Method for estimating frequency deviation in radar communication integrated system

Abstract

The invention discloses a method for estimating frequency offset in a radar communication integrated system, which is characterized by comprising the following contents: influence of carrier frequency offset on system performance; a time-frequency delay estimation algorithm; a local correlation estimation algorithm; the invention discloses a dual-stage frequency offset estimation algorithm. Aiming at the limitation in the prior art, the design and implementation of the frequency offset estimation algorithm in the RCIS are discussed, and the double-stage frequency offset estimation algorithm combined with the UW sequence phase information is also discussed, so that the limitation of a single-stage algorithm on the frequency offset estimation precision and range is effectively broken through.

Description

Technical Field

[0001] The present invention belongs to the field of frequency offset estimation methods, and specifically relates to a frequency offset estimation method in a radar-communication integrated system. Background Art

[0002] In a Radar and Communication Integration System (RCIS), Carrier Frequency Offset (CFO) (hereinafter referred to as "frequency offset") is one of the key factors affecting the system performance. The existence of frequency offset not only destroys the phase synchronization of signals, thereby leading to the deterioration of demodulation performance, but also causes inter-symbol interference and reduces the anti-interference ability of signals. Therefore, accurate estimation and correction of frequency offset are the basis for ensuring the reliability of the system and the communication quality. The technical framework of frequency offset estimation and correction usually consists of two stages: First, estimate the frequency offset value in the signal; Second, restore the phase synchronization of the signal through the reverse correction of the frequency offset value.

[0003] Frequency offset estimation algorithms usually rely on different reference sequences and signal processing methods. The core task of frequency offset estimation is to accurately capture the frequency offset information in the signal to provide necessary references for the correction stage. In fact, the implementation of frequency offset correction is not complex. Once the frequency offset value is estimated, only by taking the negative of the frequency offset value and multiplying it with the received signal can the phase recovery be completed.

[0004] In previous studies, frequency offset estimation algorithms based on training sequences have been widely applied and studied. However, in the scenario of RCIS with high bandwidth, high sampling rate and large frequency offset, existing algorithms often fail to meet the high requirements of the system for accuracy and stability. Summary of the Invention

[0005] Aiming at the limitations in the prior art, the present invention explores the design and implementation of a frequency offset estimation algorithm in RCIS, as well as a two-stage frequency offset estimation algorithm combined with the phase information of UW sequences. The method of the present invention effectively breaks through the limitations of single-stage algorithms in terms of frequency offset estimation accuracy and range.

[0006] The present invention is implemented as follows:

[0007] A frequency offset estimation method in a radar-communication integrated system, characterized in that the method includes the following contents: 1) The influence of carrier frequency offset on system performance; 2) Time-frequency delay estimation algorithm; 3) Local correlation estimation algorithm; 4) Two-stage frequency offset estimation algorithm.

[0008] Furthermore, the influence of the carrier frequency offset on system performance specifically includes the following contents:

[0009] Set the impact of phase noise to 0, that is, assume that the phase noise in the signal has been effectively suppressed, or its impact is small enough to be negligible;

[0010] Assume that during signal transmission, the received signal r n is affected by the carrier frequency offset ε; the model of the received signal can be expressed as:

[0011] r n = s n ·e j2πεn / N + v n

[0012] where s n is the transmitted symbol, e j2πεn / N is the phase rotation term caused by the frequency offset, v n is the received noise, and N is the length of the signal; the formula shows that the frequency offset causes the phase of the received signal to rotate at each sampling point, ignoring the further impact of phase noise on the received signal; converting this model to the frequency domain, assume that the signal is transformed by the N-point discrete Fourier transform (DFT) to obtain the frequency-domain signal R k :

[0013]

[0014] Substitute into the signal model:

[0015]

[0016] Further simplification gives:

[0017]

[0018] It can be seen that the frequency offset causes the phase rotation of the frequency-domain signal and generates inter-carrier interference (ICI), which affects the accuracy of frequency-domain demodulation; specifically, the phase shift caused by the frequency offset will be exacerbated in a multipath fading environment, causing interference between different sub-carriers and significantly increasing the bit error rate of the system. Continue to ignore the interference of phase noise on the signal and set it to 0;

[0019] When there is a frequency offset in the received signal at the receiving end, the constellation diagram of the received signal will rotate, which in turn affects the correct decision of the symbol; assume that the receiving end uses a single-carrier frequency-domain equalization (SC-FDE) system. In the frequency domain, the signal of each sub-carrier can be obtained through the discrete Fourier transform (DFT); when there is a frequency offset, the phase of each sub-carrier of the received signal in the frequency domain will be rotated, resulting in a deviation between the received symbol and the transmitted symbol; especially in a multipath fading channel, the phase rotation caused by the frequency offset will be superimposed with the signals of different paths, thus increasing the inter-symbol interference (ISI);

[0020] For a multipath channel, assume that the received signal is the superposition of multiple paths, and the signal of each path can be expressed as:

[0021]

[0022] where L represents the number of multipaths of the signal, and h i is the attenuation factor of the i-th path; the frequency offset will cause different phase rotations of the signals of each path, which will increase the gap between the received symbol and the ideal symbol, further causing demodulation errors;

[0023] In the SC-FDE system, the influence of the frequency offset is not only manifested as the phase rotation of the symbol, but also as the amplitude attenuation in the frequency domain; due to the frequency offset, the amplitudes of the subcarriers in the system will change, resulting in the influence on the amplitude of the received signal. This change in amplitude further reduces the signal-to-noise ratio (SNR) of the system, thereby increasing the bit error rate (BER).

[0024] In a multipath channel, the frequency offset will introduce phase rotation and amplitude attenuation; assume that after the received signal is frequency-domain equalized, the interference caused by the frequency offset can be expressed by the following formula:

[0025]

[0026] This phase rotation and amplitude attenuation will cause interference between symbols, making the received signal unable to be correctly demodulated; through the frequency offset estimation technology, the frequency offset is compensated, but if the compensation is incomplete, there will still be a certain error;

[0027] Through accurate frequency offset estimation, we can estimate the frequency offset value in the received signal and achieve frequency offset correction by taking the inverse of the frequency offset value; assume that the estimated frequency offset is The frequency offset correction process can be completed by multiplying the received signal by to complete the correction:

[0028]

[0029] This correction process effectively eliminates the phase rotation caused by the frequency offset, thereby restoring the original phase of the signal and enabling the received signal to be correctly demodulated.

[0030] Furthermore, the time-frequency delay estimation algorithm described above specifically includes the following content:

[0031] When estimating the frequency offset, based on the length of the training sequence, the range of frequency offset estimation is limited; assume that the correlation window length of the training sequence is D sampling points, and the maximum estimable frequency offset range △ε max can be derived from the following formula:

[0032]

[0033] where f s is the sampling frequency and D is the length of the correlation window; in the STF sequence, assuming the length of its correlation window is 128 samples and the sampling frequency is 64 MHz, the maximum frequency offset estimation range is:

[0034]

[0035] Therefore, the time-domain delay estimation algorithm based on the STF sequence can theoretically estimate a maximum frequency offset range of 250 kHz; the derivation of this estimation range provides theoretical support for frequency offset estimation and ensures that the system performance requirements can be met in practical applications;

[0036] The time-domain delay estimation algorithm and the frequency-domain delay estimation algorithm include the following:

[0037] 2.1. Time-domain delay estimation algorithm:

[0038] The basic idea of the time-domain delay estimation algorithm is to extract the frequency offset information by calculating the time-domain autocorrelation of the training sequence in the received signal. Assuming that the i-th symbol in the received STF (Short Training Frame) sequence is r i , the time-domain model of the received signal can be expressed as:

[0039] r i = s i ·e j2πεi / N + v i

[0040] where s i is the transmitted symbol, e j2πεi / N is the phase rotation term caused by the frequency offset ε, v i is the received noise, N is the length of the signal, and ε is the frequency offset; the frequency offset causes the received symbol to have a phase rotation in the time domain;

[0041] To estimate the frequency offset, the time-domain delay estimation algorithm obtains the frequency offset information by calculating the autocorrelation value between symbol pairs with a fixed interval I; assuming that in the STF sequence, the interval between each symbol pair is I sampling points; for the received symbols r i and r i+I , their conjugate multiplication gives the time-domain autocorrelation value:

[0042]

[0043] From the phase of the autocorrelation value, the frequency offset ε can be estimated, and the formula is as follows:

[0044]

[0045] Among them, is the estimated frequency offset value, arg(R(i)) is the phase of the autocorrelation value, and N is the sequence length (autocorrelation window size); by calculating the autocorrelation values between multiple symbol pairs and taking their average, we can obtain an accurate frequency offset estimate.

[0046] The advantage of the time-domain delay estimation algorithm is that it is simple to calculate and has strong robustness to noise; however, the accuracy of time-domain estimation is limited by the length of the training sequence. Increasing the sequence length can improve the estimation accuracy, but the accuracy of the time-domain estimation algorithm is still limited by the length of the training sequence;

[0047] 2.2 Frequency-domain delay estimation algorithm:

[0048] The frequency-domain delay estimation algorithm estimates the frequency offset by analyzing the frequency-domain characteristics of the received signal; due to the existence of the frequency offset, the received signal will generate a phase rotation in the frequency domain and cause interference (ICI) between subcarriers of different frequencies; in the RCIS system, the signal is first transformed by the discrete Fourier transform (DFT) to obtain the frequency-domain representation R k , where the frequency offset of each subcarrier is manifested as a linear change in phase;

[0049] Assume that the received signal is r n , and its frequency-domain representation is R k . Due to the existence of the frequency offset ε, the received frequency-domain signal R k can be expressed as:

[0050]

[0051] Among them, R k is the frequency-domain signal, and e j2πεn / N represents the phase rotation term caused by the frequency offset ε; the frequency offset ε will cause different phase offsets for each subcarrier of the received signal, thus affecting the correct demodulation of the frequency-domain signal;

[0052] The frequency-domain delay estimation algorithm estimates the frequency offset by calculating the frequency-domain phase difference between symbol pairs with an interval I; for the received symbols r n and r n+I , their frequency-domain representations are R k and R k+I respectively, and their phase differences can be expressed by the following formula:

[0053]

[0054] Among them, is the estimated frequency offset value, is the phase difference of the frequency-domain signal, and N is the sequence length (the size of the autocorrelation window); the advantage of this algorithm is that it can efficiently estimate the frequency offset in a complex channel environment. Especially in the case of multipath fading and strong noise, it can still provide high-precision frequency offset estimation through the maximum likelihood estimation (MLE) method.

[0055] Furthermore, the local correlation estimation algorithm specifically includes the following:

[0056] 3.1 Local peak estimation algorithm: The peak algorithm estimates the frequency offset by finding the position of the maximum peak in the cross-correlation result; assuming the cross-correlation result is R cross (i), then the estimation of the frequency offset can be calculated by the following formula:

[0057]

[0058] where i max represents the position of the maximum value in the cross-correlation function;

[0059] 3.2 Local mean estimation algorithm

[0060] To improve the accuracy of the frequency offset estimation, the cross-correlation values between multiple symbols are averaged; the mean algorithm reduces the influence of noise by accumulating the phase information of multiple cross-correlation results;

[0061] Assuming the phase differences of multiple cross-correlation functions are θ 1 , θ 2 ,... θ L , then the estimation of the frequency offset can be expressed as:

[0062]

[0063] where L is used to calculate the number of symbol pairs for averaging, and θ l is the phase difference between the l-th symbol pair; by averaging the phase differences of multiple symbol pairs, the algorithm can effectively reduce the influence of noise on the frequency offset estimation and enhance the stability of the estimation.

[0064] Furthermore, the two-stage frequency offset estimation algorithm specifically includes the following:

[0065] The two-stage frequency offset estimation algorithm first uses the time-domain sliding correlation algorithm based on the STF sequence for coarse estimation to capture a wider frequency offset range; then, it performs refined estimation on the compensated data through the time-domain sliding correlation frequency offset estimation algorithm based on the UW sequence to obtain higher frequency offset estimation accuracy;

[0066] The specific steps are as follows:

[0067] The first stage (coarse estimation): The received signal extracts the STF sequence through frame synchronization, and a time-domain delay estimation algorithm is used to coarsely estimate the frequency offset; assuming the length of the received signal is N r , the received signal is Then the autocorrelation function of the received signal and its own delay sequence can be expressed as:

[0068]

[0069] Among them, R STF (i) represents the autocorrelation function of the received sequence STF and its own delay sequence, reflecting the similarity between the received signal and the training sequence, and I is the operation correlation interval;

[0070] Through the phase information of the autocorrelation function, the estimation of the frequency offset can be achieved through the following formula:

[0071]

[0072] Among them, is the coarse estimated frequency offset value based on the STF sequence. The frequency offset estimation range in this stage is ±250 kHz, meeting the system's capture requirements for wide frequency offsets; through this coarse estimated frequency offset value the signal after the STF sequence is corrected, and the received signal after frequency offset correction is:

[0073]

[0074] The second stage (fine estimation): For the received signal that has been coarsely estimated and corrected through the STF sequence, the UW sequence is further extracted, and a time-domain delay estimation algorithm based on the UW sequence is used for fine estimation; assuming the received signal after the correction in the first stage is The autocorrelation of the corrected UW received signal and the delay of the UW sequence can be expressed as:

[0075]

[0076] The refined estimation of the frequency offset can be achieved through the following formula:

[0077]

[0078] It should be noted that in the time-domain delay estimation algorithm based on the UW sequence, the frequency offset estimation range is restricted by two key conditions;

[0079] First, the maximum range of frequency offset estimation is determined by the formula where f sLet \(f_s\) denote the sampling frequency and \(D\) denote the length of the correlation window. In this stage, the length of the correlation window is set to 64 samples, which is the length of one UW (Unique Word). In the simulation experiment, the sampling frequency is set to 64 MHz. According to the above formula, the maximum estimable frequency offset is 500 kHz.

[0080] Secondly, to ensure the effectiveness of the algorithm, the phase change within a data block should not exceed \(2\pi\). This condition can be expressed by the formula \(\Delta\varphi = 2\pi\Delta\varepsilon\cdot N\) s \(<2\pi\), where \(N\) s denotes the length of the data block. According to this condition, the calculated maximum estimable frequency offset is 125 kHz. Combining the above two conditions, we take the minimum value as the final maximum estimable frequency offset, that is, 125 kHz.

[0081] Since the frequency offset values within 250 kHz have been compensated in the first stage, the estimation range of the second stage can fully meet the system performance. Combining the estimation results of the first stage and the second stage, the final frequency offset estimation value is:

[0082]

[0083] The two - stage frequency offset estimation algorithm has significant advantages compared with the traditional single - stage estimation algorithm. In the first stage, a rough estimation is carried out through the STF sequence, which can quickly capture a large frequency offset range and has a low computational complexity. In the second stage, a fine estimation is carried out through the UW sequence to further improve the accuracy of frequency offset estimation. The simulation results show that the two - stage frequency offset estimation algorithm can effectively meet the frequency offset estimation requirements under complex channel conditions, especially having strong robustness in high - speed mobile and multipath environments. Description of the Drawings

[0084] Figure 1 It is the schematic diagram of the TSC frequency offset estimation algorithm in the frequency offset estimation method of a radar - communication integrated system of the present invention;

[0085] Figure 2 It is the schematic diagram of the FSD frequency offset estimation in the frequency offset estimation method of a radar - communication integrated system of the present invention;

[0086] Figure 3 It is the sampling point position corresponding to each peak in the embodiment of the present invention;

[0087] Figure 4 It is the schematic diagram of the peak algorithm in the frequency offset estimation method of a radar - communication integrated system of the present invention;

[0088] Figure 5 It is the schematic diagram of the local mean estimation algorithm in the frequency offset estimation method of a radar - communication integrated system of the present invention;

[0089] Figure 6 This is the schematic diagram of the two-stage frequency offset estimation algorithm in the intermediate frequency offset estimation method of a radar communication integrated system according to the present invention;

[0090] Figure 7 This is the schematic diagram of the influence of intermediate frequency offset on the bit error rate of the system in the embodiment of the present invention;

[0091] Figure 8 This is the schematic diagram of the influence of intermediate frequency offset on the system performance in the 16QAM modulation system in the embodiment of the present invention;

[0092] Figure 9 This is the schematic diagram of the influence of the number of training sequences on the performance in the embodiment of the present invention;

[0093] Figure 10 This is the schematic diagram of the influence of different algorithms on the performance in the frequency offset estimation range in the embodiment of the present invention.

[0094] Figure 11 This is the schematic diagram of the performance simulation results of fixed frequency offset when introducing a 20kHz frequency offset in the embodiment of the present invention, and respectively using time-domain delay estimation algorithm, frequency-domain delay estimation algorithm, local correlation mean algorithm and two-stage frequency offset algorithm for estimation;

[0095] Figure 12 This is the schematic diagram of the algorithm performance at different frequency offset magnitudes under the condition that the SNR is fixed at 12dB in the embodiment of the present invention;

[0096] Figure 13 This is the schematic diagram of the performance of four frequency offset estimation algorithms versus signal-to-noise ratio under the condition of a 250kHz frequency offset in the embodiment of the present invention. Detailed implementation manners

[0097] To make the purpose, technical solutions and effects of the present invention clearer and more definite, the following examples are listed to further elaborate on the present invention in detail. It should be noted that the specific implementations described herein are only used to explain the present invention and are not used to limit the present invention.

[0098] The present invention evaluates the existing algorithms and proposes an optimization scheme for the frequency offset estimation algorithm for RCIS. Specifically, it includes the following contents:

[0099] Influence of carrier frequency offset on system performance:

[0100] In modern wireless communication systems, Carrier Frequency Offset (CFO) is caused by the frequency mismatch between the transmitter and the receiver. The existence of CFO will lead to phase offset of the received signal, which in turn affects the demodulation performance of the system, especially in complex fading channel environments. The frequency offset not only introduces amplitude attenuation and phase rotation of the signal, but also may cause Inter-Symbol Interference (ISI) and Inter-Carrier Interference (ICI), thus seriously reducing the signal quality and Bit Error Rate (BER) of the system.

[0101] In the implementation process of the simulation algorithm, we assume that there is no influence of phase noise on the received signal. Therefore, in the subsequent frequency offset estimation process, the interference of phase noise on the signal is ignored. However, in practice, phase noise is also an important factor affecting signal demodulation. Nevertheless, in order to simplify the research and simulation of the frequency offset estimation algorithm, the influence of phase noise is set to 0 in this paper, that is, it is assumed that the phase noise in the signal has been effectively suppressed, or its influence is small enough to be ignored.

[0102] Assume that during the signal transmission process, the received signal r n is affected by the carrier frequency offset ε. The model of the received signal can be expressed as:

[0103] r n = s n ·e j2πεn / N + v n

[0104] where s n is the transmitted symbol, e j2πεn / N is the phase rotation term caused by the frequency offset, v n is the received noise, and N is the length of the signal. This formula shows that the frequency offset will cause the phase of the received signal to rotate at each sampling point. However, in this study, we ignore the further influence of phase noise on the received signal.

[0105] Converting this model to the frequency domain, assuming that the signal is transformed by the N-point Discrete Fourier Transform (DFT) to obtain the frequency domain signal R k :

[0106]

[0107] Substituting into the signal model:

[0108]

[0109] Further simplification gives:

[0110]

[0111] As can be seen, frequency offset causes the phase rotation of the frequency-domain signal and generates inter-carrier interference (ICI), which affects the accuracy of frequency-domain demodulation. Specifically, the phase shift caused by frequency offset may be exacerbated in a multipath fading environment, causing interference between different subcarriers and significantly increasing the bit error rate of the system. Nevertheless, in the simulations of this paper, we ignored the interference of phase noise on the signal and set it to 0, thus simplifying the research process.

[0112] When a frequency offset occurs at the receiving end of the signal, the constellation diagram of the received signal will rotate, thereby affecting the correct decision of the symbol. Assume that the single-carrier frequency-domain equalization (SC-FDE) system is used at the receiving end. In the frequency domain, the signal of each subcarrier can be obtained through the discrete Fourier transform (DFT). When there is a frequency offset, the phase of each subcarrier of the received signal in the frequency domain will be rotated, resulting in a deviation between the received symbol and the transmitted symbol. Especially in a multipath fading channel, the phase rotation caused by frequency offset will be superimposed on the signals of different paths, thus increasing the inter-symbol interference (ISI).

[0113] For a multipath channel, assume that the received signal is the superposition of multiple paths, and the signal of each path can be expressed as:

[0114]

[0115] where L represents the number of multipaths of the signal, and h i is the attenuation factor of the i-th path. Frequency offset will cause different phase rotations of the signals of each path, which will increase the gap between the received symbol and the ideal symbol, further causing demodulation errors.

[0116] In the SC-FDE system, the influence of frequency offset not only manifests as the phase rotation of the symbol, but also as the amplitude attenuation in the frequency domain. Due to the frequency offset, the amplitudes of the subcarriers in the system will change, affecting the amplitude of the received signal. This change in amplitude further reduces the signal-to-noise ratio (SNR) of the system, thereby increasing the bit error rate (BER).

[0117] In a multipath channel, frequency offset will introduce phase rotation and amplitude attenuation. Assume that after the received signal undergoes frequency-domain equalization, the interference caused by frequency offset can be expressed by the following formula:

[0118]

[0119] This phase rotation and amplitude attenuation will cause inter-symbol interference, making the received signal unable to be correctly demodulated. Through frequency offset estimation technology, we can compensate for the frequency offset, but if the compensation is incomplete, there will still be a certain error.

[0120] Through precise frequency offset estimation, we can estimate the frequency offset value in the received signal and achieve frequency offset correction by taking the inverse of the frequency offset value. Assume the estimated frequency offset is The frequency offset correction process can be achieved by multiplying the received signal with to complete the correction:

[0121]

[0122] This correction process effectively eliminates the phase rotation caused by the frequency offset, thus restoring the original phase of the signal and enabling the correct demodulation of the received signal.

[0123] Time-frequency delay estimation algorithm

[0124] The time-frequency delay estimation algorithm is one of the key technologies in frequency offset estimation, mainly estimating the frequency offset information in the system by analyzing the signal delay in the time domain or frequency domain. In RCIS, the frequency offset usually causes phase rotation of the signal and inter-carrier interference (ICI), so high-precision frequency offset estimation is crucial for system performance. The time-domain delay estimation algorithm and the frequency-domain delay estimation algorithm start from the time domain and frequency domain respectively, and estimate the frequency offset through different mathematical models.

[0125] When estimating the frequency offset, based on the length of the training sequence, the range of frequency offset estimation is limited. Assume the correlation window length of the training sequence is D sampling points, and the maximum estimable frequency offset range △ε max can be derived from the following formula:

[0126]

[0127] where, f s is the sampling frequency and D is the correlation window length. Taking the STF sequence as an example, assume its correlation window length is 128 samples and the sampling frequency is 64 MHz, then the maximum frequency offset estimation range is:

[0128]

[0129] Therefore, the time-domain delay estimation algorithm based on the STF sequence can theoretically estimate a maximum frequency offset range of 250 kHz. The derivation of this estimation range provides theoretical support for frequency offset estimation and ensures that the system performance requirements can be met in practical applications. Next, the time-domain delay estimation algorithm and the frequency-domain delay estimation algorithm will be introduced respectively.

[0130] 2.1. Time-domain delay estimation algorithm

[0131] The basic idea of the time-domain delay estimation algorithm is to extract the frequency offset information by calculating the time-domain autocorrelation of the training sequence in the received signal. Assume that the i-th symbol in the received STF (Short Training Frame) sequence is r i , the time-domain model of the received signal can be expressed as:

[0132] r i =s i ·e j2πεi / N +v i

[0133] where s i is the transmitted symbol, e j2πεi / N is the phase rotation term caused by the frequency offset ε, v i is the received noise, N is the length of the signal, and ε is the frequency offset. The frequency offset will cause the received symbols to have phase rotation in the time domain.

[0134] To estimate the frequency offset, the time-domain delay estimation algorithm estimates the frequency offset information by calculating the autocorrelation values between symbol pairs with a fixed interval I. Assume that in the STF sequence, the interval between each symbol pair is I sampling points. For the received symbols r i and r i+I , their conjugate multiplication gives the time-domain autocorrelation value:

[0135]

[0136] From the phase of the autocorrelation value, the frequency offset ε can be estimated, and the formula is as follows:

[0137]

[0138] where is the estimated frequency offset value, arg(R(i)) is the phase of the autocorrelation value, and N is the sequence length (autocorrelation window size). By calculating the autocorrelation values between multiple symbol pairs and taking their average, we can obtain an accurate frequency offset estimate.

[0139] The advantage of the time-domain delay estimation algorithm is that it is computationally simple and has strong robustness to noise. However, the accuracy of the time-domain estimation is limited by the length of the training sequence. Increasing the sequence length can improve the estimation accuracy, but the accuracy of the time-domain estimation algorithm is still limited by the length of the training sequence. The principle of the TSC frequency offset estimation algorithm is as Figure 1 shown.

[0140] 2.2 Frequency-domain delay estimation algorithm

[0141] The frequency-domain delay estimation algorithm estimates the frequency offset by analyzing the frequency-domain characteristics of the received signal. Due to the existence of the frequency offset, the received signal will generate a phase rotation in the frequency domain and cause interference (ICI) between subcarriers of different frequencies. In the RCIS system, the signal is first transformed by the discrete Fourier transform (DFT) to obtain the frequency-domain representation R k , where the frequency offset of each subcarrier is manifested as a linear change in phase.

[0142] Assume that the received signal is r n , and its frequency-domain representation is R k . Due to the existence of the frequency offset ε, the received frequency-domain signal R k can be expressed as:

[0143]

[0144] where R k is the frequency-domain signal, and e j2πεn / N represents the phase rotation term caused by the frequency offset ε. The frequency offset ε will cause different phase offsets for each subcarrier of the received signal, thus affecting the correct demodulation of the frequency-domain signal.

[0145] The frequency-domain delay estimation algorithm estimates the frequency offset by calculating the frequency-domain phase difference between symbol pairs with an interval I. For the received symbols r n and r n+I , whose frequency-domain representations are R k and R k+I respectively, their phase differences can be expressed by the following formula:

[0146]

[0147] where is the estimated frequency offset value, is the phase difference of the frequency-domain signal, and N is the sequence length (autocorrelation window size). The advantage of this algorithm is that it can efficiently estimate the frequency offset in a complex channel environment. Especially in the case of multipath fading and strong noise, it can still provide high-precision frequency offset estimation through the maximum likelihood estimation (MLE) method. The schematic diagram of the FSD frequency offset estimation is as shown in Figure 2 .

[0148] Local correlation estimation algorithm

[0149] The local correlation estimation algorithm is an effective method for estimating the frequency offset based on the cross-correlation between the received signal and a known local training sequence. In RCIS, the estimation of the frequency offset needs to be achieved through the correlation between the received signal and the known training sequence. This method can effectively improve the estimation accuracy and has good robustness especially in the case of low signal-to-noise ratio and high dynamic environment.

[0150] In the local correlation estimation algorithm, the length of the received signal is usually not equal to the length of the training sequence. To estimate the frequency offset more precisely, the frequency offset information is often extracted by performing a sliding window correlation between the received signal and the training sequence and calculating their cross-correlation function. Specifically, we use one of the Ga128 sequences in the STF sequence as the known training sequence. The length of the received signal may be greater than or less than the length of the training sequence. Therefore, when designing the algorithm, considering the length difference between the received signal and the training sequence, the cross-correlation calculation needs to be adjusted accordingly.

[0151] Assume that the length of the received signal is N r , while the length of the training sequence is N t = 128 (i.e., the length of one Ga128 sequence), and the received signal is The training sequence is The cross-correlation function between the received signal and the training sequence can be expressed as:

[0152]

[0153] where R cross (i) represents the cross-correlation function between the received signal and the training sequence at the i-th moment, represents the conjugate complex number of the m-th sample of the training sequence. Since the Gray sequence has excellent correlation characteristics, when the received sequence is aligned with the local sequence, the cross-correlation function R cross (i) reaches a peak, as shown in the following figure. A total of 17 correlation peaks are observed. The sampling point positions corresponding to each peak are as Figure 3 shown, clearly reflecting the phase information when the sequences are aligned.

[0154] The frequency offset ε will cause the phase rotation of the received signal. Therefore, the phase information of the cross-correlation function can be used to estimate the frequency offset value. According to the definition of the cross-correlation function, the estimation of the frequency offset ε can be achieved by calculating the phase difference between two adjacent symbols. The estimation formula for the frequency offset is:

[0155]

[0156] where represents the estimated frequency offset value, and arg(R cross (i + I) · R cross (i) * ) represents the phase difference of the cross-correlation function at offsets i and i + I, and I is the correlation interval.

[0157] In local correlation-based estimation algorithms, different optimization strategies can be used, such as the peak algorithm and the mean algorithm, to further improve the accuracy of frequency offset estimation. The peak algorithm estimates the frequency offset value by finding the position of the maximum value in the cross-correlation function. The mean algorithm reduces the influence of noise by accumulating the phase information of multiple cross-correlation values and utilizing its statistical characteristics.

[0158] 3.1 Local Peak Estimation Algorithm

[0159] As Figure 4 shown, the peak algorithm estimates the frequency offset by finding the position of the maximum peak in the cross-correlation result.

[0160] Assume the cross-correlation result is R cross (i), then the estimation of the frequency offset can be calculated by the following formula:

[0161]

[0162] where i max represents the position of the maximum value in the cross-correlation function.

[0163] 3.2 Local Mean Estimation Algorithm

[0164] As Figure 5 shown, to improve the accuracy of frequency offset estimation, the cross-correlation values between multiple symbols can be averaged. The mean algorithm reduces the influence of noise by accumulating the phase information of multiple cross-correlation results.

[0165] Assume the phase differences of multiple cross-correlation functions are θ 1 , θ 2 ,... θ L , then the estimation of the frequency offset can be expressed as:

[0166]

[0167] where L is used to calculate the number of symbol pairs for averaging, and θ l is the phase difference between the l-th symbol pair. By averaging the phase differences of multiple symbol pairs, the algorithm can effectively reduce the influence of noise on frequency offset estimation and enhance the stability of the estimation.

[0168] Dual-Stage Frequency Offset Estimation Algorithm

[0169] In a radar communication integrated system (RCIS), the estimation of frequency offset faces a contradiction between "range - accuracy". Traditional single - stage frequency offset estimation algorithms usually make a trade - off between the frequency offset range and the estimation accuracy, and it is difficult to meet the requirements of wide - frequency - offset capture and high - precision estimation simultaneously. For example, the algorithm based on the short training sequence (STF) can capture a wide frequency offset (such as 250 kHz), but due to noise interference and phase accumulation effects, its estimation accuracy is difficult to meet the requirements of high - reliability communication; the algorithm based on the unique word (UW) can only cover a frequency offset range below 125 kHz due to the limitations of the symbol period and the correlation window length, but it can achieve fine estimation through the phase information within the data block. To solve this problem, the present invention proposes a two - stage frequency offset estimation algorithm. By dividing the frequency offset estimation process into two stages: coarse estimation and fine estimation, a progressive compensation architecture is formed, aiming to improve the range and accuracy of frequency offset estimation.

[0170] As Figure 6 shown, the core idea of the two - stage frequency offset estimation algorithm is: First, use the time - domain sliding correlation algorithm based on the STF sequence for coarse estimation to capture a relatively wide frequency offset range; then, perform refined estimation on the compensated data through the time - domain sliding correlation frequency offset estimation algorithm based on the UW sequence to obtain higher frequency offset estimation accuracy. The specific steps are as follows:

[0171] The first stage (coarse estimation): The received signal extracts the STF sequence through frame synchronization, and uses the time - domain delay estimation algorithm to perform coarse estimation of the frequency offset. Assume the length of the received signal is N r , and the received signal is Then the autocorrelation function of the received signal and its own delayed sequence can be expressed as:

[0172]

[0173] where R STF (i) represents the autocorrelation function of the received sequence STF and its own delayed sequence, reflecting the similarity between the received signal and the training sequence, and I is the operation correlation interval.

[0174] Through the phase information of the autocorrelation function, the estimation of the frequency offset can be achieved by the following formula:

[0175]

[0176] where is the coarse - estimated frequency offset value based on the STF sequence. The frequency offset estimation range of this stage is ±250 kHz, meeting the system's requirement for wide - frequency - offset capture. Through this coarse - estimated frequency offset value correct the signal after the STF sequence, and the received signal after frequency offset correction is:

[0177]

[0178] Second stage (fine estimation): For the received signal that has been roughly estimated and corrected through the STF sequence, the UW sequence is further extracted, and a time-domain delay estimation algorithm based on the UW sequence is used for fine estimation. Assume that the received signal after the correction in the first stage is The autocorrelation between the corrected UW received signal and the delay of the UW sequence can be expressed as:

[0179]

[0180] The refined estimation of the frequency offset can be achieved through the following formula:

[0181]

[0182] It should be noted that in the time-domain delay estimation algorithm based on the UW sequence, the range of frequency offset estimation is restricted by two key conditions. First, the maximum range of frequency offset estimation is determined by the formula where f s represents the sampling frequency, and D is the length of the correlation window. In this stage, the length of the correlation window is set to 64 samples, which is the length of one UW (Unique Word). In the simulation experiment, the sampling frequency is set to 64 MHz. According to the above formula, the maximum estimable frequency offset is 500 kHz. Second, to ensure the effectiveness of the algorithm, the phase change within a data block shall not exceed 2π. This condition can be expressed by the formula △φ = 2π△ε·N s < 2π, where N s represents the length of the data block. According to this condition, the calculated maximum estimable frequency offset is 125 kHz. Combining the above two conditions, we take the minimum value as the final maximum estimable frequency offset, that is, 125 kHz.

[0183] Since the frequency offset value within 250 kHz has been compensated in the first stage, the estimation range in the second stage can fully meet the system performance. Combining the estimation results of the first stage and the second stage, the final frequency offset estimation value is:

[0184]

[0185] The two-stage frequency offset estimation algorithm has significant advantages compared with the traditional single-stage estimation algorithm. In the first stage, rough estimation is carried out through the STF sequence, which can quickly capture a large frequency offset range with relatively low computational complexity; in the second stage, fine estimation is carried out through the UW sequence to further improve the accuracy of frequency offset estimation. The simulation results show that the two-stage frequency offset estimation algorithm can effectively meet the frequency offset estimation requirements under complex channel conditions, especially having strong robustness in high-speed mobile and multipath environments.

[0186] Simulation Results and Performance Comparison

[0187] As shown in Table 1, the system simulation uses the CM1.2 channel condition and simulates two digital modulation methods, QPSK and 16QAM. In order to comprehensively evaluate the performance of each algorithm, the simulation conditions are uniformly set, including a carrier frequency of 8 GHz, a sampling frequency of 64 MHz, and a phase noise of 0. The receiving end uses MMSE frequency domain equalization under ideal channel information conditions.

[0188] Table 1 System simulation parameters

[0189] System parameters Parameter setting Physical layer symbol rate (sampling rate) 64 MSps Symbol mapping QPSK / 16QAM Frame structure IEEE 802.11ay SC PHY Channel type CM1.2 Data block length / CP length 512 / 64 Number of packets 10000 Number of data blocks per packet 256 Equalization L-MMSE frequency domain equalization

[0190] In order to verify the impact of carrier frequency offset on system performance, the necessity of frequency offset compensation and the effectiveness of the proposed algorithm, the system was first compensated for frequency offset by taking the above-mentioned time domain delay estimation algorithm as an example. By introducing frequency offsets of different sizes into the system, we compared the difference in system performance before and after compensation. The simulation results show that frequency offset compensation has a significant impact on the performance of the system under different frequency offset conditions. Specifically, when different frequency offsets (such as 10kHz, 20kHz, and 30kHz) are introduced, the bit error rate (BER) of the system shows a significant improvement, especially under higher SNR conditions, the compensated system shows better performance than the uncompensated system. This result further proves the important role of frequency offset compensation in improving system performance.

[0191] like Figure 7 As shown in the figure, in the QPSK modulation system, frequency offset has a significant impact on the bit error rate (BER) of the system. As the frequency offset increases, the BER of the uncompensated system increases significantly, especially at higher frequency offsets (such as 20kHz and 30kHz), the system performance deteriorates more significantly. This phenomenon shows that frequency offset causes the phase rotation of the received signal, thereby increasing inter-symbol interference and bit error rate. In contrast, the system performance is significantly improved after frequency offset compensation, and the BER curve tends to the ideal state of no frequency offset, which verifies the necessity of frequency offset compensation and its effectiveness in improving system performance.

[0192] Likewise Figure 8 As shown in the figure, in the 16QAM modulation system, the impact of frequency offset on system performance is also very significant. As the frequency offset increases, the uncompensated system bit error rate also rises sharply, while the compensated system shows stronger anti-interference ability and lower bit error rate. Considering that the impact and compensation effect of frequency offset in QPSK and 16QAM modulation systems are similar, and QPSK modulation is representative in performance evaluation, the subsequent simulation of algorithm performance will be based on QPSK modulation, and the effectiveness of the algorithm will be demonstrated through the estimation accuracy (NMSE).

[0193] For the algorithm described in the present invention, first, an absolute frequency offset value of 20 kHz is added to the system to simulate the influence of different numbers of Ga128 pairs on the estimation accuracy (NMSE). According to the theoretical derivation of the algorithm, the more the number of Ga128, the better the estimation accuracy (NMSE) should be. The simulation results verify this point, that is, with the increase in the number of Ga128, the estimation accuracy has been significantly improved.

[0194] As Figure 9 shown, with the increase in the number of training sequence pairs (length), the estimation accuracy (NMSE) of all algorithms shows a gradually increasing trend. However, with the increase in the number of training sequences, the amplitude of performance improvement gradually decreases.

[0195] In addition, from Figure 9 (a) or the comparison in 9(b), it can be seen that under the same number of training sequence pairs, the frequency offset estimation accuracy based on the UW sequence is significantly better than that based on the STF sequence. This indicates that the algorithm based on the UW sequence has an advantage in estimation accuracy. However, its estimation range is relatively limited. Relatively speaking, although the algorithm based on the STF sequence has slightly lower accuracy, it has an advantage in the frequency offset range. According to the foregoing theoretical analysis and subsequent simulation verification, when the number of training sequences is 15 pairs, the algorithm based on the STF sequence can already provide sufficient estimation accuracy. Therefore, in practical applications, the advantage of the STF sequence lies in its wider frequency offset estimation range, and the accuracy gap is no longer a significant problem in the case of 15 pairs of training sequences.

[0196] In the simulation of the local correlation estimation algorithm, Figure 9 (c) shows that the performance of the mean algorithm is significantly better than that of the peak algorithm. This is because the mean algorithm can effectively reduce the influence of noise on the estimation result by averaging the cross-correlation values between multiple symbols, thereby improving the stability and robustness of the algorithm. In contrast, the peak algorithm is easily interfered by noise due to relying on a single maximum correlation value, resulting in a decrease in estimation accuracy. Therefore, the mean algorithm is selected as the preferred method in subsequent simulations to improve the accuracy and stability of frequency offset estimation.

[0197] Finally, the two-stage frequency offset estimation algorithm (d) can effectively break through the trade-off limitation between the frequency offset range and estimation accuracy of the single-stage algorithm by combining the advantages of the estimation based on the STF sequence and the estimation based on the UW sequence, and is applicable to a wider range of application scenarios. However, the computational complexity of the two-stage algorithm is relatively high, which limits its application in actual implementation. Nevertheless, the two-stage frequency offset estimation algorithm still shows strong advantages in scenarios requiring high accuracy and wide frequency offset range, and its applications and optimizations in different scenarios will be further explored subsequently.

[0198] In summary, as the number of training sequence pairs increases, the estimation accuracy (NMSE) of all algorithms gradually improves, but the magnitude of performance improvement gradually decreases. When using 15 pairs of training sequences, the estimation accuracy has reached a sufficient level. Further increasing to 16 pairs of training sequences brings a slight performance improvement, but the computational complexity increases significantly. Therefore, to balance performance and computational efficiency, 15 pairs of training sequences are selected for subsequent algorithm simulations.

[0199] Based on this, the following simulations will focus on studying the performance of different algorithms in the frequency offset estimation range, such as Figure 10 shown. We will analyze the estimation capabilities of algorithms based on STF and UW sequences in different frequency offset ranges, further explore the advantages and disadvantages of each algorithm under different frequency offset conditions, as well as their applicability in practical applications.

[0200] From Figure 10 (a) and Figure 10 (b), it can be seen that the maximum frequency offset that can be estimated by the frequency offset estimation based on the STF sequence is 250 kHz, while the estimation range based on the UW sequence is limited within 125 kHz. Beyond this range, the estimation accuracy based on the UW sequence will decrease significantly, resulting in an inability to accurately estimate the frequency offset. This result indicates that the STF sequence has an obvious advantage in the frequency offset estimation range, capable of covering a wider frequency offset range, while the UW sequence has an advantage in accuracy, but its application is limited by the frequency offset range.

[0201] Figure 10 (c) shows the simulation results of the local mean correlation algorithm. It can be seen from the figure that the local mean correlation algorithm can accurately estimate when the frequency offset is small, but when the frequency offset increases to 220 kHz and 240 kHz, accurate estimation can only be achieved under relatively high signal-to-noise ratio conditions. This indicates that the estimation performance of the local correlation estimation algorithm is greatly affected by noise under high frequency offset conditions, resulting in the estimation range not reaching the theoretical maximum value and being unable to meet the system's requirements for accuracy and range. Therefore, although the local correlation estimation algorithm performs well in some scenarios, its limitation lies in the narrow frequency offset estimation range.

[0202] Figure 10 (d) shows the simulation results of the two-stage frequency offset estimation algorithm. The same as the estimation range based on the STF sequence, the two-stage frequency offset estimation algorithm can also reach an estimation range of 250 kHz, indicating that this algorithm has strong adaptability and can provide high-precision estimation within a relatively large frequency offset range. The two-stage algorithm overcomes the trade-off limitation between range and accuracy of the single-stage algorithm through staged estimation, combining the advantages of STF sequence-based estimation and UW sequence-based estimation, enabling it to maintain a high estimation accuracy within a wide frequency offset range.

[0203] In summary, each frequency offset estimation algorithm has its own advantages and disadvantages in terms of range and accuracy. The estimation based on the STF sequence performs excellently in the frequency offset range, but its accuracy is slightly inferior to that of the UW sequence. Although the local mean correlation algorithm performs well at low frequency offsets, it is greatly affected by noise, resulting in insufficient accuracy in high frequency offset estimation. The two-stage frequency offset estimation algorithm, on the other hand, shows balanced performance in terms of range and accuracy and is an ideal choice for dealing with complex frequency offset environments.

[0204] In the CM1.2 channel environment, a 20 kHz frequency offset is introduced, and the time-domain delay estimation algorithm, frequency-domain delay estimation algorithm, local correlation mean algorithm, and two-stage frequency offset algorithm are respectively used for estimation. The performance simulation results of the fixed frequency offset are as Figure 11 shown.

[0205] In the simulation results, we observe that the time-domain delay estimation algorithm and the frequency-domain delay estimation algorithm exhibit exactly the same performance. Therefore, the time-domain delay estimation algorithm is used as the general term for the time-frequency delay estimation algorithm in the following analysis. Under the condition of relatively low signal-to-noise ratio (SNR < 8 dB), the local correlation mean algorithm performs the best, followed by the two-stage frequency offset estimation algorithm, which is about 3 dB lower, while the time-domain delay estimation algorithm performs the worst, about 2 dB lower than the two-stage frequency offset estimation algorithm. This phenomenon can be attributed to the fact that the noise component of the signal is more significant at low SNR. In this case, all algorithms are subject to greater noise interference during frequency offset estimation. The time-domain delay estimation algorithm has a weak ability to suppress noise in a low SNR environment, so the estimation error is large. In contrast, the local correlation mean algorithm can more effectively reduce the influence of noise by performing cross-correlation analysis on the signal, thereby improving the estimation accuracy. The two-stage frequency offset estimation algorithm has a poor noise suppression effect when dealing with a low SNR environment, resulting in performance inferior to the local correlation mean algorithm.

[0206] As the signal-to-noise ratio increases, the signal quality improves, the influence of noise gradually decreases, and the performance gap between the algorithms also gradually converges. Figure 12 shows the algorithm performance at different frequency offset magnitudes under the condition that the SNR is fixed at 12 dB.

[0207] At this time, the performance of the time-domain delay estimation algorithm and the local correlation mean algorithm tends to be the same, but both are inferior to the two-stage frequency offset estimation algorithm. The main reason for this phenomenon is that the correlation window length of the UW sequence used in the second stage of the two-stage frequency offset estimation algorithm is relatively short, which reduces the cumulative effect of phase noise and at the same time reduces the influence of adjacent channel interference. At high SNR, the interference of noise on the correlation operation has been significantly weakened, and at this time, the advantage of the short window length is highlighted, and it can more accurately capture the instantaneous characteristics of phase changes.

[0208] Under the same simulation environment, a 250 kHz frequency offset is introduced, and the performance simulation results of the fixed frequency offset are asFigure 13 as shown

[0209] As Figure 13 shown, under the condition of 250 kHz frequency offset, the performance of the four frequency offset estimation algorithms varies with the signal-to-noise ratio (SNR). Specifically, as the SNR increases, the estimation accuracy (NMSE) of all algorithms shows a downward trend, indicating that the improvement of the signal-to-noise ratio can effectively improve the accuracy of frequency offset estimation.

[0210] Under low SNR conditions, the performance differences of the four algorithms are more obvious. The NMSE of the time-domain delay estimation algorithm and the frequency-domain delay estimation algorithm is relatively high, while the local correlation mean algorithm and the two-stage frequency offset estimation algorithm show lower NMSE values. This result shows that in a high-noise environment, the local correlation-based algorithms and the two-stage algorithms can suppress noise more effectively and provide more accurate frequency offset estimation compared with the time-domain and frequency-domain algorithms.

[0211] As the SNR further increases, the performance of all algorithms tends to approach, and the two-stage frequency offset estimation algorithm always maintains the lowest NMSE value, demonstrating its advantage in dealing with larger frequency offsets. Although the performance of the time-domain delay estimation algorithm and the frequency-domain delay estimation algorithm has improved, they still cannot reach the accuracy level of the two-stage frequency offset estimation algorithm. This verifies that the two-stage algorithm combines multiple estimation strategies and can provide higher accuracy in a wide frequency offset range.

[0212] Therefore, it can be concluded from Figure 13 this that the two-stage frequency offset estimation algorithm shows the best performance under high SNR conditions, especially suitable for complex environments that require high-precision estimation. Although other algorithms also perform well under low frequency offset and low SNR conditions, the advantage of the two-stage algorithm is more obvious when dealing with larger frequency offsets.

[0213] Through multi-scenario simulation experiments, the performance boundaries and applicability of each frequency offset estimation algorithm are clarified. The two-stage frequency offset estimation algorithm is at the highest level in terms of computational complexity, but its advantage lies in covering a wide frequency offset range from 0 to 250 kHz and showing the best estimation accuracy within this range. In contrast, the computational complexity of the time-domain delay estimation algorithm is further optimized to 45% - 60% of the two-stage frequency offset estimation algorithm. Although there is a gap of about 2 dB in its NMSE performance compared with the two-stage frequency offset estimation algorithm, it can still provide reliable estimation results in medium and high frequency offset scenarios.

[0214] From the perspective of system design, the selection of algorithms requires a trade-off between complexity and performance requirements. In the frequency offset range of 0 to 125 kHz, if resource efficiency is prioritized, the two-stage frequency offset estimation algorithm can meet the engineering requirements; while if extreme accuracy is pursued, the two-stage frequency offset estimation algorithm needs to be adopted. For the high-dynamic scenario of 125 to 250 kHz, the two-stage frequency offset estimation becomes the optimal solution due to its wide-range capture ability, while the remaining algorithms provide a compromise for low-complexity scenarios. It should be noted that when the frequency offset exceeds 250 kHz, none of the existing algorithms can meet the accuracy requirements, and a technology for suppressing out-of-range frequency offset needs to be introduced, which will be the focus of subsequent research.

[0215] In summary, the essence of optimizing the frequency offset estimation algorithm is the dynamic balance of the three-dimensional parameters of "accuracy - complexity - range". The experimental results verify the effectiveness of the scenario-based strategy: the two-stage frequency offset estimation algorithm is suitable for high-precision and wide-range requirements, while the remaining algorithms show stronger engineering adaptability in resource-constrained scenarios.

[0216] To verify the improvement effect of the proposed frequency offset estimation algorithm on system performance, the inventors constructed a full-link simulation platform for the integrated radar and communication system based on the IEEE 802.11ad protocol. Under the CM1.2 indoor line-of-sight channel model, for QPSK and 16QAM modulation schemes respectively, -87 dBc / Hz phase noise and 20 kHz carrier frequency offset were introduced, and through Monte Carlo simulation of 10,000 frames of data, the bit error rate (BER) characteristics in three scenarios of no frequency offset, uncompensated frequency offset, and compensation with different algorithms were compared and analyzed.

[0217] The above is only the preferred implementation manner of the present invention. It should be pointed out that for those of ordinary skill in the art of this technology, several improvements can be made without departing from the principle of the present invention, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A frequency offset estimation method in a radar communication integrated system, characterized in that: The method described includes the following: 1) Impact of carrier frequency deviation on system performance; 2) Time-frequency delay estimation algorithm; 3) Local correlation estimation algorithm; 4) Two-stage frequency offset estimation algorithm.

2. The frequency offset estimation method in a radar communication integrated system according to claim 1, characterized in that: The impact of the carrier frequency deviation on the system performance specifically includes the following: The influence of phase noise is set to 0, that is, it is assumed that the phase noise in the signal has been effectively suppressed, or its influence is small enough to be ignored; Assume that during the signal transmission process, the received signal r n Affected by the carrier frequency deviation ε, the model of the received signal can be expressed as: r n =s n ·e j2πεn / N +v n Among them, s n is the symbol sent, e j2πεn / N is the phase rotation term caused by frequency offset, v n is the received noise, and N is the length of the signal. The formula shows that frequency deviation will cause the phase of the received signal to rotate at each sampling point, ignoring the further impact of phase noise on the received signal. Convert this model to the frequency domain, assuming that the signal is transformed by N-point discrete Fourier transform (DFT), and obtain the frequency domain signal R k : Substitute into the signal model: Further simplifying: It can be seen that the frequency offset causes the phase rotation of the frequency domain signal and generates inter-subcarrier interference (ICI), which will affect the accuracy of frequency domain demodulation. Specifically, the phase shift caused by the frequency offset will be aggravated in a multipath fading environment, causing interference between different subcarriers, resulting in a significant increase in the system's bit error rate. We continue to ignore the interference of phase noise on the signal and set it to 0. When the signal has frequency deviation at the receiving end, the constellation diagram of the received signal will rotate, which will affect the correct judgment of the symbol. Assuming that the receiving end uses a single carrier frequency domain equalization (SC-FDE) system, in the frequency domain, the signal of each subcarrier can be obtained by discrete Fourier transform (DFT). When frequency deviation exists, the phase of each subcarrier of the received signal in the frequency domain will be rotated, resulting in a deviation between the received symbol and the transmitted symbol. Especially in multipath fading channels, the phase rotation caused by frequency deviation will be superimposed on the signals of different paths, thereby increasing inter-symbol interference (ISI). For a multipath channel, assuming that the received signal is the superposition of multiple paths, the signal of each path can be expressed as: Where L represents the number of multipaths of the signal, h i is the attenuation factor of the i-th path; the frequency offset will cause the signal of each path to produce different phase rotations, which will increase the gap between the received symbol and the ideal symbol, further causing demodulation errors; In the SC-FDE system, the impact of frequency offset is not only manifested as symbol phase rotation, but also as amplitude attenuation in the frequency domain. Due to frequency offset, the amplitude of each subcarrier in the system will change, resulting in the amplitude of the received signal being affected. This amplitude change further reduces the system's signal-to-noise ratio (SNR), thereby increasing the bit error rate (BER). In a multipath channel, frequency offset will introduce phase rotation and amplitude attenuation. Assuming that the received signal has been equalized in the frequency domain, the interference caused by frequency offset can be expressed by the following formula: This phase rotation and amplitude attenuation will cause interference between symbols, making it impossible to demodulate the received signal correctly. The frequency offset can be compensated by frequency offset estimation technology, but if the compensation is incomplete, there will still be a certain error. Through accurate frequency offset estimation, we can estimate the frequency offset value in the received signal and implement frequency offset correction by taking the inverse frequency offset value; assuming that the estimated frequency offset is The frequency offset correction process can be performed by comparing the received signal with Multiply to complete the correction: This correction process effectively eliminates the phase rotation caused by the frequency offset, thereby restoring the original phase of the signal and enabling the received signal to be correctly demodulated.

3. The frequency offset estimation method in a radar communication integrated system according to claim 1, characterized in that: The time-frequency delay estimation algorithm specifically includes the following contents: When estimating the frequency offset, the range of the frequency offset estimation is limited based on the length of the training sequence. Assuming that the correlation window length of the training sequence is D sampling points, the maximum estimable frequency offset range △ε max It can be derived from the following formula: Among them, f s is the sampling frequency, D is the correlation window length; in the STF sequence, assuming that the correlation window length is 128 samples and the sampling frequency is 64MHz, then the maximum frequency deviation estimation range is: Therefore, the time-domain delay estimation algorithm based on the STF sequence can theoretically estimate the frequency offset range up to 250kHz; the derivation of this estimation range provides theoretical support for frequency offset estimation and ensures that the performance requirements of the system can be met in practical applications; The time domain delay estimation algorithm and the frequency domain delay estimation algorithm include the following: 2.

1. Time domain delay estimation algorithm: The basic idea of ​​the time domain delay estimation algorithm is to extract the frequency offset information by calculating the time domain autocorrelation of the training sequence in the received signal; assuming that the i-th symbol in the received STF (Short Training Frame) sequence is r i , the time domain model of the received signal can be expressed as: r i =s i ·e j2πεi / N +v i Among them, s i is the symbol sent, e j2πεi / N is the phase rotation term caused by the frequency offset ε, v i is the received noise, N is the length of the signal, and ε is the frequency deviation; the frequency deviation causes the received symbols to produce phase rotation in the time domain; In order to estimate the frequency offset, the time domain delay estimation algorithm calculates the autocorrelation value between symbol pairs with a fixed interval I to obtain the frequency offset information; assuming that in the STF sequence, the interval between each symbol pair is I sampling points; for the received symbol r i and r i+I , and their conjugate multiplication gives the time domain autocorrelation value: From the phase of the autocorrelation value, the frequency offset ε can be estimated as follows: in, is the estimated frequency offset value, arg(R(i)) is the phase of the autocorrelation value, and N is the sequence length (autocorrelation window size); by calculating the autocorrelation values ​​between multiple symbol pairs and taking their average, we can get an accurate frequency offset estimate; The advantages of the time domain delay estimation algorithm are that it is simple to calculate and has strong robustness to noise; however, the accuracy of the time domain estimation is limited by the length of the training sequence. Increasing the sequence length can improve the estimation accuracy, but the accuracy of the time domain estimation algorithm is still limited by the length of the training sequence; 2.2 Frequency Domain Delay Estimation Algorithm: The frequency domain delay estimation algorithm estimates the frequency offset by analyzing the frequency domain characteristics of the received signal. Due to the existence of frequency offset, the received signal will produce phase rotation in the frequency domain and cause interference (ICI) between subcarriers of different frequencies. In the RCIS system, the signal is first transformed by discrete Fourier transform (DFT) to obtain the frequency domain representation R k , where the frequency deviation of each subcarrier is expressed as a linear change of phase; Assume that the received signal is r n , which is represented in the frequency domain as R k , due to the existence of frequency deviation ε, the received frequency domain signal R k It can be expressed as: Among them, R k is the frequency domain signal, e j2πεn / N Represents the phase rotation term caused by the frequency offset ε; the frequency offset ε will cause different phase offsets for each subcarrier of the received signal, thus affecting the correct demodulation of the frequency domain signal; The frequency domain delay estimation algorithm estimates the frequency offset by calculating the frequency domain phase difference between symbol pairs with interval I; for the received symbol r n and r n+I , whose frequency domain representation is R k and R k+I , their phase difference can be expressed by the following formula: in, is the estimated frequency offset value, is the phase difference of the frequency domain signal, and N is the sequence length (autocorrelation window size); the advantage of this algorithm is that it can efficiently estimate the frequency offset in a complex channel environment, especially in the case of multipath fading and strong noise, and can still provide high-precision frequency offset estimation through the maximum likelihood estimation (MLE) method.

4. The frequency offset estimation method in a radar communication integrated system according to claim 1, characterized in that: The local correlation estimation algorithm is specifically Includes the following: 3.1 Local peak estimation algorithm: The peak algorithm estimates the frequency offset by finding the maximum peak position in the cross-correlation result; assuming that the cross-correlation result is R cross (i), the frequency offset can be estimated by the following formula: where i max represents the position of the maximum value in the cross-correlation function; 3.2 Local mean estimation algorithm In order to improve the accuracy of frequency offset estimation, the cross-correlation values ​​between multiple symbols are averaged; the average algorithm reduces the influence of noise by accumulating the phase information of multiple cross-correlation results; Assume that the phase difference of multiple cross-correlation functions is θ1, θ2, ...θ L , then the frequency deviation estimation can be expressed as: Where L is used to calculate the number of symbol pairs on average, θ l is the phase difference between the lth symbol pair; by averaging the phase differences of multiple symbol pairs, the algorithm can effectively reduce the impact of noise on frequency offset estimation and enhance the stability of estimation.

5. The frequency offset estimation method in a radar communication integrated system according to claim 1, characterized in that: The two-stage frequency offset estimation algorithm specifically includes the following contents: The dual-stage frequency offset estimation algorithm first uses the time-domain sliding correlation algorithm based on the STF sequence for coarse estimation to capture a wider frequency offset range; then, the time-domain sliding correlation frequency offset estimation algorithm based on the UW sequence is used to refine the compensated data to obtain higher frequency offset estimation accuracy; the specific steps are as follows: The first stage (rough estimation): The received signal extracts the STF sequence through frame synchronization, and uses the time domain delay estimation algorithm to roughly estimate the frequency offset; assuming that the length of the received signal is N r , the received signal is r=[r1,r2,...,r Nr ], then the autocorrelation function of the received signal and its own delayed sequence can be expressed as: Among them, R STF (i) represents the autocorrelation function of the received sequence STF and its own delayed sequence, reflecting the similarity between the received signal and the training sequence, and I is the operational correlation interval; Through the phase information of the autocorrelation function, the frequency offset can be estimated by the following formula: in, is a rough estimate of the frequency deviation based on the STF sequence; the frequency deviation estimation range at this stage is ±250kHz, which meets the system's capture requirements for wide frequency deviation; through this rough estimate of the frequency deviation Correct the signal after the STF sequence, and the received signal after frequency offset correction is: The second stage (fine estimation): For the received signal that has been roughly estimated and corrected by the STF sequence, the UW sequence is further extracted, and a time domain delay estimation algorithm based on the UW sequence is used for fine estimation; assuming that the received signal after the correction in the first stage is The autocorrelation of the corrected UW received signal and the UW sequence delay can be expressed as: The refined estimation of frequency deviation can be achieved by the following formula: It is worth noting that in the time-domain delay estimation algorithm based on UW sequences, the range of frequency offset estimation is limited by two key conditions; First, the maximum range of frequency offset estimation is given by the formula Determine, where f s represents the sampling frequency, and D is the correlation window length. In this stage, the correlation window length is set to 64 samples, i.e., the length of a UW (Unique Word). In the simulation experiment, the sampling frequency is set to 64 MHz. According to the above formula, the maximum estimated frequency deviation is 500 kHz. Secondly, to ensure the effectiveness of the algorithm, the phase change within a data block must not exceed 2π; this condition can be obtained by the formula △φ=2π△ε·N s <2π, where N s Indicates the length of the data block; Based on this condition, the maximum estimated frequency deviation is calculated to be 125kHz; Combining the above two conditions, we take the minimum value as the final maximum estimated frequency deviation, which is 125kHz; Since the frequency deviation within 250kHz has been compensated in the first stage, the estimation range of the second stage can fully meet the system performance; combining the estimation results of the first and second stages, the final frequency deviation estimation value is: The two-stage frequency offset estimation algorithm has significant advantages over the traditional single-stage estimation algorithm. The first stage performs coarse estimation through the STF sequence, which can quickly capture a larger frequency offset range with low computational complexity. The second stage performs fine estimation through the UW sequence to further improve the accuracy of frequency offset estimation. Simulation results show that the two-stage frequency offset estimation algorithm can effectively meet the frequency offset estimation requirements under complex channel conditions, especially in high-speed mobile and multipath environments.

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