A two-step amplitude centroid correction algorithm in time delay and doppler domain for OTFS sensing system

Abstract

The present application relates to a kind of two-step amplitude centroid correction algorithm in OTFS sensing system time delay and doppler domain, the correction algorithm includes the following steps: step 1, design pilot frame structure;Step 2, the amplitude of received signal is calculated;Step 3, using three DFT samples, the centroid of discrete channel response is calculated to obtain the distance and speed of target;The correction algorithm has the superior technical effect that the present application uses more simple optimization objective function and reduces the calculation complexity of integrated signal joint precoding matrix, more suitable for large-scale antenna scene;Computer simulation shows that the method of the present application can effectively generate beam in target direction and the peak side ratio of generated beam is superior to prior art and also achieves better performance than prior art in beam detection performance.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of wireless communication technology and radar signal processing, and particularly relates to a two-step amplitude centroid correction algorithm in the time delay and Doppler domain in an OTFS sensing system. BACKGROUND

[0002] The upcoming sixth generation of mobile communication systems will be applied to a wide variety of scenarios, such as non-terrestrial networks, vehicle internet, and smart manufacturing, which require flexibility, scalability, and precise sensing capabilities. While 5G has described a positioning accuracy of 0.2m / 1m horizontally / vertically in Internet of Things applications, future applications can require higher accuracy. Traditionally, communication and sensing are implemented on different devices and frequencies. However, since the 1990s, there has been a trend of integrating these two functions into a single device due to the need for high frequencies and compact hardware. In view of this, sensing can be an inherent capability of 6G, which can help to research integrated sensing and communication (ISAC) technology.

[0003] In recent years, ISAC has attracted great attention, and most existing methods involve resource sharing and coexistence design. Traditional methods are divided into allocating resources such as time, frequency, or antennas into orthogonal spaces, and then allocating them to communication and sensing respectively. However, resource sharing fails to fully integrate sensing and communication, as they are still carried out independently. A typical method to achieve ISAC is a radar-centric coexistence design. Representative research in this field includes frequency-modulated continuous wave (FMCW) and orbital angular momentum (OAM). Recently, there has been an increasing emphasis on communication-centric coexistence design, and orthogonal frequency division multiplexing (OFDM) has the advantages of communication, including high spectral efficiency, robustness to frequency-selective fading, and low complexity equalization, and has proven acceptable sensing accuracy in low mobility scenarios. However, in high mobility scenarios, the orthogonality between subcarriers can be compromised, leading to poor performance.

[0004] Recently, a novel two-dimensional (2D) modulation technique called orthogonal time frequency space modulation (OTFS) has been proposed as a solution for high Doppler scenarios. In OTFS, each data symbol is mapped onto a delay-Doppler (DD) plane by inverse symplectic finite Fourier transform (ISFFT), which spreads each symbol over the entire time-frequency (TF) resource, facilitating full TF diversity. Since then, some pioneering research has demonstrated the potential of OTFS as a promising candidate for 6G mobile communication. To improve signal detection performance, advanced methods such as message passing (MP), variational Bayes (VB), and maximum ratio combining (MRC) have been successively introduced for OTFS signals.

[0005] The OTFS modulation technique exhibits inherent advantages for radar perception as it operates in the delay-Doppler (DD) domain where the delay and Doppler characteristics of targets can be extracted for channel estimation and perception. The main challenge associated with OTFS-ISAC is the trade-off between limited TF resources and resolution requirements. One approach involves implementing a likelihood ratio search over a set of DD grids. However, each grid point requires high-dimensional matrix multiplication, which results in a significant computational burden. Additionally, the selection bias problem has become a new challenge. When the calibration samples do not represent the entire channel response, especially in low signal-to-noise ratio (SNR) cases, this leads to a considerable degradation in perception accuracy. SUMMARY

[0006] To address the problems of the prior art, the present application proposes a two-step amplitude centroid correction algorithm in the delay and Doppler domain in an OTFS sensing system.

[0007] The method of the present application comprises the following steps:

[0008] Step 1, design a pilot frame structure;

[0009] Step 2, calculate the amplitude of the received signal;

[0010] Step 3, use three DFT samples to calculate the centroid of the discrete channel response to obtain the distance and velocity of the target.

[0011] Further, in step 1, the pilot frame structure is designed, and the pilot represented by x p is strategically positioned on the DD grid point , where u = 1, 2,..., U represents the index of the multi-pilot, for the sake of simplicity, the pilot frame is designed as follows (1):

[0012]

[0013] In combination with the guard interval around each pilot to exclude potential overlap between adjacent pilots, the length of the guard interval in the delay and Doppler axes satisfies M s ≥ l max and N g ≥ k max , where and limit the peak position within a certain region of and , in addition, a guard interval needs to be inserted to avoid the sidelobe interference from adjacent pilots, according to the delay and Doppler, the length of the guard interval is defined as N k and M l , in order to avoid the influence of Doppler spread and delay, N k × Ml The protected area.

[0014] Furthermore, in step 2, the amplitude of the received signal is represented as |y[k,l]|, and the grid Γ is divided into subgrids Γ1, ..., Γ2. U In each subgrid, peak detection is performed as follows (2):

[0015]

[0016] in, and Represents subgrid Γ u Integer Doppler and delay index.

[0017] Furthermore, in step 3, the centroid of the discrete channel response is calculated using three DFT samples to obtain the target's distance and velocity:

[0018] Step 3.1, in the sub-mesh Γ u The first step of TS-ABC executed in the process is as follows (3):

[0019]

[0020] in, Represents a delay index, and This represents three DFT samples along the time delay axis around the peak;

[0021] Step 3.2: Calculate the weighted sum of the amplitude and Doppler index of the three DFT samples along the Doppler axis, and divide the result by the sum of the amplitudes of the three DFT samples to obtain the subgrid Γ. u The Doppler index of the first calibration step is as follows (4):

[0022]

[0023] in, This represents the magnitude of three DFT samples along the Doppler axis around the peak, while Indicates the Doppler index;

[0024] Step 3.3, obtained from Step 3.2 and Step 3.1 and Subtract the pilot signal position placed in the transmitted frame from the middle, and... and The results of the first step of correction are denoted as follows: and In subgrid Γ u The second step of TS-ABC executed in the process is as follows (5)-(6):

[0025]

[0026]

[0027] Step 3.4, compare the provided DFT peak with the calibration results of each sub-grid obtained in the first step;

[0028] Step 3.5, select the second DFT sample facing the preliminary estimate for further checking, in the second calibration, calculate the statistical average of the time delay and Doppler index, and obtain the distance and velocity of the target respectively as follows (7)-(8):

[0029]

[0030]

[0031] The method of the present application has the following characteristics compared with the prior art:

[0032] 1. The method of the present application adopts a simpler optimization objective function and reduces the computational complexity of the integrated signal joint precoding matrix, which is more suitable for large-scale antenna scenarios.

[0033] 2. Computer simulation shows that the method of the present application can effectively generate a beam in the target direction, and the peak-to-side ratio of the generated beam is better than the prior art, and the performance of the beam detection is also better than the prior art.

[0034] 3. The Capon spectrum estimation method has the advantages of minimizing the power estimation of non-target angles and only retaining the power of target angles, thus producing a very high peak at the target, which is easy to set a threshold to detect the target DOA (angle of arrival). Compared with the MUSIC method, the Capon method does not need to know the number of sources, and has lower complexity. Compared with the simplest spatial FFT, the resolution is higher. Therefore, the performance of the Capon spectrum estimation method has a good trade-off between resolution and complexity, which helps to provide a simple and efficient spatial spectrum estimation for the method of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 Fig. 1 is a schematic diagram of the multi-pilot signal principle of the method of the present application;

[0036] Figure 2a Fig. 2b is a simulation schematic diagram of the probability density function of the selected bias of the method of the present application;

[0037] Figure 3a Fig. 3b is a simulation schematic diagram of the probability and loss of the selected bias during the first calibration step in the method of the present application;

[0038] Figure 4a -4b is a schematic diagram of the comparison of the MSE and SS-ABC and CRLB of the calibrated range and velocity of the method of the application;

[0039] Figure 5 -4c is a schematic diagram of the simulation of the MSE and CRLB of the velocity estimation of the fractional parameter of the method of the application;

[0040] Figure 6 -4d is a schematic diagram of the comparison of the MSE of the range estimation of the method of the application with the ML algorithm and the GLRT algorithm. DETAILED DESCRIPTION

[0041] The application will be further described in detail below with reference to the accompanying drawings. Figures 1 to 6 The application will be further described in detail below with reference to the accompanying drawings.

[0042] The method of the application comprises the following steps:

[0043] Step 1, design the pilot frame structure, by x p The pilots represented by x are strategically positioned on the DD grid points , where u = 1, 2,..., U represents the index of the multiple pilots, for the sake of simplifying the derivation, the designed pilot frame is as follows (1):

[0044]

[0045] In combination with the guard interval around each pilot, in order to exclude the potential overlap between adjacent pilots, as shown in Figure 1 The length of the guard interval in the delay and Doppler axis needs to meet M g ≥ l max and N g ≥ k max , respectively, where and The peak position is limited to a specific area of and , in addition, the guard interval needs to be inserted to avoid the sidelobe interference from adjacent pilots, the length of the guard interval is defined as N k and M l , respectively, according to the delay and Doppler, in order to avoid the influence of Doppler spread and delay, a guard zone of M k × M l is inserted in the signal;

[0046] Step 2, calculate the amplitude of the received signal, represented as |y[k, l]|, divide the grid Γ into sub-grids Γ1,..., Γ U , in each sub-grid, perform peak detection, as follows (2):

[0047]

[0048] wherein, and denote the integer Doppler and delay indices of the sub-grid u ;

[0049] Step 3, using the three DFT samples, the centroid of the discrete channel response is computed, obtaining the range and velocity of the target:

[0050] Step 3.1, the first step of TS-ABC performed in the sub-grid u is given as:

[0051]

[0052] wherein, denotes the delay index, and denotes the amplitudes of the three DFT samples along the peak around the Doppler axis;

[0053] Step 3.2, along the Doppler axis the weighted sum of the three DFT samples amplitudes and Doppler indices is computed and the result is divided by the sum of the amplitudes of the three DFT samples, obtaining the Doppler index of the first calibration step in the sub-grid u , as shown in the following equation (4):

[0054]

[0055] wherein, denotes the amplitudes of the three DFT samples along the peak around the Doppler axis, while denotes the Doppler index;

[0056] Step 3.3, from and subtract the pilots placed in the pilot positions of the transmitted frame, denoting and as the results of the first step correction, denoted as and respectively. Furthermore, the second step of TS-ABC performed in the sub-grid u is given by the following equations (5)-(6) respectively:

[0057]

[0058]

[0059] Step 3.4, the provided DFT peak is compared in detail with the calibration results of each sub-grid obtained in the first step;

[0060] Step 3.5, the second DFT sample facing the preliminary estimate is selected for further checking, in the second step calibration, the statistical average of time delay and Doppler index is calculated respectively, and finally the distance and speed of the target are calculated respectively as:

[0061]

[0062]

[0063] In the method of the present application, in order to verify the technical performance of the two-step amplitude centroid correction algorithm in the embodiment, the setting of the simulation environment and the comparison of the simulation results are further illustrated by the following experiments:

[0064] 1, selection bias

[0065] The generated random variable is subjected to 100,000 Monte Carlo experiments, assuming that the peak signal-to-noise ratio is 20dB, the probability density function is as shown in Figure 5 , it can be seen that is approximately a Gaussian random variable, under the premise that Δx l >0, the point with a larger index should be selected from the samples adjacent to the DFT peak, if , the selection bias will occur, in order to analyze the influence of different fractional indexes on the calibration accuracy, simulations are performed under different Δ l values, as shown in Fig. 2(a), it can be seen that the PDF of the first calibration step tends to deviate from the true index as Δx l increases, thereby effectively reducing the probability of selection bias, simulations are performed under different U values in Fig. 2(b), and the influence of different numbers of pilots on the calibration accuracy is investigated, it can be seen that the variance of the calibration result decreases as the number of pilots increases, which further helps to reduce the probability of selection bias;

[0066] The probability and loss of selection bias during the first calibration step are shown in Fig. 3, in the case of SS-ABC and single pilot scheme, the loss of selection bias reaches its maximum value, approximately Δx l =0.15, which indicates that for the target with such fractional time delay index, the receiver will encounter the maximum estimation bias, as shown in Fig. 3(b), due to multiple observations of the pilot response, the curve reaches a lower peak at smaller Δx l as the PSNR or the number of pilots increases.

[0067] 2, sensing performance

[0068] In FIG. 4, the MSE of distance and velocity calibrated by the TS-ABC method is compared with the SS-ABC and CRLB, and the MSE of velocity or range decreases as the PSNR increases, in addition, the trend is more obvious for targets with smaller fractional values, and is similar to the almost "ideal" curve, which indicates that the estimator of the method described in the application can effectively avoid selection bias at this point, in addition, the multi-pilot scheme helps to reduce the estimated MSE and lower limit.

[0069] At the same time, the application further analyzes the influence of the fractional parameter on the MSE and CRLB of the velocity estimation, from Figure 5 It can be seen that the gap between the estimated MSE and CRLB will be reduced by increasing the PSNR or the value of the fractional parameter; Figure 6 The MSE of the SS-ABC and TS-ABC algorithms is compared with the ML and GLRT algorithms, as Figure 6 shown, the mean square error of the ML and GLRT search algorithms decreases linearly with the increase of the peak signal-to-noise ratio, in contrast, the selection bias at low PSNR level leads to a higher MSE of distance estimation using the SS-ABC method, when the PSNR exceeds 30dB, the MSE performance of SS-ABC is similar to that of ML and GLRT methods; compared with the SS-ABC method, the TS-ABC method reduces the selection bias in the first step calibration, and needs a lower PSNR to reach the linear region, and further shows that the TS-ABC method with 16 pilots is better than other algorithms by nearly 10dB.

[0070] 3, computational complexity

[0071] The application compares the computational complexity of the TS-ABC method with the ML and GLRT methods, the total complexity of the ML method is The complexity of the GLRT method is and the complexity of the ML algorithm increases exponentially with the increase of N v M τ , in contrast, the computational complexity of the TS-ABC and SS-ABC methods increases linearly with N v M τ , which is significantly lower than that of the ML and GLRT methods.

[0072] The application is not limited by the above embodiments, the above embodiments and descriptions described in the specification are only to illustrate the principles of the application, and various changes and improvements can be made without departing from the spirit and scope of the application, and these changes and improvements all fall within the scope of the claimed application.

Claims

1. A two-step amplitude centroid correction algorithm for time delay and Doppler domain in an OTFS sensing system, the algorithm comprising the following steps: Step 1, Design the pilot frame structure: By x p The pilot signals are strategically positioned at DD grid points. Above, where u = 1, 2, ..., U represents the index of the multiple pilots, the pilot frame is designed as follows (1): By combining the guard interval around each pilot to eliminate potential overlap between adjacent pilots, the length of the guard interval in the time delay and Doppler axis respectively satisfies M g ≥l max and N g ≥k max ,in, and Limit the peak position to and Within a specific region, a guard interval is also required to avoid sidelobe interference from adjacent pilots. The length of the guard interval is defined as N based on the time delay and Doppler effect. k and M l To avoid the effects of Doppler dispersion and time delay, N is inserted into the signal. k ×M l The protected area; Step 2, calculate the amplitude of the received signal: The amplitude of the received signal is represented as |y[k,l]|, and the grid Γ is divided into subgrids Γ1,…,Γ. U In each subgrid, peak detection is performed as follows (2): in, and Represents subgrid Γ u Integer Doppler and delay index; Step 3: Using three DFT samples, calculate the centroid of the discrete channel response to obtain the target's distance and velocity. Step 3.1, in the sub-mesh Γ u The first step of TS-ABC executed in the process is as follows (3): in, Represents a delay index, and This represents three DFT samples along the time delay axis around the peak; Step 3.2: Calculate the weighted sum of the amplitude and Doppler index of the three DFT samples along the Doppler axis, and divide the result by the sum of the amplitudes of the three DFT samples to obtain the subgrid Γ. u The Doppler index of the first calibration step is as follows (4): in, This represents the magnitude of three DFT samples along the Doppler axis around the peak, while Indicates the Doppler index; Step 3.3, obtained from Step 3.2 and Step 3.1 and Subtract the pilot signal position placed in the transmitted frame from the middle, and... and The results of the first step of correction are denoted as follows: and In subgrid Γ u The second step of TS-ABC executed in the process is as follows (5)-(6): Step 3.4: Compare the provided DFT peak with the calibration results of each subgrid obtained in the first step; Step 3.5: Select the second DFT sample from the initial estimate for further examination. In the second calibration step, calculate the statistical average of the time delay and Doppler index to obtain the target's distance and velocity as follows (7)-(8):

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