A carrier frequency offset estimation method based on fully connected neural network

Abstract

The present invention relates to a carrier frequency offset estimation method based on a fully connected neural network. By utilizing a fully connected neural network, carrier frequency offset estimation is performed directly based on the data portion of the received signal in a data-driven manner. This problem is considered a regression problem. The main processing steps are: first, feature extraction is performed from the received signal affected by the carrier frequency offset at the receiver to obtain sample features for training the neural network; then, the neural network is trained using the samples, and a gradient descent algorithm is executed to find the optimal parameters; finally, the trained neural network is used on a test set to estimate the carrier frequency offset. Simulations show that compared with traditional carrier frequency offset estimation methods, the present invention can improve bandwidth efficiency and achieve higher estimation accuracy.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a carrier frequency offset estimation method based on a fully connected neural network in an orthogonal frequency division multiplexing communication system. Background Art

[0002] Orthogonal Frequency Division Multiplexing (OFDM) has been widely used in mobile communication systems (such as 4G and 5G) because of its high spectrum utilization and ability to combat multipath effects. The basic idea of ​​the OFDM system is to use multiple subcarriers for parallel transmission, and introduce a cyclic prefix (CP) to make the signal resistant to multipath fading. The OFDM system does not use a separate bandwidth-limiting filter and oscillator for each subchannel. Instead, it uses multi-carrier modulation to make the subcarriers overlap with each other in the spectrum, thereby transmitting high-speed serial data in parallel at a low speed, improving the spectrum efficiency of the system during transmission. Multiple subcarrier signals that overlap in the spectrum can be generated using the Nyquist criterion, but this method is complex to implement, has high hardware costs, and is not suitable for practical applications. The success of the OFDM system is based on the digital implementation of analog methods, that is, the modulation and demodulation of OFDM are realized by using the inverse discrete Fourier transform (IDFT) and discrete Fourier transform (DFT) respectively. In order to improve the computational efficiency of the system, the inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) are generally used instead of IDFT and DFT.

[0003] To achieve parallel transmission of multiple carriers, OFDM technology must ensure strict orthogonality between the subcarriers. However, during OFDM signal transmission, due to the inherent physical characteristics of the crystal oscillators used to generate carriers in the transmitter and receiver, it is difficult to generate carriers with the same frequency. Therefore, OFDM signals are affected by carrier frequency offset (CFO). CFO destroys the orthogonality between the subcarriers of the OFDM signal, causing inter-carrier interference (ICI). As a result, the original signal cannot be accurately restored at the receiving end, which reduces the performance of the OFDM communication system.

[0004] Regarding carrier frequency offset estimation, traditional cyclic prefix-based CFO estimation methods utilize the phase difference between the cyclic prefix in the received signal and the repeated portion of the OFDM signal. This method's estimation accuracy is affected by the cyclic prefix length: the longer the cyclic prefix, the more accurate the CFO estimation result. However, as additional data beyond the valid data, the cyclic prefix occupies a certain amount of channel bandwidth during signal transmission and increases computational overhead. Therefore, the primary problem addressed by the present invention is how to more accurately estimate the carrier frequency offset from the received signal while conserving communication bandwidth. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a carrier frequency offset estimation method based on a fully connected neural network, which can more accurately estimate the carrier frequency offset from a received signal while saving communication bandwidth.

[0006] The technical solution adopted by the present invention is a carrier frequency offset estimation method based on a fully connected neural network, which comprises the following steps:

[0007] S1. In the OFDM system of point-to-point communication, the transmitter sends a string of random information bit sequences S = {b1, b2, ..., b s}, where b s ∈{0,1}, s is the number of information bits sent by the transmitter at one time;

[0008] S2. Perform baseband signal modulation on the information bit sequence S. The information bit sequence S is mapped to constellation symbols X = {X[1], X[2], ..., X[k]}, where k is the number of constellation symbols. M represents the baseband signal modulation order; performing an inverse discrete Fourier transform (IFFT) on the constellation symbol to obtain an OFDM symbol, the expression of the lth OFDM symbol is: in, N represents the number of IFFT points, x l [n] represents the nth time domain sampling point in the lth OFDM symbol, 1≤n≤N; a length of N is added before the OFDM symbol. cp The length of the OFDM symbol after adding the cyclic prefix is: N s =N cp +N; the OFDM symbol after adding the cyclic prefix is ​​transmitted in the channel and received by the receiver; the expression of the lth OFDM symbol received by the receiver affected by the channel and the carrier frequency offset is: in, Represents the convolution operation, 1≤n≤N s, h represents the multipath channel gain, its length is 1≤m≤L, L represents the number of tap coefficients of the multipath channel gain, 1≤x≤L+N s -1 represents the total length of the OFDM symbol time domain sampling points received by the receiver, ε is the normalized carrier frequency offset, and -0.5<ε<0.5; when the channel is flat fading, h has only one tap coefficient, when the channel is frequency selective fading, h has multiple tap coefficients, that is, h=[h[1],h[2],…,h[L]]; in order to eliminate interference between OFDM symbols, it is necessary to ensure that the length of the cyclic prefix is ​​greater than the length of the multipath channel gain, that is, N cp >L; w[x] means the mean is 0 and the variance is σ 2 The complex Gaussian white noise is

[0009] S3, extract the time domain sampling point of the data part from the lth OFDM symbol received by the receiver, which is affected by the channel and carrier frequency offset, and record it as y l [n], 1≤n≤N; and from each y l [n] is extracted from the real part and the imaginary part, and the extracted real part and the imaginary part are used to form the sample features for training the carrier frequency offset estimation neural network; the sample features are expressed as: [R(y l [n]),I(y l [n])], whose dimension is 1×2N, where R(*) represents the real part operation, I(*) represents the imaginary part operation, and N is the number of IFFT points.

[0010] S4. Send multiple random information bit sequences S at the transmitter, and execute steps S2 to S3 to obtain the sample features corresponding to each random information bit sequence S. All the obtained sample features are combined into a sample feature matrix: where N f Represents the total number of OFDM symbols sent, that is, the number of times the random information bit sequence is sent. The dimension of the feature matrix is ​​N f ×2N; the label of the sample is the true value of the carrier frequency offset that affects each OFDM symbol. The label matrix used to train the network is composed of the label of each sample. The dimension of the label matrix is ​​N f ×1;

[0011] S5. Select a fully connected neural network as a deep learning model of the carrier frequency offset estimation neural network; the fully connected neural network has Layer, specifically including 1 input layer, hidden layers and 1 output layer; each neuron on each layer of the fully connected neural network represents a weighted nonlinear transformation of all output values ​​of the previous layer, and the weight matrix between the l-1th layer and the lth layer is defined as The dimension of the weight matrix is ​​n l ×n l-1 , where n l and n l-1 Respectively represent the number of neurons in the lth layer and the l-1th layer, Represents the weight value between the nth neuron in the lth layer and the nth neuron in the l-1th layer. The bias vector on the lth layer is defined as The dimension of the bias vector is n l ×1, where Represents the nth bias value in the lth layer; in order to ensure the nonlinearity of the neural network, the neurons in the hidden layer use the ReLU activation function, the expression is: ReLU(x) = max(0,x), and the neurons in the output layer use the tanh activation function, the expression is:

[0012] S6: Input the feature matrix Y and label matrix E obtained in step S4 into the fully connected neural network in step S5 for training. The output of the fully connected neural network is the carrier frequency offset estimation matrix The expression is: where θ l Represents the set of all neuron parameters on the lth layer in the neural network, that is, Function g l Represents the nonlinear transformation performed on the lth layer in the neural network, specifically expressed as: The set of parameters in all layers of the neural network is defined as The loss function Loss(θ) of the fully connected neural network is the label matrix E and the carrier frequency offset estimation matrix The mean square error (MSE) between: in, represents the mathematical expectation, ||*|| represents the two-norm; finally, the gradient descent algorithm is executed to update the parameter set θ so that the loss function is minimized, that is, Among them, α>0 represents the learning rate, Represents the calculation of the gradient of the loss function.

[0013] Compared with the traditional carrier frequency offset estimation method based on cyclic prefix, the method of the present invention

[0014] The beneficial effects of the present invention are as follows: the traditional carrier frequency offset estimation method is completed by using the phase difference information between the cyclic prefix part in the time domain sampling of the receiving end and the corresponding data sampling, so the estimation accuracy of the traditional estimation method depends on the length of the cyclic prefix; but the cyclic prefix, as data other than effective information, will occupy additional channel bandwidth during the signal transmission process; the method of the present invention directly uses the sampling points of the data part to complete the estimation of the carrier frequency offset, and the length of the cyclic prefix can be selected to be greater than the minimum value of the channel delay extension, so the method of the present invention can improve the bandwidth efficiency of communication; the method of the present invention proposes a carrier frequency offset estimation scheme based on a fully connected neural network in a data-driven manner under the framework of deep learning, and the scheme has higher estimation accuracy than the traditional estimation method in a Gaussian white noise channel environment; the current deep learning framework cannot process complex value data, and the method of the present invention proposes a method for processing complex value data, which extracts the real part and imaginary part of the complex signal to form new sample features, and uses a single neural network to receive the time domain sampling signal to complete the estimation of the carrier frequency offset. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flow chart of a carrier frequency offset estimation method based on a fully connected neural network according to the present invention;

[0016] Figure 2 A system block diagram of an OFDM system for point-to-point communication in the present invention;

[0017] Figure 3 Schematic diagram of the structure of the carrier frequency offset estimation neural network model in the present invention;

[0018] Figure 4 Schematic diagram of feature extraction for received time domain sampling signals in the present invention;

[0019] Figure 5 A comparison diagram of using a carrier frequency offset estimation neural network and a cyclic prefix-based estimation method to complete CFO estimation and calculate the bit error rate of the entire communication system in an OFDM communication system in the present invention;

[0020] Figure 6 A comparison diagram of using a carrier frequency offset estimation neural network and a cyclic prefix-based estimation method to complete CFO estimation and calculate the bit error rate of the entire communication system in an OFDM communication system in the present invention;

[0021] Figure 7 This is a comparison chart of the bit error rate performance of the carrier frequency offset estimation neural network in the entire OFDM communication system under different hyperparameters in the present invention. DETAILED DESCRIPTION

[0022] The invention will be further described below with reference to the accompanying drawings and in combination with specific implementations, so that those skilled in the art can implement the invention with reference to the description. The protection scope of the invention is not limited to the specific implementations.

[0023] The embodiment of the present invention provides a carrier frequency offset estimation method based on a fully connected neural network, such as Figure 1 As shown, the method comprises the following steps:

[0024] S1. In the OFDM system of point-to-point communication, the transmitter sends a string of random information bit sequences S = {b1, b2, ..., b s}, where b s ∈{0,1}, s is the number of information bits sent by the transmitter at one time;

[0025] S2. Perform baseband signal modulation on the information bit sequence S. The information bit sequence S is mapped to constellation symbols X = {X[1], X[2], ..., X[k]}, where k is the number of constellation symbols. M represents the baseband signal modulation order; performing an inverse discrete Fourier transform (IFFT) on the constellation symbol to obtain an OFDM symbol, the expression of the lth OFDM symbol is: in, N represents the number of IFFT points, x l [n] represents the nth time domain sampling point in the lth OFDM symbol, 1≤n≤N; a length of N is added before the OFDM symbol. cp The length of the OFDM symbol after adding the cyclic prefix is: N s =N cp +N; the OFDM symbol after adding the cyclic prefix is ​​transmitted in the channel and received by the receiver; the expression of the lth OFDM symbol received by the receiver affected by the channel and the carrier frequency offset is: in, Represents the convolution operation, 1≤n≤N s , h represents the multipath channel gain, its length is 1≤m≤L, L represents the number of tap coefficients of the multipath channel gain, 1≤x≤L+N s -1 represents the total length of the OFDM symbol time domain sampling points received by the receiver, ε is the normalized carrier frequency offset, and -0.5<ε<0.5; when the channel is flat fading, h has only one tap coefficient, when the channel is frequency selective fading, h has multiple tap coefficients, that is, h=[h[1],h[2],…,h[L]]; in order to eliminate interference between OFDM symbols, it is necessary to ensure that the length of the cyclic prefix is ​​greater than the length of the multipath channel gain, that is, N cp >L; w[x] means the mean is 0 and the variance is σ 2The complex Gaussian white noise is

[0026] S3, extract the time domain sampling point of the data part from the lth OFDM symbol received by the receiver, which is affected by the channel and carrier frequency offset, and record it as y l [n], 1≤n≤N; and from each y l [n] is extracted from the real part and the imaginary part, and the extracted real part and the imaginary part are used to form the sample features for training the carrier frequency offset estimation neural network; the sample features are expressed as: [R(y l [n]),I(y l [n])], whose dimension is 1×2N, where R(*) represents the real part operation, I(*) represents the imaginary part operation, and N is the number of IFFT points.

[0027] S4. Send multiple random information bit sequences S at the transmitter, and execute steps S2 to S3 to obtain the sample features corresponding to each random information bit sequence S. All the obtained sample features are combined into a sample feature matrix: where N f Represents the total number of OFDM symbols sent, that is, the number of times the random information bit sequence is sent. The dimension of the feature matrix is ​​N f ×2N; the label of the sample is the true value of the carrier frequency offset that affects each OFDM symbol. The label matrix used to train the network is composed of the label of each sample. The dimension of the label matrix is ​​N f ×1;

[0028] S5. Select a fully connected neural network as a deep learning model of the carrier frequency offset estimation neural network; the fully connected neural network has Layer, specifically including 1 input layer, hidden layers and 1 output layer; each neuron on each layer of the fully connected neural network represents a weighted nonlinear transformation of all output values ​​of the previous layer, and the weight matrix between the l-1th layer and the lth layer is defined as The dimension of the weight matrix is ​​n l ×n l-1 , where n l and n l-1 Respectively represent the number of neurons in the lth layer and the l-1th layer, Represents the weight value between the nth neuron in the lth layer and the nth neuron in the l-1th layer. The bias vector on the lth layer is defined as The dimension of the bias vector is n l ×1, where Represents the nth bias value in the lth layer; in order to ensure the nonlinearity of the neural network, the neurons in the hidden layer use the ReLU activation function, the expression is: ReLU(x) = max(0,x), and the neurons in the output layer use the tanh activation function, the expression is:

[0029] S6: Input the feature matrix Y and label matrix E obtained in step S4 into the fully connected neural network in step S5 for training. The output of the fully connected neural network is the carrier frequency offset estimation matrix The expression is: where θ l Represents the set of all neuron parameters on the lth layer in the neural network, that is, Function g l Represents the nonlinear transformation performed on the lth layer in the neural network, specifically expressed as: The set of parameters in all layers of the neural network is defined as The loss function Loss(θ) of the fully connected neural network is the label matrix E and the carrier frequency offset estimation matrix The mean square error (MSE) between: in, represents the mathematical expectation, ||*|| represents the two-norm; finally, the gradient descent algorithm is executed to update the parameter set θ so that the loss function is minimized, that is, Among them, α>0 represents the learning rate, Represents the calculation of the gradient of the loss function.

[0030] As shown in Table 1 below, Table 1 shows the hyperparameters saved by the carrier frequency offset estimation neural network when the OFDM system bit error rate performance is optimal:

[0031] Table 1

[0032]

[0033] In order to verify the feasibility and effectiveness of the method of the present invention, a specific experimental simulation is given to illustrate.

[0034] The channel environment of the experimental simulation is a Gaussian white noise channel. The OFDM signal frame structure at the transmitting end adopts the 802.11a standard, with the number of subcarriers N=64 and the cyclic prefix length N cp= 16, the number of IFFT / FFT points is 64, and the modulation method on each subcarrier is BPSK. Considering that only one OFDM symbol is transmitted in an OFDM frame, the impact of carrier frequency offset is assumed to be constant within each OFDM symbol, but the carrier frequency offset varies between OFDM frames. To ensure the generalization ability of the neural network under different signal-to-noise ratios, we generate 10,000 time-domain received samples every 5 dB within the receive signal-to-noise ratio range of 0 to 40 dB as network training data. The training set, validation set, and test set are generated in a 10:1:1 ratio.

[0035] like Figure 5 As shown in Figure 2, the mean square error performance of the traditional CP-based CFO estimation method and the method of the present invention is compared. The mean square error is an indicator to measure the accuracy of CFO estimation. Figure 5 It can be seen from the figure that under various signal-to-noise ratios, the method of the present invention has better MSE performance.

[0036] like Figure 6 As shown in the figure, the bit error rate performance comparison of the traditional CP-based CFO estimation method and the method of the present invention in the entire OFDM communication system is shown. Figure 6 It can be seen from the figure that when the signal-to-noise ratio is greater than 7 dB, the OFDM system using the method of the present invention has a significant improvement in bit error rate performance.

[0037] like Figure 7 As shown in the figure, we varied the number of hidden layers and neurons in the network to verify the BER performance of the neural network under different hyperparameters. The OFDM system achieved optimal BER performance when the number of hidden layers was 1 and the number of neurons was 1024. In theory, the learning ability of a neural network increases with the depth of the network model. However, in practice, increasing model depth also increases network complexity, and also introduces the risks of gradient vanishing and overfitting. Therefore, selecting appropriate hyperparameters is crucial. Furthermore, when the signal-to-noise ratio (SNR) is below 7dB, the BER performance difference between different hyperparameters is only 0.5dB. In this case, a simpler network structure can be selected to reduce model complexity.

Claims

1. A carrier frequency offset estimation method based on a fully connected neural network, characterized by: The method comprises the following steps: S1. In the OFDM system of point-to-point communication, the transmitter sends a string of random information bit sequences S = {b1, b2, ..., b s }, where b s ∈{0,1}, s is the number of information bits sent by the transmitter at one time; S2. Perform baseband signal modulation on the information bit sequence S. The information bit sequence S is mapped to constellation symbols X = {X[1], X[2], ..., X[k]}, where k is the number of constellation symbols. M represents the baseband signal modulation order; performing an inverse discrete Fourier transform (IFFT) on the constellation symbol to obtain an OFDM symbol, the expression of the lth OFDM symbol is: in, N represents the number of IFFT points, x l [n] represents the nth time domain sampling point in the lth OFDM symbol, 1≤n≤N; a length of N is added before the OFDM symbol. cp The length of the OFDM symbol after adding the cyclic prefix is: N s =N cp + N; the OFDM symbol after adding the cyclic prefix is ​​transmitted in the channel and received by the receiver; the expression of the lth OFDM symbol received by the receiver affected by the channel and the carrier frequency offset is: in, Represents the convolution operation, 1≤n≤N s , h represents the multipath channel gain, its length is 1≤m≤L, L represents the number of tap coefficients of the multipath channel gain, 1≤x≤L+N s -1 represents the total length of the OFDM symbol time domain sampling points received by the receiver, ε is the normalized carrier frequency offset, and -0.5<ε<0.5; when the channel is flat fading, h has only one tap coefficient, when the channel is frequency selective fading, h has multiple tap coefficients, that is, h=[h[1],h[2],…,h[L]]; in order to eliminate interference between OFDM symbols, it is necessary to ensure that the length of the cyclic prefix is ​​greater than the length of the multipath channel gain, that is, N cp >L; w[x] means the mean is 0 and the variance is σ 2 The complex Gaussian white noise is S3, extract the time domain sampling point of the data part from the lth OFDM symbol received by the receiver, which is affected by the channel and carrier frequency offset, and record it as y l [n], 1≤n≤N; and from each y l [n] is extracted from the real part and the imaginary part, and the extracted real part and the imaginary part are used to form the sample features for training the carrier frequency offset estimation neural network; the sample features are expressed as: [R(y l [n]),I(y l [n])], its dimension is 1×2N, where R(*) represents the real part operation, I(*) represents the imaginary part operation, and N is the number of IFFT points; S4. Send multiple random information bit sequences S at the transmitter, and execute steps S2 to S3 to obtain the sample features corresponding to each random information bit sequence S. All the obtained sample features are combined into a sample feature matrix: where N f Represents the total number of OFDM symbols sent, that is, the number of times the random information bit sequence is sent. The dimension of the feature matrix is ​​N f ×2N; the label of the sample is the true value of the carrier frequency offset that affects each OFDM symbol. The label matrix used to train the network is composed of the label of each sample. The dimension of the label matrix is ​​N f ×1; S5. Select a fully connected neural network as a deep learning model of the carrier frequency offset estimation neural network; the fully connected neural network has Layer, specifically including 1 input layer, hidden layers and 1 output layer; each neuron on each layer of the fully connected neural network represents a weighted nonlinear transformation of all output values ​​of the previous layer, and the weight matrix between the l-1th layer and the lth layer is defined as The dimension of the weight matrix is ​​n l ×n l-1 , where n l and n l-1 Respectively represent the number of neurons in the lth layer and the l-1th layer, Represents the weight value between the nth neuron in the lth layer and the nth neuron in the l-1th layer. The bias vector on the lth layer is defined as The dimension of the bias vector is n l ×1, where Represents the nth bias value in the lth layer; the neurons in the hidden layer select the ReLU activation function, the expression is: ReLU(x)=max(0,x), and the neurons in the output layer select the tanh activation function, the expression is: S6: Input the feature matrix Y and label matrix E obtained in step S4 into the fully connected neural network in step S5 for training. The output of the fully connected neural network is the carrier frequency offset estimation matrix The expression is: where θ l Represents the set of all neuron parameters on the lth layer in the neural network, that is, Function g l Represents the nonlinear transformation performed on the lth layer in the neural network, specifically expressed as: ReLU(W1Y+b1), l=1, ReLU(W l (g l-1 (g l-2 θ l-1 ))+b l ), The set of parameters in all layers of the neural network is defined as The loss function Loss(θ) of the fully connected neural network is the label matrix E and the carrier frequency offset estimation matrix The mean square error (MSE) between: in, represents the mathematical expectation, ||*|| represents the two-norm; finally, the gradient descent algorithm is executed to update the parameter set θ so that the loss function is minimized, that is, Among them, α>0 represents the learning rate, Represents the calculation of the gradient of the loss function.

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