Channel estimation program, channel estimation method, and information processing device

Abstract

Reduce the number of bit errors. [Solution] The processing unit 12 calculates the estimated value of the channel (h p Using a first function that represents the expected number of bit errors (E[number of bit errors]) in the transmitted signal reconstructed from the received signal using ), the first value (h) of the channel that minimizes this expected value is determined. Emin A second function (a) determines the first value and finds a correction value whose product with the true value of the channel is the first value. * Using (h,σ), the first correction value (a) for the first estimate of the channel * (h p Determine σ).

Description

[Technical Field]

[0001] The present invention relates to a channel estimation program, a channel estimation 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, techniques have been proposed to estimate transmission path coefficients based on the signal output by a filter that suppresses signal components in a specific frequency band of the received signal in a wireless communication system (see, for example, Patent Document 1). Furthermore, techniques have been proposed to correct channel estimates by multiplying them by carrier frequency offset estimates (see, for example, Patent Document 2). Additionally, techniques have been proposed to calculate weighting coefficients that minimize the bit error rate when maximum likelihood detection is performed in the receiver, multiply these coefficients by the modulated signal, and output them as the transmitted signal (see, for example, Patent Document 3). Finally, techniques have been proposed to determine the number of subcarriers that minimizes the average bit error rate (see, for example, Patent Document 4).

[0004] Furthermore, methods have been proposed to estimate channel values ​​using machine learning models based on DNNs (Deep Neural Networks) (see, for example, Non-Patent Document 1). [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2013-141142 [Patent Document 2] U.S. Patent Application Publication No. 2004 / 0156422 [Patent Document 3] Japanese Patent Publication No. 2007-306532 [Patent Document 4] U.S. Patent Application Publication No. 2009 / 0147749 [Non-patent literature]

[0006] [Non-Patent Document 1] Mehran Soltani, Vahid Pourahmadi, Ali Mirzaei, and Hamid Sheikhzadeh,“Deep Learning-Based Channel Estimation”, IEEE COMMUNICATIONS LETTERS, VOL. 23, NO. 4, APRIL 2019 [Overview of the project] [Problems that the invention aims to solve]

[0007] Even when machine learning models are used to accurately estimate channel values, the estimated channel value that minimizes the expected number of bit errors may differ from the true channel value. One aspect of this is the aim to reduce the number of bit errors. [Means for solving the problem]

[0008] In one aspect, a channel estimation program is provided that causes a computer to perform the following steps: determine a first value of the channel that minimizes the expected number of bit errors in a transmitted signal reconstructed from a received signal using an estimated channel value, using a first function that represents the expected number of bit errors in the transmitted signal reconstructed from a received signal using an estimated channel value; and determine a first correction value for the first estimated channel value using a second function that finds a correction value whose product with the true value of the channel is the first value. [Effects of the Invention]

[0009] One aspect is that it can reduce the number of bit errors. [Brief explanation of the drawing]

[0010] [Figure 1] This figure shows an example of a channel estimation 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 diagram shows the relationship between the transmitted signal and the reconstructed transmitted signal. [Figure 9] This figure shows the relationship between the transmitted signal and the reconstructed transmitted signal when a=1. [Figure 10] This diagram shows the relationship between the transmitted signal and the reconstructed transmitted signal when a > 1. [Figure 11] This figure shows an example of generating the function a*(h,σ). [Figure 12] This figure shows an example of correcting channel estimates. [Figure 13] This is a flowchart showing the processing procedure for the channel estimation method according to the second embodiment. [Figure 14] 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]

[0011] 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 channel estimation method according to the first embodiment. The channel estimation method according to the first embodiment is a method for obtaining an estimated channel value that can reduce the number of bit errors.

[0012] Figure 1 shows an information processing device 10 for implementing the channel estimation method according to the first embodiment. The information processing device 10 can implement the channel estimation method according to the first embodiment by, for example, executing a channel estimation program.

[0013] The information processing device 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 is, for example, a memory or storage device of the information processing device 10. The processing unit 12 is, for example, a processor of the information processing device 10. The information processing device 10 may have multiple processors. Some of the multiple processes performed by the information processing device 10 may be executed on different processors.

[0014] The memory unit 11 stores the learning data 11a. The learning data 11a includes, for example, values ​​related to noise in the propagation path of the transmitted signal, the true value of the channel, the position of the transmitted signal in the complex plane, and the modulation scheme.

[0015] Received signal (y D ) and the transmitted signal (x D The relationship between ) is expressed by the following equation (1).

[0016]

number

[0017] In equation (1), h D represents the true value of the channel, and n represents the complex noise value. “n~CN(0,2σ 2 )” means that n has a mean of 0 and a variance of 2σ. 2 This means it follows a complex normal distribution. Note that 2σ 2 =10 -SNR[db] / 10 SNR stands for signal-to-noise ratio.

[0018] In Zero-Forcing (ZF) demodulation, the transmitted signal x ZF ) to be restored is represented by y D and the channel estimation value h p ) according to the following Equation (2).

[0019]

Mathematics

[0020] Figure 2 is a diagram showing an example of a restored transmitted signal. In Figure 2, on a complex plane where the horizontal axis represents the real axis (Re) and the vertical axis represents the imaginary axis (Im), the expected value (E[x ZF ) of the restored transmitted signal is shown together with the value of x D . In Figure 2, circle 17 represents the magnitude of variance caused by x ZF .

[0021] x ZF 's value, when separated into the real part (Re x ZF ) and the imaginary part (Im x ZF ), follows a two-dimensional normal distribution as represented by the following Equation (3).

[0022]

Mathematics

[0023] In Equation (3), H r ΣH rT can be expressed as Equation (5) using Equation (4).

[0024]

Mathematics

[0025]

Mathematics

[0026] 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.

[0027] 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 system, 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.

[0028] Figure 4 shows an example of channel estimation using the OFDM method. The matrix H represents the estimated channel values ​​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.

[0029] 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 DNN-based machine learning model, the matrix H p There is a method to obtain this. The machine learning model uses matrix H p and the matrix H representing the true values ​​of the channel D The Euclidean distance between (||H) and (||H) D -H p The system is trained to minimize ||2).

[0030] However, even when machine learning models are used to accurately estimate channel values, the estimated channel value that minimizes the expected number of bit errors may differ from the true channel value. The reason for this will be explained later (see Figures 8-10).

[0031] Therefore, one approach is to consider the matrix of channel values ​​that minimizes the expected value of bit errors as the image, and then compare that matrix with matrix H p One approach is to train a machine learning model so that the Euclidean distance between the two points is minimized.

[0032] However, as mentioned above, machine learning models for channel estimation use low-resolution images (matrix H ls From ) the true image (matrix H D This attempts to reconstruct the image. Therefore, machine learning models that attempt to reconstruct an image different from the true image may not be able to learn sufficiently, which can result in an increase in the number of bit errors.

[0033] Therefore, in the channel estimation method according to the first embodiment, the processing unit 12 performs the following processing. The processing unit 12 performs the channel estimation method according to the processing procedure shown in the channel estimation program, for example. The processing procedure of the channel estimation method performed by the processing unit 12 is as follows.

[0034] Step S1: The processing unit 12 uses a first function that represents the expected value of the number of bit errors (E[number of bit errors]) in the transmitted signal reconstructed from the received signal using the estimated channel value to determine the first value of the channel that minimizes this expected value. Hereinafter, the first function will be called the bit error function. Also, the first value is h Emin This is how it is written. The transmitted signal is given by the estimated channel (h) as in equation (2). p It can be reconstructed from the received signal using ).

[0035] The expected value of the number of bit errors is h p The value of, modulation scheme, value of σ (or SNR), h D The value of x on the complex planeD It changes depending on the position. Figure 5 shows an example of the number of bit errors. In Figure 5, the modulation scheme is QPSK (Quadrature Phase Shift Keying), and x D An example is shown where the value of lies in region 1 on the complex plane.

[0036] 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.

[0037] 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.

[0038] x D 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.

[0039] 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.

[0040]

number

[0041] The bit error function is h p The value of σ (or SNR), h D value, x D This is a function that represents the expected number of bit errors, which is determined according to the position and modulation scheme. The bit error function is given by E[number of bit errors]=f(h p ;σ,h D ,x D It can be expressed as (position, modulation scheme). The bit error function accurately represents the expected number of bit errors for the estimated channel.

[0042] The processing unit 12 determines the value of σ (or SNR), h D value, x D The learning data 11a, whose position and modulation scheme are known, is applied to the bit error function. Then the processing unit 12 h D Multiple h around p By calculating E[bit error count] for the value of , we can determine the channel value that minimizes E[bit error count].

[0043] Figure 1 shows an example of the calculation result of the expected value of E [bit error count] using multiple sample points. In calculation results 15a and 15b, “Re hp-hD” is 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 value of the number of bit errors. Calculation result 15b is the result of looking at calculation result 15a from a different perspective.

[0044] In the example of calculation result 15b, the sample point 16 is among a plurality of h p values, h Emin represents . For h at sample point 16 Emin is h p -h D is 0, h p is different from that. That is, h Emi ≠h D .

[0045] Note that when the learning data 11a includes data for 1000 RB, for example, for n=14×12×1000 symbols, the expected value of E[number of bit errors] is calculated. The shape of the set of sample points differs depending on the value of σ, the value of h D value, x D position, or the difference in modulation scheme.

[0046] Step S2: The processing unit 12 uses a second function (hereinafter, function a * expressed as (h,σ)) to determine a correction value (a p ) for a certain estimated channel value (h * (h p ,σ)). Function a * (h,σ) is a function representing a correction value whose product with the true channel value (h D ) is h Emin .

[0047] The estimated channel value (h p ) is acquired from a trained machine learning model that estimates the true channel value (h D ). For example, as shown in Fig. 4, the machine learning model regards the matrix H ls as a low-resolution image, and is a DNN-based machine learning model that obtains the matrix H p by performing high-resolution processing. The machine learning model uses the matrix H p and the matrix H representing the true channel value D Euclidean distance between (||H D -H p ||2) is learned (trained) to be minimized.

[0048] Furthermore, machine learning models such as CNNs (Convolutional Neural Networks), RNNs (Recurrent Neural Networks), and DNNs such as Transformers can be used. Information about the machine learning model may be stored in the memory unit 11. For example, the values ​​of parameters such as weights and biases for each layer of the DNN may be stored as information about the machine learning model.

[0049] The processing unit 12 calculates values ​​related to noise in the propagation path of the transmitted signal (for example, variance (σ)). 2 )) and h D h according to the value Emin Based on the value of function a * (h,σ) can be determined. The value related to noise and h D The value of h Emin The value is obtained from the calculation result of the process in step S1.

[0050] function a * Let (h,σ), for example, a * (h,σ) = a1(σ) 2 -a2)exp(a3|h|)+a4 can be used. a1~a4 are fitting parameters. Function a * A more specific example of how to determine (h,σ) will be discussed later (see Figure 11).

[0051] Step S3: The processing unit 12 calculates the estimated value of the channel (h p ) for which the correction value (a * (h p The estimated value is corrected by multiplying it by σ). This completes the channel estimation method process. The processing unit 12 then uses the corrected channel estimate obtained in step S3 to calculate the transmission signal (x) using equation (2). ZF You may restore the value of ).

[0052] According to the channel estimation method described above, the channel value (h) that minimizes the expected number of bit errors is EminThe true value of the channel (h) is predetermined. D The product of ) is h Emin Function a represents the correction value that results in this. * Using (h,σ), estimate the channel (h p Correction value a for ) * (h p ,σ) is determined. This determines h D and h Emin The increase in the number of bit errors caused by the difference can be suppressed, and the number of bit errors can be reduced. Also, the predetermined function a * By using (h,σ), the computational load when correcting the channel estimate can be reduced.

[0053] [Second Embodiment] Next, a second embodiment will be described. The information processing device 100 of the second embodiment determines an estimated number of channels that can reduce the number of bit errors. The information processing device 100 may be a client device or a server device. The information processing device 100 may also be called a computer.

[0054] 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.

[0055] 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".

[0056] 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.

[0057] 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).

[0058] 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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.

[0063] 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.

[0064] 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, h Emin Determination unit 111, function a * (h,σ) determination unit 112, learning model memory unit 113, channel estimation unit 114, correction value determination unit 115, h p It has a correction unit 116.

[0065] The learning data storage unit 110 and the learning model storage unit 113 are implemented using, for example, memory areas allocated in RAM 102 or HDD 103. Emin Determination unit 111, function a * (h,σ) determination unit 112, channel estimation unit 114, correction value determination unit 115, h p The correction unit 116 is implemented, for example, using a program module executed by the processor 101.

[0066] The learning data storage unit 110 stores learning data. The learning data includes, for example, values ​​related to noise in the propagation path of the transmitted signal, the true value of the channel, the position of the transmitted signal in the complex plane, and the modulation scheme.

[0067] h Emin The determination unit 111 determines the value of the channel that minimizes the expected value of the number of bit errors (E[number of bit errors]) h Emin Determine h Emin The determination unit 111 applies the above-mentioned learning data to the bit error function shown in the first embodiment, h D Multiple h around p By calculating E[bit error count] for the value of h Emin To decide.

[0068] function a * The (h,σ) determination unit 112 determines the function a * Determine (h,σ). Function a * (h,σ) is the true value of the channel (h DThe product of ) is h Emin This is a function that represents the correction value. Function a * The (h,σ) determination unit 112 determines the variance (σ 2 ) and h D The value of h Emin Based on the value of function a * (h,σ) can be determined. Variance (σ) 2 ) and h D h according to the value Emin The value of h Emin This is obtained from the calculation results by the determination unit 111.

[0069] The learning model memory unit 113 stores information about the trained machine learning model. For example, a CNN, RNN, or DNN such as a Transformer can be used as the machine learning model.

[0070] When performing channel estimation in the OFDM method, the machine learning model uses a matrix H, for example, as shown in Figure 4. ls By treating it as a low-resolution image and performing high-resolution processing, matrix H p This is a machine learning model using a DNN that obtains the matrix H. p and the matrix H representing the true values ​​of the channel D The Euclidean distance between (||H) and (||H) D -H p The model is trained to minimize ||2). Information about a trained machine learning model includes, for example, the values ​​of parameters such as the weights and biases for each layer of the DNN.

[0071] The channel estimation unit 114 uses the trained machine learning model to h p The channel estimation unit 114 estimates, for example, matrix H in the machine learning model. ls Input the matrix H from the machine learning model. p Obtain the matrix H. p The h of each symbol p Includes.

[0072] The correction value determination unit 115 determines the function a *Using (h,σ), the h obtained by the estimation unit 144 p Correction value for (a * (h p Determine σ). h p The correction unit 116 uses the h estimated by the channel estimation unit 114. p The correction value determination unit 115 multiplies this by the correction value determined by the correction value determination unit 115, p Correct it.

[0073] (h Emin ga h D (For different reasons) As described in the first embodiment, the channel value (h) that minimizes the expected number of bit errors is Emin ) is h D This may not always be the case. The reasons for this are explained below.

[0074] Figure 8 shows the relationship between the transmitted signal and the reconstructed transmitted signal. Figure 8 shows an example where the modulation scheme is 16QAM (Quadrature Amplitude Modulation). The transmitted signal to be restored (x ZF ) is expressed by the above equation (2). The expected value of the number of bit errors is h p =ah D The minimum occurs when a > 0. Using a, equation (2) can be expressed as equation (7) below.

[0075]

number

[0076] However, when a < 1, from equation (7), the restored transmitted signal (x ZF The value of the transmitted signal (x D The deviation from the value of ) becomes larger. Also, the magnitude of the noise increases. Therefore, the expected value of the bit error count deteriorates.

[0077] Figure 9 shows the relationship between the transmitted signal and the reconstructed transmitted signal when a=1. If a=1, hp =h D The transmitted signal (x ZF The value of the transmitted signal (x D This matches the value of ). In Figure 9, circle 120 is x ZF Variance due to (σ 2 This represents the size of x. In 16QAM, x ZF The variance of the function increases as you move away from the origin where both the imaginary and real parts are zero.

[0078] Figure 10 shows the relationship between the transmitted signal and the reconstructed transmitted signal when a > 1. When a > 1, x ZF The value of x D Although the deviation from the value becomes larger, the variance represented by circle 121 becomes smaller than when a=1, resulting in a smaller noise level. Therefore, the expected value of the bit error count may be smaller than when a=1.

[0079] For these reasons, the channel value (h) that minimizes the expected number of bit errors is Emin ) but, h D This may differ. (function a * (Example of generating (h,σ)) Figure 11 shows the function a * This figure shows an example of generating (h,σ). Figure 11 shows h D The absolute value of (denoted as |h|) and σ 2 a according to the value * An example of the calculation result is shown using multiple sample points. * is, h D ×a * =h Emin It is a scalar value that satisfies the following condition.

[0080] Variance (σ 2 ) and h D h according to the value Emin The value of h Emin This is obtained from the calculation results by the determination unit 111. * is, a * =h Emin / h DIt can be obtained from the formula. By performing a function fitting on a set of sample points as shown in Figure 11, the function a * (h,σ) is obtained. Function a * Let (h,σ), for example, a * (h,σ) = a1(σ) 2 -a2)exp(a3|h|)+a4 can be used. a1~a4 are fitting parameters. In Figure 11, the fitted function a * (h,σ) is shown. In the fitting results in Figure 11, the RMSE (Root Mean Squared Error) is 0.272, which represents the set of sample points relatively well.

[0081] (Example of correcting channel estimates) Figure 12 shows an example of correcting the estimated channel value. The channel estimation unit 114 applies a matrix H as shown in Figure 4 to the trained machine learning model 130. ls By inputting, matrix H p Obtain the following. Machine learning model 130 uses matrix H p and matrix H D Since it is learned to minimize the Euclidean distance between and , matrix H p h of each symbol included p The value of h D It will be approximately equal to the value of .

[0082] function a * (h,σ) is the true value of the channel (h D The product of ) is h Emin To represent the correction value, matrix H D Each h D Function a corresponding to * By multiplying by the value of (h,σ), h Emin Matrix H Emin You can obtain this.

[0083] When restoring the transmitted signal, h D This is unknown. Therefore, matrix H p Each h p Function a for* (h,σ) value (correction value a) * (h p The correction is performed by multiplying by σ). As shown in Figure 12, the matrix H before correction p The matrix X of the transmitted signal is reconstructed using this method. ZF X ZF =Y D / H p This is expressed as follows. In contrast, the matrix H of the corrected transmitted signal p ×a * (h p The matrix X of the transmitted signal is reconstructed using σ. ZF* X ZF* =Y D / H p ×a * (h p It is expressed as σ).

[0084] (Estimation method procedure) Figure 13 is a flowchart showing the processing procedure of the channel estimation method according to the second embodiment.

[0085] 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.

[0086] Step S11: The information processing device 100 applies the above training data to the bit error function, h D Multiple h around p By calculating E[bit error count] for the value of h Emin To decide.

[0087] Step S12: The information processing device 100 is h Emin Based on the calculation results, for example, by the method shown in Figure 11, the function a * Determine (h, σ). Step S13: The information processing device 100 uses the trained machine learning model to h p We estimate this.

[0088] Step S14: The information processing device 100 performs function a * Using (h,σ), the h obtained by the estimation unit 144 p Correction value for (a * (h p Determine σ). Step S15: The information processing device 100 processes the h estimated in the processing of step S13. p In contrast, the a determined in the process of step S14 * (h p By multiplying by σ, h p Correct it.

[0089] The information processing device 100 uses, for example, a matrix H as shown in Figure 12. p h of each symbol p The corrected value may be stored in RAM102 or HDD103. h p The corrected value may be transmitted to another computer via network 107a.

[0090] This concludes the processing of the channel estimation method according to the second embodiment. The information processing device 100 then processes the corrected h p Using the transmission signal (x ZF ) may be restored. According to the channel estimation method of the second embodiment, the true value of the channel (h D The product of ) is h Emin Function a represents the correction value that results in this. * (h,σ) is predetermined, and function a * Estimated channel (h) using (h,σ) p Correction value a for ) * (h p ,σ) is determined. This determines h D and h Emin The increase in the number of bit errors caused by the difference can be suppressed, and the number of bit errors can be reduced. Also, the predetermined function a * By using (h,σ), the computational load when correcting the channel estimate can be reduced.

[0091] (Evaluation results) Figure 14 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 14, matrix H ls By treating it as a low-resolution image and performing high-resolution processing using a DNN-based machine learning model, the matrix H p The evaluation results obtained using a conventional method are compared with the evaluation results obtained using the method of this embodiment.

[0092] As shown in Figure 14, applying the method of this embodiment results in fewer bit errors than the conventional method. In other words, the number of bit errors can be reduced by applying the method of this embodiment.

[0093] (modified version) The machine learning model may be trained using a function that approximates the bit error function as the loss function, based on the simulation results using the above bit error function (for example, calculation results 15a, 15b shown in Figure 1). For example, a function g such as the one in equation (8) below can be used.

[0094]

number

[0095] Function g is an extension of the Easom function. i ya c i These are the fitting parameters. The machine learning model is trained to minimize the sum of the functions g determined for each SNR and modulation scheme.

[0096] The value of such a function g is h p =h D Since it is minimized when, similar to the channel estimation method according to the second embodiment, the function a * A correction using (h,σ) can be applied. 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]

[0097] 10 Information Processing Devices 11 Storage section 11a Training data 12 Processing Units 15a,15b Calculation results 16 sample points

Claims

1. Using a first function that represents the expected number of bit errors in the transmitted signal reconstructed from the received signal using the estimated channel value, a first value of the channel that minimizes the expected value is determined. A first correction value for the first estimated value of the channel is determined using a second function that finds a correction value whose product with the true value of the channel is the first value. A channel estimation program that uses a computer to perform the processing.

2. The channel estimation program according to claim 1, which corrects the first estimated value by multiplying the first estimated value by the first correction value.

3. The channel estimation program according to claim 1, wherein the second function is determined based on the first value corresponding to the true value and a value relating to noise in the propagation path of the transmitted signal.

4. The channel estimation 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 true value, the position of the transmitted signal in the complex plane, or the modulation scheme.

5. The channel estimation program according to claim 1, wherein the first estimated value is obtained from a trained machine learning model that estimates the true value.

6. Computers Using a first function that represents the expected number of bit errors in the transmitted signal reconstructed from the received signal using the estimated channel value, a first value of the channel that minimizes the expected value is determined. A first correction value for the first estimated value of the channel is determined using a second function that finds a correction value whose product with the true value of the channel is the first value. Channel estimation method.

7. A processing unit that determines a first value of the channel that minimizes the expected number of bit errors in the transmitted signal reconstructed from the received signal using the estimated value of the channel, using a first function that represents the expected value of the number of bit errors in the transmitted signal reconstructed from the received signal using the estimated value of the channel, and determines a first correction value for the first estimated value of the channel using a second function that finds a correction value whose product with the true value of the channel is the first value, An information processing device having

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