

[0002] With the rapid development of wireless communication technology and its expanding application scenarios, jungle communication, as a special scenario, presents new challenges to communication technologies. In the jungle environment, signal transmission is affected by dense vegetation, complex terrain, and multipath effects, leading to problems such as signal attenuation, scattering, and delay spread, which seriously affect the reliability, signal quality, and transmission efficiency of communication. Existing communication technologies have many shortcomings in dealing with these complex environments and are unable to meet the high-efficiency and reliable requirements of jungle communication.

[0003] In jungle communication scenarios, GFDM (Generalized Frequency Division Multiplexing) technology exhibits unique advantages. As an emerging multi-carrier modulation technology, GFDM is an extension and improvement upon the classic OFDM (Orthogonal Frequency Division Multiplexing) technology. Its excellent out-of-band radiation suppression capability reduces the absorption and scattering effects of vegetation on signals; its flexible time-frequency resource allocation characteristics allow it to adapt to dynamic channel changes in jungle environments. Simultaneously, GFDM technology also holds great potential in ranging and positioning, providing new solutions for integrated sensing applications in jungle environments.

[0004] In GFDM technology, the roll-off factor, cyclic prefix, and subcarriers are key parameters affecting the bit error rate and bandwidth utilization of GFDM. By designing the roll-off factor, sidelobe levels can be effectively reduced, false targets caused by clutter can be decreased, and out-of-band radiation can be suppressed to reduce the absorption and scattering effects of vegetation on the signal. Optimizing the cyclic prefix length can achieve a balance between combating multipath interference and maintaining spectral efficiency, reducing inter-symbol interference and inter-subcarrier interference. Reasonably configuring the number of subcarriers can further improve the system's flexibility and bandwidth utilization.

[0005] The synergistic optimization of these parameters can not only significantly reduce the communication bit error rate and increase the symbol transmission rate, but also enhance the sensing distance resolution and velocity resolution, effectively reducing measurement errors. In jungle scenarios, the practical application of GFDM technology is limited by the rigidity of existing parameter optimization methods. Existing GFDM systems typically use fixed raised cosine roll-off coefficients and static cyclic prefix configurations. To achieve specific communication requirements, repeated trials are often necessary, making the workload complex. Summary of the Invention

[0006] To overcome the above problems, this invention provides a GFDM waveform design method for jungle communication systems. This method mainly covers two parts: a performance testing module and a waveform design module. Through careful construction and parameter optimization of each module, it aims to improve the overall performance of the jungle communication system, fully leverage the potential of GFDM technology, and meet the diverse needs of jungle communication.

[0007] A GFDM waveform design method for jungle communication systems includes the following:

[0008] Part 1: Performance Testing

[0009] In a GFDM jungle communication system, the receiver will test the bit error rate and symbol transmission rate of the GFDM jungle communication system based on the known pilot signals transmitted by the transmitter, so as to construct a utility function as a joint evaluation index for both; the specific steps are as follows:

[0010] Step 1.1: At the transmitting end, the input binary data stream is mapped to complex symbols D∈C through M-QAM modulation. K×M Where C represents the complex set, K is the number of subcarriers, and M is the number of subsymbols; pulse shaping is performed through a raised cosine roll-off filter to generate a time-domain signal x(t);

[0011] Step 1.2, let the original symbol sequence transmitted by the sending end be x[n], n=0,1,...,L n -1, where L n Let L be the sequence length. cp =L n Let cp represent the code length used for the cyclic prefix, then the symbol x after adding the prefix... cp [n] is represented as:

[0012]

[0013] Step 1.3, assume the channel's impulse response is b[n] and its length is L. h The received signal y[n] after adding the cyclic prefix is ​​represented as:

[0014]

[0015] In the formula, w[n] represents additive noise;

[0016] Step 1.4: The receiving end recovers the complex symbol D into a symbol using matched filtering. After demodulation, a binary data stream is obtained. The bit error rate (BER) is calculated by comparing it with the data from the sending end (b). tx and receiver b rx Bit difference calculation:

[0017]

[0018] In the formula b tx b is the number of bits to send. rx Where N is the number of bits received, μ is the total number of bits, and i represents a number from 1 to N.

[0019] Step 1.5, Symbol transmission rate R S The value is determined by the number of subcarriers K, the symbol period, and the proportion of the cyclic prefix β, and the calculation formula is as follows:

[0020]

[0021] In the formula For the cyclic prefix time T CP With symbol period T S The ratio;

[0022] II. Waveform Design Section

[0023] In a GFDM jungle communication system, the utility function is identified, and a genetic algorithm is applied to optimize waveform design parameters—cyclic prefix and roll-off coefficient—stepwise. Specifically, this includes the following:

[0024] Step 2.1, let B r This represents the bit error rate (BER) calculated by the receiver after demodulation, which is simplification of BER to B. r R s Representing the symbol transmission rate, a linear combination of the two is constructed as the utility function:

[0025] F=ω1·B r -ω2·R s

[0026] In the formula, ω1 and ω2 are used as weighting coefficients to balance the relative importance of transmission rate and communication error rate in the utility function;

[0027] Because there is an order of magnitude difference between the communication error rate and the transmission rate, normalization processing is necessary to make B r and R s They are respectively mapped to the interval [0,1]; where B r The formula for normalization is as follows:

[0028]

[0029] In the formula B real B represents the actual bit error rate calculation result. max The maximum permissible bit error rate;

[0030] R s The formula for normalization is as follows:

[0031]

[0032] In the formula R real R is the result of the actual transmission rate calculation. max R is the theoretical maximum permissible transmission rate. min This represents the theoretical minimum permissible transmission rate.

[0033] Step 2.2, optimize waveform design parameters step by step.

[0034] Step 2.21: The roll-off factor α is set to a fixed value, and optimization is performed on the cyclic prefix cp:

[0035] For the GFDM jungle communication system, keeping other waveform parameters unchanged, the GA algorithm is embedded into the communication system. The cyclic prefix cp is optimized using a custom utility function, with the utility function determined in step 2.1 used as the fitness function and cp as the decision variable. Its scope is defined as [γ]. min ,γ max ], where γ min It is the self-defined minimum cp value, γ max It is a self-defined maximum value of CP, and the values ​​of decision variables are continuously adjusted to make the fitness function optimal;

[0036] Step 2.22, Optimization of the roll-off factor α of the pulse shaping filter.

[0037] Take the optimal solution cp obtained from the cyclic prefix optimization in step 2.21 when the optimal utility function is achieved. opt ; will cp opt As a cyclic prefix in the constant waveform parameters of the GFDM jungle communication system, with other constant waveform parameters set unchanged, the GA algorithm is called to optimize the roll-off factor α for the same utility function, and its range is set to [α]. min ,α max ], where α min It is the self-defined minimum value of α, α max It is the maximum value of α as defined by the user.

[0038] The frequency response function of the raised cosine roll-off filter in step 1.1 is:

[0039]

[0040] In the formula T s For the symbol period, R s For symbol transmission rate, and f is the frequency, α is the roll-off factor, and 0≤α≤1.

[0041] In step 1.4, as needed, the receiving end can recover the complex symbol D into a symbol using matched filtering and frequency domain equalization.

[0042] The solution process for optimizing the cyclic prefix cp in step 2.21 is as follows:

[0043] Step a: Randomly generate a set number of first-generation CP values ​​within a defined range as initial candidate solutions, and calculate B for each CP using the performance testing section. r and R s For these two performance indicators, the corresponding utility function F is obtained. The individuals in the F values ​​that account for the top ρ% are retained in ascending order to obtain the set of cp values, and other solutions are discarded.

[0044] Step b involves simulating a genetic process to generate the next generation of individuals for the set of cp values. This genetic process is divided into two parts: crisscross inheritance and variation inheritance. Crosscross inheritance involves randomly selecting two solutions from the set of cp values ​​multiple times and taking the median to generate a new solution. Variation inheritance involves randomly selecting one solution from the set of cp values ​​multiple times and adding a perturbation Δcp to each selected solution. The perturbation has a mean of 0 and a standard deviation of 0. The Gaussian distributed random variables are superimposed, and the resulting solutions are used as the new solutions.

[0045] Step c: Combine the set of cp values ​​and the new solution as a new set of cp values ​​and iterate over step b.

[0046] Step d continues until the specified number of iterations is reached, at which point the final value of the cyclic prefix cp and the extreme value of the utility function F are obtained.

[0047] In step a, a batch of P is randomly generated within a set range. sum The first-generation cp value of each individual is used as the initial candidate solution. The total number of new individuals in step b is required to be P. son =P sum • (1-ρ%), the proportion of new individuals generated by crossover in the total number of new individuals required is δ%, and the proportion of new individuals generated by mutation in the total number of new individuals required is (1-δ%).

[0048] The optimization process for the roll-off coefficient α of the pulse shaping filter in step 2.22 is as follows:

[0049] Step a: Randomly generate a specified number of α values ​​within a set range as initial candidate solutions, and use the performance test module to calculate B under each α. r and R s These two performance indicators are used to obtain the corresponding utility function F. The individuals in the F values ​​that account for the top ρ% are retained in ascending order to obtain the set of α values, while other solutions are discarded.

[0050] Step b involves simulating the genetic process to generate the next generation of individuals for the set of α values. This genetic process is divided into two parts: crisscross inheritance and variation inheritance. Crosscross inheritance involves randomly selecting two solutions from the set of α values ​​multiple times and taking the median to generate a new solution. Variation inheritance involves randomly selecting one solution from the set of α values ​​multiple times and adding a perturbation Δα to each selected solution. The perturbation has a mean of 0 and a standard deviation of 0. The Gaussian distributed random variables are superimposed, and the resulting solutions are used as the new solutions.

[0051] Step c: Combine the set of α values ​​and the new solution as a new set of α values ​​and iterate over step b.

[0052] Step d continues until the specified number of iterations is reached. At this point, the final roll-off coefficient α of the pulse shaping filter and the ultimate value of the utility function F after waveform step-by-step optimization are obtained.

[0053] In step a, a batch of P is randomly generated within a set range. sum The first-generation α value is used as the initial candidate solution, and the total number of new individuals in step b is required to be P. son =P sum • (1-ρ%), the proportion of new individuals generated by crossover in the total number of new individuals required is δ%, and the proportion of new individuals generated by mutation in the total number of new individuals required is (1-δ%).

[0054] The beneficial effects of this invention are:

[0055] Based on the various impacts of jungle environments on signal transmission, this invention proposes a systematic solution integrating dynamic parameter optimization and adaptive utility functions using GFDM technology. It employs the GA algorithm to optimize the parameters of the GFDM system step-by-step, obtaining the optimal parameter settings for the GFDM system, thereby improving the communication quality of radio waves in jungle environments. Furthermore, it allows for specific waveform design based on different performance requirements. Using high-precision ranging and positioning technology based on GFDM signals, it can provide accurate location information for personnel and equipment, while simultaneously achieving efficient data transmission and stable environmental perception. This comprehensively enhances the communication and sensing performance of the GFDM system in complex jungle environments, achieving optimal parameter settings for the GFDM communication system under various conditions. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the content of the embodiments of the present invention and these drawings without creative effort.

[0057] Figure 1 This is a graph showing the changing trend of the utility function F under different cp values ​​in Embodiment 2 of the present invention.

[0058] Figure 2 This is a graph showing the changing trend of the utility function F under different algebraic α values ​​in Embodiment 2 of the present invention. Detailed Implementation

[0059] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0060] Example 1

[0061] A GFDM waveform design method for jungle communication systems includes the following:

[0062] Part 1: Performance Testing

[0063] A performance testing module is constructed in the GFDM jungle communication system. The receiver will test the bit error rate and symbol transmission rate of the GFDM jungle communication system based on the known pilot signal transmitted by the transmitter, so as to construct a utility function as a joint evaluation index for both. The specific steps are as follows:

[0064] Step 1.1: At the transmitting end, the input binary data stream is mapped to complex symbols D∈C through M-QAM modulation. K×M Where C represents the complex set, K is the number of subcarriers, and M is the number of subsymbols; pulse shaping is performed using a raised cosine roll-off filter (Roll-off factor α) to generate a time-domain signal x(t), where the frequency response function of the raised cosine roll-off filter is:

[0065]

[0066] In the formula T s For the symbol period, R s For symbol transmission rate, and f is the frequency, α is the roll-off factor, and 0≤α≤1;

[0067] In a jungle communication environment, the received signal is:

[0068] y(t)=h(t)*x(t)+n(t) (1)

[0069] In the formula, y(t) represents the time-domain data of the signal received at the receiver, h(t) represents the unit impulse response model of the jungle communication channel, and n(t) represents the noise, which has a mean of 0 and a variance of σ. 2 Gaussian noise;

[0070] Step 1.2, let the original symbol sequence transmitted by the sending end be x[n], n = 0, 1, ..., L n -1, where L n Let L be the sequence length. cp =L n Let cp represent the code length used for the cyclic prefix, then the symbol x after adding the prefix... cp [n] is represented as:

[0071]

[0072] In GFDM systems, the main function of the cyclic prefix cp is to combat inter-symbol interference (ISI) and inter-subcarrier interference (ICI) to ensure system performance.

[0073] Step 1.3, assuming the channel's impulse response is h[n] and its length is L h The received signal y[n] after adding the cyclic prefix is ​​represented as:

[0074]

[0075] In the formula, w[n] is additive noise, while cp avoids the interference caused by the overlap of x(nl) and x(n), and l is the symbol delay caused by multipath effect;

[0076] Step 1.4: The receiver recovers the complex symbol D into a symbol using matched filtering and frequency domain equalization (if necessary). After demodulation, a binary data stream is obtained. The bit error rate (BER) is calculated by comparing it with the data from the sending end (b). tx and receiver b rx Bit difference calculation:

[0077]

[0078] In the formula b tx b is the number of bits to send. rx Where N is the number of bits received, μ is the total number of bits, and i represents a number from 1 to N.

[0079] Regarding the bit error rate (BER), multipath effects can cause inter-symbol interference (ISI) and inter-subcarrier interference (ICI), leading to an increase in the BER. When the duration T of the CP prefix... cp Satisfy T cp ≥τ maxAt this time, the delay spread caused by multipath can be limited to within cp, and the orthogonality of subcarriers can be maintained by using the Discrete Fourier Transform (DFT), reducing ICI, while also assisting in symbol synchronization and channel estimation, thus reducing the communication bit error rate, τ max Maximum delay spread for multipath channels;

[0080] For symbol transmission rate R s Its commonly used spectral efficiency Measurement; due to cp insertion, the duration of the GFDM symbol changes from T. s Increase to T s +T cp Information rate With the transmission bandwidth B constant, T cp The larger R is b The smaller T is, the lower η is, and the lower the transmission rate; if T cp Too short a signal can lead to an increase in the bit error rate of communication, requiring a reduction in the information rate to ensure performance, which will also indirectly reduce the transmission rate. Therefore, a trade-off must be struck between the two to optimize system performance. The roll-off factor α of the pulse shaping filter is another important parameter in waveform design. A reasonable roll-off factor can effectively reduce inter-symbol interference while controlling the signal's spectral width, achieving a balance between spectral efficiency and out-of-band suppression.

[0081] For the bit error rate (BER), the roll-off factor α plays a role by affecting inter-symbol interference (ISI). When α is small, the raised cosine roll-off filter has a long tail in its impulse response, resulting in large ISI and making the receiver susceptible to interference from adjacent symbols, thus increasing the BER. When α is large, the tail is short, reducing ISI, but the increased bandwidth may lead to a decrease in the signal-to-noise ratio (SNR), which in turn increases the BER. Therefore, it is necessary to select an appropriate α value based on the actual channel conditions to achieve a balance between ISI and SNR in order to reduce the BER.

[0082] For symbol transmission rate R s Spectral efficiency η is a key indicator for measuring signal transmission rate, and its calculation formula is as follows: This indicates that α is inversely proportional to the spectral efficiency η, where M is the modulation base; as α increases, the signal bandwidth... An increase in α leads to a decrease in spectral efficiency, resulting in a drop in system transmission rate; conversely, a decrease in α leads to an increase in transmission rate.

[0083] Step 1.5, Symbol transmission rate R S The value is determined by the number of subcarriers K, the symbol period, and the proportion of the cyclic prefix β, and the calculation formula is as follows:

[0084]

[0085] In the formula For the cyclic prefix time T CP With symbol period T S The ratio;

[0086] II. Waveform Design Section

[0087] In order to design GFDM waveforms that meet the different needs of jungle communication in complex jungle environments, it is necessary to determine the utility function for different performance requirements. The joint utility function for different requirements can have different forms and can be customized. In the GFDM jungle communication system, the utility function is confirmed, and the waveform design parameters, namely the cyclic prefix and roll-off coefficient, are optimized step by step using a genetic algorithm.

[0088] Utility function identification for different performance requirements;

[0089] In the complex environment of jungle channels, the utility function can be defined in three ways depending on the context, as follows:

[0090] 1. Using the bit error rate (BER) and sensing resolution (R) as the main indicators, the BER reflects the reliability of communication, while the sensing resolution reflects the system's accuracy in detecting targets. A function is constructed... The smaller the BER and the larger the R, the larger the utility function value will be, which means that the communication reliability and sensing capability are both good at this time; ω1 and ω2 are weighting coefficients, and satisfy ω1+η2=1, which are used to adjust the importance of communication performance and sensing performance in the utility function, respectively.

[0091] 2. Using sensing resolution R and spectral efficiency SE as the main indicators, sensing resolution reflects the system's detection accuracy of the target, while spectral efficiency reflects the degree of utilization of spectrum resources. A function F = η1·R + η2·SE is constructed, where a larger R indicates higher sensing accuracy; SE is spectral efficiency, measured in bits per second per hertz (bps / Hz). A larger SE value indicates a stronger ability of the system to transmit data per unit of spectrum resources, and more efficient utilization of spectrum resources; ω1 and ω2 are weighting coefficients, satisfying ω1 + η2 = 1, used to adjust the importance of bit error rate and spectral efficiency in the utility function, respectively. When R and SE are larger, the utility function value F is larger, representing that both sensing accuracy and spectrum resource utilization efficiency are good at this time.

[0092] 3. Using the communication bit error rate (BER) and transmission rate (R) as the basis... S As the primary indicator, the bit error rate (BER) is related to the reliability of communication quality, while the transmission rate directly reflects the speed of data transmission. The function F = ω1·BER - ω2·R is constructed. S Here, a smaller BER value means a lower probability of data errors during communication, and higher communication reliability; R SBER is the transmission rate, measured in bits per second (bps). A higher BER indicates a larger data transmission rate per unit time, meaning faster data transmission speed. η1 and η2 are weighting coefficients that satisfy η1 + η2 = 1. Their function is to adjust the relative importance of BER and transmission rate in the utility function. A smaller BER indicates a higher R... S The larger the value, the smaller the utility function value F, indicating that the communication reliability and data transmission speed are both in a better state.

[0093] This embodiment selects the third case to construct the utility function, which specifically includes the following:

[0094] Step 2.1, let B r This represents the bit error rate (BER) calculated by the receiver after demodulation, which is simplification of BER to B. r R s Representing the symbol transmission rate, a linear combination of the two is constructed as the utility function:

[0095] F=ω1·B r -ω2·R s

[0096] In the formula, ω1 and ω2 are used as weighting coefficients to balance the relative importance of transmission rate and communication error rate in the utility function; when B is the minuend r Decrease, while the subtrahend R s When the value increases, the utility function is minimized. At this point, the system simultaneously satisfies a low communication error rate and a high transmission rate, thus achieving the desired communication effect.

[0097] Because there is an order of magnitude difference between the communication error rate and the transmission rate, normalization processing is necessary to make B r and R s They are respectively mapped to the interval [0,1]; where B r The formula for normalization is as follows:

[0098]

[0099] In the formula B real B represents the actual bit error rate calculation result. max The maximum permissible bit error rate;

[0100] R s The formula for normalization is as follows:

[0101]

[0102] In the formula R real R is the result of the actual transmission rate calculation. max R is the theoretical maximum permissible transmission rate. minThis represents the theoretical minimum permissible transmission rate.

[0103] Normalized bit error rate and normalized transmission rate eliminate dimensional differences through normalization, ensuring that each metric has equal importance in the utility function.

[0104] Step 2.2, optimize waveform design parameters step by step.

[0105] Step 2.21: The roll-off factor α is set to a fixed value (not exceeding the set range), and optimization is performed on the cyclic prefix cp:

[0106] For the GFDM jungle communication system with a performance testing module, keep other waveform parameters unchanged, and set the parameter values ​​as shown in Table 1 of the specific implementation plan. Embed the GA algorithm into the communication system, optimize the cyclic prefix cp using a custom utility function, use the utility function determined in step 2.1 as the fitness function, and use cp as the decision variable, specifying its range as [γ]. min ,γ max ], where γ min It is the self-defined minimum cp value, γ max It is a self-defined maximum value of CP, and the values ​​of decision variables are continuously adjusted to make the fitness function optimal;

[0107] The specific solution process is as follows:

[0108] Step a: Randomly generate a batch with a total number of P within a set range. sum Using the first-generation CP value as the initial candidate solution, the B value under each CP is calculated using the performance testing section. r and R s These two performance metrics yield the corresponding utility function F. The cp value with the best utility function value, i.e., the smaller F value, is retained. That is, individuals with the highest F values, arranged in ascending order, are retained to obtain the set of cp values. In the genetic algorithm, such cp values ​​can be understood as individuals with high fitness, and other solutions are discarded.

[0109] Step b: For the set of cp values, simulate the genetic process to generate the next generation of individuals. The total number of new individuals is required to be P. son =P sum ·(1-ρ%), where heredity is divided into two parts: crisscross inheritance and variation inheritance. Crosscross inheritance refers to randomly selecting two solutions from the set of cp values ​​multiple times and taking the median to generate a new solution. The proportion of new individuals generated by crisscross in the total number of new individuals required is δ%. Variation inheritance refers to randomly selecting one solution from the set of cp values ​​multiple times and superimposing a perturbation Δcp on each selected solution. The perturbation satisfies a mean of 0 and a standard deviation of . The Gaussian distributed random variable is superimposed and the solution is taken as the new solution. The proportion of the new individuals generated by the mutation in the total number of new individuals is (1-δ%).

[0110] Step c: Combine the set of cp values ​​and the new solution as a new set of cp values ​​and iterate over step b.

[0111] Step d continues until the specified number of iterations is reached. With each iteration, the solution is continuously optimized, ultimately outputting the cp value with the highest fitness, thus improving system performance. The entire process is similar to natural selection, allowing good solutions to evolve into the optimal solution through "propagation" and "mutation." At this point, a solution that simultaneously satisfies a low communication bit error rate B is obtained. r and higher transmission rate R s The final value of the cyclic prefix cp, and the extreme values ​​of the utility function F;

[0112] Step 2.22, Optimization of the roll-off factor α of the pulse shaping filter.

[0113] Take the optimal solution cp obtained from the cyclic prefix optimization in step 2.21 when the optimal utility function is achieved. opt ; will cp opt As a cyclic prefix in the constant waveform parameters of the GFDM jungle communication system, with other constant waveform parameters set unchanged, the GA algorithm is called to optimize the roll-off factor α for the same utility function, and its range is set to [α]. min ,α max ], where α min It is the self-defined minimum value of α, α max It is the self-defined maximum value of α; the specific solution process is as follows:

[0114] Step a: Randomly generate a specified number of α values ​​within a set range as initial candidate solutions, and use the performance test module to calculate B under each α. r and R s These two performance indicators are used to obtain the corresponding utility function F. The α value with the best utility function value, i.e., the smaller F value, is retained. That is, individuals with the top ρ% of F values ​​are retained in ascending order, and the set of α values ​​is obtained. Such α values ​​can be understood as individuals with high fitness in the genetic algorithm. Then other solutions are discarded.

[0115] Step b: For the set of α values, simulate the genetic process to generate the next generation of individuals. The total number of new individuals is required to be P. son =P sum·(1-ρ%), where heredity is divided into two parts: crisscross inheritance and variation inheritance. Crosscross inheritance involves randomly selecting two solutions from the set of α values ​​multiple times and taking the median to generate a new solution. The proportion of new individuals generated by crisscross in the total number of new individuals required is δ%. Variation inheritance refers to randomly selecting a solution from the set of α values ​​multiple times and superimposing a perturbation Δα on each selected solution. The perturbation has a mean of 0 and a standard deviation of 0. The Gaussian distributed random variable is superimposed to obtain the new solution; the proportion of the new individuals generated by the mutation in the total number of new individuals is (1-δ%).

[0116] Step c: Combine the set of α values ​​and the new solution as a new set of α values ​​and iterate over step b.

[0117] Step d continues until the specified number of iterations is reached. With each iteration, the solution is continuously optimized, eventually outputting the α value with the highest fitness, thus improving system performance. At this point, a solution that simultaneously satisfies a low bit error rate B is obtained. r and higher transmission rate R s The final value of the roll-off coefficient α of the pulse shaping filter, and the ultimate value of the utility function F after waveform step-by-step optimization.

[0118] Example 2

[0119] A GFDM waveform design method for jungle communication systems includes the following:

[0120] Step 1: Construction of utility functions in jungle communication systems.

[0121] Constructing a GFDM communication system in a jungle environment requires careful consideration of the characteristics of jungle channels. Jungle channels exhibit complex multipath effects and delay spread, and their signals are easily attenuated by dense vegetation. In this communication system construction, the jungle channel is simulated using a Rayleigh distribution, and its power spectral density function is:

[0122]

[0123] Where γ is the channel gain, σ 2 This represents the channel variance.

[0124] To optimize system communication efficiency and transmission reliability, a utility function that comprehensively considers bit error rate (BER) and transmission rate is selected. Weighting coefficients ω1 = 0.65 and ω2 = 0.35 are set, with BER being considered more important than transmission rate. BER and symbol transmission rate are normalized to map them to the [0,1] interval, ensuring that each indicator has equal importance in the utility function. For the BER normalization process, the maximum permissible BER B is... max =0.01, minimum permissible bit error rate B min=0.0001; For the transmission rate normalization process, since the transmission rate and the cyclic prefix have a typical inverse relationship, the theoretical maximum allowable transmission rate R is set to 0.0001. max Minimum cp value γ min The corresponding transmission rate, the theoretical minimum permissible transmission rate R min The maximum cp value γ max The corresponding transmission rate. Other key parameter settings for the communication system are shown in Table 1.

[0125] Table 1

[0126] variable describe Simulation value settings <![CDATA[ω1]]> Bit error rate weight 0.65 <![CDATA[ω2]]> Transmission rate weight 0.35 <![CDATA[γ max ]]> Maximum cyclic prefix 99(％) <![CDATA[γ min ]]> Minimum Cyclic Prefix 1(％) SNR Signal-to-noise ratio 25 dB K Number of subcarriers 512 M Number of sub-symbols 15 α Cosine roll-off factor 0.6 Mu Modulation bit number 4

[0127] Step 2: Distributed optimization of waveform design parameters

[0128] (1) Optimization for the cyclic prefix (cp)

[0129] For a given target utility function, the cyclic prefix cp is optimized. Its scope is [γ]. min ,γ max = [0.01, 0.99]. The GA algorithm iteratively calculates the cp value within this interval. The basic parameters of the GA algorithm are set as follows: the total number of individuals in each generation is P. sum =20, and the proportion of individuals retained after each generation of selection is ρ% = 5%, then the total number of new individuals in the next generation is P. son =P sum • (1-ρ%) = 19, where the proportion of new individuals generated by crossover is δ% = 80%, and the proportion of new individuals generated by mutation is (1-δ%) = 20%. The iteration count is set to 20. Through simulation, the changing trend of the utility function F under different generation cp values ​​is observed. The relevant results are as follows: Figure 1 As shown in the figure, the optimal individual achieving the best utility function in each generation, along with its cp value and utility function result, is recorded. With increasing iterations, the optimal cp curve of the cyclic prefix of the GFDM system tends to converge, while the utility function value shows a fluctuating downward trend, indicating that the genetic algorithm successfully optimizes the parameter cp. In the final generation, the final optimal solution of the system is obtained as cp. opt =0.0842, corresponding to a utility function value F = 4.228651. This result indicates that when designing the GFDM waveform with a cyclic prefix of 8.42%, a high symbol transmission rate and a low bit error rate can be achieved in jungle communication systems.

[0130] (2) Optimization of the roll-off factor (α) of the pulse shaping filter

[0131] For the established target utility function, the roll-off factor α is further optimized. The basic parameters are shown in Table 2 unless otherwise specified, and the cyclic prefix is ​​set to the aforementioned optimal value cp. opt=0.0842. Its value range is set to [α]. min ,α max Given the interval [0.1, 0.9], the GA algorithm is used to iteratively calculate the α value within this interval. The basic parameters of the GA algorithm are set as follows: the total number of individuals in each generation is P. sum =20, and the proportion of individuals retained after each generation of selection is ρ% = 5%, then the total number of new individuals in the next generation is P. son =P sum • (1-ρ%) = 19, where the proportion of new individuals generated by crossover is δ% = 80%, and the proportion of new individuals generated by mutation is (1-δ%) = 20%. The iteration count is set to 20. Through simulation, the changing trend of the utility function F under different α values ​​is observed. The relevant results are as follows: Figure 2 As shown in the figure, the optimal individual achieving the best utility function in each generation, along with its α value and utility function result, is recorded. With increasing iterations, the optimal α curve of the roll-off coefficient of the pulse shaping filter in the GFDM system tends to converge, while the utility function value shows a fluctuating downward trend. This indicates that the genetic algorithm successfully optimized the parameter α. In the final generation, the final optimal solution of the system is obtained as α... opt =0.1181, corresponding to a utility function value F = 0.476374. This result shows that when the GFDM waveform is designed with a cyclic prefix of 8.42% and a roll-off factor of 11.81%, a high symbol transmission rate and a low bit error rate can be achieved in jungle communication systems.

[0132] Table 2

[0133] variable describe Simulation value settings <![CDATA[ω1]]> Bit error rate weight 0.65 <![CDATA[ω2]]> Transmission rate weight 0.35 <![CDATA[α max ]]> Maximum cyclic prefix 99(％) <![CDATA[α min ]]> Minimum Cyclic Prefix 1(％) SNR Signal-to-noise ratio 25 dB K Number of subcarriers 512 M Number of sub-symbols 15 cp Cyclic prefix 8.42(％) Mu Modulation bit number 4

[0134] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the scope of protection of the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, any person skilled in the art can make equivalent substitutions or changes based on the technical solution and inventive concept of the present invention within the scope of the technology disclosed in the present invention. These simple modifications are all within the scope of protection of the present invention.

Claims

1. A GFDM waveform design method for jungle communication systems, characterized in that, Includes the following: Part 1: Performance Testing In a GFDM jungle communication system, the receiver will test the bit error rate and symbol transmission rate of the GFDM jungle communication system based on the known pilot signals transmitted by the transmitter, so as to construct a utility function as a joint evaluation index for both; the specific steps are as follows: Step 1.1: At the transmitting end, the input binary data stream is mapped to complex symbols D∈C through M-QAM modulation. K×M Where C represents the complex set, K is the number of subcarriers, and M is the number of subsymbols; pulse shaping is performed through a raised cosine roll-off filter to generate a time-domain signal x(t); Step 1.2, let the original symbol sequence transmitted by the sending end be x[n], n=0,1,...,L n -1, where L n Let L be the sequence length. cp =L n Let cp represent the code length used for the cyclic prefix, then the symbol x after adding the prefix... cp [n] is represented as: Step 1.3, assuming the channel's impulse response is h[n] and its length is L h The received signal y[n] after adding the cyclic prefix is ​​represented as: In the formula, w[n] represents additive noise; Step 1.4: The receiving end recovers the complex symbol D into a symbol using matched filtering. After demodulation, a binary data stream is obtained. The bit error rate (BER) is calculated by comparing it with the data from the sending end (b). tx and receiver b rx Bit difference calculation: In the formula b tx b is the number of bits to send. rx Where N is the number of bits received, μ is the total number of bits, and i represents a number from 1 to N. Step 1.5, Symbol transmission rate R S The value is determined by the number of subcarriers K, the symbol period, and the proportion of the cyclic prefix β, and the calculation formula is as follows: In the formula For the cyclic prefix time T CP With symbol period T S The ratio; II. Waveform Design Section In a GFDM jungle communication system, the utility function is identified, and a genetic algorithm is applied to optimize waveform design parameters—cyclic prefix and roll-off coefficient—stepwise. Specifically, this includes the following: Step 2.1, let B r This represents the bit error rate (BER) calculated by the receiver after demodulation, which is simplification of BER to B. r R s Representing the symbol transmission rate, a linear combination of the two is constructed as the utility function: F=ω1·B r -ω2·R s In the formula, ω1 and ω2 are used as weighting coefficients to balance the relative importance of transmission rate and communication error rate in the utility function; Because there is an order of magnitude difference between the communication error rate and the transmission rate, normalization processing is necessary to make B r and R s They are respectively mapped to the interval [0,1]; where B r The formula for normalization is as follows: In the formula B real B represents the actual bit error rate calculation result. max The maximum permissible bit error rate; R s The formula for normalization is as follows: In the formula R real R is the result of the actual transmission rate calculation. max R is the theoretical maximum permissible transmission rate. min This represents the theoretical minimum permissible transmission rate. Step 2.2, optimize waveform design parameters step by step. Step 2.21: The roll-off factor α is set to a fixed value, and optimization is performed on the cyclic prefix cp: For the GFDM jungle communication system, keeping other waveform parameters unchanged, the GA algorithm is embedded into the communication system. The cyclic prefix cp is optimized using a custom utility function, with the utility function determined in step 2.1 used as the fitness function and cp as the decision variable. Its scope is defined as [γ]. min ,γ max ], where γ min It is the self-defined minimum cp value, γ max It is a self-defined maximum value of CP, and the values ​​of decision variables are continuously adjusted to make the fitness function optimal; Step 2.22, Optimization of the roll-off factor α of the pulse shaping filter. Take the optimal solution cp obtained from the cyclic prefix optimization in step 2.21 when the optimal utility function is achieved. opt ; will cp out As a cyclic prefix in the constant waveform parameters of the GFDM jungle communication system, with other constant waveform parameters set unchanged, the GA algorithm is called to optimize the roll-off factor α for the same utility function, and its range is set to [α]. min ,α max ], where α min It is the self-defined minimum value of α, α max It is the maximum value of α as defined by the user.

2. The GFDM waveform design method for jungle communication systems according to claim 1, characterized in that, The frequency response function of the raised cosine roll-off filter in step 1.1 is: In the formula T s For the symbol period, R s For symbol transmission rate, and f is the frequency, α is the roll-off factor, and 0≤α≤1.

3. The GFDM waveform design method for jungle communication systems according to claim 1, characterized in that, In step 1.4, as needed, the receiving end can recover the complex symbol D into a symbol using matched filtering and frequency domain equalization.

4. The GFDM waveform design method for jungle communication systems according to claim 1, characterized in that, The solution process for optimizing the cyclic prefix cp in step 2.21 is as follows: Step a: Randomly generate a set number of first-generation CP values ​​within a defined range as initial candidate solutions, and calculate B for each CP using the performance testing section. r and R s For these two performance indicators, the corresponding utility function F is obtained. The individuals in the F values ​​that account for the top ρ% are retained in ascending order to obtain the set of cp values, and other solutions are discarded. Step b involves simulating a genetic process to generate the next generation of individuals for the set of cp values. This genetic process is divided into two parts: crisscross inheritance and variation inheritance. Crosscross inheritance involves randomly selecting two solutions from the set of cp values ​​multiple times and taking the median to generate a new solution. Variation inheritance involves randomly selecting one solution from the set of cp values ​​multiple times and adding a perturbation Δcp to each selected solution. The perturbation has a mean of 0 and a standard deviation of 0. The Gaussian distributed random variables are superimposed, and the resulting solutions are used as the new solutions. Step c: Combine the set of cp values ​​and the new solution as a new set of cp values ​​and iterate over step b. Step d continues until the specified number of iterations is reached, at which point the final value of the cyclic prefix cp and the extreme value of the utility function F are obtained.

5. The GFDM waveform design method for jungle communication systems according to claim 4, characterized in that, In step a, a batch of P is randomly generated within a set range. sum The first-generation cp value of each individual is used as the initial candidate solution. The total number of new individuals in step b is required to be P. son =P sum • (1-ρ%), the proportion of new individuals generated by crossover in the total number of new individuals required is δ%, and the proportion of new individuals generated by mutation in the total number of new individuals required is (1-δ%).

6. The GFDM waveform design method for jungle communication systems according to claim 1, characterized in that, The optimization process for the roll-off coefficient α of the pulse shaping filter in step 2.22 is as follows: Step a: Randomly generate a specified number of α values ​​within a set range as initial candidate solutions, and use the performance test module to calculate B under each α. r and R s These two performance indicators are used to obtain the corresponding utility function F. The individuals in the F values ​​that account for the top ρ% are retained in ascending order to obtain the set of α values, while other solutions are discarded. Step b involves simulating the genetic process to generate the next generation of individuals for the set of α values. This genetic process is divided into two parts: crisscross inheritance and variation inheritance. Crosscross inheritance involves randomly selecting two solutions from the set of α values ​​multiple times and taking the median to generate a new solution. Variation inheritance involves randomly selecting one solution from the set of α values ​​multiple times and adding a perturbation Δα to each selected solution. The perturbation has a mean of 0 and a standard deviation of 0. The Gaussian distributed random variables are superimposed, and the resulting solutions are used as the new solutions. Step c: Combine the set of α values ​​and the new solution as a new set of α values ​​and iterate over step b. Step d continues until the specified number of iterations is reached. At this point, the final roll-off coefficient α of the pulse shaping filter and the ultimate value of the utility function F after waveform step-by-step optimization are obtained.

7. The GFDM waveform design method for jungle communication systems according to claim 6, characterized in that, In step a, a batch of P is randomly generated within a set range. sum The first-generation α value is used as the initial candidate solution, and the total number of new individuals in step b is required to be P. son =P sum • (1-ρ%), the proportion of new individuals generated by crossover in the total number of new individuals required is δ%, and the proportion of new individuals generated by mutation in the total number of new individuals required is (1-δ%).

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