Learning program, learning method, and information processing device

Abstract

Reduce the number of bit errors. [Solution] The memory unit 11 stores the training data 11a. The processing unit 12 determines a first function (bit error function) that represents the expected number of bit errors in the transmitted signal reconstructed from the received signal using the estimated channel value. The processing unit 12 determines the expected number of bit errors for multiple candidate channel estimates using the training data 11a and the first function, and determines a second function that approximates the first function based on the determined expected value. The processing unit 12 trains a machine learning model using the second function as the loss function, using the training data 11a.

Description

[Technical Field]

[0001] The present invention relates to a learning program, a learning method, and an information processing device. [Background technology]

[0002] In wireless communication methods such as OFDM (Orthogonal Frequency Division Multiplexing), fading can degrade the received signal, potentially causing bit errors in the reconstructed transmitted signal. Therefore, channel values ​​that reflect fading characteristics are estimated, and the transmitted signal is reconstructed using these estimated channel values ​​and the received signal.

[0003] Conventionally, a technique has been proposed to generate a machine learning model using the transmission path response or data based on the transmission path response of an OFDM-type received signal as an explanatory variable, and the required C / N (Carrier-to-Noise Ratio) degradation amount in the transmission path as the objective variable (see, for example, Patent Document 1). In addition, a technique has been proposed to suppress jammer signals using a neural network trained to convert a complex number sequence of a received signal into a real number image and remove image noise (see, for example, Patent Document 2). Furthermore, channel estimation techniques using neural networks have also been proposed (see, for example, Patent Documents 3 and 4). [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2024-46875 [Patent Document 2] Japanese Patent Publication No. 2020-150539 [Patent Document 3] U.S. Patent Application Publication No. 2024 / 0259121 [Patent Document 4] U.S. Patent Application Publication No. 2023 / 0261910 [Overview of the project] [Problems that the invention aims to solve]

[0005] When using machine learning models to accurately estimate channel values, the number of parameters in the machine learning model increases, leading to increased computational load, memory usage, and overhead. On the other hand, in order to reduce the number of bit errors, it may not be necessary to estimate channel values ​​with high accuracy.

[0006] One aspect of this is the aim to reduce the number of bit errors. [Means for solving the problem]

[0007] In one aspect, a learning program is provided that causes a computer to perform the following steps: determine a first function that represents the expected number of bit errors in a transmitted signal reconstructed from a received signal using channel estimates; determine the expected values ​​for a plurality of candidates for the estimate using training data and the first function; determine a second function that approximates the first function based on the determined expected values; and train a machine learning model using the training data with the second function as the loss function. [Effects of the Invention]

[0008] One aspect is that it can reduce the number of bit errors. [Brief explanation of the drawing]

[0009] [Figure 1] This figure shows an example of a learning method according to the first embodiment. [Figure 2] This figure shows an example of a restored transmitted signal. [Figure 3] This diagram illustrates the basic units of signals in the OFDM scheme. [Figure 4] This figure shows an example of channel estimation using the OFDM method. [Figure 5] This figure shows an example of the number of bit errors. [Figure 6]This is a block diagram showing an example of hardware for an information processing device. [Figure 7] This is a block diagram showing examples of functions of an information processing device. [Figure 8] This figure shows the relationship between the difference between the estimated and true channel values ​​and the expected number of bit errors. [Figure 9] This figure shows an example of a simulation result for the expected number of bit errors. [Figure 10] This figure shows an example of the expected value of the averaged bit error count when the modulation scheme is QPSK. [Figure 11] This figure shows an example of the expected value of the averaged bit error count when the modulation scheme is 16QAM (Quadrature Amplitude Modulation). [Figure 12] This figure shows an example of the fitting result to function g when the modulation scheme is QPSK. [Figure 13] This figure shows an example of the fitting result to function g when the modulation scheme is 16QAM. [Figure 14] This is a flowchart showing the processing procedure of the learning method according to the second embodiment. [Figure 15] This figure shows the evaluation results illustrating the relationship between the number of parameters in a machine learning model and the number of bit errors. [Modes for carrying out the invention]

[0010] The embodiments for carrying out the invention will be described below with reference to the drawings. [First Embodiment] Figure 1 shows an example of a learning method according to the first embodiment. The learning method according to the first embodiment trains a machine learning model to output an estimate of the channel that can reduce the number of bit errors.

[0011] Note that FIG. 1 shows an information processing apparatus 10 for implementing the learning method according to the first embodiment. The information processing apparatus 10 can implement the learning method according to the first embodiment, for example, by executing a learning program.

[0012] The information processing apparatus 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 is, for example, a memory or a storage device included in the information processing apparatus 10. The processing unit 12 is, for example, a processor included in the information processing apparatus 10. The information processing apparatus 10 may include a plurality of processors. One process among the plurality of processes performed by the information processing apparatus 10 and another process may be executed by different processors, respectively.

[0013] The storage unit 11 stores learning data 11a. The learning data 11a includes, for example, a value relating to noise in a propagation path of a transmission signal, a channel value, a position of the transmission signal on a complex plane, and a modulation scheme.

[0014] Received signal y D ) and transmission signal x D ) The relationship is expressed by the following equation (1).

[0015]

Math

[0016] In equation (1), h D represents a channel value, and n represents a complex noise value. “n~CN(0, 2σ 2 )” means that n follows a complex normal distribution with a mean of 0 and a variance of 2σ 2 . Note that 2σ 2 = 10 -SNR[db] / 10 holds. SNR is the signal-to-noise ratio.

[0017] In zero-forcing (ZF: Zero-Forcing) demodulation, a reconstructed transmission signal (x ZF ) is obtained from y D and an estimated channel value (h pUsing ), it can be expressed as follows: (2)

[0018]

number

[0019] Figure 2 shows an example of a reconstructed transmitted signal. In Figure 2, the expected value (E[x[x]) of the reconstructed transmitted signal is shown on the complex plane, where the horizontal axis is the real axis (Re) and the vertical axis is the imaginary axis (Im). ZF ]) but x D It is shown together with x ZF The value of is the real part (Re x ZF ) and the imaginary part (Im x ZF When divided into ), it follows a two-dimensional normal distribution, as shown in equation (3) below.

[0020]

number

[0021] In equation (3), H r ΣH rT This can be expressed using equation (4) as shown in equation (5).

[0022]

number

[0023]

number

[0024] For example, σ in equation (1) can be used as a value relating to the noise contained in the training data 11a. By the way, in the OFDM method, the basic unit of the signal (called RB (Resource Block)) is determined by fixed time intervals and frequency intervals.

[0025] Figure 3 illustrates the basic unit of a signal in the OFDM method. 1RB consists of a 14x12 symbol signal, with 12 symbols in the frequency direction and 14 symbols in the time direction. Furthermore, in the OFDM method, the signal of the symbol at a predetermined position is considered the pilot signal (labeled "PT" in Figure 3). The pilot signal is a known x to the receiving end. D This includes the value (fixed value). Therefore, the Least Square (LS) estimate of the channel in the pilot signal symbol (h ls ) is h ls =y D / x D It can be expressed as follows.

[0026] Figure 4 shows an example of channel estimation using the OFDM method. The estimated channel value H for the entire RB. p One way to obtain this is by using the h symbol in the pilot signal. ls (Figure 4 h) ls 31 ,h ls 33 Using (etc.), the matrix H has the estimated channel values ​​of other symbols set to 0. ls One method is to use two-dimensional linear interpolation.

[0027] Furthermore, as a more accurate estimation method, matrix H ls By treating it as a low-resolution image and performing high-resolution processing using a machine learning model based on a Deep Neural Network (DNN), H p There are methods to obtain this (see, for example, reference 1 below).

[0028] Reference 1: Mehran Soltani, Vahid Pourahmadi, Ali Mirzaei, and Hamid Sheikhzadeh, “Deep Learning-Based Channel Estimation”, IEEE COMMUNICATIONS LETTERS, VOL. 23, NO. 4, APRIL 2019. However, when attempting to accurately estimate channel values ​​using a machine learning model, the number of parameters in the machine learning model increases, leading to increased computational load, memory usage, and overhead.

[0029] On the other hand, to reduce the number of bit errors, it may not be necessary to estimate the channel values ​​with high precision. Figure 5 shows an example of the number of bit errors. In Figure 5, the modulation scheme of the transmitted signal is QPSK (Quadrature Phase Shift Keying), and x D However, an example is shown that lies in region 1 on the complex plane.

[0030] If the modulation scheme is QPSK, x D The bit value of is x D It is represented by which of the regions 1 to 4 on the complex plane it lies in. D However, if both the real and imaginary parts are in the positive region 1, the bit value is "00". D However, if it lies in region 2 where the real part is negative and the imaginary part is positive, the bit value is "10". D However, if the real part is positive and the imaginary part is negative, the bit value is "01". D However, when both the real and imaginary parts are located in the negative region 4, the bit value is "11". In this way, x on the complex plane D The bit value is determined by its position.

[0031] Expected value of the restored transmitted signal (E[x ZF ]) but x D If it is located in the same region as x, no bit error occurs, D If it is located in a different region, a bit error occurs. For example, as shown in Figure 5, E[x ZF ] is x D If it is located in the same region 1 as E[x ZF If ] is located in region 2 or 3, the number of bit errors will be 1, and if it is located in region 4, the number of bit errors will be 2.

[0032] xD When p is located in region 1 on the complex plane, i to x ZF If the value of is the probability that falls into region i, then the expected value of the number of bit errors (E[number of bit errors]) can be expressed as E[number of bit errors] = 0 × p1 + p2 + p3 + 2 × p4.

[0033] p i This can be calculated using the aforementioned two-dimensional normal distribution. For example, p1 can be expressed by the following equation (6) using the error function erf.

[0034]

number

[0035] As mentioned above, x ZF The value of x D If it is located in the same region, the bit error count will be 0. In other words, by improving the accuracy of channel estimation x ZF The value of x D It is sometimes possible to reduce the number of bit errors without having to approach the specified value. By leveraging this degree of flexibility, it is possible to train a machine learning model to reduce the number of bit errors even with a relatively small number of parameters.

[0036] The processing unit 12 executes the learning method, for example, according to the processing procedure shown in the learning program. The processing procedure of the learning method executed by the processing unit 12 is as follows: Step S1: The processing unit 12 determines a first function (hereinafter referred to as the bit error function) that represents the expected number of bit errors in the transmitted signal to be restored. The transmitted signal can be restored from the received signal using the channel estimate, as shown in equation (2).

[0037] As mentioned above, the expected value of the number of bit errors is h p The value of, modulation scheme, value of σ (or SNR), h D value, x D It changes depending on the position. Therefore, the bit error function determined by the processing unit 12 is h pThe value of, modulation scheme, value of σ (or SNR), h D value, x D This is a function that represents the expected number of bit errors determined by the position of the bit. The bit error function is E[number of bit errors]=f(h p ;σ,h D ,x D It can be written as (position, modulation scheme).

[0038] One method is for the processing unit 12 to use the bit error function as the loss function of the machine learning model, where ΣE[number of bit errors]=Σf(h p ;σ,h D ,x D One approach is to train a machine learning model to minimize the position (position, modulation scheme).

[0039] However, in training data 11a, the modulation scheme, σ value, and h are used for the signal of all symbols. D value, x D While the position of is known, when actually reconstructing the transmitted signal, h D value, x D The position is unknown. Which position of x on the complex plane? D Since it is uncertain whether a bit error will be transmitted, an averaged bit error function is used at each position. For example, in the case of the modulation scheme QPSK, the bit error function is 1 / 4(f QPSK,1 +…+f QPSK,4 )(h p ;σ,h D ) is used. f QPSK,i is, x D This is the bit error function when the element is located in region i.

[0040] However, during restoration, h determines the shape of the bit error function. D Since the value of is unknown, h in training data 11a D Using this method to train a machine learning model can lead to overfitting, potentially resulting in a high number of bit errors. Furthermore, averaging the bit error function across channel values ​​increases the complexity of the formula.

[0041] Therefore, in the learning method according to the first embodiment, the processing unit 12 performs the processing from step S2 onward as shown in Figure 1. Step S2: After determining the bit error function, the processing unit 12 uses the training data 11a and the bit error function to determine h p Determine the expected number of bit errors (E[number of bit errors]) for multiple candidates. p h D A value around this value is used. E[bit error count] is determined for each symbol in the training data 11a.

[0042] Figure 1 shows an example of the expected number of bit errors determined for n symbols, represented by multiple sample points. “Re hp-hD” means h p The real part and h D It represents the difference in the real parts, and “Im hp-hD” means h p The imaginary part and h D This represents the difference in the imaginary parts. “E[Number of BE]” represents the expected number of bit errors. The value of σ and h between each symbol. D value, x D The shape of the sample point set differs depending on the position or modulation method.

[0043] Furthermore, if the training data 11a contains 1000 RBs worth of data, the expected value of E[bit error count] is determined for n=14×12×1000 symbols. Step S3: The processing unit 12 determines a second function that approximates the bit error function based on the expected value of the determined number of bit errors.

[0044] For example, the processing unit 12 averages the sample points of the expected number of bit errors for each SNR and modulation scheme. Then, the processing unit 12 determines the function fitted to the averaged sample points as the second function.

[0045] Figure 1 shows an example of the second function obtained when the noise (SNR) range is N1 and the modulation scheme is QPSK. Such a second function is given by E[number of bit errors]=f(hp ;σ,h D ,x D position and modulation scheme), it is a simpler function (for example, a function with fewer parameters).

[0046] Step S4: The processing unit 12 trains a machine learning model that uses the second function as a loss function with the training data 11a. As the machine learning model, for example, DNNs such as CNN (Convolutional Neural Network), RNN (Recurrent Neural Network), and Transformer can be used. The processing unit 12 trains the machine learning model such that the sum of loss functions obtained for each SNR and each modulation scheme is minimized. Accordingly, as shown in FIG. 4, when known channel values of some symbols are input, a machine learning model that outputs channel estimation values for all symbols can be obtained. Information of the machine learning model after training may be stored in the storage unit 11. For example, values of parameters such as weights and biases for each layer of the DNN are stored as information of the machine learning model.

[0047] According to the above training method, as described above, x ZF the value of is located in the same region as x D , the degree of freedom in channel estimation is utilized that the number of bit errors may be zero even if the value of x ZF is not brought close to the value of x D to improve channel estimation accuracy. This degree of freedom is reflected in the second function determined as described above. Furthermore, the second function has a gentler shape than the mean squared error function. By training a machine learning model using this second function as a loss function, the number of bit errors can be reduced even when using a machine learning model with a small number of parameters.

[0048] [Second Embodiment] Next, a second embodiment will be described. In the second embodiment, the information processing device 100 trains a machine learning model to reduce the number of error bits. The machine learning model outputs estimated channel values ​​for all symbols when given known channel values ​​for some symbols as input. The information processing device 10 may be a client device or a server device. The information processing device 100 may also be called a computer.

[0049] Figure 6 is a block diagram showing an example of the hardware of an information processing device. The information processing device 100 includes a processor 101 connected to a bus, RAM (Random Access Memory) 102, HDD (Hard Disk Drive) 103, GPU (Graphics Processing Unit) 104, input interface 105, media reader 106, and communication interface 107. The processor 101 corresponds to the processing unit 12 of the first embodiment. The RAM 102 or HDD 103 corresponds to the storage unit 11 of the first embodiment.

[0050] The processor 101 is a processor such as a GPU or CPU (Central Processing Unit) that includes arithmetic circuits for executing program instructions. The processor 101 loads at least a portion of the program and data stored in the HDD 103 into the RAM 102 and executes the program. The processor 101 may have multiple processor cores. The information processing device 100 may also have multiple processors. The processor that executes one of the multiple processes performed by the information processing device 100 may be different from the processor that executes a different process from the multiple processes. A processor may also be called a processor circuitry. A collection of multiple processors (multiprocessor) may also be called a "processor".

[0051] RAM 102 is a volatile semiconductor memory that temporarily stores programs executed by the processor 101 and data used for calculations by the processor 101. The information processing device 100 may have a type of volatile memory other than RAM.

[0052] The HDD 103 is a non-volatile storage device that stores software programs such as the operating system (OS), middleware, and application software, as well as data. The information processing device 100 may have other types of non-volatile storage, such as flash memory or an SSD (Solid State Drive).

[0053] The GPU 104 works in conjunction with the processor 101 to perform image processing and outputs the image to the display device 104a connected to the information processing device 100. The display device 104a is, for example, a CRT (Cathode Ray Tube) display, a liquid crystal display, an organic EL (Electro Luminescence) display, or a projector. Other types of output devices, such as a printer, may also be connected to the information processing device 100.

[0054] Furthermore, the GPU 104 may be used as a GPGPU (General Purpose Computing on Graphics Processing Unit). The GPU 104 can execute programs in response to instructions from the processor 101. The information processing device 100 may have volatile semiconductor memory other than RAM 102 as GPU memory.

[0055] The input interface 105 receives input signals from an input device 105a connected to the information processing device 100. The input device 105a is, for example, a mouse, a touch panel, or a keyboard. Multiple input devices may be connected to the information processing device 100.

[0056] The media reader 106 is a reading device that reads programs and data recorded on the recording medium 106a. The recording medium 106a is, for example, a magnetic disk, an optical disk, or semiconductor memory. Magnetic disks include flexible disks (FD) and HDDs. Optical disks include CDs (Compact Discs) and DVDs (Digital Versatile Discs). The media reader 106 copies the programs and data read from the recording medium 106a to other recording media such as RAM 102 or HDD 103. The read programs may be executed by the processor 101.

[0057] The recording medium 106a may be a portable recording medium. The recording medium 106a may be used for distributing programs and data. The recording medium 106a and the HDD 103 may also be called computer-readable recording media.

[0058] The communication interface 107 communicates with other information processing devices via the network 107a. The communication interface 107 may be a wired communication interface connected to a wired communication device such as a switch or router, or a wireless communication interface connected to a wireless communication device such as a base station or access point.

[0059] Next, the functions of the information processing device 100 will be described. Figure 7 is a block diagram showing an example of the functions of an information processing device. The information processing device 100 includes a learning data storage unit 110, a bit error function determination unit 111, a simulation unit 112, an approximation function determination unit 113, a machine learning unit 114, and a learning model storage unit 115. The learning data storage unit 110 and the learning model storage unit 115 are implemented using, for example, memory areas allocated in RAM 102 or HDD 103. The bit error function determination unit 111, the simulation unit 112, the approximation function determination unit 113, the machine learning unit 114, and the learning model storage unit 115 are implemented using, for example, program modules executed by the processor 101.

[0060] The learning data storage unit 110 stores learning data. The learning data includes, for example, a value related to noise in a propagation path of a transmission signal, a channel value, a position of the transmission signal on a complex plane, and a modulation scheme.

[0061] The bit error function determining unit 111 determines a bit error function representing an expected value of the number of bit errors in a restored transmission signal. The bit error function is expressed as E[number of bit errors]=f(h p ;σ,h D ,x D position, modulation scheme).

[0062] The simulation unit 112 uses the learning data and the bit error function to determine an expected value of the number of bit errors (E[number of bit errors]) for a plurality of candidates of h p through simulation. Values around h p are used as the plurality of candidates of h D . E[number of bit errors] is determined for each symbol of the learning data. When performing channel estimation in OFDM wireless communication, data of 14×12 symbols per RB is used as learning data (refer to the aforementioned FIG. 3).

[0063] The approximate function determining unit 113 determines an approximate function approximating the bit error function based on the determined expected value of the number of bit errors. The approximate function corresponds to the second function in the first embodiment. A specific example of the method for determining the approximate function will be described later.

[0064] The machine learning unit 114 trains a machine learning model that uses the approximate function as a loss function, using the learning data. As the machine learning model, for example, a DNN such as a CNN, an RNN, or a Transformer can be used. The machine learning unit 114 trains the machine learning model such that the sum of loss functions determined for each SNR and each modulation scheme is minimized.

[0065] The learning model memory unit 115 stores information about the machine learning model after it has been learned (trained). For example, the values ​​of parameters such as weights and biases for each layer of a DNN are stored as information about the machine learning model.

[0066] As described in the first embodiment, in order to reduce the number of bit errors, it is sometimes not necessary to match the estimated value of the channel with the true value of the channel. The reasons for this will be explained in detail below.

[0067] (Reasons why the estimated value of the channel does not need to match the true value of the channel) Below, we consider the problem of minimizing the sum of bit errors in two signals (symbols). This minimization problem is expressed by the following equation (7).

[0068]

number

[0069] In equation (7), f1(h p 1) is the estimated value of the channel (h p This is the expected number of bit errors for 1). f2(h p 2) is the estimated value of the channel (h p This is the expected number of bit errors for (2). θ is a parameter of a DNN, which is an example of a machine learning model. ls 1,h ls 2 is the estimated LS value of the channel in the pilot signal symbol (see Figure 4 above). ls 1,h ls 2 is the input to the DNN.

[0070] Figure 8 shows the relationship between the difference between the estimated and true values ​​of the channel and the expected number of bit errors. The horizontal axis represents the estimated value (h p ) and true value (h D ) difference (h p -h D The real part of ) is on the vertical axis, and h is on the vertical axis. p -h D This represents the imaginary part of the difference between the two.

[0071] Set 120 is h p and h D h p This represents the set. The set 120 is represented by the following equation (8).

[0072]

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[0073] On the other hand, h for which the expected value of the number of bit errors is 0. p The set is represented by the following equation (9).

[0074]

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[0075] h p 1∈D Dist When f1(h p Since 1) = 0, the min of equation (7) θ f1(h p 1) + f2(h p The value of (2) is given by the following equation (10).

[0076]

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[0077] h p 1∈D res When f1(h p Since 1) = 0, the min of equation (7) θ f1(h p 1) + f2(h p The value of (2) is given by the following equation (11).

[0078]

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[0079] Here, D Dist ⊆Dres Therefore, the following relationship (12) holds true.

[0080]

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[0081] In other words, h p 1 to h D If there is little need to get close to 1, the number of bit errors in the other signal can be reduced. Note that f1(h p The same applies if there is no region where 1)=0. In this case, D Dist and D res Instead of equations (8) and (9), this can be expressed by the following equations (13) and (14).

[0082]

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[0083]

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[0084] h p 1∈D Dist When f1(h p 1) Since ≤ ε, the min of equation (7) θ f1(h p 1) + f2(h p The value of (2) is given by the following equation (15).

[0085]

number

[0086] h p 1∈D res When f1(h p 1) Since ≤ ε, the min of equation (7) θ f1(h p 1) + f2(h pThe value of (2) is given by the following equation (16).

[0087]

number

[0088] Here, D Dist ⊆D res If so, the relationship in equation (12) above holds. As mentioned above, x ZF The value of x D If it is located in the same region, the number of bit errors will be 0, so D Dist ⊆D res It can be expected that this will hold true.

[0089] (Example of simulation results for the expected number of bit errors) Figure 9 shows an example of the simulation results for the expected number of bit errors. Figure 9 shows simulation results 130a1 to 130an. “Re hp-hD” means h p The real part and h D It represents the difference in the real parts, and “Im hp-hD” means h p The imaginary part and h D It represents the difference in the imaginary parts. “E[Number of BE]” represents the expected value of the number of bit errors.

[0090] When estimating the channel in OFDM wireless communication, for example, using 1000 RBs of training data, the expected number of bit errors is determined for each of the n = 14 × 12 × 1000 symbols. The shape of the set of sample points is determined by the h of the training data. p The value of, modulation scheme, value of σ (or SNR), h D value, or x D It varies depending on the location.

[0091] (Example of a method for determining an approximation function) The approximation function determination unit 113 averages the expected number of bit errors for each SNR or modulation scheme.

[0092] Figure 10 shows an example of the expected value of the averaged bit error when the modulation scheme is QPSK. Figure 11 shows an example of the expected value of the averaged bit error when the modulation scheme is 16QAM. In Figures 10 and 11, various h over multiple SNR ranges are shown. P The calculation results of the expected number of bit errors averaged over the given values ​​are shown. In the examples in Figures 10 and 11, averaging is performed for each 1 dB SNR range.

[0093] In Figure 10, calculation result 140a1 is the calculated expected value of the averaged number of bit errors for a modulation scheme of QPSK with an SNR of -10dB or higher and less than -9dB. Calculation result 140a2 is the calculated expected value of the averaged number of bit errors for a modulation scheme of QPSK with an SNR of 10dB or higher and less than 11dB. Calculation result 140a3 is the calculated expected value of the averaged number of bit errors for a modulation scheme of QPSK with an SNR of 29dB or higher and less than 30dB.

[0094] In Figure 11, calculation result 140b1 is the calculated expected value of the average number of bit errors for a modulation scheme of 16QAM with an SNR of -10dB or higher and less than -9dB. Calculation result 140b2 is the calculated expected value of the average number of bit errors for a modulation scheme of 16QAM with an SNR of 10dB or higher and less than 11dB. Calculation result 140b3 is the calculated expected value of the average number of bit errors for a modulation scheme of 16QAM with an SNR of 29dB or higher and less than 30dB.

[0095] The shape of the set of sample points representing the averaged expected number of bit errors is less pronounced than the shape of the set of expected number of bit errors shown in Figure 9. Next, the approximation function determination unit 113 determines an approximation function that approximates the error bit function by performing function fitting on the averaged expected value. The set of sample points shown in Figures 10 and 11 fits well to a function g represented by, for example, the following equation (17).

[0096]

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[0097] Function g is an extension of the Easom function. i ya c i These are the fitting parameters. Figure 12 shows an example of fitting results to function g when the modulation scheme is QPSK. Figure 13 shows an example of fitting results to function g when the modulation scheme is 16QAM. Figures 12 and 13 show the fitting results to the calculated expected value of the averaged number of bit errors for multiple SNR ranges shown in Figures 10 and 11.

[0098] In Figure 12, fitting results 150a1 and 150b1 are fitting results for calculation result 140a1, which is the expected value of the averaged number of bit errors with a modulation scheme of QPSK and an SNR of -10dB or higher and less than -9dB. Fitting results 150a2 and 150b2 are fitting results for calculation result 140a2, which is the expected value of the averaged number of bit errors with a modulation scheme of QPSK and an SNR of 10dB or higher and less than 11dB. Fitting results 150a3 and 150b3 are fitting results for calculation result 140a3, which is the expected value of the averaged number of bit errors with a modulation scheme of QPSK and an SNR of 29dB or higher and less than 30dB. Fitting results 150b1 to 150b3 are simplified representations of fitting results 150a1 to 150a3 viewed from a different perspective.

[0099] In Figure 13, fitting results 151a1 and 151b1 are fitting results for calculation result 140b1, which is the expected value of the averaged number of bit errors for a modulation scheme of 16QAM in the range of -10dB to less than -9dB. Fitting results 151a2 and 151b2 are fitting results for calculation result 140b2, which is the expected value of the averaged number of bit errors for a modulation scheme of 16QAM in the range of 10dB to less than 11dB. Fitting results 151a3 and 151b3 are fitting results for calculation result 140b3, which is the expected value of the averaged number of bit errors for a modulation scheme of 16QAM in the range of 29dB to less than 30dB. Note that fitting results 151b1 to 151b3 are simplified representations of fitting results 151a1 to 151a3 viewed from a different perspective.

[0100] As shown in Figures 12 and 13, in both fitting results, h p -h D The function value is minimized when the real and imaginary parts are 0. Furthermore, the shape of the function obtained from the fitting results is sharper when using 16QAM than when using QPSK. Also, in 16QAM, the shape becomes sharper as the SNR value increases.

[0101] Another example of an approximation function is h p -h D We can use a function that takes its minimum value when both the real and imaginary parts are 0, and which is also a downward-facing parabola. An example of such a function is the Sphere function.

[0102] (Learning method steps) Figure 14 is a flowchart showing the processing procedure of the learning method according to the second embodiment. Step S10: The information processing device 100 acquires training data. The training data may be acquired from the recording medium 106a or acquired (received) from another computer via the network 107a. The acquired training data is stored in the RAM 102 or HDD 103.

[0103] Step S11: The information processing device 100 uses a bit error function (E[number of bit errors]=f(h) that represents the expected number of bit errors in the transmitted signal to be restored. p ;σ,h D ,x D Determine the position and modulation scheme.

[0104] Step S12: The information processing device 100 uses the training data and bit error function to perform a simulation, as shown in Figure 9, h p Determine the expected number of bit errors (E[number of bit errors]) for multiple candidates.

[0105] Step S13: The information processing device 100 averages the expected number of bit errors for each modulation scheme or SNR, as shown in Figures 10 and 11. Step S14: The information processing device 100 determines the approximate function by fitting the function g to sample points of the expected value of the averaged number of bit errors, as shown in Figures 12 and 13.

[0106] Step S15: The information processing device 100 trains a machine learning model using the training data, with the approximation function as the loss function. The information processing device 100 trains the machine learning model so that the sum of the loss functions obtained for each SNR and modulation scheme (sum of functions g (Σg)) is minimized. As a result, a machine learning model is obtained that outputs estimated channel values ​​for all symbols when known channel values ​​for some symbols are input, as shown in Figure 4.

[0107] The obtained machine learning model information (for example, parameter values ​​such as weights and biases for each layer of the DNN) is stored, for example, in RAM 102 or HDD 103. The machine learning model information may also be transmitted to other computers via network 107a.

[0108] This completes the processing of the learning method according to the second embodiment. The information processing device 100 then uses the learned machine learning model to estimate the channel LS value (h) of the pilot signal symbol in RB. ls ) An inference process may be performed to obtain an estimate of the total channel of RB. Furthermore, the information processing device 100 may reconstruct the transmitted signal based on the channel estimate obtained in the inference process and the received signal.

[0109] (Evaluation results) Figure 15 shows the evaluation results illustrating the relationship between the number of parameters and the number of bit errors in a machine learning model. As mentioned above, in Figure 15, matrix H ls By treating it as a low-resolution image and performing high-resolution processing using a DNN-based machine learning model, H p The evaluation results obtained using a conventional method are compared with the evaluation results obtained using the method of this embodiment.

[0110] When the number of parameters is reduced, applying the method of this embodiment results in fewer bit errors than conventional methods. In other words, by applying the method of this embodiment, the number of bit errors can be suppressed even when the number of parameters is reduced and overhead is decreased.

[0111] The above describes one aspect of the learning program, learning method, and information processing device of the present invention based on embodiments, but these are merely examples and the invention is not limited to those described above. [Explanation of symbols]

[0112] 10 Information Processing Devices 11 Storage section 11a Training data 12 Processing Units

Claims

1. Using the estimated channel, we determine a first function that represents the expected number of bit errors in the transmitted signal reconstructed from the received signal. The expected values ​​for multiple candidate estimates are determined using the training data and the first function. Based on the determined expected value, a second function is determined that approximates the first function. A machine learning model with the second function described above as the loss function is trained using the training data. A learning program that instructs a computer to perform a task.

2. The learning program according to claim 1, wherein the value of the first function is determined according to the estimated value, the value relating to noise in the propagation path of the transmitted signal, the value of the channel, the position of the transmitted signal in the complex plane, or the modulation scheme.

3. The learning program according to claim 1, wherein the learning data includes values ​​relating to noise in the propagation path of the transmitted signal, the channel value, the position of the transmitted signal in the complex plane, and the modulation scheme.

4. The process for determining the second function is as follows: A process to average the expected values ​​for each noise value in the propagation path of the transmitted signal, or for each modulation scheme, The process involves determining the second function by performing function fitting on the averaged expected value, The learning program according to claim 1, including the following:

5. The learning program according to claim 4, wherein the function fitting is performed using the Easom function.

6. The learning program according to claim 4, wherein the learning process for learning the machine learning model is performed such that the sum of the second function determined for each of the noise values ​​or each of the modulation schemes is minimized.

7. Computers Using the estimated channel, we determine a first function that represents the expected number of bit errors in the transmitted signal reconstructed from the received signal. The expected values ​​for multiple candidate estimates are determined using the training data and the first function. Based on the determined expected value, a second function is determined that approximates the first function. A machine learning model with the second function described above as the loss function is trained using the training data. Learning methods.

8. A memory unit that stores learning data, A processing unit that determines a first function representing the expected number of bit errors in a transmitted signal reconstructed from a received signal using channel estimates, determines the expected values ​​for a plurality of candidate estimates using the training data and the first function, determines a second function that approximates the first function based on the determined expected values, and trains a machine learning model using the training data with the second function as the loss function. An information processing device having

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