High-precision frequency offset estimation compensation method without data assistance under low signal-to-noise ratio

Abstract

The application relates to a low-signal-noise-ratio non-data-aided high-precision frequency offset estimation compensation method, belonging to the technical field of high-speed data transmission. The method comprises the following steps: performing order reduction operation on input signals to obtain four-phase constellation point signals; converting the signals from a rectangular coordinate system to a polar coordinate system; performing segmented FFT calculation on the signals to obtain signal superposition spectrum and perform peak value searching to obtain a periodogram peak value index; obtaining a coarse frequency offset estimation value according to the spectrum peak value index and other information, and completing coarse frequency offset compensation; performing order reduction demodulation operation and resampling on the compensated signals; performing segmented FFT calculation on the resampled signals, and obtaining a peak value index of the signals according to signal superposition spectrum; and performing fine frequency offset estimation according to the compensated peak value index, an extraction factor and other parameters such as the number of FFT points, and completing compensation on the signals. The application can perform high-precision frequency offset estimation in a low-signal-noise-ratio environment, effectively improves demodulation performance, and is suitable for wideband satellite communication systems and satellite high-speed data transmission systems.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-speed data transmission and specifically relates to a high-precision frequency offset estimation compensation method for non-data aided low signal-to-noise ratio, which is used in a wideband satellite communication system and a satellite high-speed data transmission system. BACKGROUND

[0002] Since the 21st century, with the wide popularization of broadband Internet, the continuous innovation and replacement of communication technology, and the development of satellite payload technology and multimedia technology, the wideband satellite communication system and the high-speed data transmission system have become an important research and development direction. The DVB-S2X standard proposed by the European Telecommunication Standardization Organization adds multiple use scenarios compared with the previous DVB-S2 standard, such as a very small aperture terminal (VSAT) characterized by VLSNR, an IP voice transmission characterized by superframe hopping beam, a cellular backhaul network, etc. In addition, in the face of complex and diversified application scenarios, DVB-S2X can automatically select and provide the optimal modulation and demodulation scheme by combining adaptive modulation and coding technology (ACM), further optimize the satellite link, and obtain greater efficiency improvement, and approach the theoretical Shannon limit as much as possible.

[0003] The continuous improvement of global satellite communication service quality and the demand for high-throughput and high-speed information transmission make the available space spectrum resources increasingly scarce. At present, in order to meet the demand for higher data transmission rate, higher spectrum utilization rate high-order modulation modes such as 16APSK, 32APSK, and a maximum of 256APSK are used, and more efficient coding and decoding modes such as BCH code and LDPC code are also used, which further improves the demodulation signal-to-noise ratio threshold requirement. These factors make it a valuable research direction to estimate and compensate the frequency offset and phase offset of the signal with high precision in a poor signal-to-noise ratio environment, otherwise it will become a bottleneck of signal reception and demodulation, and seriously affect the normal operation of other modules of the demodulation system.

[0004] For the research of carrier recovery algorithm, it can be divided into the following three algorithms according to whether the pilot data and coding information are used: one is a data aided method (Data Aided, DA) which uses the pilot information in the current data frame for correlation calculation and then performs carrier synchronization, another is a non-data aided method (NonData Aided, NDA) which does not directly use known prior data, and the third method is a coding aided algorithm (Code Aided, CA) which generally uses decoding soft information or uses related modulation information to estimate the correlation parameters.

[0005] Data-aided (DA) algorithms mainly use known information such as pilot blocks in data frames, such as L&R algorithm, M&M algorithm, Fitz algorithm, Kay algorithm, L&W algorithm, etc. Although the L&R algorithm and the Fitz algorithm have good anti-noise performance, the estimation range is small and the estimation accuracy is poor. Kay, L&W algorithm also only expands the estimation range, and is poor in anti-noise ability and estimation accuracy. And this kind of algorithm needs to use a large amount of pilot block data, which will cause a certain degree of loss of data frame transmission capacity. The code-aided (CA) algorithm was first proposed by Wangrok.Oh et al. in 2001. Its essence is to combine the decoding soft information output by the decoder with the iteration performance and synchronization to assist in carrier phase offset frequency offset estimation. This algorithm has good performance in low SNR environment, but it has obvious drawbacks. It needs to use multiple decoding iterations, which brings a certain time delay processing problem, affects the running efficiency of the whole system and has large calculation complexity, and the complex iteration structure will further increase the implementation complexity of FPGA.

[0006] The non-data-aided method is based on the maximum likelihood theory, and uses discrete time observation to estimate the frequency information of the single-tone signal. As a relatively classic algorithm, the DD algorithm takes the phase-locked loop as the core, and estimates and compensates the data frequency offset through the combination of decision, phase discrimination and loop filtering, but it is difficult to discriminate the phase for some high-order modulation modes, and the whole loop needs certain data to train and converge. Low SNR will cause decision error and lead to lock loss. In the low SNR scenario, the traditional frequency offset estimation algorithm is difficult to apply, especially in the case of no prior data and multiple modulations. The application has certain advantages in the scene, and can perform high-precision and stable frequency offset estimation and compensation on OPSK data and 8PSK / 8APSK data under the condition that the ESN0 is-3dB and 6dB respectively, and has low calculation complexity and is easy to implement. SUMMARY

[0007] The technical problem to be solved by the application is:

[0008] Under the condition of low SNR, in order to overcome the influence of random noise, the traditional frequency offset estimation algorithm generally uses data-aided (DA) algorithm to extract carrier correlation information through pilot data, but the estimation accuracy of this kind of algorithm is easily affected by SNR, and there is no pilot mode data frame in satellite communication system and high-speed data transmission system. In these integrated scenarios, the traditional frequency offset estimation algorithm is difficult to apply directly,

[0009] In view of the problems of the above frequency offset estimation method under low signal-to-noise ratio condition, the application provides a non-data-aided high-precision frequency offset estimation compensation method under low signal-to-noise ratio.

[0010] In order to solve the above technical problems, the technical scheme adopted by the application is:

[0011] A non-data-aided high-precision frequency offset estimation compensation method under low signal-to-noise ratio, characterized in that it comprises:

[0012] S1: performing order reduction operation on the input signal to obtain a four-phase constellation point signal;

[0013] S2: converting the signal obtained in S1 from a rectangular coordinate system to a polar coordinate system, amplifying the phase by 4 times, and then remapping it to a rectangular coordinate system to obtain a signal without modulation information;

[0014] S3: performing segmented FFT calculation on the signal obtained in S2 to obtain signal superimposed spectrum and perform peak value search to obtain periodogram peak value index;

[0015] S4: obtaining a coarse frequency offset value according to the frequency spectrum peak value index obtained in S3, FFT point number and modulation order, and completing coarse frequency offset compensation;

[0016] S5: performing order reduction demodulation operation of S1-S2 on the compensated signal obtained in S4, and performing resampling with decimation factor S to obtain a signal with sampling rate f s / S;

[0017] S6: performing segmented FFT calculation on the resampled signal obtained in S5, obtaining its peak value index according to the signal superimposed spectrum, and then performing interpolation calculation to obtain an index compensation factor to approximate the actual position of the peak value;

[0018] S7: performing fine frequency offset estimation according to the compensated peak value index, decimation factor S and FFT point number parameters and completing compensation of the signal.

[0019] Further technical scheme of the application: the S1 further comprises before it:

[0020] S0: performing timing recovery and frame synchronization processing on the received data symbol to eliminate symbol timing offset and obtain the data to be corrected, and simultaneously obtaining corresponding modulation mode information, wherein the modulation mode comprises non-QPSK.

[0021] Further technical scheme of the application: if the modulation mode is non-QPSK, the S1 is specifically:

[0022] The Mth power downgrading operation is performed on the outer loop constellation point of the input signal to obtain a four-phase constellation point consistent with QPSK modulation.

[0023] The further technical solution of the application is that the Mth power downgrading operation is performed on the outer loop constellation point of the input signal to obtain a four-phase constellation point consistent with QPSK modulation, comprising:

[0024] If the modulation type of the data to be corrected is 8PSK or 8APSK, the 2nd power downgrading operation is performed on the outer loop constellation point corresponding to the symbol; if the converted constellation point has a phase difference of π / 4 compared with the standard QPSK constellation point, the phase compensation is performed on the constellation point to obtain a four-phase constellation point consistent with QPSK phase.

[0025] If the modulation type of the data to be corrected is 16APSK, the value of M in the downgrading algorithm is represented as:

[0026] M=Y / 4

[0027] Wherein, Y is the number of outer loop data points corresponding to the data constellation; then the inner and outer circle power thresholds are determined, the Mth power downgrading operation is performed on the outer circle signal greater than the threshold, and the inner circle signal less than the power threshold is set to 0; if the converted constellation point has a phase difference of π / 4 compared with the standard QPSK constellation point, the phase compensation is performed on the constellation point to obtain a four-phase constellation point consistent with QPSK modulation.

[0028] The further technical solution of the application is that the S2 comprises:

[0029] S21: energy normalization is performed on the signal to obtain a signal s1(i);

[0030] S22: the s1(i) is converted from the rectangular polar coordinate system to the polar coordinate system to obtain the phase information θ of the signal i =2πf d iT s +φ0+φ z , wherein f d is the modulation frequency information, φ0 is the initial phase, and φ z is the phase domain Gaussian white noise component.

[0031] The 4-fold amplification is performed on θ i to remove the signal modulation information to obtain:

[0032] 4θ i =8πf d iT s +4φ0+4φ z

[0033] Mapping to the rectangular coordinate system has:

[0034] s2(i)=exp(j(8πfd iT s +4φ0+4φ z ).

[0035] A further technical solution of the present invention: S3 includes:

[0036] The signal s2(i) is segmented with the number of FFT calculation points N as the length, and FFT transformation is performed on each segment of the signal, which can be expressed as follows:

[0037]

[0038] Among them, h n is a segmented signal, k=0,1,…,N-1;

[0039] Using the formula |F k |=F k F k * / N obtains the spectrum amplitude, superimposes and sums the spectrum amplitudes of all data segments, and searches for the maximum peak index k in the summed spectrum result max1 .

[0040] A further technical solution of the present invention: S4 includes:

[0041] The estimated expression of frequency deviation obtained from the maximum likelihood estimation theory is as follows:

[0042]

[0043] Where, T s is the sampling interval, k max1 is the spectrum peak index, N is the number of FFT points, M is the QPSK modulation index, and the rough estimate of frequency offset

[0044] A further technical solution of the present invention: S6 includes:

[0045] S61: Divide the resampled signal x(n)′ into segments of length N, and obtain the peak index k of the signal superposition spectrum according to the steps in S3 max2 ;

[0046] S62: Refine the spectrum between the indexes on both sides of the peak; specifically, first calculate the spectrum amplitude point corresponding to each signal segment |X N (k max2 ±0.5)|For this segment of signal [k max2 -1,k max2 +1]; by filling the suffix of each signal with all 0 data of length N, the formula Calculate the |X of each signal segment N (kmax2 ±0.5), and finally sum average

[0047] S63: calculate compensation factor δ, and compensate peak index k max2 by compensation of the decimal part to make it more approximate to the actual spectrum peak position; specifically, combining the FFT calculation expression and the frequency offset estimation expression, another form of the FFT expression is obtained:

[0048]

[0049] Wherein, k max is the peak index, Δf is the frequency offset value, T s is the sampling interval, N is the FFT calculation point number, and θ is the initial phase of the data; then The value of the compensation factor δ is between-0.5 and 0.5, and the following relationship is obtained:

[0050]

[0051] According to the simplification of the above formula according to the properties of trigonometric functions, the following formula is obtained:

[0052]

[0053] The expression for calculating the compensation factor δ is:

[0054]

[0055] Finally, the peak index after compensation by δ is expressed as: k max =k max2 -δ.

[0056] Further technical solutions of the application: the S7 comprises:

[0057] According to the maximum likelihood estimation theory, the relationship between the fine frequency offset estimation value and the compensated peak index is as follows:

[0058]

[0059] Wherein, f s is the sampling interval, k max is the compensated spectrum peak index, N is the FFT transform point number, M is the QPSK modulation index, S is the resampling decimation factor, and the fine frequency offset estimation value is

[0060] A low SNR non-data-aided high-precision frequency offset estimation compensation method is applied to a wideband satellite communication physical layer demodulation system carrier recovery.

[0061] The application has the following advantages:

[0062] The application relates to a non-data-aided high-precision frequency offset estimation compensation method under low signal-to-noise ratio, which can be applied to carrier recovery in a wideband satellite physical layer demodulation system without using known prior data and comprises the following steps: performing M times of power reduction on a signal subjected to symbol timing recovery and frame synchronization to obtain a four-phase constellation point signal; performing energy normalization operation on the signal, converting the signal from a rectangular coordinate system into a polar coordinate form, expanding the phase data of the signal by 4 times, remapping the signal into the rectangular coordinate system, and obtaining a signal without modulation information; segmenting the signal according to the FFT point number, completing FFT transformation on each segment of the signal, accumulating the spectrum of the signal, searching for a peak value according to the accumulated spectrum of the signal, and obtaining a periodogram peak value index; obtaining a coarse frequency offset estimation value according to the spectrum peak value index, the FFT point number, the modulation order and other information, and completing first-stage coarse compensation of the signal; performing the same power reduction and demodulation operation on the signal subjected to coarse offset compensation, and performing resampling with an extraction factor S to obtain a signal with a sampling rate of f s / S; performing segmental FFT calculation on the resampled signal and accumulating the spectrum of the signal, searching for a peak value according to the accumulated spectrum, and obtaining a peak value index; performing interpolation calculation to obtain an index compensation factor and approximate the actual position of the peak value; performing fine frequency offset estimation according to the compensated peak value index, the extraction factor S and the FFT point number and other parameters, and completing compensation of the signal. The application can perform high-precision frequency offset estimation under low signal-to-noise ratio, effectively improve demodulation performance, and be suitable for wideband satellite communication systems and satellite high-speed data transmission systems. BRIEF DESCRIPTION OF DRAWINGS

[0063] The accompanying drawings are included to provide a further understanding of the embodiments, and are incorporated in and constitute a part of this specification, illustrate embodiments of the application, and together with the description serve to explain the principles of the application, and should not be considered limiting of the application's scope, as numerous embodiments can be made of the application.

[0064] Figure 1 FIG. 1 is a schematic diagram of a low signal-to-noise ratio non-data-aided high-precision frequency offset estimation compensation method provided by an embodiment of the application.

[0065] Figure 2 FIG. 2 is a flowchart of a low signal-to-noise ratio non-data-aided high-precision frequency offset estimation compensation method provided by an embodiment of the application.

[0066] Figure 3 FIG. 3 is a schematic diagram of 8PSK data power reduction operation provided by an embodiment of the application.

[0067] Figure 4 FIG. 4 is a schematic diagram of residual frequency offset size of a coarse frequency offset estimation module provided by an embodiment of the application: (1) QPSK data; (2) 8PSK data.

[0068] Figure 5Figure is a residual frequency offset size case diagram of the fine frequency offset estimation module provided by the embodiment of the present application: (1) QPSK data; (2) 8PSK data.

[0069] Figure 6 Figure is a frequency offset estimation range diagram of the frequency offset estimation method provided by the embodiment of the present application for QPSK data and 8PSK data under different signal-to-noise ratios: (1) QPSK data; (2) 8PSK data. DETAILED DESCRIPTION

[0070] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0071] The present application provides a method capable of non-data-aided high-precision frequency offset estimation compensation under low signal-to-noise ratio conditions. Please refer to Figure 1 and Figure 2 , Figure 1 Figure is a diagram of the non-data-aided high-precision frequency offset estimation compensation method provided by the present application under low signal-to-noise ratio conditions, Figure 2 Figure is a flowchart of the non-data-aided high-precision frequency offset estimation compensation method provided by the present application under low signal-to-noise ratio conditions. As Figure 1 shown: the technical problem to be solved is realized by the following technical solution, specifically including:

[0072] S1: performing a reduction operation on the input signal to obtain a four-phase constellation point signal;

[0073] S2: converting the signal from a rectangular coordinate system to a polar coordinate system, and amplifying the phase by 4 times, and then remapping it to a rectangular coordinate system to obtain a signal without modulation information;

[0074] S3: performing segmented FFT calculation on the signal to obtain signal superimposed spectrum and perform peak value search to obtain a periodogram peak value index;

[0075] S4: obtaining a coarse frequency offset value according to the spectrum peak value index, the FFT point number, the modulation order and other information, and completing coarse frequency offset compensation;

[0076] S5: performing the reduction and demodulation operation of S1-S2 on the compensated signal, and performing resampling with a decimation factor of S to obtain a signal with a sampling rate of f s / S;

[0077] S6: segmenting the resampling signal, obtaining the peak value index according to the signal superimposed spectrum, and then performing interpolation calculation to obtain the index compensation factor, and approximating the actual position of the peak value;

[0078] S7: performing fine frequency offset estimation according to the compensated peak value index, the decimation factor S and the FFT point number and other parameters, and completing compensation of the signal;

[0079] In an embodiment of the present application, before the S1, further comprising:

[0080] S0: the data signal for frequency offset estimation needs to pass through a symbol timing recovery module to eliminate the influence of sampling, and then needs to pass through a frame synchronization module to obtain the modulation mode information of the data.

[0081] The S1 includes performing order reduction operation on the input signal to obtain a four-phase constellation point signal. If the modulation mode of the input signal is QPSK, no operation is needed, and if the modulation mode is not QPSK modulation, M times multiplication order reduction operation is needed to obtain a four-phase constellation point signal, wherein the value of M can be set as the ratio of the data outer ring constellation point number to 4.

[0082] If the modulation type of the data to be corrected is 8PSK or 8APSK, 2 times order reduction operation is needed on the symbol corresponding outer ring constellation point, that is, M=2, and if there is a phase difference of π / 4 between the obtained constellation point and the QPSK standard constellation point, phase compensation is needed on the constellation point to obtain a four-phase constellation point consistent with the QPSK phase. Taking 8PSK modulation as an example, the constellation point can be represented as c k = rexp(j(2π / 8·i)) i=0,1,2...7, and after 2 times calculation on the outer ring data, it becomes: k 2 = rexp(j(2π / 4·i1)) i1=0,1,2,3. According to the formula, π / 4 angle rotation is needed on the order-reduced constellation point to obtain a four-phase constellation point consistent with the QPSK modulation. As shown in the 8PSK data order reduction operation diagram, wherein (1) is an 8PSK constellation diagram, and (2) is a four-phase constellation diagram after order reduction calculation. Figure 3

[0083] If the modulation type of the data to be corrected is 16APSK, the value of M in the order reduction algorithm can be represented as:

[0084] M=Y / 4

[0085] ​​Wherein, Y is the outer ring data points corresponding to the data constellation. Next, according to the data power threshold τ, the outer ring signal greater than the threshold is calculated by M times to reduce the order, and the inner ring signal less than the power threshold is set to 0. Taking 16APSK as an example, the outer ring constellation point can be expressed by the following formula:

[0086] c k = rexp(j(2π / 12·i+π / 12)), i=0, 1, 2...11

[0087] The 3 times reduction operation is performed on it, and the formula is as follows:

[0088] c k = r 3 exp(j(2π / 4·i+π / 4)), i=0, 1, 2, 3

[0089] It can be seen from the formula that the distribution state of the processed constellation point has been converted to QPSK form, only the amplitude is different, which does not affect the subsequent operation. If there is a phase difference of π / 4 between the converted constellation point and the QPSK constellation point, the phase compensation needs to be performed on the constellation point to obtain the four-phase constellation point consistent with the QPSK phase.

[0090] The S2 includes the following specific steps:

[0091] S21: Energy normalization is performed on the data after the order reduction in S1 to obtain the signal s1(i).

[0092] S22: The s1(i) is converted from the rectangular polar coordinate system to the polar coordinate system to obtain the phase information θ i = 2πf d iT s + φ0+ φ z , wherein f d is the modulation frequency information, φ0is the initial phase, and φ z is the phase domain Gaussian white noise component. Then, θ i is amplified by 4 times to remove the signal modulation information to obtain:

[0093] 4θ i = 8πf d iT s + 4φ0+ 4φ z

[0094] Mapping it to the rectangular coordinate system has:

[0095] s2(i)=exp(j(8πf d iT s + 4φ0+ 4φ z )

[0096] Compared with performing a fourth-power nonlinear transformation on the signal to remove the modulation information, directly multiplying the phase domain information of the signal by four times can eliminate the amplification effect of the amplitude term on the noise and appropriately reduce the signal-to-noise ratio threshold.

[0097] The S3 includes segmenting the signal s2(i) by the number of FFT points N and performing FFT transformation on each segment of the signal, which can be expressed as follows:

[0098]

[0099] Among them, h n is a segmented signal, k=0,1,…,N-1.

[0100] Then use the formula |F k |=F k F k * / N is used to obtain the spectrum amplitude. Compared with directly taking the absolute value of the FFT result, the spectrum amplitude obtained by this method has better separation. Next, the spectrum amplitudes of all data segments are summed to reduce the influence of random noise on the spectrum results. Finally, the maximum peak index k is searched in the summed spectrum results. max1 .

[0101] The step S4 includes obtaining a rough estimate of the frequency offset based on the obtained peak index and the maximum likelihood estimation theory. The specific expression is as follows:

[0102]

[0103] In the above formula, T s is the sampling interval, k max1 is the spectrum peak index, N is the number of FFT points, M is the QPSK modulation index, and the rough estimate of frequency offset is Δf1.

[0104] The S5 includes performing the down-modulation operation of S1 to S2 on the data after the coarse bias compensation, and then resampling with a decimation factor of S to obtain the signal x(n)′. At this time, the signal sampling rate is reduced to f s / S.

[0105] The S6 includes the following specific steps:

[0106] S61: Divide the resampled signal into segments of length N, and obtain the peak index k of the signal superposition spectrum according to the steps in S3 max2 .

[0107] S62: Refine the spectrum between the indexes on both sides of the peak. Specifically, first calculate the spectrum amplitude point corresponding to each signal segment |X N (k max2 ±0.5)|For this segment of signal [k max2 -1,kmax2 +1] between the spectrum is refined. Since the FFT amplitude |X N (k max2 ±0.5)| corresponds to the amplitude |X 2N (2k max2 ±1)| of the 2N-point FFT, each segment of the signal can be padded with N all-0 data at the end, and the |X of each segment of the signal can be calculated by the formula N (k max2 ±0.5)|, and finally the summation average is obtained

[0108] S63: The compensation factor δ is calculated, and the peak index k max2 is compensated by the compensation of the decimal part to make it closer to the actual spectrum peak position. Specifically, in combination with the FFT calculation expression and the frequency offset estimation expression, another form of the FFT expression can be obtained:

[0109]

[0110] where k max is the peak index, Δf is the frequency offset value, T s is the sampling interval, N is the FFT calculation point number, and θ is the data initial phase. Then The value of the compensation factor δ is between -0.5 and 0.5, and the following relationship can be obtained:

[0111]

[0112] In addition, for the sine function sinx, when x tends to 0, the value of sinx is approximately x. Therefore, according to the properties of trigonometric functions, it can be simplified as:

[0113]

[0114] At this time, the ratio of |X 2N (2k1+1)| and |X 2N (2k1-1)| is easily obtained Further, the expression of the compensation factor δ is obtained as follows:

[0115]

[0116] Finally, the peak index after compensation using δ can be expressed as: k max = k max2 - δ.

[0117] The relationship between the frequency offset fine estimation value and the compensated peak index according to the maximum likelihood estimation theory is as follows:

[0118]

[0119] wherein f s is the sampling interval, k max is the compensated spectral peak index, N is the FFT transform point number, M is the QPSK modulation index, S is the resampling decimation factor, and the fine frequency offset estimation value is Δf2.

[0120] According to Δf2, compensation of the signal is completed.

[0121] The effect of the non-data-aided high-precision frequency offset estimation compensation method of embodiment one under low signal-to-noise ratio is illustrated through a simulation experiment.

[0122] The simulation experiment of the embodiment is performed under MATLAB2023a software, the data modulation mode adopts QPSK and 8PSK, the data frame structure adopts MODCOD132 and MODCOD142 in the DVB-S2X system, the added normalized frequency offset is 0.002 and 0.004 respectively, 1024-point FFT is adopted, the resampling decimation factor is set to 8, and the simulation adopts an additive white Gaussian noise channel.

[0123] Simulation content and result analysis:

[0124] Figure 4 (1) and (2) are the residual frequency offset distribution of the coarse frequency offset estimation of QPSK data and 8PSK data under the conditions of ES / N0 at -4dB and -3dB and ES / N0 at 5dB and 6dB. It can be seen that under the condition of ESN0 of -3dB, for QPSK data, the residual frequency offset of the coarse offset estimation module can still be controlled at the order of 10 -5 Under the condition of ESN0 of 5dB, for 8PSK data, the residual frequency offset of the coarse offset estimation module can also be controlled at the order of 10 -5 It can be seen that under the condition of low signal-to-noise ratio, the residual frequency offset after coarse frequency offset estimation can also be stably controlled at a small order.

[0125] Figure 5 (1) and (2) are the residual frequency offset distribution of the fine frequency offset estimation of QPSK data and 8PSK data under the conditions of ESN0 in the range of -3dB to -1dB and ESN0 in the range of 6dB to 8dB. It can be seen from the CDF curve that when the data modulation mode is QPSK, the residual frequency offset can be stably controlled at the order of 10 -6 Under the condition of -3dB; at the same time, when the data modulation mode is 8PSK, the residual frequency offset can also be stably controlled at the order of 10 -6 Under the condition of 6dB. After coarse frequency offset estimation and fine frequency offset estimation, even under the condition of low signal-to-noise ratio, the residual frequency offset can be stably controlled at the order of 10-7 to 10 -6 It has good performance.

[0126] Figure 6 (1) and (2) are the frequency offset estimation ranges for QPSK data and 8PSK data at different signal-to-noise ratios. It can be seen that the theoretical frequency offset estimation range of the algorithm can be achieved even at low signal-to-noise ratios.

[0127] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present invention, and these modifications or replacements should all be included in the scope of protection of the present invention.

Claims

1. A non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio, characterized in that: include: S1: Perform order reduction operation on the input signal to obtain the four-phase constellation point signal; S2: Convert the signal obtained in S1 from the rectangular coordinate system to the polar coordinate system, amplify its phase by 4 times, and then remap it to the rectangular coordinate system to obtain a signal without modulation information; S3: Perform segmented FFT calculation on the signal obtained in S2 to obtain the signal superposition spectrum and perform peak search to obtain the periodogram peak index; S4: Obtain a rough frequency offset estimate based on the spectrum peak index, FFT points, and modulation order obtained in S3, and complete the coarse frequency offset compensation. S5: Perform the demodulation operation of S1 to S2 on the compensated signal obtained by S4, and perform the decimation factor S The resampling rate is signal; S6: Perform segmented FFT calculation on the resampled signal obtained in S5, obtain its peak index based on the signal superposition spectrum, and then perform interpolation calculation to obtain the index compensation factor to approximate the actual position of the peak; S7: According to the peak index after compensation, the extraction factor And the FFT point number parameters are used to perform fine frequency offset estimation and complete signal compensation.

2. The non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to claim 1, characterized in that: The S1 also includes: S0: The received data symbols are subjected to timing recovery and frame synchronization processing to eliminate the symbol timing deviation to obtain the data to be corrected, and the corresponding modulation mode information is obtained at the same time, and the modulation mode includes non-QPSK.

3. The non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to claim 2, characterized in that: If the modulation mode is not QPSK, the S1 is specifically: Do the outer ring constellation points of the input signal The power reduction operation is performed to obtain the four-phase constellation points consistent with QPSK modulation.

4. The non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to claim 3, characterized in that: Do the outer ring constellation points of the input signal The power reduction operation obtains the four-phase constellation points consistent with QPSK modulation, including: If the modulation type of the data to be corrected is 8PSK or 8APSK, it is necessary to perform a quadratic reduction operation on the outer ring constellation points corresponding to its symbols; if the converted constellation points are different from the QPSK standard constellation points If the phase difference is greater than , the constellation point needs to be phase compensated to obtain a four-phase constellation point consistent with the QPSK phase; If the modulation type of the data to be corrected is 16APSK, then the The value is expressed as: in, The number of outer ring data points corresponding to the data constellation diagram; then the inner and outer ring power thresholds need to be defined, and the outer ring signal greater than the threshold is The order is reduced, and the inner circle signal less than the power threshold is set to 0; if the converted constellation point is compared with the QPSK standard constellation point If the phase difference is greater than , the constellation point needs to be phase compensated to obtain a four-phase constellation point consistent with QPSK modulation.

5. The non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to claim 1, characterized in that: The S2 includes: S21: Normalize the signal energy to obtain the signal ; S22: Convert the rectangular polar coordinate system to the polar coordinate system to obtain the phase information of the signal ,in, is the sampling interval, is the modulation frequency information, is the initial phase, is the phase domain Gaussian white noise component; right Amplify by 4 times to remove the signal modulation information and get: Mapping it to the rectangular coordinate system is: 。 6. The non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to claim 1, characterized in that: The S3 includes: Calculate the number of points in FFT is the length, for the signal Divide the signal into segments and perform FFT transformation on each segment, which can be expressed as follows: in, is a segmented signal, ; Using the formula Obtain the spectrum amplitude, superimpose and sum the spectrum amplitudes of all data segments, and search for the maximum peak index in the summed spectrum result .

7. The non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to claim 1, characterized in that: The S4 includes: The estimated expression of frequency deviation obtained from the maximum likelihood estimation theory is as follows: Where, is the sampling interval, is the spectrum peak index, is the number of FFT points, is the QPSK modulation index, the rough estimate of frequency offset .

8. The non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to claim 1, characterized in that: The S6 includes: S61: For the resampled signal by Segment the signal into segments of length and obtain the peak index of the signal superposition spectrum according to the steps in S3 ; S62: Refine the spectrum between the indices on both sides of the peak; specifically, first calculate the spectrum amplitude point corresponding to each segment of the signal For this signal The spectrum between is refined; by filling the suffix of each signal with a length of All 0 data, according to the formula Calculate the signal of each segment , and finally sum and average to obtain ; S63: Calculate compensation factor , and index the peak Compensation is performed to make it closer to the actual spectrum peak position by compensating the fractional part. Specifically, by combining the FFT calculation expression and the frequency offset estimation expression, another form of the FFT expression is obtained: in, is the peak index, is the frequency deviation value, is the sampling interval, The number of points for FFT calculation, is the initial phase of the data; then ; Compensation factor For values ​​between -0.5 and 0.5, the following relationship is obtained: According to the properties of trigonometric functions, the above formula can be simplified as follows: Calculating the compensation factor The expression is: Last use The peak index after compensation is expressed as: .

9. The non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to claim 1, characterized in that: The S7 includes: According to the maximum likelihood estimation theory, the relationship between the fine frequency offset estimate and the peak index after compensation is as follows: in, is the sampling interval, is the spectrum peak index after compensation, is the number of FFT transformation points, is the QPSK modulation index, is the resampling decimation factor, and the frequency deviation fine estimate is .

10. An application of the non-data-aided high-precision frequency offset estimation and compensation method under low signal-to-noise ratio according to any one of claims 1 to 9, characterized in that Applied to carrier recovery in the physical layer demodulation system of broadband satellite communications.

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