阅读说明：本技术 基于fft的分步递进高精度频率估计方法 (FFT-based step-by-step progressive high-precision frequency estimation method ) 是由 王晓婷 白鹤峰 李文屏 苏曼 周永彬 武磊磊 侯滨可 邵富杰 于 2020-05-07 设计创作，主要内容包括：本发明涉及一种基于FFT的分步递进高精度频率估计方法,包括以下步骤：a.发送端在数据起始位置插入同步导引p(n)(n＝0,1,…,N-1),N为同步导引长度,之后等间隔M插入导频符号q(n)(n＝0,1,…)；b.接收端对同步导引共轭相关得到恒模序列m(n)＝p(n)p*(n),对m(n)进行N点FFT得M(k),根据采样率fs1和|M(k)|最大值所对应位置,计算频率初步估计值fΔ1；c.根据所述频率初步估计值fΔ1对后续接收数据进行频谱搬移,从搬移后的接收数据中提取导频符号q′(n),与本地导频符号共轭相关得到待估计序列v<Sub>L</Sub>(n)＝q′(n)q<Sup>*</Sup>(n),n＝0,1,…,L-1,L为提取的导频符号长度,再次进行FFT频率估计,得到频率估计值fΔ2,进而计算最终的精确频率估计值为fΔ＝fΔ1+fΔ2。根据本发明的基于FFT的分步递进高精度频率估计方法,易于实现,复杂度低。(The invention relates to a step-by-step progressive high-precision frequency estimation method based on FFT, which comprises the following steps of: a. the transmitting end inserts a synchronization pilot p (N) (0, 1, …, N-1) at the data start position, where N is the synchronization pilot length, and then inserts pilot symbols q (N) (0, 1, …) at equal intervals M; b. the receiving end synchronously leads conjugate correlation to obtain a constant modulus sequence m (N) ═ p (N), performs N-point FFT on m (N) to obtain M (k), and calculates a frequency initial estimation value f delta 1 according to the sampling rate fs1 and the position corresponding to the maximum value of | M (k) |; c. carrying out spectrum shifting on subsequent received data according to the frequency preliminary estimation value f delta 1, extracting a pilot frequency symbol q' (n) from the shifted received data, and carrying out conjugate correlation with a local pilot frequency symbol to obtain a sequence v to be estimated L (n)＝q′(n)q * And (n), wherein n is 0,1, …, L-1 and L are the lengths of the extracted pilot symbols, the FFT frequency estimation is performed again to obtain a frequency estimation value f delta 2, and then the final accurate frequency estimation value f delta is calculated to be f delta 1+ f delta 2.)

1. A step-by-step progressive high-precision frequency estimation method based on FFT comprises the following steps:

a. the transmitting end inserts a synchronization pilot p (N) (0, 1, …, N-1) at the data start position, where N is the synchronization pilot length, and then inserts pilot symbols q (N) (0, 1, …) at equal intervals M;

b. the receiving end synchronously leads conjugate correlation to obtain a constant modulus sequence m (N) ═ p (N), performs N-point FFT on m (N) to obtain M (k), and calculates a frequency initial estimation value f delta 1 according to the sampling rate fs1 and the position corresponding to the maximum value of | M (k) |;

c. carrying out spectrum shifting on subsequent received data according to the frequency preliminary estimation value f delta 1, extracting a pilot frequency symbol q' (n) from the shifted received data, and carrying out conjugate correlation with a local pilot frequency symbol to obtain a sequence v to be estimated_L(n)＝q′(n)q^*And (n), where n is 0,1, …, L-1, and L are pilot symbol lengths extracted, FFT frequency estimation is performed again to obtain a frequency estimation value f Δ 2, and a final precise frequency estimation value f Δ is calculated as f Δ 1+ f Δ 2.

2. The FFT-based step-and-step advanced high-precision frequency estimation method as claimed in claim 1, wherein in the step b, a maximum value f of the first-step frequency estimation is calculated based on the transmission symbol rate fsym and the synchronization pilot length_max1And coarse estimation accuracy f_min1Expressed as:

calculating a frequency initial estimation value f delta 1 by adopting a rectangular window and FFT estimation method, wherein the process is as follows:

3. the FFT-based step-by-step progressive high-precision frequency estimation method according to claim 2, wherein in the step c, the method of performing spectrum shifting on the subsequent received data according to the preliminary frequency estimation value f Δ 1 comprises:

frequency value f estimated in a first step_Δ1Generating local oscillation signals at a receiving end, carrying out difference frequency spectrum shifting on subsequent received data r (n) to obtain r' (n), wherein the process is represented as:

wherein Re represents the real part of the expression, r^*(n) represents the orthogonal component of r (n).

4. The FFT-based step-and-step advanced high-precision frequency estimation method according to claim 3, wherein in the step c, a second-step maximum frequency estimation value fj is calculated based on the transmission symbol rate fsym and the CPLD_max2And coarse estimation accuracy f_min2Expressed as:

5. the FFT-based step-and-step progressive high-precision frequency estimation method of claim 4, wherein the second step frequency estimation maximum value f_max2And the first step coarse estimation accuracy f_min1The following relationship needs to be satisfied: f. of_min1≤f_max2；

The relationship that the pilot symbol insertion interval M and the synchronization pilot length N need to satisfy is derived and expressed as follows:

6. the FFT-based step-and-step progressive high-precision frequency estimation method according to claim 4, wherein the sending end determines a pilot symbol insertion interval M and a pilot symbol length L extracted by the receiving end according to a transmitted symbol rate fsym.

7. The FFT-based step-and-step advanced high precision frequency estimation method according to any of claims 1 to 6, wherein the synchronization pilot p (n) and the pilot symbol q (n) are symbol identifications known to the determined both the transmitting and receiving parties.

Technical Field

The invention relates to the technical field of wireless communication, in particular to a step-by-step progressive high-precision frequency estimation method based on FFT.

Background

With the development of society and the arrival of information age, digital wireless communication with 0 and 1 transmission is a major information transfer method at present, and is widely applied to various scenes. The uncertainty of the wireless transmission channel and the digital transceiver device itself poses a challenge to the reliability of digital communication, wherein the frequency offset between the transceiver devices is one of the problems that seriously affect the performance of digital communication, and when serious, the communication is blocked. Therefore, how to effectively estimate the frequency offset of the received data at the receiving end becomes a key for ensuring stable and reliable communication.

Since the precision of the frequency source used in the system is limited, the local oscillation signal generated by the system for quadrature digital down-conversion is a free oscillation signal with fixed frequency, and is influenced by various factors in practical application, and the actual output frequency is different from the ideal frequency, so that the frequency of the local oscillation signal cannot be completely consistent with the carrier frequency of the input signal, and a frequency difference is necessarily generated. On the other hand, if the receiver is in a moving state, the doppler effect caused by the relative motion will cause a certain deviation between the carrier frequency of the signal received by the receiver and the carrier frequency of the transmitted signal, i.e. doppler shift. When the relative motion of the transmitter and the receiver approaches each other, the frequency of the signal received by the receiver is higher than the frequency of the transmitted signal; when the relative motion of the transmitter and the receiver moves away from each other, the frequency of the signal received by the receiver will be lower than the frequency of the transmitted signal, i.e. the doppler effect.

Methods of implementing frequency estimation can be divided into two broad categories: hardware circuit based frequency measurement and discrete fourier transform based spectrum analysis. The former detects the signal waveform estimation frequency through a hardware circuit, is greatly influenced by noise, is difficult to adapt to high-precision requirements, and has higher cost; the latter is widely used because the FFT increases the operation speed, and the estimation accuracy mainly depends on the sampling rate and the data length.

At present, most of frequency estimation methods applied in practice are based on FFT, for example, algorithm design for spectrum refinement and calculation complexity improvement on the basis of discrete Fourier transform is disclosed in ShouRev, Tuyaqing, He Li 'DTFT spectrum refinement characteristic analysis and rapid algorithm design' electronic and information science report, Volume 33, phase 6, page number 1395-1400, Jacobsen E, Kootokokohos P 'Fast, acquisition frequency estimators' IEEE SIGNA L PROCESSASGMAGAIZINE, Volume 24, 2007, Pages: 123-.

With the development of mobile communication services such as high-speed railways, highways, low and medium orbit satellites and the like, the application requirements of wireless mobile communication in a high dynamic scene are increasing day by day and are not limited to simple voice communication, and high-speed data transmission such as videos, images, mobile internet and the like becomes an urgent need at present. However, the conditions of the mobile communication channel in a high dynamic scene are more complex and variable, and especially, the relative motion speed of the transmitting and receiving parties is high, which inevitably generates a large doppler shift, deepens the intersymbol interference of the system, reduces the demodulation performance of the receiving end, and seriously affects the reliability of the system transmission. At present, the range and the precision of the receiving end for estimating the data frequency offset are contradictory, the two are difficult to meet the requirements at the same time, and how to further improve the estimation precision under the condition of ensuring the frequency estimation range is a problem to be solved urgently for realizing stable and reliable high-dynamic wireless mobile communication.

Disclosure of Invention

The invention aims to solve the problems and provides a step-by-step progressive high-precision frequency estimation method based on FFT.

In order to achieve the above object, the present invention provides a step-by-step progressive high-precision frequency estimation method based on FFT, comprising the following steps:

a. the transmitting end inserts a synchronization pilot p (N) (0, 1, …, N-1) at the data start position, where N is the synchronization pilot length, and then inserts pilot symbols q (N) (0, 1, …) at equal intervals M;

b. the receiving end synchronously leads conjugate correlation to obtain a constant modulus sequence m (N) ═ p (N), performs N-point FFT on m (N) to obtain M (k), and calculates a frequency initial estimation value f delta 1 according to the sampling rate fs1 and the position corresponding to the maximum value of | M (k) |;

c. carrying out spectrum shifting on subsequent received data according to the frequency preliminary estimation value f delta 1, extracting a pilot frequency symbol q' (n) from the shifted received data, and carrying out conjugate correlation with a local pilot frequency symbol to obtain a sequence v to be estimated_L(n)＝q′(n)q^*And (n), where n is 0,1, …, L-1, and L are pilot symbol lengths extracted, FFT frequency estimation is performed again to obtain a frequency estimation value f Δ 2, and a final precise frequency estimation value f Δ is calculated as f Δ 1+ f Δ 2.

According to an aspect of the invention, in said step b, a maximum frequency estimate f of the first step is calculated based on the transmitted symbol rate fsym and the synchronization pilot length_max1And coarse estimation accuracy f_min1Expressed as:

calculating a frequency initial estimation value f delta 1 by adopting a rectangular window and FFT estimation method, wherein the process is as follows:

according to an aspect of the present invention, in the step c, the method for performing spectrum shifting on subsequent received data according to the preliminary frequency estimation value f Δ 1 includes:

frequency value f estimated in a first step_Δ1Generating local oscillation signals at a receiving end, carrying out difference frequency spectrum shifting on subsequent received data r (n) to obtain r' (n), wherein the process is represented as:

wherein Re represents the real part of the expression, r^*(n) represents the orthogonal component of r (n).

According to an aspect of the invention, in said step c, a second maximum frequency estimate f is calculated based on the transmitted symbol rate fsym and the synchronization pilot length_max2And coarse estimation accuracy f_min2Expressed as:

according to an aspect of the invention, the second step frequency estimates the maximum value f_max2And the first step coarse estimation accuracy f_min1The following relationship needs to be satisfied: f. of_min1≤f_max2；

The relationship that the pilot symbol insertion interval M and the synchronization pilot length N need to satisfy is derived and expressed as follows:

according to an aspect of the present invention, the sender determines the pilot symbol insertion interval M and the pilot symbol length L extracted by the receiver according to the transmitted symbol rate fsym.

According to one aspect of the invention, the synchronization pilot p (n) and the pilot symbol q (n) are known symbol identifiers for certain transceivers.

The step-by-step progressive high-precision frequency estimation method based on the FFT comprises the steps of designing the synchronous pilot length and the interval of pilot symbols according to the estimation precision requirement, realizing the frequency estimation based on the fast Fourier transform, carrying out data spectrum shifting by combining with the rough frequency estimation, extracting the pilot symbols to carry out the fine frequency estimation, and integrating the two estimation results to obtain the final frequency estimation value. Compared with the related technical method, the invention has the advantages that: the method is closely combined with the inherent frame structure characteristics of communication transmission data, has no other additional requirements, is easy to realize and has low complexity; the pilot frequency symbol insertion interval and the extraction length can be flexibly designed according to the system requirements to change the final frequency estimation precision; the estimation method adopted by the two-step frequency estimation is flexible, a rectangular window acceleration fast Fourier transform estimation method with simple calculation can be adopted, the structure and the calculation are simple, and hardware resources are saved; the simple integration of the two-step frequency estimation results is the final high-precision frequency estimation value. Through simulation verification, on the basis of synchronization of a communication system, the method can realize the estimation precision of approaching the Clalmelo limit, and can be less than 1 Hz.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.

FIG. 1 schematically shows a flow chart of an FFT-based step-and-step progressive high-precision frequency estimation method according to the present invention;

FIG. 2 is a schematic representation of the location of synchronization pilot and pilot symbols in synchronization frames and data frames according to one embodiment of the present invention;

FIG. 3 schematically illustrates a flow chart of a method for estimating a preliminary estimate of frequency according to one embodiment of the present invention;

fig. 4 schematically shows a flow chart of spectrum shifting of the subsequently received data r (n) according to an embodiment of the present invention.

Detailed Description

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments will be briefly described below. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.

In describing embodiments of the present invention, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in an orientation or positional relationship that is based on the orientation or positional relationship shown in the associated drawings, which is for convenience and simplicity of description only, and does not indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and thus, the above-described terms should not be construed as limiting the present invention.

The present invention is described in detail below with reference to the drawings and the specific embodiments, which are not repeated herein, but the embodiments of the present invention are not limited to the following embodiments.

Fig. 1 schematically shows a flow chart of an FFT-based step-wise progressive high-precision frequency estimation method according to the present invention. As shown in fig. 1, the FFT-based step-by-step high-precision frequency estimation method according to the present invention comprises the following steps:

a. the transmitting end inserts a synchronization pilot p (N) (0, 1, …, N-1) at the data start position, where N is the synchronization pilot length, and then inserts pilot symbols q (N) (0, 1, …) at equal intervals M;

b. the receiving end synchronously leads conjugate correlation to obtain a constant modulus sequence m (N) ═ p (N), performs N-point FFT on m (N) to obtain M (k), and calculates a frequency initial estimation value f delta 1 according to the sampling rate fs1 and the position corresponding to the maximum value of | M (k) |;

c. according to the frequency initial estimation value f delta 1Continuously receiving data and carrying out spectrum shifting, extracting pilot frequency symbol q' (n) from the shifted received data, and obtaining a sequence v to be estimated by conjugate correlation with the local pilot frequency symbol_L(n)＝q′(n)q^*And (n), where n is 0,1, …, L-1, and L are pilot symbol lengths extracted, FFT frequency estimation is performed again to obtain a frequency estimation value f Δ 2, and a final precise frequency estimation value f Δ is calculated as f Δ 1+ f Δ 2.

In the invention, a sending end carries out continuous framing, including synchronous guidance and pilot symbol insertion, sets the length N of the synchronous guidance, the insertion interval M of the pilot symbol and the transmission symbol rate fsym.

The inserted synchronization pilot and pilot symbols have no special format requirement, the synchronization pilot is consistent with a conventional synchronization header, and the pilot symbols can be continuous '1' or a specific pseudo-random sequence.

According to an embodiment of the present invention, in the step b, the maximum frequency estimation value f of the first step is calculated according to the transmission symbol rate and the synchronization pilot length_max1And coarse estimation accuracy f_min1Expressed as follows:

the frequency value is calculated by adopting a rectangular window and FFT estimation method, and the process is as follows:

according to one embodiment of the invention, in step c, the frequency value f estimated in the first step_Δ1Generating local oscillation signal at receiving end, shifting difference frequency spectrum for subsequent received data r (n) to obtain r' (n), the process is expressed as follows:

wherein Re represents the real part of the expression, r^*(n) represents the orthogonal component of r (n).

From moving toTo extract pilot symbols q' (n) of length L, i.e. to reduce the data sampling rate to f_symFrequency estimation is performed as in the first step, first with the conjugate q of the received pilot symbols and the local pilot symbols^*(n) multiplying to obtain an estimated sequence v_L(n), then FFT frequency estimation is carried out, and an accurate estimation value f is obtained through calculation_Δ2The maximum range of the step frequency estimation and the achievable accuracy are respectively f_max2And coarse estimation accuracy f_min2The calculation is as follows:

to ensure inheritance between the two frequency estimates, the second estimate the maximum range f_max2And the first step coarse estimation accuracy f_min1The following relationship needs to be satisfied:

f_min1≤f_max2

further derivation yields the relation that the pilot symbol insertion interval M and the synchronization pilot length N need to satisfy, which is expressed as follows:

finishing two-step frequency estimation of data with different sampling rates to obtain corresponding frequency estimation values (frequency values have positive and negative parts), and adding the frequency estimation values to obtain a final high-precision frequency estimation value, namely: f. of_Δ＝f_Δ1+f_Δ2。

The above-described method of the present invention is described in detail below with reference to the accompanying drawings in a specific embodiment.

The synchronization pilot and pilot symbol insertion, FFT frequency estimation and spectrum shifting processes of the present invention are further described below.

The sync pilot length N is determined by the communication system according to the application scenario and the system performance requirement, the pilot symbol insertion interval M and the receiver extraction length L are determined by the frequency estimation accuracy requirement, the larger the product of M and L is, the higher the frequency estimation accuracy is, and the larger the L invariant M is, the smaller the calculation complexity is.

Let the symbol rate fsym of the communication system be 1MBps, the sync pilot is M sequence with length N511, and the pilot symbol insertion interval is M128 symbols, i.e. two pilot symbols are spaced M/f apart in time_sym0.000128 (sec). The sync pilot is at the start of the sync frame and the pilot symbols are uniformly inserted in the sync frame and the data frame as shown in fig. 2.

The receiving end completes strict time and symbol synchronization through synchronous pilot correlation peak detection, further realizes optimal sampling at a symbol rate fsym, and obtains received data r (n) which comprises received synchronous pilot, data and pilot symbols.

The received synchronization pilot is multiplied by the conjugate of the local pilot at the receiving end (since the inserted synchronization pilot is m sequence, the conjugate is the pilot itself) to obtain the symbol sequence m (N) input to the FFT frequency estimation module, and since m (N) has a length N of 511, in order to perform FFT operation, 0 needs to be added at the end. If the total frequency offset generated by the transmission channel is 101020Hz, according to the estimation method in fig. 3, K is first calculated to be K-26, and then the frequency estimated in the first step is f_Δ1＝101760Hz。

And obtaining a coarse estimation frequency value, and performing frequency offset correction, namely frequency spectrum shifting, on subsequent received data r (n), wherein the process is as shown in fig. 4. For convenience of implementation, the received data is r_i(n) and r_q(n) two orthogonal paths, r (n) is in complex representation form: r (n) ═ r_i(n)+jr_q(n) of (a). The frequency spectrum shifting module generates a frequency of-f delta₁Of orthogonal local oscillator signals, i.e. cos (2 π f)_Δ1n/f_sym) And-sin (2 π f)_Δ1n/f_sym) The complex number is expressed in the form ofThe residual frequency offset after the frequency spectrum shifting is-740 Hz, and the sampling rate of the extracted pilot frequency symbol is f_symSetting the extracted pilot symbol length L to 1024 according to the requirement of estimation accuracy,/M7812.5 Hz., and then performing the second step of frequency estimation from fig. 3, wherein the frequency estimation value is calculated asf_Δ2-740.05Hz, and the final frequency estimate f is obtained_Δ＝f_Δ1+f_Δ2101019.5 Hz. Therefore, the variable sampling rate high-precision frequency estimation method can set the pilot frequency symbol length according to the precision requirement and realize the frequency estimation with any precision.

The variable sampling rate high-precision frequency estimation method provided by the embodiment of the invention can flexibly design the pilot frequency symbol insertion interval and the extraction length according to requirements, simultaneously meet the requirements of calculation complexity and estimation precision, realize high-precision frequency estimation through two-step FFT calculation, and effectively solve the problem of high dynamic frequency offset correction of mobile communication.

The step-by-step progressive high-precision frequency estimation method based on the FFT comprises the steps of designing the synchronous pilot length and the interval of pilot symbols according to the estimation precision requirement, realizing the frequency estimation based on the fast Fourier transform, carrying out data spectrum shifting by combining with the rough frequency estimation, extracting the pilot symbols to carry out the fine frequency estimation, and integrating the two estimation results to obtain the final frequency estimation value. Compared with the related technical method, the invention has the advantages that: the method is closely combined with the inherent frame structure characteristics of communication transmission data, has no other additional requirements, is easy to realize and has low complexity; the pilot frequency symbol insertion interval and the extraction length can be flexibly designed according to the system requirements to change the final frequency estimation precision; the estimation method adopted by the two-step frequency estimation is flexible, a rectangular window acceleration fast Fourier transform estimation method with simple calculation can be adopted, the structure and the calculation are simple, and hardware resources are saved; the simple integration of the two-step frequency estimation results is the final high-precision frequency estimation value. Through simulation verification, on the basis of synchronization of a communication system, the method can realize the estimation precision of approaching the Clalmelo limit, and can be less than 1 Hz.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.