阅读说明：本技术 一种星地异源扩跳频载波捕获频率补偿方法及系统 (Satellite-ground heterogeneous spread spectrum frequency hopping carrier capture frequency compensation method and system ) 是由 白力舸 方凯 焦荣惠 柴源 宋振飞 杨冬雪 李天然 于 2021-06-29 设计创作，主要内容包括：本发明公开了一种星地异源扩跳频载波捕获频率补偿方法及系统,其中,该方法包括如下步骤：得到含有载波频偏的信号；对去除噪声的信号进行最大似然估计得到频偏估计值和相偏估计值；进行二分法划分处理得到二分法划分处理后的频偏估计值；得到实际相偏；根据实际相偏得到下一个含有载波频偏的信号的相偏估计值,根据下一个含有载波频偏的信号的相偏估计值得到下一个含有载波频偏的信号的修正的相偏估计值,根据下一个含有载波频偏的信号的修正的相偏估计值得到下一个含有载波频偏的信号的修正的频偏修正值。本发明解决了在地面接收端初始扩跳频同步过程中,动态多普勒载波频偏估计误差随时间和码元数量增加而增大从而影响接收性能的问题。(The invention discloses a satellite-ground heterogeneous spread-spectrum frequency hopping carrier capture frequency compensation method and a system, wherein the method comprises the following steps: obtaining a signal containing carrier frequency offset; carrying out maximum likelihood estimation on the signal without the noise to obtain a frequency offset estimation value and a phase offset estimation value; carrying out dichotomy division processing to obtain a frequency deviation estimated value after the dichotomy division processing; obtaining actual phase deviation; and obtaining a phase deviation estimated value of the next signal containing the carrier frequency deviation according to the actual phase deviation, obtaining a corrected phase deviation estimated value of the next signal containing the carrier frequency deviation according to the phase deviation estimated value of the next signal containing the carrier frequency deviation, and obtaining a corrected frequency deviation corrected value of the next signal containing the carrier frequency deviation according to the corrected phase deviation estimated value of the next signal containing the carrier frequency deviation. The invention solves the problem that the receiving performance is influenced because the estimation error of the dynamic Doppler carrier frequency offset is increased along with the increase of time and the number of code elements in the initial spreading frequency hopping synchronization process of a ground receiving end.)

1. A satellite-to-ground heterogeneous spread spectrum frequency hopping carrier acquisition frequency compensation method is characterized by comprising the following steps:

the method comprises the following steps: completing initial spreading and frequency hopping synchronization of carrier waves by ADC sampling, digital frequency conversion and matched filtering of received intermediate frequency signals to obtain signals containing carrier frequency offset;

step two: removing noise influence from the signal containing the carrier frequency offset in the step one to obtain a noise-removed signal; performing maximum likelihood estimation on the signal without the noise to obtain a frequency offset estimation value and a phase offset estimation value;

step three: according to the residual frequency offset obtained in the first step and the frequency offset estimation value obtained in the second step, carrying out bisection division processing to obtain a frequency offset estimation value after the bisection division processing;

step four: resolving phase ambiguity of an initial phase difference in a signal containing carrier frequency offset through a preset unique code, and obtaining actual phase offset according to a phase offset estimation value;

step five: and obtaining a phase deviation estimated value of the next signal containing the carrier frequency deviation according to the actual phase deviation, obtaining a corrected phase deviation estimated value of the next signal containing the carrier frequency deviation according to the phase deviation estimated value of the next signal containing the carrier frequency deviation, and obtaining a corrected frequency deviation corrected value of the next signal containing the carrier frequency deviation according to the corrected phase deviation estimated value of the next signal containing the carrier frequency deviation.

2. The method according to claim 1, wherein the method comprises the steps of: in step one, the expression of the signal containing the carrier frequency offset is as follows:

where Δ f is the residual frequency offset, T_bN (k) N (0,2 σ) for a symbol period²) Is additive complex white Gaussian noise, and the variance of the in-phase component and the quadrature component of the additive complex white Gaussian noise are sigma²θ is the initial phase difference, A_kIs the instantaneous amplitude, alpha, due to the influence of noise_kIs added phase noise due to the influence of noise, phi_kIs the phase of the modulation phi_kE {0, pi }, k is an integer of the time domain position of the signal, and L is the maximum length of the signal.

3. The method according to claim 1, wherein the method comprises the steps of: in step two, the frequency deviation estimated valueComprises the following steps:

where f is the signal frequency.

4. The method according to claim 1, wherein the method comprises the steps of: in step two, the phase deviation estimation valueComprises the following steps:

wherein r'_kFor a noise-removed signal, k is an integer number of time-domain positions of the signal.

5. The method according to claim 1, wherein the method comprises the steps of: in step three, the residual frequency deviation delta f is distributed at-f_max～+f_maxIn between, so is at_max～+f_maxSearching for delta f, combining the maximum likelihood estimation expression of the frequency deviation in the step two, if f is_s1＝f_maxMaximum likelihood estimation of/2>f_s2＝-f_maxThe maximum likelihood estimation of/2 is to make the dichotomy estimation value f_smid＝f_s1Otherwise, let dichotomyEstimate f_smid＝f_s2When the nth calculation is carried out, the precision reaches f_max/2ⁿObtaining the frequency deviation estimated value after the dichotomy division processingWherein f is_maxIs the absolute value of the maximum frequency deviation range, f_s1Is the first point selected in the dichotomy process, f_s2Is the second point selected in the dichotomy process, f_smidThe absolute value of the maximum frequency deviation estimated value obtained by the bisection method.

6. The method according to claim 1, wherein the method comprises the steps of: in step five, the expression of the phase offset estimation value of the next signal containing carrier frequency offset is:

wherein the content of the first and second substances,is the phase-offset estimate of the next signal containing the carrier frequency offset,an initial phase offset estimate of the signal containing the carrier frequency offset obtained by the search algorithm,the initial frequency offset estimation value is obtained through a search algorithm.

7. The method according to claim 1, wherein the method comprises the steps of: in step five, the expression of the corrected phase-offset estimation value of the next signal containing carrier frequency offset is:

wherein the content of the first and second substances,is the phase-offset estimate of the next signal containing the carrier frequency offset,is a modified phase-offset estimate of the next signal containing carrier frequency offset.

8. The method according to claim 1, wherein the method comprises the steps of: in step five, the expression of the corrected frequency offset correction value of the next signal containing carrier frequency offset is:

wherein the content of the first and second substances,for the initial frequency offset estimation value obtained by the search algorithm,a frequency offset correction value for correction of a next signal containing carrier frequency offset.

9. A satellite-to-ground heterogeneous spread spectrum frequency hopping carrier acquisition frequency compensation system, comprising:

the first module is used for completing the initial spreading and hopping synchronization of the carrier wave through ADC sampling, digital frequency conversion and matched filtering of the received intermediate frequency signal to obtain a signal containing carrier frequency offset;

a second module for frequency-shifting the carrier-containing frequency in the first moduleRemoving noise influence from the signal to obtain a noise-removed signal; carrying out maximum likelihood estimation on the signal without the noise to obtain a frequency deviation estimation valueSum phase deviation estimate

A third module, configured to obtain a residual frequency offset Δ f from the first module and a frequency offset estimation value from the second moduleCarrying out dichotomy division processing to obtain a frequency deviation estimated value after the dichotomy division processing;

a fourth module, configured to resolve phase ambiguity for the initial phase difference θ in the signal containing the carrier frequency offset by using a preset unique code, and perform phase ambiguity resolution according to the phase offset estimation valueObtaining actual phase deviation;

and the fifth module is used for obtaining a phase deviation estimated value of the next signal containing the carrier frequency deviation according to the actual phase deviation, obtaining a corrected phase deviation estimated value of the next signal containing the carrier frequency deviation according to the phase deviation estimated value of the next signal containing the carrier frequency deviation, and obtaining a corrected frequency deviation corrected value of the next signal containing the carrier frequency deviation according to the corrected phase deviation estimated value of the next signal containing the carrier frequency deviation.

10. The system according to claim 9, wherein the system further comprises: the expression for the signal containing the carrier frequency offset is as follows:

where Δ f is the residual frequencyPartial, T_bN (k) N (0,2 σ) for a symbol period²) Is additive complex white Gaussian noise, and the variance of the in-phase component and the quadrature component of the additive complex white Gaussian noise are sigma²θ is the initial phase difference, A_kIs the instantaneous amplitude, alpha, due to the influence of noise_kIs added phase noise due to the influence of noise, phi_kIs the phase of the modulation phi_kE {0, pi }, k is an integer of the time domain position of the signal, and L is the maximum length of the signal.

Technical Field

The invention belongs to the technical field of digital communication, and particularly relates to a satellite-ground heterogeneous spread-spectrum frequency hopping carrier capture frequency compensation method and system.

Background

In spread spectrum frequency hopping satellite-to-ground communication, a carrier synchronization stage in a ground receiving system is a very critical stage. The carrier synchronization means that during coherent demodulation, a receiver needs to provide a coherent carrier with the same frequency and phase as a modulation carrier of a transmitter, and the carrier acquisition process is carrier synchronization. Because relative motion exists between the ground receiver and the satellite, Doppler frequency offset can be caused, the capturing and tracking performance of carrier waves can be influenced, and de-spread and demodulation of the receiver can not be finished. Therefore, whether the communication system can work effectively or not and whether the demodulation result can reach the required bit error rate precision or not depends on the quality of the system carrier synchronization performance to a great extent. In the satellite-ground communication process, due to the influence of factors such as satellite-ground time non-homologous sources, channel noise, signal types and doppler effect, a difference value, called carrier frequency offset, generally exists between the estimated value of the carrier frequency during ground carrier synchronization and the carrier center frequency of the received signal.

For the spread spectrum frequency hopping system, the ground receiving channel needs to perform ADC sampling on the input intermediate frequency signal in sequence, then perform digital frequency conversion (digital de-hopping), matched filtering, frequency hopping and spread spectrum synchronization, carrier synchronization and BPSK demodulation on the sampled digital signal, and complete frame synchronization and remove phase ambiguity by using the frame synchronization code. The demodulation result is sent to a decoding module for decoding, and finally, the decoding result is output and sent to the rear end for digital signal processing.

At present, in the synchronization process of frequency hopping and spread spectrum of a ground receiving end, the estimation of carrier frequency offset is not accurate, and the actual frequency offset also changes randomly along with time due to the acceleration of Doppler frequency offset. Due to the existence of frequency deviation, a demodulated signal constellation diagram is twisted to a certain degree, and the phenomenon becomes more obvious along with the increase of time and the number of code elements. When a received intermediate frequency signal has a larger frequency offset, the demodulation of the signal is seriously affected, so that the demodulation process of a receiving end cannot be completed.

Disclosure of Invention

The technical problem solved by the invention is as follows: the method and the system overcome the defects of the prior art, provide a satellite-ground heterogeneous spread-spectrum frequency hopping carrier capture frequency compensation method and a system, and solve the problem that the receiving performance is influenced because the dynamic Doppler carrier frequency offset estimation error is increased along with the increase of time and the number of code elements in the initial spread-spectrum frequency hopping synchronization process of a ground receiving end.

The purpose of the invention is realized by the following technical scheme: a satellite-to-ground heterogeneous spread spectrum frequency hopping carrier acquisition frequency compensation method comprises the following steps: the method comprises the following steps: completing initial spreading and frequency hopping synchronization of carrier waves by ADC sampling, digital frequency conversion and matched filtering of received intermediate frequency signals to obtain signals containing carrier frequency offset; step two: removing noise influence from the signal containing the carrier frequency offset in the step one to obtain a noise-removed signal; carrying out maximum likelihood estimation on the signal without the noise to obtain a frequency deviation estimation valueSum phase deviation estimateStep three: according to the residual frequency deviation delta f obtained in the step one and the frequency deviation estimated value in the step twoCarrying out dichotomy division processing to obtain a frequency deviation estimated value after the dichotomy division processing; step four: decoding phase ambiguity of initial phase difference theta in signal containing carrier frequency offset through preset unique code, and estimating value according to phase offsetObtaining actual phase deviation; step five: and obtaining a phase deviation estimated value of the next signal containing the carrier frequency deviation according to the actual phase deviation, obtaining a corrected phase deviation estimated value of the next signal containing the carrier frequency deviation according to the phase deviation estimated value of the next signal containing the carrier frequency deviation, and obtaining a corrected frequency deviation corrected value of the next signal containing the carrier frequency deviation according to the corrected phase deviation estimated value of the next signal containing the carrier frequency deviation.

In the above method for compensating the acquisition frequency of the satellite-to-ground heterogeneous spread-spectrum frequency hopping carrier, in the first step, the expression of the signal containing the carrier frequency offset is as follows:

where Δ f is the residual frequency offset, T_bN (k) N (0,2 σ) for a symbol period²) Is additive complex white Gaussian noise, and the variance of the in-phase component and the quadrature component of the additive complex white Gaussian noise are sigma²θ is the initial phase difference, A_kIs the instantaneous amplitude, alpha, due to the influence of noise_kIs added phase noise due to the influence of noise, phi_kIs the phase of the modulation phi_kE {0, pi }, k is an integer of the time domain position of the signal, and L is the maximum length of the signal.

In the method for compensating the acquisition frequency of the satellite-ground heterogeneous spread-spectrum frequency hopping carrier, in the second step, the frequency offset estimation valueComprises the following steps:

where f is the signal frequency.

In the satellite-ground heterogeneous spread-spectrum frequency hopping carrier capture frequency compensation method, in the step two, the phase deviation estimated valueComprises the following steps:

wherein r is_k' is a signal for removing noise, and k is an integer of a time domain position of the signal.

In the satellite-ground heterogeneous spread spectrum frequency hopping carrier capture frequency compensation method, in the third step, the residual frequency deviation delta f is distributed in-f_max～+f_maxIn between, so is at_max～+f_maxSearching for delta f, combining the maximum likelihood estimation expression of the frequency deviation in the step two, if f is_s1＝f_maxMaximum likelihood estimation of/2>f_s2＝-f_maxThe maximum likelihood estimation of/2 is to make the dichotomy estimation value f_smid＝f_s1Otherwise, let dichotomy estimate f_smid＝f_s2When the nth calculation is carried out, the precision reaches f_max/2ⁿObtaining the frequency deviation estimated value after the dichotomy division processingWherein f is_maxIs the absolute value of the maximum frequency deviation range, f_s1Is the first point selected in the dichotomy process, f_s2Is the second point selected in the dichotomy process, f_smidThe absolute value of the maximum frequency deviation estimated value obtained by the bisection method.

In the satellite-ground heterogeneous spread-spectrum frequency hopping carrier capture frequency compensation method, in step five, the expression of the phase offset estimation value of the next signal containing carrier frequency offset is as follows:

wherein the content of the first and second substances,is the phase-offset estimate of the next signal containing the carrier frequency offset,an initial phase offset estimate of the signal containing the carrier frequency offset obtained by the search algorithm,the initial frequency offset estimation value is obtained through a search algorithm.

In the satellite-to-ground heterogeneous spread spectrum frequency hopping carrier acquisition frequency compensation method, in step five, the expression of the corrected phase offset estimation value of the next signal containing carrier frequency offset is as follows:

wherein the content of the first and second substances,is the phase-offset estimate of the next signal containing the carrier frequency offset,is a modified phase-offset estimate of the next signal containing carrier frequency offset.

In the above method for compensating the acquisition frequency of the satellite-to-ground heterogeneous spread-spectrum frequency hopping carrier, in step five, the expression of the corrected frequency offset correction value of the next signal containing carrier frequency offset is:

wherein the content of the first and second substances,for the initial frequency offset estimation value obtained by the search algorithm,a frequency offset correction value for correction of a next signal containing carrier frequency offset.

Satellite-ground heterogenous expanding jumpA frequency carrier acquisition frequency compensation system, comprising: the first module is used for completing the initial spreading and hopping synchronization of the carrier wave through ADC sampling, digital frequency conversion and matched filtering of the received intermediate frequency signal to obtain a signal containing carrier frequency offset; the second module is used for removing noise influence from the signal containing the carrier frequency offset in the first module to obtain a noise-removed signal; carrying out maximum likelihood estimation on the signal without the noise to obtain a frequency deviation estimation valueSum phase deviation estimateA third module, configured to obtain a residual frequency offset Δ f from the first module and a frequency offset estimation value from the second moduleCarrying out dichotomy division processing to obtain a frequency deviation estimated value after the dichotomy division processing; a fourth module, configured to resolve phase ambiguity for the initial phase difference θ in the signal containing the carrier frequency offset by using a preset unique code, and perform phase ambiguity resolution according to the phase offset estimation valueObtaining actual phase deviation; and the fifth module is used for obtaining a phase deviation estimated value of the next signal containing the carrier frequency deviation according to the actual phase deviation, obtaining a corrected phase deviation estimated value of the next signal containing the carrier frequency deviation according to the phase deviation estimated value of the next signal containing the carrier frequency deviation, and obtaining a corrected frequency deviation corrected value of the next signal containing the carrier frequency deviation according to the corrected phase deviation estimated value of the next signal containing the carrier frequency deviation.

In the satellite-to-ground heterogeneous spread spectrum frequency hopping carrier capture frequency compensation method, the expression of the signal containing carrier frequency offset is as follows:

whereinΔ f is the residual frequency offset, T_bN (k) N (0,2 σ) for a symbol period²) Is additive complex white Gaussian noise, and the variance of the in-phase component and the quadrature component of the additive complex white Gaussian noise are sigma²θ is the initial phase difference, A_kIs the instantaneous amplitude, alpha, due to the influence of noise_kIs added phase noise due to the influence of noise, phi_kIs the phase of the modulation phi_kE {0, pi }, k is an integer of the time domain position of the signal, and L is the maximum length of the signal.

Compared with the prior art, the invention has the following beneficial effects:

(1) the invention carries out maximum likelihood estimation on the initial frequency offset and the phase offset, so that the variance of the obtained estimator is the Cramer-Rao (Cramer-Rao) boundary. The Claimei-Roman boundary is the lower limit of the variance of all unbiased estimates, so the estimation algorithm of the invention has the theoretically optimal performance.

(2) The invention can meet the design requirement of high frequency precision by dividing the residual frequency offset by dichotomy.

(3) The invention completes the whole carrier tracking synchronization process by correcting the accumulated phase error of the continuous data section due to inaccurate frequency offset estimation.

Drawings

Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:

fig. 1 is an information processing flow of a reception channel.

Fig. 2 is a carrier synchronization structure based on a frequency offset estimation and compensation algorithm.

Fig. 3 is a schematic diagram of carrier synchronization tracking.

Fig. 4 is a hybrid spread spectrum system tracking loop architecture.

Detailed Description

Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. The following detailed description of embodiments of the invention refers to the accompanying drawings and examples.

The embodiment provides a satellite-ground heterogeneous spread-spectrum frequency hopping carrier capture frequency compensation method, which solves the problem that in the initial spread-spectrum frequency hopping synchronization process of a ground receiving end, the receiving performance is influenced because the estimation error of dynamic Doppler carrier frequency offset is increased along with the increase of time and the number of code elements, and comprises the following steps:

the method comprises the following steps: completing initial spreading and frequency hopping synchronization of carrier waves by ADC sampling, digital frequency conversion and matched filtering of received intermediate frequency signals to obtain signals containing carrier frequency offset; wherein the content of the first and second substances,

the expression for the signal containing the carrier frequency offset is as follows:

where Δ f is the residual frequency offset, T_bN (k) N (0,2 σ) for a symbol period²) Is additive complex white Gaussian noise, and the variance of the in-phase component and the quadrature component of the additive complex white Gaussian noise are sigma²θ is the initial phase difference, A_kIs the instantaneous amplitude, alpha, due to the influence of noise_kIs added phase noise due to the influence of noise, phi_kIs the phase of the modulation phi_kE {0, pi }, wherein k is an integer representing the time domain position of the segment of the signal, and L is the maximum value of k, namely the maximum length of the signal;

step two: removing noise influence from the signal containing the carrier frequency offset in the step one to obtain a noise-removed signal; carrying out maximum likelihood estimation on the signal without the noise to obtain a frequency deviation estimation valueSum phase deviation estimateWherein the content of the first and second substances,

if the influence of noise is not considered, there are:

definition of r_k′：

Wherein r is_kR (k) when k is constant, n' (k) is equivalent noise and can be approximately considered to be in a Gaussian distribution, and as can be seen from the expression, r_k' can be approximately regarded as a single carrier. Thereby obtaining the frequency deviation maximum likelihood estimation valueComprises the following steps:

maximum likelihood estimate of initial phaseComprises the following steps:

wherein f is the signal frequency;

step three: according to the residual frequency deviation delta f obtained in the step one and the frequency deviation estimated value in the step twoThe dichotomy division processing is carried out to obtain the frequency deviation estimated value after the dichotomy division processingWherein the content of the first and second substances,

the residual frequency deviation delta f is distributed in-f_max～+f_maxIn between, so is at_max～+f_maxSearching for delta f, combining the maximum likelihood estimation expression of the frequency deviation in the step two, if f is_s1＝f_maxMaximum likelihood estimation of/2>f_s2＝-f_maxThe maximum likelihood estimation of/2 is to make the dichotomy estimation value f_smid＝f_s1Otherwise, let dichotomy estimate f_smid＝f_s2When the nth calculation is carried out, the precision reaches f_max/2ⁿObtaining the frequency deviation estimated value after the dichotomy division processingWherein f is_maxIs the absolute value of the maximum frequency deviation range, f_s1Is the first point selected in the dichotomy process, f_s2Is the second point selected in the dichotomy process, f_smidObtaining an absolute value of a maximum frequency deviation estimated value by a bisection method;

step four: decoding phase ambiguity of initial phase difference theta in signal containing carrier frequency offset through preset unique code, and estimating value according to phase offsetObtaining actual phase deviation;

step five: obtaining a phase deviation estimated value of a next signal containing carrier frequency deviation according to actual phase deviation, obtaining a corrected phase deviation estimated value of the signal according to the phase deviation estimated value of the next signal containing carrier frequency deviation, and obtaining a corrected frequency deviation corrected value of the next signal containing carrier frequency deviation according to the corrected phase deviation estimated value of the next signal containing carrier frequency deviation; wherein the content of the first and second substances,

the expression of the phase offset estimation value of the next signal containing carrier frequency offset is:

an initial phase offset estimate of the signal containing the carrier frequency offset obtained by the search algorithm,for the initial frequency offset estimation value obtained by the search algorithm,

the expression of obtaining the corrected phase deviation estimated value of the next signal containing the carrier frequency deviation by utilizing the maximum likelihood estimation is as follows:

the expression for obtaining the corrected frequency offset correction value of the next signal containing carrier frequency offset at the same time is:

fig. 1 shows a carrier synchronization structure based on a frequency offset estimation and compensation algorithm. The intermediate frequency signal sequentially passes through three steps of ADC sampling, digital frequency conversion and matched filtering, and after initial jump-spread synchronization and de-spread, a signal containing data information and carrier frequency offset is obtained, which can be expressed as:

wherein Δ f is the residual frequency deviation, T_bN (k) N (0,2 σ) for a symbol period²) Is additive complex white Gaussian noise, and the variance of the in-phase component and the quadrature component of the additive complex white Gaussian noise are sigma²θ is the initial phase difference, A_kDue to the influence of noiseInstantaneous amplitude, α_kIs added phase noise due to the influence of noise, phi_kIs the phase of the modulation phi_k∈{0,π}。

If the influence of noise is not considered, there are:

it can be seen that the modulation information is removed. Definition of r_k′：

n' (k) is an equivalent noise that can be approximated as following a gaussian distribution. Can see r_k' is a form of a single carrier contaminated with Gaussian white noise, from which r can be derived_kThe expression for the maximum likelihood estimate of frequency and initial phase is:

after the initial spreading and hopping synchronization, Δ f has been reduced to a certain extent, which can be expressed as being distributed at-f_max～+f_maxIn between, so only need be at-f_max～+f_maxSearching for Δ f. When calculating for the first time, respectively order f_s1＝f_maxA/2 and f_s2＝-f_max/2, calculated from the above formula_s1＝f_maxMaximum likelihood estimate U of/2_s1And f_s2＝-f_maxMaximum likelihood estimate U of/2_s2Then compare U_s1And U_s2Size of (1), if U_s1>U_s2If so, let f_smid＝f_s1Otherwise, order f_smid＝f_s2(ii) a Then proceed to the firstSecond calculation, calculating time order f_s1＝f_smid+f_max/4，f_s2＝f_smid-f_max/4, likewise from U_sCalculating to obtain U_s1And U_s2Then compare U_s1And U_s2Size of (1), if U_s1>U_s2If so, update f_smid＝f_s1Otherwise, order f_smid＝f_s2(ii) a So doing, when the nth calculation is performed, let f_s1＝f_smid+f_max/2ⁿ，f_s2＝f_smid-f_max/2ⁿFrom U_sCalculating to obtain U_s1And U_s2Then compare U_s1And U_s2Size of (1), if U_s1>U_s2If so, let f_smid＝f_s1Otherwise, order f_smid＝f_s2. As to how many times the specific n is taken, the frequency precision required to be achieved depends on, and the convergence process of the algorithm is very fast, and the precision reaches f after n times of calculation_max/2ⁿ。

For f after the last search_smidThe estimated value of the frequency offset can be obtained asEstimate outThe initial phase offset can then be estimated. Since the phase determined is periodic, one period is often [ - π, π), and soThe phase value of (1) is [ -pi/2, pi/2), so the obtained initial phase deviation is phase-fuzzy, that is, the actual phase deviation isTwo possibilities. The phase ambiguity can only be removed by a known unique code, which is known from the BPSK-modulated mapping rule, if originally modulatedOne path of data is I whenWhen the data obtained by demodulation isWhen in useThen, two paths of data obtained by demodulation areTherefore, when searching the unique code, the above two states of the unique code can be searched at the corresponding positions, that is, the phase ambiguity can be corrected according to the search result, and the frame synchronization can be completed.

After the estimation of the initial frequency offset and the initial phase offset is completed, the frequency offset needs to be tracked in the demodulation process, otherwise, the phase difference accumulated due to the frequency offset tracking error may exceed the phase interval between two adjacent constellation points, thereby causing the demodulation result to be inverted and wrong.

The tracking still uses the algorithm based on the maximum likelihood estimation, as shown in fig. 3, the data is divided into several continuous segments: and the data section 1, the data section 2 and the data section 3 … … estimate the phase error accumulated in each data section due to inaccurate frequency offset estimation, and then correct the frequency offset estimation value by using the estimated phase error, thereby completing carrier synchronization tracking.

Fig. 2 is a schematic diagram of carrier synchronization tracking.Andif the initial phase offset and the initial frequency offset are obtained by the previous search algorithm, the phase offset estimation value of the first data of the data segment 1 obtained by the initial phase offset and the initial frequency offset is:but because ofThe estimated inaccuracy or the actual phase-offset value of the first data of the data section 1 has deviated due to a change in frequencyTherefore, need to re-estimateAnd correct itUsing maximum likelihood estimation, we obtain:

and simultaneously obtaining a correction value of the frequency offset as follows:

in the following demodulation, the above method is continuously applied to the data segment 2, the data segment 3, and the like, so that the carrier synchronization tracking process can be completed, and the final tracking loop of the hybrid spread spectrum system is shown in fig. 4.

Since the estimation algorithm used in this scheme is essentially a maximum likelihood estimation, the variance of the resulting estimate is the Cramer-Rao (Cramer-Rao) bound. The Claimei-Roman boundary is the lower limit of the variance of all unbiased estimates, so the estimation algorithm of the method has the optimal performance.

Estimating variance using normalized frequency offsetSum-phase-offset estimation varianceAs a measure ofFrequency offset estimatorSum phase offset estimatorCriteria for performance. Normalized frequency offset estimatorThe variance of (c) is:

in the formulaIs the signal-to-noise ratio (signal power normalized to 1). Phase offset estimatorThe variance of (c) is:

it can be seen that, the accuracy of the above estimation algorithm for initial frequency offset and initial phase offset depends on the signal-to-noise ratio and the length of the data used for estimation, and because of the existence of the frequency offset acceleration, the length of the data used for estimation cannot be infinitely long, so that a compromise can be obtained between the required estimation performance and the frequency offset acceleration during the actual test and satellite-ground communication, and the estimation accuracy is improved by lengthening the length of the data used for estimation under the condition of low signal-to-noise ratio.

AboutThe maximum likelihood estimation formula has no analytic solution, only a search algorithm can be adopted, and in order to increase the search speed, reduce the calculation amount of the algorithm and increase the convergence speed, a dichotomy is adopted for searching.

Because the hopping of the frequency hopping frequency causes the hopping of the pseudo-doppler at the receiving end, the tracking of the spread spectrum frequency hopping signal is adversely affected, and the carrier wave cannot be tracked by adopting the traditional frequency-locked loop and phase-locked loop structures. The direct spreading code and the hopping spreading code in the received signal are coherent, that is, the number of direct spreading codes contained in one hopping time slot is a fixed integer number of PN codes, and the hopping codes are correlated with time. The time of frequency change of the local frequency hopping DDS can be accurately obtained by utilizing the time correlation of the PN code and the frequency hopping signal code of the direct spread spectrum sequence signal. Thus, after the pseudo code synchronization is completed, the hopping code is substantially synchronized.

The carrier frequency hopping speed is high, the frequency hopping frequency points are multiple, and in order to ensure the coherence of frequency hopping signals, digital direct frequency synthesis (DDS) is adopted to generate carriers. The direct digital synthesis DDS is a frequency synthesis technology based on waveform storage, introduces an advanced data processing theory and method into the field of frequency synthesis, and is a third generation frequency synthesis technology following direct frequency synthesis and indirect frequency synthesis. The DDS has the advantages that: the bandwidth is wide, the frequency conversion time is short, the frequency resolution is high, the full digitalization structure is convenient to integrate, the output phase is continuous, and the frequency, the phase and the amplitude can be programmed. Under the condition that the reference clock is accurate, a stable sine wave with adjustable frequency and phase can be generated, and the generation of a local frequency hopping source can be directly completed by matching with the FPGA, so that the debounce is completed.

Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.