Method for target detection and parameter estimation in a through-the-wall radar system

Abstract

The application is a target detection and parameter estimation method of a sensing integrated system, aiming to solve the target detection and fractional Doppler and time delay parameter estimation problems of an OTFS sensing integrated system, and the method comprises the following steps: step one, a sensing integrated signal is generated at the sending end; step two, the receiver receives the echo signal and processes it; step three, a threshold map is generated through an integer time delay and Doppler detection network based on a convolutional neural network to perform target detection; and step four, fractional Doppler and time delay indexes are estimated. The target detection and parameter estimation method of the OTFS sensing integrated system based on deep learning has the following advantages: compared with the commonly used CFAR detection algorithm, the detection performance of the integer time delay and Doppler detection network is better. In addition, compared with the differential algorithm considering only integer Doppler and time delay and considering fractional Doppler and time delay, the relative distance and speed estimated by the fractional estimation network are more accurate.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of communication and sensing integration, and particularly relates to a target detection and parameter estimation method for an OTFS (Orthogonal Time Frequency Space) integrated sensing and communication system based on deep learning. BACKGROUND

[0002] With the development of information technology, the technology vision of Internet of Vehicles, unmanned aerial vehicle network, etc. is gradually becoming a reality. These emerging application scenarios require high reliable communication capability and high precision sensing capability. In addition, the rapid increase in the number of communication devices leads to a shortage of spectrum resources. In order to solve these problems, the concept of integrated sensing and communication (ISAC) is proposed. ISAC integrates the functions of communication and sensing, which can actively recognize and analyze the characteristics of the channel during the transmission of information, and then sense the physical characteristics of the surrounding environment. Compared with the system separating communication and sensing, it has many advantages, such as saving spectrum resources, reducing hardware cost and power consumption, and reducing device size, etc.

[0003] In order to realize ISAC, waveform design and signal processing are very important issues. Many studies are based on Orthogonal Frequency Division Multiplexing (OFDM) to realize ISAC. However, high Doppler effect in high-speed mobile scenarios can greatly increase the inter-carrier interference of OFDM systems, resulting in performance degradation. In this context, OTFS has attracted widespread attention because of its significant advantages in resisting time-frequency domain selective fading, and can still maintain good communication performance in high-speed mobile scenarios. Moreover, OTFS works in the delay-Doppler domain, and the parameters of its impulse channel response are delay and Doppler. The distance and velocity parameters concerned in radar sensing can be derived from delay and Doppler. One of the main challenges of OTFS-ISAC system is that in real scenarios, the real Doppler and delay of the target are often not integer multiples of the resolution, resulting in fractional Doppler and delay errors. In addition, the number of potential targets in the sensing scenario is usually unknown. Therefore, how to effectively detect targets and reduce the estimation error in the presence of fractional Doppler and delay is a technical problem to be solved. SUMMARY

[0004] Technical problem: In view of the deficiencies of the prior art, the application provides a target detection and parameter estimation method for an OTFS integrated sensing and communication system based on deep learning, aiming to solve the problems of target detection and fractional Doppler and delay parameter estimation of the OTFS integrated sensing and communication system.

[0005] Technical scheme: The target detection and parameter estimation method of the integrated sensing and communication system of the application considers a single-input single-output (SISO) OTFS-ISAC system of a single-base radar, and comprises the following steps:

[0006] Step one: The sending end generates an integrated sensing and communication signal, a sending signal model is constructed for the base station sending OTFS signal scene,

[0007] Step two: The receiver receives the echo signal and processes it, and an echo signal model is constructed for the base station receiving echo signal scene,

[0008] Step three: A threshold map is generated by an integer time delay and Doppler detection network based on a convolutional neural network to perform target detection, and the problems of sensing target detection and integer Doppler and time delay estimation are solved,

[0009] Step four: Fractional Doppler and time delay index is estimated to solve the problems of fractional Doppler and time delay estimation, and achieve more fine parameter estimation effect.

[0010] Among them,

[0011] The step one is specifically:

[0012] 1.5. The signal source generates data bits X DD ∈C NM , C represents a complex matrix, N and M represent the number of time slots and subcarriers of each OTFS frame respectively, and their values are determined according to the specific system design; the data bits are placed on the time delay-Doppler plane, and the time delay-Doppler plane is represented as:

[0013]

[0014] In the formula, 1 / NT and 1 / MΔf represent the sampling interval of the Doppler axis and the time delay axis respectively, or the resolution of the Doppler frequency shift and the time delay; MΔf represents the bandwidth occupied by each frame, and NT represents the duration of each frame; Δf is the subcarrier spacing, T is the symbol duration, and TΔf=1 is satisfied; k and l represent the Doppler domain and the time delay index respectively; the values of N, M, Δf and T are determined according to the specific system design;

[0015] 1.6. X DD is converted from the time delay-Doppler domain to the time-frequency domain by the inverse symplectic finite Fourier transform ISFFT to obtain the time-frequency domain sending symbol matrix X TF ∈C N×M ; X TF [n,m]∈X TF represents the sending symbol at the nth time index and the mth frequency index, and is as follows

[0016]

[0017] In the formula, n = 0, ..., N-1, m = 0, ..., M-1;

[0018] 1.7. Applying the Heisenberg transform to the transmitted symbol in the time-frequency domain can convert it into a continuous-time baseband signal s(t), as shown in the following equation.

[0019]

[0020] In the formula, g tx It is a pulse shaping filter with a duration of T, i.e., g tx (t) = 0, t < 0, t > T;

[0021] 1.8. Up-convert the continuous-time baseband signal s(t) to obtain the time-domain transmitted signal s. T (t),

[0022]

[0023] In the formula, f c For carrier frequency.

[0024] Step two specifically involves:

[0025] 2.1. Down-convert the echo signal to obtain the time-domain baseband received signal r(t), as shown in the following equation.

[0026]

[0027] In the formula, z(t) is additive white Gaussian noise with a one-sided power spectral density (PSD) of N0, h(τ,ν) is the complex channel impulse response in the time-delay-Doppler domain, and τ and ν are the round-trip time delay and Doppler frequency shift, respectively, and their formulas are as follows:

[0028]

[0029] In the formula, P represents the number of perceived targets, and h i The complex channel gain of the path represented by the i-th target; δ(·) represents the Dirac function; τ i and ν i Representing the round-trip time delay and Doppler shift of the i-th target, respectively, the formula is:

[0030]

[0031] In the formula, R i Let V be the relative distance between the i-th target and the transmitter. i Let be the relative radial velocity between the i-th target and the transmitter, and c be the speed of light; and are the delay index and Doppler index of the ith target, respectively, where l i ∈Z and k i ∈Z are integer parts of the indices, Z represents the set of integers; ι i ∈[-0.5,0.5] and κ i ∈[-0.5,0.5] are fractional parts of the indices; when ι i = 0 and κ i = 0, i.e., the delay and Doppler shift of the target are both integer multiples of the resolution, the target is located at the grid points of the delay-Doppler plane; when ι i ≠ 0 or κ i ≠ 0, i.e., the delay and Doppler shift of the target are both fractional multiples of the resolution, the target is located between the grid points of the delay-Doppler plane;

[0032] 2.2. Apply the Wigner-Ville transform to the received signal to obtain the expression Y TF (t,f) in the time-frequency domain,

[0033]

[0034] where g rx (t) is the receive pulse-shaping filter, A grx,r (t,f) is the cross ambiguity function between g rx (t) and the received signal, is the definition symbol, indicating that the former is defined by the latter;

[0035] 2.3. Sample Y TF (t,f) to obtain the discrete expression Y TF [n,m],

[0036]

[0037] 2.4. Convert Y TF [n,m] to the delay-Doppler domain received symbol Y DD [k,l]∈Y DD , Y DD ∈C N×M is the delay-Doppler domain received symbol matrix, Y DD [k,l] is as follows

[0038]

[0039] Under the ideal pulse-shaping filter condition, the input-output relationship of the baseband transmitted modulation symbol and the received modulation symbol is as follows

[0040] where Z DD [k, l] is additive complex Gaussian white noise in delay-Doppler domain with mean 0 and variance σ 2 ; h ω [k, l] is effective channel response in delay-Doppler domain,

[0041]

[0042]

[0043] where and are the delay index and Doppler index of the ith target respectively, and l' and k' are variables needed for calculation, representing the index in delay and Doppler domain respectively;

[0044] 2.5. Two-dimensional pulse compression is performed on the received signal, which is essentially to perform correlation operation on Y DD along the delay axis and Doppler axis respectively using known transmitted symbols, to obtain matrix U; U[k, l] e U is the element in the kth row and the lth column of matrix U, and its expression is

[0045]

[0046] where * represents conjugate operation, [] N and [] M represent modulo N and modulo M operation respectively;

[0047] 2.6. Circular shift operation is performed on U along the Doppler axis, so that the zero axis of Doppler index is located in the center of the delay-Doppler plane;

[0048] The third step is specifically:

[0049] 3.1. U is split into two real number matrices according to real part and imaginary part as two inputs of the integer delay and Doppler detection network, to generate input tensor I = [U R , U I ]; where U R and U I are the matrix composed of the real part of each element in U and the matrix composed of the imaginary part of each element in U respectively;

[0050] 3.2. The input first passes through two residual blocks, which introduce a residual connection, allowing the input to skip certain residual blocks to enter the next part of the network. Convolutional neural networks are used in the residual blocks, and there are 5 convolutional neural network (CNN) layers in each residual block. Each CNN layer uses a 3*3 size convolution kernel, and the output feature map has a length and width of C1 and C2, respectively, which are equal in value to the number of time slots N and the number of subcarriers M. Except for the last CNN layer, the output feature map of the remaining CNN layers must pass through group normalization (GN). GN divides the channels into different groups in the channel dimension, then calculates the mean and variance of each group to achieve normalization, thereby reducing the computational load of the model and accelerating convergence. Parametric rectified linear unit (PReLU) is used for parameter correction.

[0051]

[0052] The output of the first four CNN layers is normalized to introduce nonlinearity. The fifth CNN layer reduces the number of channels of the feature map to two, consistent with the input of the residual block. The output of the residual block is represented as:

[0053] Q(x) = P(x) + x (38)

[0054] where Q(x) is the output of each residual block, including the original input x of the residual block and the output P(x) after a series of layers. The ReLU function is used as the activation function at the end of each residual block, as follows:

[0055] ReLU(x) = Max(0, x) (39)

[0056] where Max() represents the maximum value.

[0057] The last part of the network is a single convolutional layer with a 3*3 kernel size, an input channel of 2, and an output channel of 1, which reduces the dimension of the output of the residual block to form the final network output, i.e., the threshold map.

[0058] 3.3. In the offline training phase, the neural network is trained using end-to-end supervised learning, treating U as a low-resolution image composed of the target map and the threshold map, i.e., |U| = T P + T N , where T P is the target map, in which the amplitudes of all grid points except those of the target integer Doppler and time delay are 0, T N is the threshold map, in which only the grid points of the target integer Doppler and time delay retain the noise amplitude, and the amplitudes of the remaining grid points are the same as |U|. T N is also the label for network training, and the mean square error is used as the loss function:

[0059]

[0060] where D is the number of samples in each batch, is the threshold map of the network output, the optimizer used in the training process is Adam, which is a gradient descent optimizer designed to adjust the learning rate of each parameter by calculating the first and second moment estimates of the gradient, so as to achieve more efficient network training;

[0061] 3.4. In the online estimation stage, input I into the trained network to obtain the target detection threshold map

[0062] 3.5. According to the threshold map, the integer Doppler and time delay index of the target are obtained;

[0063] The fourth step is specifically:

[0064] 4.1. The five data points centered on the integer target obtained in the previous step are input into the fractional time delay and Doppler estimation network, and the real and imaginary parts are input separately;

[0065] 4.2. The fractional estimation network has four layers, the first layer is the input layer with 10 neurons, the fourth layer output layer has 1 neuron, and its output is activated by the 0.5*tanh function, the hidden layers in the middle have Q1 and Q2 neurons respectively, and are activated by the tanh function, the expression of the tanh function is:

[0066]

[0067] e x is the exponential function with real number e as the base, e -x is the negative exponential function of real number, e≈2.71828,

[0068] 4.3. In the offline training stage, the neural network is trained by supervised learning, and the Adam optimizer is used to adjust the network weights and biases, and the mean square error is used as the loss function, and its expression is

[0069]

[0070] where T F is the true value of the fractional index, is the network estimation value of the fractional index, and E is the number of samples in each batch;

[0071] 4.4. In the online estimation stage, the real and imaginary parts of the five data points centered on the integer target obtained in the previous step are input into the trained network to obtain the estimated value of the fractional index

[0072] Step five: calculate relative distance and relative velocity, this step includes the following flow:

[0073] 5.1. Relative distance R i Calculation

[0074]

[0075] 5.2. Relative velocity V i Calculation

[0076]

[0077] Advantages: the target detection and parameter estimation method of the OTFS-ISAC system based on deep learning proposed in the present application has the following advantages: compared with the commonly used CFAR (Constant False Alarm Rate) detection algorithm, the detection performance of the integer time delay and Doppler detection network is better. In addition, compared with the difference algorithm considering only integer Doppler and time delay and considering fractional Doppler and time delay, the relative distance and velocity estimated by the fractional estimation network are more accurate. BRIEF DESCRIPTION OF DRAWINGS

[0078] Figure 1 The target detection and parameter estimation flowchart of the OTFS-ISAC system based on deep learning provided by the present application;

[0079] Figure 2 The integer time delay and Doppler detection network structure provided by the present application;

[0080] Figure 3 The fractional time delay and Doppler estimation network structure provided by the present application;

[0081] Figure 4 The detection result simulation comparison chart under different SNRs provided by the present application; Figure 4 (a) in the detection result simulation comparison chart under SNR=5dB, Figure 4 (b) in the detection result simulation comparison chart under SNR=0dB, Figure 4 (c) in the detection result simulation comparison chart under SNR=-5dB, Figure 4 (d) in the detection result simulation comparison chart under SNR=-10dB.

[0082] Figure 5 The error and resolution ratio simulation comparison chart under different SNRs provided by the present application. DETAILED DESCRIPTION

[0083] The specific embodiments of the present application are described in further detail below with M = 32, N = 32, 4QAM modulation, carrier frequency of 24 GHz, and subcarrier spacing Δf of 39 kHz as an example, in combination with the drawings of the specification, as shown in Figure 1 、 Figure 2 、 Figure 3 .

[0084] Step one: the sending end generates a sensing-integrated signal, and this step includes the following processes:

[0085] (1) The signal source generates data bits X DD ∈C N×M , C represents a complex matrix, and N and M represent the number of time slots and subcarriers of each OTFS frame respectively, M = 32, N = 32. The data bits are placed on the delay-Doppler plane, X DD [k,l]∈X DD represents the transmitted symbol on the kth Doppler index and the lth delay index. The delay-Doppler plane is represented as

[0086]

[0087] In the formula, 1 / NT and 1 / MΔf represent the sampling interval of the Doppler axis and the delay axis respectively, which can also be regarded as the resolution of the Doppler frequency shift and the delay. MΔf represents the bandwidth occupied per frame, and NT represents the duration of each frame. Δf is the subcarrier spacing, T is the symbol duration, and TΔf = 1 is satisfied.

[0088] (2) Convert X DD from the delay-Doppler domain to the time-frequency domain by inverse symplectic finite Fourier transform (ISFFT) to obtain the time-frequency domain transmitted symbol matrix X TF ∈C N ×M , X TF [n,m]∈X TF represents the transmitted symbol on the nth time index and the mth frequency index, as follows

[0089]

[0090] In the formula, n = 0, …, N-1, m = 0, …, M-1.

[0091] (3) Applying the Heisenberg transform to the transmitted symbol in the time-frequency domain can convert it into a continuous time baseband signal s(t), as follows

[0092]

[0093] In the formula, gtx is a pulse shaping filter.

[0094] (4) up-convert the continuous-time baseband signal s(t) to obtain the time-domain transmit signal s T (t),

[0095]

[0096] where f c is the carrier frequency.

[0097] Step two: the receiver receives the echo signal and processes it, and this step includes the following processes:

[0098] (1) down-convert the echo signal to obtain the time-domain baseband received signal r(t), as follows:

[0099] r(t) = ∫∫h(τ, v)e j2πν(t-τ) s(t - τ) dτ dv + z(t) (49)

[0100] where z(t) is additive white Gaussian noise with a one-sided power spectral density PSD of N0, and h(τ, v) ∈ C is a complex channel impulse response in the delay-Doppler domain, and its formula is

[0101]

[0102] where P is the number of sensing targets, h i is the complex channel gain of the path represented by the i-th target. δ(·) represents the Dirac function. τ i and v i represent the round-trip delay and Doppler shift of the i-th target, respectively, and their formulas are

[0103]

[0104] where R i is the relative distance between the i-th target and the transmitter, V i is the relative radial velocity of the i-th target and the transmitter, and c is the speed of light. and are the delay index and the Doppler index of the i-th target, respectively, where l i ∈ Z and k i ∈ Z are the integer parts of the indices, and Z represents the set of integers.

[0105] ι i ∈ [-0.5, 0.5] and κ i ∈ [-0.5, 0.5] are the decimal parts of the indices.

[0106] (2) Apply Wigner transform to the received signal to get the expression Y TF (t,f) in time-frequency domain

[0107]

[0108] where g rx (t) is the receive pulse-shaping filter, A grx,r (t,f) is the cross ambiguity function between g rx (t) and the received signal, is defined as the former is defined by the latter.

[0109] (3) Sampling Y TF (t,f) can get the discrete expression Y

[0110] Y TF [n,m] = Y TF (t,f)| t＝nT,f＝mΔf (53)

[0111] (4) Convert Y TF [n,m] to the received symbol Y DD [k,l] in delay-Doppler domain by using Symplectic Finite Fourier Transform (SFFT) DD , Y DD ∈ C N×M is the matrix of received symbol in delay-Doppler domain, Y DD [k,l] is given by

[0112]

[0113] Under the condition of ideal pulse-shaping filter, the input-output relationship between the transmitted and received modulation symbols in baseband is given by

[0114]

[0115] where Z DD [k,l] is the additive complex Gaussian white noise in delay-Doppler domain with mean 0 and variance σ 2 . h ω [k,l] is the effective channel response in delay-Doppler domain,

[0116]

[0117] where is the sampling function when the transmitter and receiver use the same rectangular window.

[0118]

[0119] (5) Two-dimensional pulse compression is performed on the received signal, which is essentially using known transmitted symbols to correlate Y DD along the delay axis and the Doppler axis respectively, to obtain matrix U. U[k, l] e U is the element in the kth row and the lth column of matrix U, and its expression is

[0120]

[0121] where (·) * denotes the conjugate operation, [·] N and [·] M denote the modulo N and modulo M operations respectively.

[0122] (6) Perform a cyclic shift operation on U along the Doppler axis to make the Doppler index zero axis located in the center of the delay-Doppler plane.

[0123] Step three: generate a threshold map through an integer time delay and Doppler target detection network based on a convolutional neural network, and perform target detection. This step includes the following processes:

[0124] (1) Split U into two real value matrices according to the real part and the imaginary part as the inputs of the integer time delay and Doppler detection network, to generate input tensor I = [U R ,U I ]. Wherein U R and U I are the matrix composed of the real part of each element in U and the matrix composed of the imaginary part of each element in U.

[0125] (2) Figure 2 shows the structure of the integer time delay and Doppler detection network. The input first passes through two residual blocks. The residual block introduces a residual connection, allowing the input to skip some residual blocks and enter the next part of the network. Convolutional neural networks are used in the residual block, and there are 5 convolutional neural network (CNN) layers in each residual block. Each CNN layer uses a 3*3 size convolution kernel, and the output feature map has a length and width of C1 and C2 respectively, C1 and C2 are equal in value to the time slot number N and the subcarrier number M in the previous text. Except for the last CNN layer, the output feature map of the remaining CNN layers needs to pass through group normalization (GN). GN divides the channels into different groups in the channel dimension, and then calculates the mean and variance in each group to achieve normalization, thereby reducing the computational amount of the model and accelerating the convergence. parametric rectified linear unit (PReLu)

[0126]

[0127] The output of the first four CNN layers is normalized to introduce nonlinearity, where a = 0.25. The fifth CNN layer reduces the number of channels of the feature map to two channels, consistent with the input of the residual block. The output of the residual block can be expressed as

[0128] Q(x) = P(x) + x (60)

[0129] where Q(x) is the output of each residual block, including the original input x of the residual block and the output P(x) after a series of layers. The ReLU function is used at the end of each residual block as an activation function, as follows.

[0130] ReLU(x) = Max(0, x) (61)

[0131] where Max(·) represents the maximum value.

[0132] The last of the network is a single convolutional layer with a kernel size of 3*3. Its input channel is 2 and the output channel is 1, so that the output of the residual block is reduced in dimension to form the final network output, i.e., the threshold map.

[0133] (3) In the offline training phase, the neural network is trained by end-to-end supervised learning. The modulus of U is regarded as a low-resolution image composed of the target map and the threshold map, i.e., |U| = T P + T N , where T P is the target map, and the amplitudes of all grid points in the target map except for the grid points where the target integer Doppler and time delay are located are all 0. T N is the threshold map, and the amplitudes of all grid points in the threshold map except for the grid points where the target integer Doppler and time delay are located are all noise amplitudes, and the amplitudes of the remaining grid points are the same as |U|. T N is also the label for network training. The mean square error is used as the loss function:

[0134]

[0135] where D is the number of samples in each batch, is the threshold map output by the network. The optimizer used in the training process is Adam (Adaptive Moment Estimation), which is a gradient descent optimizer designed to adjust the learning rate of each parameter by calculating the first and second moment estimates of the gradient, thereby achieving more efficient network training.

[0136] (4) In the online estimation phase, I is input into the trained network to obtain the target detection threshold map T N .

[0137] (5) Target detection according to the threshold map, and obtain the integer Doppler and time delay index of the target.

[0138] The above steps are explained in detail as follows:

[0139] In the example, M = 32 and N = 32, so the size of each layer of the integer time delay and Doppler target detection network is 32*32. In the offline training stage, the size of each batch is 512, and the learning rate of the Adam optimizer is 0.001. 30000 OTFS frames constitute the training set, and the signal-to-noise ratio SNR (Signal-to-noise Ratio) is -10dB, -5dB, and 0dB, respectively, with 10000 data for each SNR. The training set focuses on the multi-target situation, and the number of targets in each OTFS frame is randomly generated from 1 to 9. The maximum distance of the target is 3785 meters, and the absolute value of the maximum speed of the target is 118 meters / second. In the online estimation stage, the test set covers the SNR from -10dB to 5dB with an interval of 5dB. There are 1000 test data for each SNR, and the number of targets in each OTFS frame is randomly generated from 1 to 9.

[0140] The selected algorithms for comparison are the commonly used CFAR detection algorithms, including CA-CFAR (Cell Averaging-CFAR), GO-CFAR (Greatest of CFAR), and SO-CFAR (Smallest of CFAR). The training interval of the three CFAR algorithms is 2*2, and the protection interval is 4*4. The detection performance is measured by the detection rate P d and the false alarm rate P fa .

[0141]

[0142] Figure 4 The detection results of the network and other algorithms under different SNRs with random target numbers are shown. It is obvious that the network is superior to the CFAR algorithms regardless of the SNR. For example, in Figure 4 (b), when the false alarm rate is 10 -4 %, the detection rate of the neural network is about 0.68, while the best GO-CFAR among the other algorithms is about 0.17. Overall, as the SNR decreases, the results of all algorithms decrease, but the results of the neural network are always superior to those of the other algorithms.

[0143] Step four: Estimate the fractional Doppler and time delay index, which includes the following processes:

[0144] (1) Take the five data points centered on the integer target obtained in the previous step as the input data of the fractional time delay and Doppler estimation network, and input the real and imaginary parts separately.

[0145] (2) The network structure for score estimation is as follows Figure 3 As shown, it consists of four layers. The first layer is the input layer with 10 neurons. The fourth layer is the output layer with 1 neuron, whose output is activated using the 0.5*tanh function. The middle hidden layers have Q1 and Q2 neurons respectively, both activated using the tanh function. The expression for the tanh function is:

[0146]

[0147] (3) In the offline training phase, the neural network is trained using supervised learning, and the Adam optimizer is used to adjust the network weights and biases. Mean squared error is used as the loss function, and its expression is:

[0148]

[0149] In the formula, T F The true value of the fraction index. For the network estimate indexed by score, E represents the number of samples per batch.

[0150] (4) In the online estimation stage, the real and imaginary parts of the five data points centered on the integer target obtained in the previous step are input into the trained network to obtain the estimated value of the score index.

[0151] The steps described above will be explained in detail below:

[0152] The hidden layers of the network each have Q1 = Q2 = 32 neurons. During offline training, the batch size is 128, and the learning rate of the Adam optimizer is 0.0001. The training set consists of 40,000 data points, including 10,000 data points each for SNR = -10dB, -5dB, 0dB, and 5dB. The target number for each OTFS frame is also randomly generated from 1 to 9.

[0153] During the online evaluation phase, the test set covered SNRs ranging from -10dB to 15dB, with 5dB intervals. To compare the impact of different target numbers on the results, for each SNR, the number of targets in the OTFS frames was randomly generated as 4, 6, and 1 to 9. The maximum target distance was 3785 meters, and the absolute value of the maximum target velocity was 118 m / s. Each SNR had 1000 OTFS frames. Note that latency and Doppler are not distinguished here because they cause similar energy leakage patterns.

[0154] The comparisons in this section include results considering only integers (assuming the integer estimates are correct, with rounding down) and differencing-based methods. Figure 5The ratio of the root mean square error (RMSE) to the resolution is shown for different SNRs, without distinguishing between time delay and Doppler. Figure 5 It can be clearly observed that the error of the fractional estimation network is significantly better than the integer-only and difference-based methods for different SNRs, indicating that the network is effective for fractional estimation.

[0155] Step five: Calculate the relative distance and relative velocity, this step includes the following flow:

[0156] (1) Relative distance R i is calculated.

[0157]

[0158] (2) Relative velocity V i is calculated.

[0159]

[0160] The specific embodiments described herein are merely illustrative of the spirit of the present application. Those skilled in the art can make various modifications or supplements to the described specific embodiments or replace them with similar ways, without departing from the spirit of the present application or exceeding the scope defined by the appended claims.

Claims

1. A method for target detection and parameter estimation of a combined sensing system, characterized in that, The method comprises the following steps: Step one: the sending end generates a sensing integration signal, constructs a sending signal model for the base station sending OTFS signal scene, Step two: the receiver receives the echo signal and processes it, constructs an echo signal model for the base station receiving echo signal scene, Step three: generate a threshold map through an integer time delay and Doppler detection network based on a convolutional neural network to perform target detection, solve the problems of sensing target detection and integer Doppler and time delay estimation, specifically: 3.

1. With the known transmitted symbols, Y is correlated along the delay axis and the Doppler axis, respectively, to obtain matrix U; Y DD DD is the delay-Doppler domain received symbol matrix; U is split into two real matrices as the real and imaginary parts, which are the two inputs to the integer delay and Doppler detection network, resulting in input tensor I = [U R ,U I ]​ where U R and U I are the matrices of the real parts and imaginary parts of each element of U, respectively. 3.

2. The input first passes through two residual blocks, the residual block introduces a residual connection, allowing the input to skip certain residual blocks and enter the next part of the network, a convolutional neural network is used in the residual block, and there are 5 convolutional neural network (CNN) layers in each residual block; each CNN layer uses a 3*3 size convolution kernel, and the output feature map has a length and width of C1 and C2, respectively, C1 and C2 are equal in value to the number of time slots N and the number of subcarriers M, except for the last CNN layer, the output feature map of the remaining CNN layers needs to pass through group normalization (GN); GN divides the channels into different groups in the channel dimension, then calculates the mean and variance of each group to achieve normalization, thereby reducing the computational complexity of the model and accelerating convergence; the parameter rectified linear unit (PReLU) is used for the nonlinear introduction of the normalized output of the first four CNN layers; the fifth CNN layer reduces the number of channels of the feature map to two, consistent with the input of the residual block, and the output of the residual block is represented as: Q(x)=P(x)+x (2) Where Q(x) is the output of each residual block, including the original input x of the residual block and the output P(x) after passing through a series of layers; the ReLU function is used as the activation function at the end of each residual block, as follows ReLU(x)=Max(0,x) (3) Where Max() represents the maximum value; The last part of the network is a single convolutional layer with a 3*3 kernel size, an input channel of 2 and an output channel of 1, which reduces the dimension of the output of the residual block and forms the final network output, i.e., the threshold map; 3.

5. Perform target detection according to the threshold map to obtain the integer Doppler and time delay index of the target; 3.

3. Offline training phase, train the neural network by end-to-end supervised learning method, take U as a low resolution image composed of target image and threshold image, that is |U| = T P + T N , in which, T P is the target image, the amplitude of the grid point except the integer Doppler and time delay of the target in the target image is 0, T N is the threshold image, the amplitude of the grid point except the integer Doppler and time delay of the target in the threshold image only retains the noise amplitude, and the amplitude of the remaining grid points is the same as |U|, T N is also the label of network training, and the mean square error is used as the loss function: In the formula, D is the number of samples of each batch, is the threshold map of the network output, the optimizer used in the training process is Adam, which is a gradient descent optimizer, aiming to adjust the learning rate of each parameter by calculating the first moment estimate and second moment estimate of the gradient, so as to realize more efficient network training; 3.

4. In the online estimation phase, I is input into the trained network to obtain the target detection threshold map Step four: estimate the fractional Doppler and time delay index to solve the fractional Doppler and time delay estimation problem and achieve more precise parameter estimation, specifically: 4.

1. Use the five data points centered on the integer target obtained in the previous step as the input data of the fractional time delay and Doppler estimation network, and input the real and imaginary parts separately; 4.

2. The fractional estimation network has four layers, the first layer is the input layer with 10 neurons, the fourth layer output layer has 1 neuron, and its output uses the 0.5*tanh function as the activation function, the hidden layers in the middle have Q1 and Q2 neurons respectively, and both use the tanh function as the activation function, the expression of the tanh function is: 4.

3. In the offline training stage, the neural network is trained in a supervised learning manner, and the Adam optimizer is used to adjust the network weights and biases, and the mean square error is used as the loss function, whose expression is e x is the exponential function with base the real number e, e -x is the negative exponential function with base the real number e, e ≈ 2.71828, Step five: calculate the relative distance and relative velocity, which includes the following processes: In the formula, T F is a real value of the fraction index, is a network estimated value of the fraction index, and E is the number of samples per batch. 4.

4. In the online estimation stage, the real and imaginary parts of the five data points centered on the integer target obtained in the previous step are input into the trained network to obtain the estimated value of the fractional index ​ 5.

1. Relative distance R i Calculation 5.

2. Relative speed V i Calculations c is the speed of light; and are the time and Doppler indices of the ith target, respectively, where l i ∈ Z and k i ∈ Z are the integer part of the indices, Z represents the set of integers; ι i ∈ [-0.5, 0.5] and κ i ∈ [-0.5, 0.5] are the fractional part of the indices; M represents the number of subcarriers, Δf is the subcarrier spacing, NT represents the duration of each frame, f c is the carrier frequency.

2. The target detection and parameter estimation method of a combined sensing system according to claim 1, wherein, The step one is specifically: 1.

1. Source generates data bits X DD ∈ C N×M C represents a complex matrix, N and M represent the number of slots and subcarriers of each OTFS frame respectively, whose values are determined according to specific system design; data bits are placed on the delay-Doppler plane, which is represented as: where 1 / NT and 1 / MΔf represent the resolution of Doppler shift and time delay, respectively; MΔf represents the bandwidth occupied per frame, and NT represents the duration of each frame. Δf is the subcarrier spacing, T is the symbol duration, and satisfies TΔf = 1; k and l represent the indexes of Doppler domain and time delay respectively; the values of N, M, Δf and T are determined according to the specific system design; 1.

2. Transforming X by the inverse finite sine Fourier transform ISFFT DD From the delay-Doppler domain to the time-frequency domain, resulting in a time- frequency domain transmit symbol matrix X TF ∈ C N×M ; X TF [n,m]∈X TF denotes the transmitted symbol at the nth time index and the mth frequency index, as follows In the formula, n = 0,..., N-1, m = 0,..., M-1; 1.

3. Applying the Heisenberg transform to the transmitted symbol in the time-frequency domain can convert it into a continuous-time baseband signal s(t), as follows where g tx is a pulse-shaping filter with duration T, i.e. g tx (t) = 0, t < 0, t > T 1.

4. up-conversion of the continuous-time baseband signal s(t) to obtain the time-domain transmit signal s(t) T (t), where f c is the carrier frequency.

3. The target detection and parameter estimation method of a combined sensing system according to claim 2, characterized in that, The step two is specifically: 2.

1. Down-conversion of the echo signal to obtain the time-domain baseband received signal r(t), as follows r(t) = ∫∫ h(τ, v) e j2πν(t-τ) s(t - τ) dτ dv + z(t) (13) In the formula, z(t) is an additive white Gaussian noise, the one-sided power spectral density PSD is N0, h(τ,ν) is a complex channel impulse response in the delay-Doppler domain, τ,ν is the round-trip delay and Doppler shift, and the formula is where P is the number of targets, h i is the complex channel gain of the path represented by the i-th target; δ(·) denotes the Dirac function; τ i and v i represent the round-trip delay and the Doppler shift of the i-th target, respectively, and are given by where R i is the relative distance between the ith target and the transmitter, V i is the relative radial velocity of the ith target and the transmitter, and c is the speed of light. and are the time delay index and Doppler index of the ith target, respectively, where l i ∈ Z and k i ∈ Z are the integer part of the index, and Z represents the set of integers. i ∈ [-0.5, 0.5] and κ i ∈ [-0.5, 0.5] are the fractional part of the index; when ι i = 0 and κ i = 0, i.e., the time delay and Doppler shift of the target are both integer multiples of the resolution, the target is located at the grid points of the time delay-Doppler plane; when ι i ≠ 0 or κ i ≠ 0, i.e., the time delay and Doppler shift of the target are both fractional multiples of the resolution, the target is located between the grid points of the time delay-Doppler plane. 2.

2. Applying the Wigner transform to the received signal gives the representation Y(t,f) in the time-frequency domain TF (t,f), where g rx (t) is a receive pulse-shaping filter, A grx,r (t,f) is g rx (t) is the cross ambiguity function between g For the sake of definition, it is stated that the former is defined by the latter. 2.

3. On Y TF (t,f) is sampled to obtain a discrete representation Y TF [n,m], 2.

4. Using a Sine Finite Fourier Transform, SFFT, to transform Y TF [n,m] into the received symbols Y in the delay-Doppler domain DD [k,l] ∈ Y DD , Y DD ∈ C N×M is the received symbol matrix in the delay-Doppler domain, Y DD [k,l] as follows Under the condition of ideal pulse shaping filter, the input-output relationship of the baseband transmitted modulation symbol and the received modulation symbol is as follows wherein Z DD [k, l] is additive complex Gaussian white noise in the delay-Doppler domain with mean 0 and variance σ 2 ; h ω [k, l] is the effective channel response in the delay-Doppler domain, wherein is the sampling function when the same rectangular window is used for the transmitting and receiving ends; wherein and are the delay and Doppler indices of the ith target, respectively, and l' and k' are variables needed for the computation, representing the indices in the delay and Doppler domains, respectively. 2.

5. Two-dimensional pulse compression is performed on the received signal, which is essentially using the known transmitted symbols to correlate Y DD The correlation operation results in matrix U; U[k, l] e U is the element in the kth row and the lth column of matrix U, which is expressed as wherein * represents a conjugate operation, N and M represent modulo N and modulo M operations, respectively; 2.

6. Circularly shift U along the Doppler axis to make the Doppler index zero axis located in the center of the time-delay-Doppler plane.

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