A method and system for blind estimation of sampling frequency error in a non-cooperative scenario

Abstract

The application discloses a sampling frequency error blind estimation method and system in a non-cooperative scene, and relates to the technical fields of wireless communication and signal processing. The method comprises the following steps: the method acquires an OFDM receiving signal adopting non-circular modulation under non-synchronous sampling; the segmented conjugate cyclic autocorrelation function is calculated by using the complementary second-order statistical characteristics of the non-circular signal, and the autocorrelation accumulation is performed on the segmented conjugate cyclic autocorrelation function; the cost function is constructed by summing and modulating on the effective time delay set; the multi-window accumulation of the cost function is performed by introducing the multi-search window structure, the window length corresponding to the maximum accumulation value is searched exhaustively, and the offset basic cyclic frequency estimation value is obtained; and finally, the sampling frequency offset estimation value is calculated according to the deviation from the ideal basic cyclic frequency. The application does not depend on pilot symbols, fully utilizes the higher density cyclic impulse characteristics of the non-circular signal, and significantly improves the estimation precision under the conditions of low signal-to-noise ratio and short observation length.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and signal processing technology, and in particular to a blind estimation method and system for sampling frequency error in non-cooperative scenarios. Background Technology

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology is a key technology in modern communications due to its high spectral efficiency and resistance to multipath interference. When the sampling clocks at the transmitter and receiver mismatch, a sampling frequency offset (SFO) occurs. SFO severely degrades channel estimation accuracy and system performance.

[0003] Most existing SFO estimations rely on pilot symbols or other prior information from the transmitter. In non-cooperative communication scenarios, the receiver cannot obtain prior information, necessitating blind estimation methods. Therefore, blind SFO estimation methods have significant research value and engineering implications.

[0004] Among existing blind SFO estimation methods, SFO estimation based on cyclic stationarity is an important class of methods. This type of method utilizes the standard cyclic autocorrelation of the signal, and the number of periodic impulse features that can be used is limited. Its performance deteriorates sharply in some challenging communication environments (such as low signal-to-noise ratio and short observation length).

[0005] In recent years, non-circular signals have been widely used in systems with limited interference or satellite communications. OFDM signals with non-circular subcarrier modulation possess conjugate cyclostationary characteristics, containing a higher density of cyclic impulse features. Their application value in engineering practice, especially in blind synchronization, has not been previously explored. Therefore, it is necessary to propose a new blind SFO estimation method for OFDM signals to fully utilize the conjugate cyclostationary characteristics of non-circular OFDM signals and improve the accuracy of SFO estimation. Summary of the Invention

[0006] To address this, embodiments of the present invention provide a blind sampling frequency error estimation method and system for non-cooperative scenarios, which solves the problems of insufficient estimation accuracy of existing OFDM blind SFO estimation methods based on standard cyclic autocorrelation functions under conditions of low signal-to-noise ratio and short observation length, and the inability of the receiver to obtain prior information such as pilot symbols in non-cooperative communication scenarios.

[0007] To address the aforementioned technical problems, embodiments of the present invention provide a blind estimation method for sampling frequency error in non-cooperative scenarios, the method comprising: The discrete-time received signal obtained by the receiving end under asynchronous sampling conditions is acquired, wherein the subcarrier of the received signal adopts a non-circular modulation method; By utilizing the complementary second-order statistical properties of non-circular signals, the received signal is segmented, and the segmented conjugate cyclic autocorrelation function is calculated. The piecewise conjugate cyclic autocorrelation function is subjected to autocorrelation accumulation processing to obtain the autocorrelation estimate of the conjugate cyclic autocorrelation function after autocorrelation. The conjugate cyclic autocorrelation estimator after autocorrelation is summed and moduloed over the effective time delay set to construct a cost function to characterize the cyclic frequency; A multi-search-window structure is introduced, which divides the normalized cyclic frequency range into multiple search windows. The cost function values ​​are accumulated at the corresponding positions of each search window to obtain a refined cost function with multi-window accumulation. The window length that maximizes the refined cost function value is then exhaustively searched to obtain the offset basic cyclic frequency estimate. The sampling frequency offset estimate is calculated based on the deviation between the offset basic cycle frequency estimate and the ideal basic cycle frequency without offset.

[0008] Preferably, the received signal is an orthogonal frequency division multiplexing signal with subcarriers using non-circular modulation, wherein the non-circular modulation includes any one of BPSK modulation, unbalanced QPSK modulation, or pulse amplitude modulation; the expression of the received signal is: ; in, For the receiving end at the 1st Discrete-time signal obtained at each sampling time point The useful data duration for OFDM symbols, The total duration of a single OFDM symbol satisfies ,in For the protection interval duration; The actual sampling interval at the receiving end. For the number of subcarriers, This is the subcarrier index number, with values ​​ranging from... arrive ; For the first The first OFDM symbol Modulated data carried on each subcarrier The subcarrier complex exponent indicates that the frequency domain data is modulated onto the corresponding orthogonal subcarrier frequency; This is the OFDM symbol number, with values ​​ranging from negative infinity to positive infinity; For real-valued pulse shaping functions, The current sampling time of the receiving end and the number of sampling times. The time difference between the start times of each symbol This is additive noise, representing interference in the channel.

[0009] Preferably, the piecewise conjugate cyclic autocorrelation function is calculated as follows: ; in, Indicates the loop frequency to be searched. and delay variables Under these conditions, for conjugate signals The value of the cyclic autocorrelation function obtained by piecewise estimation; This is the start time index of the current segment. The segment length, To receive the signal at the current accumulation time The sample values, In order to receive signals in advance The sample values ​​at each sampling time. The complex exponential rotation factor is used for frequency filtering of the accumulated results; the segment length Greater than the absolute value of the largest delay in the effective delay set, i.e. ,in To ensure that the effective time delay set is non-zero for the conjugate cyclic autocorrelation function.

[0010] Preferably, an autocorrelation delay parameter is used. Autocorrelation operation is performed on the piecewise conjugate cyclic autocorrelation function to obtain the expression of the autocorrelation conjugate cyclic autocorrelation function: ; in, This represents the value of the conjugate cyclic autocorrelation function after autocorrelation. The total length of the received signal. This is a complex conjugate operation; let the autocorrelation delay parameter be equal to the segment length, i.e. .

[0011] Preferably, the range of the time delay variable is limited to: ,in To ensure that the effective time delay set contains a non-zero conjugate cyclic autocorrelation function, the conjugate cyclic autocorrelation estimates after autocorrelation are summed and moduloed on the effective time delay set to establish a cost function characterizing the offset cyclic frequency: ; in, The cost function value is given; when the observation length is sufficiently large and the segment length is appropriate, the cost function exhibits periodic pulse peaks at the offset cyclic frequency.

[0012] Preferably, the method of introducing a multi-search-window structure, dividing the normalized cyclic frequency range into multiple search windows, and accumulating the cost function values ​​at corresponding positions in each search window to obtain a refined cost function with multi-window accumulation includes: Normalize the cycle frequency range Evenly divided into There are 1 search window, each with a length of 1. And satisfy The cost function values ​​are accumulated at the corresponding positions in each search window to obtain a refined cost function with multi-window accumulation. ; in, To refine the cost function value, This represents the total number of search windows. For window indexing, For the first The starting frequency position of each search window.

[0013] Preferably, the search window length The boundary constraints must be met. ; in, The basic cycle frequency, For the number of subcarriers, The length of the cyclic prefix is ​​given; the boundary constraints are used to ensure that the search window can effectively capture the basic cyclic frequency and its associated harmonics.

[0014] Preferably, the method for obtaining the estimated value of the offset basic cycle frequency is as follows: By comparing the accumulated values ​​of the refined cost function under different window lengths, an exhaustive search is performed to find the window length that maximizes the value of the refined cost function, and this window length is used as an estimate of the basic cycle frequency. ; in, This is the basic cycle frequency estimate.

[0015] Preferably, the sampling frequency offset estimate is based on the offset basic cycle frequency estimate. With the ideal fundamental cycle frequency that has not deviated Deviation calculation between: ; in, This is the estimated value for the sampling frequency offset.

[0016] This invention also provides a blind estimation system for sampling frequency error in non-cooperative scenarios. This system is used to implement the aforementioned blind estimation method for sampling frequency error in non-cooperative scenarios, specifically including: The signal acquisition module is used to acquire the discrete-time received signal obtained by the receiver under asynchronous sampling conditions, wherein the subcarrier of the received signal adopts a non-circular modulation method; The segmented conjugate cyclic autocorrelation calculation module is used to segment the received signal and calculate the segmented conjugate cyclic autocorrelation function by utilizing the complementary second-order statistical properties of non-circular signals. The autocorrelation accumulation module is used to perform autocorrelation accumulation processing on the piecewise conjugate cyclic autocorrelation function to obtain the autocorrelation estimate of the conjugate cyclic autocorrelation after autocorrelation. The cost function construction module is used to sum and take the modulus of the conjugate cyclic autocorrelation estimate after autocorrelation on the effective time delay set to construct a cost function to characterize the cyclic frequency. An enhanced grid search module is used to introduce a multi-search window structure, divide the normalized cyclic frequency range into multiple search windows, accumulate the cost function values ​​at the corresponding positions of each search window to obtain a refined cost function with multi-window accumulation, and exhaustively search for the window length that maximizes the refined cost function value to obtain the offset basic cyclic frequency estimate. The sampling frequency offset estimation module is used to calculate the sampling frequency offset estimate based on the deviation between the offset basic cycle frequency estimate and the ideal basic cycle frequency without offset.

[0017] As can be seen from the above technical solutions, this invention application has the following beneficial effects: (1) Significantly improves the SFO estimation accuracy under low signal-to-noise ratio and short observation length. This invention fully utilizes the conjugate cyclostationary characteristics of non-circular OFDM signals, whose conjugate autocorrelation function contains a number of periodic impulse features in the time delay-time domain. Compared to the standard autocorrelation function, which only has More impact points This provides richer cyclic stationarity information for blind SFO estimation. Simulation results show that, at a signal-to-noise ratio of -6dB, the mean square error of this invention is 3 to 5 orders of magnitude lower than that of traditional methods.

[0018] (2) Effective suppression of noise interference through quadratic autocorrelation accumulation. This invention performs autocorrelation accumulation processing on the piecewise conjugate cyclic autocorrelation function, taking... This allows useful signals to be superimposed in phase and noise to be randomly canceled, further enhancing the peak characteristics at the cyclic frequency and improving the reliability of cyclic frequency detection under weak signal conditions.

[0019] (3) Enhanced grid search is used to focus harmonic energy and improve the robustness of estimation under limited samples. This invention introduces a multi-search window structure and takes advantage of the fact that non-circular signals have related harmonics at integer multiples of the basic cyclic frequency to collect and accumulate the harmonic energy scattered at various points on the frequency axis. This effectively avoids the problem of single-peak search being easily interfered with by noise pseudo-peaks. It can still converge quickly under extremely low signal-to-noise ratio (-10dB) conditions and has strong engineering adaptability. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Referring to the drawings will make the features and advantages of the present invention clearer. The drawings are illustrative and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of a blind estimation method for sampling frequency error in a non-cooperative scenario provided by the present invention; Figure 2 This is a comparison diagram of the autocorrelation impulse distribution of the standard autocorrelation function and the piecewise conjugate cyclic autocorrelation function proposed in this invention in the time-delay domain, wherein (a) is the autocorrelation impulse distribution diagram of the standard autocorrelation function in the time-delay domain, and (b) is the autocorrelation impulse distribution diagram of the piecewise conjugate cyclic autocorrelation function proposed in this invention in the time-delay domain; Figure 3 This is a comparison of the peak distribution of the cost function based on standard cyclic autocorrelation in the embodiments of the present invention and the cost function based on conjugate cyclic autocorrelation proposed in the present invention, wherein (a) is the peak distribution of the cost function based on standard cyclic autocorrelation and (b) is the peak distribution of the cost function based on conjugate cyclic autocorrelation proposed in the present invention. Figure 4 This is a comparison chart of the mean square error of the method of the present invention and the traditional method using standard cyclic stationarity under different normalized SFO conditions in the embodiments of the present invention; Figure 5 This is a comparison chart of the mean square error of the method of the present invention and the traditional method using standard cyclic stationarity under different signal-to-noise ratio conditions in the embodiments of the present invention; Figure 6 This is a block diagram of a blind estimation system for sampling frequency error in a non-cooperative scenario provided by the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Example 1: To address the shortcomings of existing OFDM blind SFO estimation methods based on the standard cyclic autocorrelation function, such as insufficient estimation accuracy under low signal-to-noise ratio and short observation length conditions, and the inability of the receiver to obtain prior information such as pilot symbols in non-cooperative communication scenarios, this invention proposes a blind estimation method for sampling frequency error in non-cooperative scenarios. Figure 1 As shown, the method includes the following steps: S1: Obtain the discrete-time received signal obtained by the receiving end under asynchronous sampling conditions, wherein the subcarrier of the received signal adopts a non-circular modulation method; S2: Utilize the complementary second-order statistical properties of non-circular signals to segment the received signal and calculate the segmented conjugate cyclic autocorrelation function; S3: Perform autocorrelation accumulation processing on the piecewise conjugate cyclic autocorrelation function to obtain the autocorrelation estimate of the conjugate cyclic autocorrelation after autocorrelation. S4: Summate the conjugate cyclic autocorrelation estimates after autocorrelation on the effective time delay set and take the modulus to construct a cost function to characterize the cyclic frequency; S5: Introduce a multi-search-window structure, divide the normalized cyclic frequency range into multiple search windows, accumulate the cost function values ​​at the corresponding positions of each search window to obtain a refined cost function with multi-window accumulation, and exhaustively search for the window length that maximizes the refined cost function value to obtain the offset basic cyclic frequency estimate. S6: Calculate the sampling frequency offset estimate based on the deviation between the offset basic cycle frequency estimate and the ideal basic cycle frequency without offset.

[0023] As can be seen from the above technical solution, this invention proposes a blind estimation method for sampling frequency error in non-cooperative scenarios. This method first acquires the OFDM received signal using non-circular modulation under asynchronous sampling, and calculates a piecewise conjugate cyclic autocorrelation function using its complementary second-order statistical properties to extract cyclic impulse features that are denser than the standard autocorrelation, providing rich periodic information for estimation. Then, the piecewise function undergoes autocorrelation accumulation processing, setting the hysteresis parameter equal to the piecewise length, so that useful signals are superimposed in phase and noise is randomly canceled, thereby further enhancing the peak features at the cyclic frequency. Next, a cost function is constructed by summing and moduloing over the effective delay set, converging the cyclic energy scattered under different delays into a single peak curve. Then, an enhanced grid search with multiple search windows is introduced, dividing the normalized cyclic frequency range into multiple windows. The cost function values ​​at corresponding positions of each window are accumulated, utilizing the characteristic that non-circular signals have harmonics at integer multiples of the fundamental frequency to achieve energy focusing. The estimated value of the offset basic cyclic frequency is obtained by exhaustively searching for the window length corresponding to the maximum accumulated value. Finally, the estimated sampling frequency offset is calculated based on the deviation between this estimated value and the ideal basic cyclic frequency. This method does not rely on prior information such as pilot symbols, and makes full use of the high-density conjugate cyclic stationary characteristics of non-circular signals, which significantly improves the estimation accuracy and robustness under conditions of low signal-to-noise ratio and short observation length.

[0024] Further, in step S1, the discrete-time received signal obtained by the receiving end under asynchronous sampling conditions is acquired, wherein the subcarrier of the received signal adopts a non-circular modulation method.

[0025] Specifically, in non-cooperative communication scenarios, the receiving end obtains discrete-time received signals under asynchronous sampling conditions. The received signal is an orthogonal frequency division multiplexing (OFDM) signal with subcarriers using non-circular modulation. The non-circular modulation method includes any one of BPSK modulation, unbalanced QPSK modulation, or pulse amplitude modulation. The signals generated by the above modulation methods have non-circular characteristics, and their complementary second-order statistics are not zero, which provides a physical basis for the present invention to utilize conjugate cyclostationarity.

[0026] The received signal The expression is: ; in, For the receiving end at the 1st Discrete-time signal obtained at each sampling time point The useful data duration for OFDM symbols, The total duration of a single OFDM symbol satisfies , The protection interval duration (i.e., the duration corresponding to the cyclic prefix length); This is the actual sampling interval at the receiving end. Due to the mismatch between the sampling clocks at the transmitting and receiving ends, Sampling interval with the transmitter There is a deviation between them, and this deviation is the sampling frequency offset that this invention aims to estimate; For the number of subcarriers, This is the subcarrier index number, with values ​​ranging from... arrive ; For the first The first OFDM symbol The modulated data carried on each subcarrier is non-circularly modulated. The subcarrier complex exponent indicates that the frequency domain data is modulated onto the corresponding orthogonal subcarrier frequency; This is the OFDM symbol number, with values ​​ranging from negative infinity to positive infinity, representing a continuously transmitted symbol stream; For real-valued pulse shaping functions, a rectangular window function is used in this embodiment. hour ,otherwise , used to define the start and end range of a single OFDM symbol; The current sampling time of the receiving end and the number of sampling times. The time difference between the start times of each symbol is used to determine which OFDM symbol's effective range the current sampling point belongs to; This is additive noise, representing interference in the channel.

[0027] The transmitter will modulate the non-circular data Mapped to On each subcarrier, a time-domain continuous signal is formed through OFDM modulation. The receiver uses its own clock. Perform asynchronous sampling to obtain discrete points The formula uses a double summation (first summing each subcarrier) to achieve this. Summation, then for each symbol Summation), and using a rectangular window Determine which symbol interval the current sampling point falls within, and then finally add the noise. Generate a receive sequence carrying sampling frequency offset information. .

[0028] Furthermore, in step S2, the received signal is segmented using the complementary second-order statistical properties of the non-circular signal, and the segmented conjugate cyclic autocorrelation function is calculated.

[0029] Since the complementary second-order statistics of non-circular signals are not zero, their conjugate cyclic autocorrelation function exhibits a periodic peak structure composed of isolated impulses and tilted impulse lines. This step utilizes this property to segment the received signal obtained in step S1 and calculate the segmented conjugate cyclic autocorrelation function.

[0030] Specifically, for the loop frequency to be searched and delay variables , will receive signal Divided into lengths of The function is divided into multiple segments, and the conjugate cyclic autocorrelation function is calculated for each segment. The segmented conjugate cyclic autocorrelation function... Calculate as follows: ; in, Indicates the loop frequency to be searched. and delay variables Under these conditions, for conjugate signals The cyclic autocorrelation function value obtained by piecewise estimation; subscript The superscript indicates the conjugate operation on the signal, which is the core feature that distinguishes this invention from the traditional standard cyclic autocorrelation method—utilizing the complementary second-order statistical properties (conjugate correlation) of non-circular signals rather than ordinary autocorrelation; The cycle frequency variable to be searched (normalized candidate frequencies, search range is within) arrive (between); within square brackets This is the start time index of the current segment (the position of the sliding window). A fixed time delay (lag, representing the time difference between the current sample and the previous sample) is used. (correlation of individual samples) The segment length; To receive the signal at the current accumulation time The sample values, In order to receive signals in advance Sample values ​​at each sampling time; The complex exponential twitch factor (Fourier analysis kernel) is used to filter the frequency of the accumulated results—when searching for candidate frequencies. When the exponential term is equal to the actual cyclic frequency in the signal, it will cause the product to... The DC component in the middle is coherently accumulated, in Sharp peaks are generated in the middle; if If there is a mismatch, the cumulative result will approach zero.

[0031] To ensure that the segmented window can completely encompass all relevant operations under all effective delays, the segment length... It must be greater than the absolute value of the largest delay in the effective delay set, i.e. ,in This constraint ensures that the effective time delay set is such that the conjugate cyclic autocorrelation function is not zero. It guarantees that each segmented window contains at least one complete "current value - historical value" pairing cycle for correlation calculations, avoiding computational failures and boundary effects caused by insufficient window length.

[0032] It should be noted that here It is a continuously changing test frequency, and the algorithm will... Constantly changing within the scope Substitute the values ​​into the formula to calculate. Only when... The value of is exactly equal to the actual fundamental cyclic frequency in the received signal after being affected by the sampling frequency offset. Only when the complex exponential twitch factor is completely synchronized with the internal periodicity of the signal will the accumulated result show a sharp peak.

[0033] Further, in step S3, the piecewise conjugate cyclic autocorrelation function is subjected to autocorrelation accumulation processing to obtain the autocorrelation estimate of the conjugate cyclic autocorrelation function.

[0034] The result obtained in step S2 Although the cyclic frequency information is already included, it still contains a large amount of residual noise and sidelobe interference. To further enhance the peak characteristics corresponding to the cyclic frequency and suppress the influence of noise, this step performs a second autocorrelation accumulation process on the piecewise conjugate cyclic autocorrelation function.

[0035] Specifically, autocorrelation delay parameters are used. Autocorrelation operation is performed on the piecewise conjugate cyclic autocorrelation function, that is, along the time axis in step S2. The segmented conjugate cyclic autocorrelation function values ​​obtained by sliding are considered as a new time series. Periodicity is extracted from this series again to obtain the expression for the conjugate cyclic autocorrelation function after autocorrelation: ; in, The value of the conjugate cyclic autocorrelation function after autocorrelation (fancy lettering) (This represents the enhanced estimator after two autocorrelation accumulation processes). The total length of the received signal. This is a complex conjugate operation. The lower bound for summation starts from... Start, Limit The end is because the formula contains the same... and To ensure indexing It will not exceed the limit (less than zero), and at the same time ensures Since its length does not exceed the total length of the signal, the boundaries at both ends are shrunk inwards. Each sample point ensures that complete and valid paired data can be obtained in each operation.

[0036] The physical essence of this step is: to compare the "preliminary correlation value at the current moment" with the "past..." Multiplying the conjugates of the initial correlation values ​​at time points is equivalent to performing another autocorrelation operation on the correlation function in the time domain, i.e., "correlation of correlations". Through this operation, noise is further canceled out due to its randomness, while the true cyclic frequency components are enhanced by in-phase superposition due to their stable periodicity.

[0037] In this embodiment, the autocorrelation delay parameter is set to be equal to the segment length, i.e. This is because the cyclic impulse characteristics of non-circular OFDM signals exhibit a periodic beat on the time axis that corresponds to the segment length. and During matching, in the formula and If the impulse position falls precisely in phase, the product results in coherent accumulation (a sharp increase in peak value); if the two are not equal, misalignment cancellation can easily occur, reducing peak detection performance. Therefore... It is the optimal parameter configuration for accurately obtaining the cycle frequency.

[0038] Further, in step S4, the conjugate cyclic autocorrelation estimate after autocorrelation is summed and moduloed on the effective time delay set to construct a cost function for characterizing the cyclic frequency.

[0039] The result obtained in step S3 It is still a two-dimensional data structure (the horizontal axis represents candidate frequencies). The vertical axis represents time delay. This step restricts the range of the time delay variable to... Information from all time delay dimensions is aggregated on the effective time delay set to construct a one-dimensional cost function.

[0040] Specifically, the range of the time delay variable is limited to: ,in This is the effective time delay set that ensures the conjugate cyclic autocorrelation function is not zero. For non-circular OFDM signals, this effective time delay set includes... The number of impulse points carrying periodic information is far greater than the number found only in the standard autocorrelation function. There are several impact points (of which) (where is the cyclic prefix length), which provides richer cyclic stationarity information for this invention and is an important foundation for achieving high-precision SFO estimation. The conjugate cyclic autocorrelation estimators after autocorrelation are summed and moduloed on the effective time delay set to establish a cost function characterizing the offset cyclic frequency: ; in, The cost function value is the overall energy index that brings together multiple "hidden periodic cues" scattered across different time delay axes.

[0041] It should be noted that the modulo operation It plays a crucial role here: It is a complex number, containing both amplitude and phase information. Due to different time delays corresponding During accumulation, the phase may become disordered due to factors such as channel and timing deviations. If complex numbers are added directly, components of different phases may cancel each other out (or even cancel out to zero). Taking the modulus before summing ensures that the "energy contribution" at each time delay is positive, achieving incoherent accumulation (energy accumulation), thus forming a sharp and stable peak at the true cyclic frequency. When the observation length is sufficiently large and the segment length is appropriate, the cost function... Offset cycle frequency The structure will exhibit extremely sharp periodic pulse peaks.

[0042] like Figure 2 As shown, for non-circular OFDM signals, the piecewise conjugate cyclic autocorrelation function of this invention exhibits a periodic peak structure composed of isolated impulses and tilted impulse lines. , Within the defined time delay-time region, the number of impulse points containing periodic information in the standard autocorrelation function is: The number of impulse points containing periodic information in the conjugate autocorrelation function of this invention is Therefore, the conjugate autocorrelation function contains more information than the standard autocorrelation function. An impulse point carrying periodic information provides richer cyclic stationarity information for blind SFO estimation.

[0043] like Figure 3 As shown, according to steps S2 to S4, under the condition that the signal-to-noise ratio is set to 5dB, the conjugate cost function curve of the received signal is calculated. Meanwhile, a cost function based on traditional standard autocorrelation was introduced as a control group. Although the cost function based on traditional standard autocorrelation has a zero cycle frequency... There is an extremely high spurious peak at this point, but this peak does not shift with SFO and therefore contributes nothing to SFO estimation. However, the true SFO information is found at the various shifted post-cycle frequency characteristic points. The cost function constructed in this invention It exhibits a denser and sharper pulse peak structure than the traditional standard autocorrelation cost function, which lays a solid foundation for high-precision frequency search in the subsequent steps of this invention.

[0044] Furthermore, in step S5, a multi-search window structure is introduced to divide the normalized cyclic frequency range into multiple search windows. The cost function values ​​are accumulated at the corresponding positions of each search window to obtain a refined cost function with multi-window accumulation. The window length that maximizes the refined cost function value is then exhaustively searched to obtain the offset basic cyclic frequency estimate.

[0045] The cost function constructed in step S4 Although it exhibits a sharp peak at the true cyclic frequency, under low signal-to-noise ratio (SNR) conditions (e.g., -10 dB), a single peak can still be overwhelmed by noise. Furthermore, the conjugate cyclic autocorrelation function of non-circular OFDM signals not only at the fundamental cyclic frequency... There is a sharp pulse at that point, and at its integer multiples (i.e.) The frequency spectrum also exhibits periodic impulse peaks (i.e., correlated harmonics). This step utilizes the widespread nature of these harmonics by introducing an enhanced grid search method—a multi-search-window structure—to gather the harmonic energy scattered across the frequency axis, thereby enhancing the locking onto weak peak signals.

[0046] Specifically, the normalized cycle frequency range Evenly divided into There are 1 search window, each with a length of 1. And satisfy The cost function values ​​are accumulated at the corresponding positions in each search window to obtain a refined cost function with multi-window accumulation: ; in, To refine the cost function value, the independent variable is the window length. Rather than frequency This reflects the fact that when the candidate basic cycle frequency is At that time, all its harmonic positions ( The average cumulative strength of the original cost function value at point ( ); This represents the total number of search windows. For window indexing; For the first The starting frequency position of each search window—when The starting position is (Zero frequency point), when The starting position is ,when The starting position is And so on, the first The starting point of each window is located on the frequency axis. The physical meaning of this formula is: within the candidate window length... Below, on the frequency axis respectively The original cost function is extracted at these equally spaced locations. The values ​​are then summed and averaged.

[0047] If the candidate window length Exactly equal to the true offset fundamental cycle frequency Then the starting position of the window Precisely aligned to the frequency axis At each location, the energy accumulated is the energy at the peak of each harmonic. It will be extremely large (coherent superposition). If Not equal to If the starting positions of these windows fall on the sidelobes or noise floor of each harmonic peak, the cumulative result will only be the noise level. In this way, it is equivalent to repeatedly verifying the weak signal. Next, the signal-to-noise ratio was obtained. A gain of times.

[0048] To ensure the search window can effectively capture the fundamental cyclic frequency and its associated harmonics, while avoiding the inclusion of irrelevant frequency components due to an excessively large window or the inclusion of noise spurious peaks due to an excessively small window, the length of the search window is [specified]. The boundary constraints must be met. ; in, The true fundamental cycle frequency after being affected by the sampling frequency offset. For the number of subcarriers, This is the length of the cyclic prefix. This boundary constraint ensures the search window length. It should be neither less than the fundamental frequency (otherwise, false noise peaks will be captured), nor greater than the fundamental frequency and... The product (to prevent the window span from being too large, which would cause the loss of effective harmonics or the introduction of interference components) thus reasonably limits the search space.

[0049] Then, the accumulated values ​​of the refined cost function under different window lengths are compared, and an exhaustive search is performed to find the window length that maximizes the value of the refined cost function. This window length is then used as an estimate of the basic cycle frequency. ; in, This is the basic cycle frequency estimate. After this step of enhanced grid search, the original problem of finding the "highest single peak" is transformed into finding the "value that maximizes the cumulative value". "This more robust optimization problem significantly improves the detection capability at low signal-to-noise ratios and limited sample conditions with high cyclic frequency."

[0050] Further, in step S6, a sampling frequency offset estimate is calculated based on the deviation between the offset basic cycle frequency estimate and the ideal basic cycle frequency without offset.

[0051] Normalized sampling frequency offset (SFO) is defined as the sampling interval at the receiver. Sampling interval with the transmitter The relative deviation between them: .

[0052] Ideal cycle frequency with SFO An offset will occur, and the cycle frequency after the offset will change. satisfy: .

[0053] Therefore, the SFO estimation problem can be transformed into the problem of estimating the offset cycle frequency. Based on the offset basic cycle frequency estimate obtained in step S5... With the ideal fundamental cycle frequency that has not deviated The deviation between them is used to calculate the estimated sampling frequency offset: ; in, This is an estimate of the sampling frequency offset. Ideal fundamental cycle frequency. The fundamental cycle frequency is determined by the OFDM system parameters; for non-circular modulated OFDM signals, it is [value missing]. (After normalization), among which This represents the total number of samples for a single OFDM symbol.

[0054] Thus, this invention completes the entire processing flow from asynchronous sampling received signal to sampling frequency offset estimation, realizing blind SFO estimation in non-cooperative scenarios that does not rely on pilot symbols and prior information.

[0055] Furthermore, to verify the effectiveness of the method of the present invention, this embodiment verifies the method of the present invention through computer simulation (based on MATLAB). The OFDM system configuration parameters are as follows: number of subcarriers. Circular prefix length The length of a single OFDM symbol is Set the number of OFDM symbols to be transmitted. The subcarrier mapping employs unbalanced quadrature phase shift keying (QPSK) modulation, and different non-circularity values ​​are set as follows: , , The non-circularity is This is equivalent to one-dimensional linear modulation such as BPSK. The signal segment length and hysteresis length are set as follows: Window length for enhanced grid search Search scope set to arrive The search advance step size is set to All numerical evaluation curves are in The average value was obtained after several independent Monte Carlo trials.

[0056] like Figure 4 As shown, let the signal-to-noise ratio be... The normalized SFO range is arrive This paper examines the blind estimation mean square error (MSE) of the proposed SFO estimation algorithm using conjugate cyclic stationarity (ICB-SFS) at different SFO levels. Simultaneously, a traditional cyclic stationarity SFO estimation algorithm (CB-SFS) employing an enhanced grid search and a simple linear search of the cost function are introduced as comparative benchmarks. Simulation results show that, throughout the entire SFO variation range, the estimation error of the ICB-SFS algorithm is consistently lower than that of the CB-SFS algorithm using enhanced grid search. arrive Order of magnitude. By decreasing the non-circularity to and It was found that the performance decreased as the non-circularity decreased, but the method of the present invention outperformed the blind estimation method based on traditional cyclostationarity across the entire parameter range, proving the universality of the technical solution and its adaptability to signals with different non-circularity.

[0057] like Figure 5 As shown, in the second set of simulations, the normalized SFO is fixed at 100%. The signal-to-noise ratio range is set to to Simulation results show that the CB-SFS algorithm exhibits an extremely high error step in the low signal-to-noise ratio region, leading to a sharp deterioration in estimation performance. In contrast, the algorithm described in this invention operates with a non-circularity of [missing information]. At that time, arrive It converged within the extremely low signal-to-noise ratio range, demonstrating strong noise robustness. When the signal-to-noise ratio reached... When the above is true, the present invention has a non-circularity of and Under these conditions, the estimation error directly reaches an extremely low lower bound. The above simulation results fully demonstrate that the method described in this invention, by utilizing the higher density of cyclic impulse features in conjugate cyclic autocorrelation and combining it with an enhanced grid search multi-window energy accumulation strategy, can effectively enhance the cyclic frequency detection capability under limited sample and low signal-to-noise ratio conditions, and significantly improve the blind estimation accuracy of sampling frequency offset.

[0058] Example 2: This invention provides a blind estimation system for sampling frequency error in non-cooperative scenarios. This system is used to implement the blind estimation method for sampling frequency error in non-cooperative scenarios described in Embodiment 1 above. Figure 6 As shown, it specifically includes: The signal acquisition module 100 is used to acquire the discrete-time received signal obtained by the receiving end under asynchronous sampling conditions, wherein the subcarrier of the received signal adopts a non-circular modulation method. This module corresponds to the function of step S1 in Embodiment 1, and the expression of the acquired received signal is as described above, including timing error information caused by sampling frequency offset.

[0059] The piecewise conjugate cyclic autocorrelation calculation module 200 is used to segment the received signal and calculate the piecewise conjugate cyclic autocorrelation function by utilizing the complementary second-order statistical properties of non-circular signals. This module corresponds to the function of step S2 in Embodiment 1. Calculate the piecewise conjugate cyclic autocorrelation function, where the piecewise length is... Must meet .

[0060] The autocorrelation accumulation module 300 is used to perform autocorrelation accumulation processing on the piecewise conjugate cyclic autocorrelation function to obtain the autocorrelation estimate of the conjugate cyclic autocorrelation. This module corresponds to the function of step S3 in Embodiment 1, according to... Perform calculations, and Configure the parameters to the optimal level.

[0061] The cost function construction module 400 is used to sum and take the modulus of the conjugate cyclic autocorrelation estimate after autocorrelation over the effective time delay set to construct a cost function characterizing the cyclic frequency. This module corresponds to the function of step S4 in Embodiment 1, according to... Construct a cost function within the effective delay set. The energy information of each time delay dimension is aggregated.

[0062] The enhanced grid search module 500 is used to introduce a multi-search window structure, dividing the normalized cyclic frequency range into multiple search windows. The cost function values ​​are accumulated at corresponding positions in each search window to obtain a refined cost function with multi-window accumulation. The module then exhaustively searches for the window length that maximizes the refined cost function value, thereby obtaining an estimate of the offset basic cyclic frequency. This module corresponds to the function of step S5 in Embodiment 1, according to... Calculate the refined cost function under boundary constraints. We exhaustively search for the optimal window length and then... Obtain the basic cycle frequency estimate.

[0063] The sampling frequency offset estimation module 600 is used to calculate the sampling frequency offset estimate based on the deviation between the offset basic cycle frequency estimate and the ideal basic cycle frequency without offset. This module corresponds to the function of step S6 in Embodiment 1, according to... Calculate the estimated sampling frequency offset.

[0064] This embodiment provides a blind estimation system for sampling frequency error in a non-cooperative scenario, used to implement the aforementioned blind estimation method for sampling frequency error in a non-cooperative scenario. Therefore, the specific implementation of the blind estimation system for sampling frequency error in a non-cooperative scenario can be found in the previous embodiment section of the blind estimation method for sampling frequency error in a non-cooperative scenario. For example, the signal acquisition module 100, the piecewise conjugate cyclic autocorrelation calculation module 200, the autocorrelation accumulation module 300, the cost function construction module 400, the enhanced grid search module 500, and the sampling frequency offset estimation module 600 are respectively used to implement steps S1, S2, S3, S4, S5, and S6 in the aforementioned blind estimation method for sampling frequency error in a non-cooperative scenario. Therefore, the specific implementation can be referred to the description of the corresponding embodiments. To avoid redundancy, it will not be repeated here.

[0065] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0066] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0067] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0068] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A blind estimation method for sampling frequency error in non-cooperative scenarios, characterized in that, include: The discrete-time received signal obtained by the receiving end under asynchronous sampling conditions is acquired, wherein the subcarrier of the received signal adopts a non-circular modulation method; By utilizing the complementary second-order statistical properties of non-circular signals, the received signal is segmented, and the segmented conjugate cyclic autocorrelation function is calculated. The piecewise conjugate cyclic autocorrelation function is subjected to autocorrelation accumulation processing to obtain the autocorrelation estimate of the conjugate cyclic autocorrelation function after autocorrelation. The conjugate cyclic autocorrelation estimator after autocorrelation is summed and moduloed over the effective time delay set to construct a cost function to characterize the cyclic frequency; A multi-search-window structure is introduced, which divides the normalized cyclic frequency range into multiple search windows. The cost function values ​​are accumulated at the corresponding positions of each search window to obtain a refined cost function with multi-window accumulation. The window length that maximizes the refined cost function value is then exhaustively searched to obtain the offset basic cyclic frequency estimate. The sampling frequency offset estimate is calculated based on the deviation between the offset basic cycle frequency estimate and the ideal basic cycle frequency without offset.

2. The blind estimation method for sampling frequency error in non-cooperative scenarios according to claim 1, characterized in that, The received signal is an orthogonal frequency division multiplexing signal with subcarriers using non-circular modulation, wherein the non-circular modulation method includes any one of BPSK modulation, unbalanced QPSK modulation, or pulse amplitude modulation; the expression of the received signal is: ； in, For the receiving end at the 1st Discrete-time signal obtained at each sampling time point The useful data duration for OFDM symbols, The total duration of a single OFDM symbol satisfies ,in For the protection interval duration; The actual sampling interval at the receiving end. For the number of subcarriers, This is the subcarrier index number, with values ​​ranging from... arrive ; For the first The first OFDM symbol Modulated data carried on each subcarrier The subcarrier complex exponent indicates that the frequency domain data is modulated onto the corresponding orthogonal subcarrier frequency; This is the OFDM symbol number, with values ​​ranging from negative infinity to positive infinity; For real-valued pulse shaping functions, The current sampling time of the receiving end and the number of sampling times. The time difference between the start times of each symbol This is additive noise, representing interference in the channel.

3. The blind estimation method for sampling frequency error in non-cooperative scenarios according to claim 1, characterized in that, The piecewise conjugate cyclic autocorrelation function is calculated as follows: ； in, Indicates the loop frequency to be searched. and delay variables Under these conditions, for conjugate signals The value of the cyclic autocorrelation function obtained by piecewise estimation; This is the start time index of the current segment. The segment length, To receive the signal at the current accumulation time The sample values, In order to receive signals in advance The sample values ​​at each sampling time. The complex exponential rotation factor is used for frequency filtering of the accumulated results; the segment length Greater than the absolute value of the largest delay in the effective delay set, i.e. ,in To ensure that the effective time delay set is non-zero for the conjugate cyclic autocorrelation function.

4. The blind estimation method for sampling frequency error in non-cooperative scenarios according to claim 3, characterized in that, Using autocorrelation delay parameters Autocorrelation operation is performed on the piecewise conjugate cyclic autocorrelation function to obtain the expression of the autocorrelation conjugate cyclic autocorrelation function: ； in, This represents the value of the conjugate cyclic autocorrelation function after autocorrelation. The total length of the received signal. This is a complex conjugate operation; let the autocorrelation delay parameter be equal to the segment length, i.e. .

5. The blind estimation method for sampling frequency error in non-cooperative scenarios according to claim 4, characterized in that, Limit the range of delay variables to ,in To ensure that the effective time delay set contains a non-zero conjugate cyclic autocorrelation function, the conjugate cyclic autocorrelation estimates after autocorrelation are summed and moduloed on the effective time delay set to establish a cost function characterizing the offset cyclic frequency: ； in, The cost function value is given; when the observation length is sufficiently large and the segment length is appropriate, the cost function exhibits periodic pulse peaks at the offset cyclic frequency.

6. The blind estimation method for sampling frequency error in non-cooperative scenarios according to claim 1, characterized in that, The method of introducing a multi-search-window structure, dividing the normalized cyclic frequency range into multiple search windows, and accumulating the cost function values ​​at corresponding positions in each search window to obtain a refined cost function with multi-window accumulation includes: Normalize the cycle frequency range Evenly divided into There are 1 search window, each with a length of 1. And satisfy The cost function values ​​are accumulated at the corresponding positions in each search window to obtain a refined cost function with multi-window accumulation. ； in, To refine the cost function value, This represents the total number of search windows. For window indexing, For the first The starting frequency position of each search window.

7. The blind estimation method for sampling frequency error in non-cooperative scenarios according to claim 6, characterized in that, The search window length The boundary constraints must be met. ； in, The basic cycle frequency, For the number of subcarriers, The length of the cyclic prefix is ​​given; the boundary constraints are used to ensure that the search window can effectively capture the basic cyclic frequency and its associated harmonics.

8. The blind estimation method for sampling frequency error in non-cooperative scenarios according to claim 6, characterized in that, The method for obtaining the estimated value of the offset basic cycle frequency is as follows: By comparing the accumulated values ​​of the refined cost function under different window lengths, an exhaustive search is performed to find the window length that maximizes the value of the refined cost function, and this window length is used as an estimate of the basic cycle frequency. ； in, This is the basic cycle frequency estimate.

9. The blind estimation method for sampling frequency error in non-cooperative scenarios according to claim 8, characterized in that, The sampling frequency offset estimate is based on the offset fundamental cycle frequency estimate. With the ideal fundamental cycle frequency that has not deviated Deviation calculation between: ； in, This is the estimated value for the sampling frequency offset.

10. A blind estimation system for sampling frequency error in non-cooperative scenarios, characterized in that, The system is used to implement the blind estimation method for sampling frequency error in non-cooperative scenarios as described in any one of claims 1 to 9, comprising: The signal acquisition module is used to acquire the discrete-time received signal obtained by the receiver under asynchronous sampling conditions, wherein the subcarrier of the received signal adopts a non-circular modulation method; The segmented conjugate cyclic autocorrelation calculation module is used to segment the received signal and calculate the segmented conjugate cyclic autocorrelation function by utilizing the complementary second-order statistical properties of non-circular signals. The autocorrelation accumulation module is used to perform autocorrelation accumulation processing on the piecewise conjugate cyclic autocorrelation function to obtain the autocorrelation estimate of the conjugate cyclic autocorrelation after autocorrelation. The cost function construction module is used to sum and take the modulus of the conjugate cyclic autocorrelation estimate after autocorrelation on the effective time delay set to construct a cost function to characterize the cyclic frequency. An enhanced grid search module is used to introduce a multi-search window structure, divide the normalized cyclic frequency range into multiple search windows, accumulate the cost function values ​​at the corresponding positions of each search window to obtain a refined cost function with multi-window accumulation, and exhaustively search for the window length that maximizes the refined cost function value to obtain the offset basic cyclic frequency estimate. The sampling frequency offset estimation module is used to calculate the sampling frequency offset estimate based on the deviation between the offset basic cycle frequency estimate and the ideal basic cycle frequency without offset.

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