CN102655491A - Frequency shift estimation method and system for coherent demodulation frequency shift keying modulating signals - Google Patents
Frequency shift estimation method and system for coherent demodulation frequency shift keying modulating signals Download PDFInfo
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Abstract
The invention relates to the field of digital wireless communication and discloses a frequency shift estimation method and system for coherent demodulation frequency shift keying modulating signals. According to the method and the system, prefix signals of GFSK (Gaussian Frequency Shift Keying)/FSK (Frequency Shift Keying) signals are designed to a string of fixed-length codes with altering 0 and 1, and according to the prefix signals, an ideal receiving signal c(i) can be completely eliminated from an x(i) under the condition that a receiver does not need to copy the ideal receiving signal c(i), thereby solving the problem that as the frequency modulation index of the GFSK/FSK signal can not be obtained accurately and can change along with time and temperatures, a receiving terminal can not accurately copy the ideal receiving signal c(i), so as to improve the accuracy of the frequency shift evaluation. Therefore, by virtue of the iteration-combination of frequency evaluation results of R(N), R(2N),..., R (KN), the phase ambiguousness caused by the large frequency shift can be eliminated, and the precision of the frequency shift evaluation can be improved further.
Description
Technical Field
The invention relates to the field of digital wireless communication, in particular to the field of signal processing, and specifically relates to a frequency offset estimation method and system for coherent demodulation frequency shift keying modulation signals.
Background
In the field of digital wireless communication, frequency offset estimation is one of the commonly used signal processing methods.
Since the carrier frequencies between the base station and the mobile station, or between the mobile station and the mobile station, are unlikely to be absolutely equal, there is a relatively fixed frequency offset between the actual received signal and the desired received signal at the receiver. Such frequency offsets are detrimental in the field of digital wireless communications, which can reduce the accuracy of channel estimation and cause an increase in bit error rate. Therefore, in a digital wireless communication system, a receiver usually needs to perform frequency offset estimation according to an uplink received signal, and then perform frequency offset compensation to eliminate various harmful effects caused by frequency offset.
For signal modulation, amplitude keying ASK, frequency shift keying FSK/GFSK, phase shift keying PSK are classified.
The basic principle is that a carrier signal and a digital baseband signal are used to interact (different modulation modes and calculation formulas), a high-frequency signal which is modulated is obtained at a transmitting output end, and demodulation is needed to recover the original digital baseband signal at a receiving end.
The fundamental difference between the two demodulation methods is that coherent demodulation must recover a coherent carrier, and the coherent carrier and the modulated signal are used to obtain the original digital baseband signal, and the coherent carrier has the same frequency and phase as the carrier signal originally modulated by the baseband signal at the transmitting end, while noncoherent demodulation does not need to recover the coherent carrier, and therefore, the method is simpler than the coherent demodulation method. However, in most cases, the coherent demodulation method has a better demodulation effect.
Coherent demodulation refers to the multiplication of a reference signal, which is coherent with a carrier frequency (has the same frequency and phase), and the carrier frequency by a multiplier.
For example, the original signal a is modulated with the carrier frequency cos (ω t + θ) to obtain a signal Acos (ω t + θ);
when a coherent (same frequency and phase) reference signal cos (ω t + θ) is introduced during demodulation, the following results are obtained:
Acos(ωt+θ)cos(ωt+θ)
using the sum and difference formula
A*1/2*[cos(ωt+θ+ωt+θ)+cos(ωt+θ-ωt-θ)]
=A*1/2*[cos(2ωt+2θ)+cos(0)]
=A/2*[cos(2ωt+2θ)+1]
=A/2+A/2cos(2ωt+2θ)
And filtering the high-frequency signal cos (2 omega t +2 theta) by using a low-pass filter to obtain an original signal A.
Coherent demodulation therefore requires receiver and carrier synchronization.
While non-coherent demodulation does not use multipliers and does not require receiver and carrier synchronization.
When the demodulation method is noncoherent demodulation, it is not necessary to accurately estimate the frequency offset. For coherent demodulation, the performance of the receiver can be greatly improved, but the frequency offset must be accurately estimated.
We will represent the received GFSK/FSK signal as:
where c (i) represents the ideal received signal, fdRepresents frequency offset, theta represents phase offset, T represents sampling time interval, and n (i) represents noise.
Since the frequency modulation index of the GFSK/FSK signal deviates from its standard value by a large error (10% or more), which changes the phase of the GFSK/FSK signal and thus the value of c (i), it is difficult to accurately estimate the frequency offset in the prior art.
ArrayComm corporation: "Method and apparatus for the determination of directional analysis using an important source and spatial processing", inventors: barratt; CraigH (Redwood City, CA); farzaneh; farrad (San Francisco, CA); parish; david M (LosAltos, CA), published day: 23/04/1998, publication No.: WO 98/17037 describes a method for frequency offset estimation, which performs frequency offset estimation in the order of a large-span coarse search and then a small-span fine search within a range of possible frequency offsets.
The method uses a section of known signal to carry out frequency offset estimation, and the cost function is the error power between the actual received signal and the ideal signal after adding the detection frequency offset. When the error power is minimum, the used detection frequency offset value is the estimation value of the frequency offset estimation.
When the method is applied to actual engineering, the position of the known signal needs to be estimated in the received signal, so that the complexity of the method is increased, and the probability of abnormal conditions is increased, namely: when the signal position estimation is known to be wrong, the frequency offset estimation result of the method is wrong.
The present invention provides a new frequency offset estimation method and system to improve or solve the above-mentioned problems.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a frequency offset estimation method for coherent demodulation frequency shift keying modulation signals, which can completely remove c (i) from x (i) without copying ideal received signals c (i), thereby avoiding the problem that the ideal received signals c (i) cannot be accurately copied at the receiving end due to the fact that the frequency modulation index of the GFSK/FSK signal cannot be accurately obtained and can change with time and temperature, and improving the accuracy of frequency offset estimation.
The invention solves the technical problems through the technical scheme that:
there is provided a frequency offset estimation method for coherent demodulation of a frequency shift keying modulated signal, the method comprising the steps of:
providing a GFSK/FSK signal;
setting a prefix of the provided GFSK/FSK signal as a code with alternating 0 and 1 of fixed length to become a prefix signal x (i);
providing an infinite response low pass filter, wherein the prefix signal x (i) passes through the infinite response low pass filter, and the signal after passing through the infinite response low pass filter is a filtered signal x' (i) = fIIR-LPF[x(i)]；
Carrying out complex conjugate multiplication and accumulation operation on the filtered prefix signals to obtain a group of signals R (N), R (2N), … and R (KN) which eliminate phase changes generated by '0' and '1' in the prefix signals and only leave phase changes generated by frequency offset;
performing frequency estimation on the R (N), R (2N), …, R (KN) to obtain a frequency offset estimation value
As an improvement of the above method, the complex conjugate multiplication operation performed on the filtered prefix signal is calculated as follows: :
rN(iN)=x′(i0+iN+N)[x′(i0+iN)]*
r2N(i2N)=x′(i0+i2N+2N)[x′(i0+i2N)]*
…
rKN(iKN)=x′(i0+iKN+KN)[x′(i0+iKN)]*
where L is a multiple of the sampling rate compared to the GFSK/FSK symbol rate, N is a factor of L, i0Is the starting point of the available prefix signal, ikN=0,1，...,2MKNL-1 is determined by the length of the available prefix signal, K is the system complexity and estimation precision, and is taken from 1 to the maximum precision value which represents complex conjugation; wherein, M is a coefficient related to the complexity and the estimation accuracy of the system, and can be a constant or a correction coefficient changing according to the complexity of the system, 2MKNL-1 can be viewed as a limit on the length of the prefix signal, which is related to the system complexity, a multiple of the symbol rate;
for r obtained by the above algorithmN(iN)，r2N(i2N)，…，rKN(iKN) The following addition is performed:
…
by performing frequency offset estimation on the calculated R (N), R (2N), …, R (KN) combinations with certain intervals, higher frequency estimation accuracy can be achieved with smaller K, and thus the system complexity is greatly reduced.
As an improvement of the above method, the cutoff frequency of the infinite response low pass filter can be lower than the bandwidth of the GFSK/FSK signal.
As an improvement of the method, a factor N, which is a multiple L of the sampling rate compared to the GFSK/FSK symbol rate, is taken as
Is determined, i.e., the value of N can satisfy the conditional expression, wherein fd maxT is the sampling time interval for the maximum possible frequency offset of the GFSK/FSK signal. Since N takes on value
Therefore, as long as r (n) has no phase ambiguity, a large frequency offset can be estimated.
As an improvement of the above method, the value of N is greater at high signal-to-noise ratios than at low signal-to-noise ratios.
As an improvement of the above method, the frequency estimation results of R (N), R (2N), …, R (kn) are combined by the following iterations:
starting from i =2 to i ═ N:
wherein,
as a result of the frequency offset estimation of step i, piFor an intermediate variable used in the estimation process of step i, a is a constant greater than 0 but less than 1. The iterative combination is used for eliminating phase ambiguity caused by large frequency offset, so that the precision of frequency offset estimation can be further improved.
The present invention further provides a frequency offset estimation system using the frequency offset estimation method for coherent demodulation of frequency shift keying modulated signals, the system comprising: the device comprises a signal generator, a signal coding unit, an infinite response low-pass filter, a prefix signal calculation unit and a frequency estimator;
the signal generator is used for providing a GFSK/FSK signal;
the signal coding unit sets the prefix of the provided GFSK/FSK signal to be 0 and 1 alternating codes with fixed length to be a prefix signal x (i);
the infinite response low-pass filter receives the prefix signal x (i) and filters the prefix signal to obtain a filtered signal x' (i) = fIIR-LPF[x(i)]；
The prefix signal calculation unit performs complex conjugate multiplication and accumulation operation on the filtered prefix signals to obtain a group of signals R (N), R (2N), … and R (KN), wherein the signals are obtained by eliminating phase changes generated by '0' and '1' in the prefix signals and only leaving the phase changes generated by frequency offset;
the frequency estimator performs frequency estimation on the R (N), R (2N), …, R (KN) to obtain a frequency offset estimation value
Compared with the prior art, the invention has the following advantages: the prefix signal of the GFSK/FSK signal is designed into a string of {0,1,0, 1} codes with fixed length, and the use of the prefix code enables a receiver to completely remove c (i) from x (i) under the condition that an ideal received signal c (i) does not need to be copied, so that the problem that the ideal received signal c (i) cannot be accurately copied at a receiving end due to the fact that the frequency modulation index of the GFSK/FSK signal cannot be accurately obtained and can change along with time and temperature is solved, and the accuracy of frequency offset estimation is improved. Because an infinite response low-pass filter is used to reduce noise in x (i) before calculating R (N), R (2N), …, R (KN), and a combination of R (N), R (2N), …, R (KN) with certain intervals is used to estimate frequency offset, higher frequency estimation precision can be achieved with smaller K, and thus system complexity is greatly reduced. The invention can also estimate larger frequency offset, can achieve higher estimation precision under the condition of low signal-to-noise ratio and estimate the optimal sampling point of coherent demodulation.
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Fig. 1 is a flow chart of a frequency offset estimation method of coherently demodulating a frequency shift keyed modulated signal according to a first embodiment of the invention;
fig. 2 is a logic diagram of a frequency offset estimation system for coherently demodulating a frequency shift keyed modulated signal in accordance with a third embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, it will be appreciated by those of ordinary skill in the art that numerous technical details are set forth in order to provide a better understanding of the present application in various embodiments of the present invention. However, the technical solutions claimed in the claims of the present application can be implemented without these technical details and with various changes and modifications based on the following embodiments.
A first embodiment of the present invention relates to a method for estimating a frequency offset of a coherent demodulation frequency shift keying modulated signal, as shown in fig. 1, which specifically includes the following steps:
step S101, providing a GFSK/FSK signal;
in the present embodiment, the received GFSK/FSK signal is represented as:
where c (i) represents the ideal received signal, fdRepresents frequency offset, theta represents phase offset, T represents sampling time interval, and n (i) represents noise.
For GFSK/FSK signals, the common demodulation scheme is noncoherent, so there is no need to estimate the frequency offset accurately. Coherent demodulation can greatly improve the performance of the receiver, but the frequency offset must be accurately estimated. Since the frequency modulation index of the GFSK/FSK signal deviates from its standard value by a large error (10% or more), which changes the phase of the GFSK/FSK signal and thus the value of c (i), it is difficult to accurately estimate the frequency offset in the prior art.
Since the frequency modulation index of the GFSK signal cannot be accurately obtained and changes with time and temperature, the ideal received signal c (i) cannot be accurately copied at the receiving end, and c (i) cannot be completely removed from x (i), thereby affecting the accuracy of frequency offset estimation.
In step S102, a series of fixed-length codes with 0 and 1 alternating, such as {0,1,0,1, · 0,1} codes, is set in the prefix of the provided GFSK/FSK signal to become a prefix signal x (i). The use of the prefix code allows us to completely remove c (i) from x (i) without duplicating the ideal received signal c (i), thereby improving the accuracy of the frequency offset estimation.
In order to reduce the noise in the prefix signal, the prefix signal is first passed through an infinite response low-pass filter to obtain a filtered signal x' (i) = fIIR-LPF[x(i)]Namely, step S103 is executed.
Wherein the cut-off frequency of the infinite response low-pass filter can be properly lower than the bandwidth of the GFSK/FSK signal. The infinite response low pass filter is used because of the low complexity of the infinite response filter. In addition, the frequency offset estimation algorithm used in the present embodiment is not affected by phase distortion caused by the infinite response filter.
Then, in step S104, the filtered prefix signal is subjected to complex conjugate multiplication and accumulation operation to obtain a set of signals R (N), R (2N), …, R (kn) with the phase changes caused by '0' and '1' in the prefix signal eliminated and only the phase changes caused by frequency offset remained.
Specifically, the complex conjugate multiplication of the filtered prefix signal is performed by the following calculation formula:
rN(iN)=x′(i0+iN+N)[x′(i0+iN)]*
r2N(i2N)=x′(i0+i2N+2N)[x′(i0+i2N)]*
…
rKN(iKN)=x′(i0+iKN+KN)[x′(i0+iKN)]*
in the present embodiment, it is assumed that the sampling rate is L times the GFSK/FSK symbol rate, and N is a factor of L. In the above formula, i0Is the starting point of the available prefix signal, ikN=0,1，...,2MKNL-1 is determined by the length of the available prefix signal, K is the system complexity and estimation precision, and is taken from 1 to the maximum precision value which represents complex conjugation; m is a coefficient related to the complexity and the estimation accuracy of the system, and can be a constant or a correction coefficient which changes according to the complexity of the system, 2MKNL-1 can be viewed as a limit on the length of the prefix signal, which is related to the system complexity, a multiple of the symbol rate.
Then, r obtained by the above calculation is addedN(iN)，r2N(i2N)，…，rKN(iKN) The following addition is performed:
…
due to the fact thatikNCovering MkNThe phase changes of "0" and "1" are opposite to each other in the GFSK/FSK signal, and therefore, the addition will eliminate the phase changes of "0" and "1" and only leave the phase changes generated by the frequency offset. Thus, no matter how the frequency modulation index of the GFSK/FSK signal changes, the ideal received signal c (i) is not required to be duplicated at the receiving end, and c (i) can be completely removed from x (i), so that the frequency offset can be accurately estimated.
After obtaining a group of signals R (N), R (2N), …, R (KN) with the phase changes generated by '0' and '1' in the prefix signals eliminated and only the phase changes generated by frequency offset, carrying out frequency estimation on the obtained signals R (N), R (2N), …, R (KN) to obtain the frequency offset estimation value
Namely, step S105 is performed.
Since the infinite response low pass filter correlates the noise contained in the adjacent data in x' (i), the value of N in this embodiment can be determined by the following criteria:
1.
that is, the value of N can satisfy the conditional expression, wherein fd maxThe maximum possible frequency deviation of the GFSK/FSK signal is shown, and T is a sampling time interval;
2. the value of N is larger than that of N in the case of low signal-to-noise ratio when the signal-to-noise ratio is high; moreover, the larger the value of N is, the better the N is under the condition of high signal-to-noise ratio; the value of N should be slightly reduced in case of low signal-to-noise ratio.
Compared with the prior art, the prefix signal of the GFSK/FSK signal is designed into a string of {0,1,0,1,. 0,1} codes with fixed length in the embodiment. The use of the prefix code enables the receiver to completely remove c (i) from x (i) without copying the ideal received signal c (i), thereby avoiding the problem that the frequency modulation index of the GFSK/FSK signal cannot be accurately obtained and can change along with time and temperature, so that the ideal received signal c (i) cannot be accurately copied at the receiving end, and improving the accuracy of frequency offset estimation.
Because an infinite response low-pass filter is used to reduce noise in x (i) before calculating R (N), R (2N), …, R (KN), and a combination of R (N), R (2N), …, R (KN) with certain intervals is used to estimate frequency offset, higher frequency estimation precision can be achieved with smaller K, and thus system complexity is greatly reduced.
In addition, such as the formulaAs shown, in the present embodiment, as long as r (n) has no phase ambiguity, a large frequency offset can be estimated. For r obtained by complex conjugate multiplicationN(iN)，r2N(i2N)，…，rKN(iKN) The processing may also estimate the best sampling point for coherent demodulation.
A second embodiment of the present invention relates to a frequency offset estimation method for coherent demodulation of a frequency shift keying modulated signal. The second embodiment is further improved on the basis of the first embodiment, and the improvement is mainly as follows: in the second embodiment of the present invention, the frequency offset estimation results of R (N), R (2N), …, R (kn) are combined iteratively to eliminate phase ambiguity caused by large frequency offset, so as to further improve the accuracy of frequency offset estimation.
Specifically, the present embodiment uses the following algorithm to eliminate the phase ambiguity caused by the large frequency offset, and iteratively combines the frequency estimation results of R (N), R (2N), …, R (kn) to achieve a higher estimation accuracy:
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2. starting from i =2 to i ═ N:
wherein,
as a result of the frequency offset estimation of step i, piFor an intermediate variable used in the estimation process of step i, a is a constant greater than zero but less than one. The value of a in the formula is optimized according to the signal-to-noise ratio condition, so that the precision of frequency estimation can be further increased.
Since the frequency estimation results of R (N), R (2N), …, R (kn) are combined by iteration in the present embodiment, a higher estimation accuracy can be achieved under the condition of a low signal-to-noise ratio.
The steps of the above methods are divided for clarity, and the implementation may be combined into one step or split some steps, and the steps are divided into multiple steps, so long as the steps contain the same logical relationship, which is within the protection scope of the present patent; it is within the scope of the patent to add insignificant modifications to the algorithms or processes or to introduce insignificant design changes to the core design without changing the algorithms or processes.
A third embodiment of the present invention relates to a frequency offset estimation system using the frequency offset estimation method for coherently demodulating a frequency shift keying modulated signal according to the first embodiment of the present invention, as shown in fig. 2, the system including: the device comprises a signal generator, a signal coding unit, an infinite response low-pass filter, a prefix signal calculation unit and a frequency estimator;
wherein, the signal generator is used for providing a GFSK/FSK signal;
the signal coding unit sets the prefix of the provided GFSK/FSK signal as 0 and 1 alternating codes with fixed length to be a prefix signal x (i);
an infinite response low-pass filter receives the prefix signal x (i) and filters the prefix signal to obtain a filtered signal x' (i) = fIIR-LPF[x(i)](ii) a Wherein the cutoff frequency of the infinite response low-pass filter is lower than the bandwidth of the GFSK/FSK signal.
The prefix signal calculation unit performs complex conjugate multiplication and accumulation operation on the filtered prefix signals to obtain a group of signals R (N), R (2N), … and R (KN), wherein the phase changes generated by '0' and '1' in the prefix signals are eliminated, and only the phase changes generated by frequency offset are left;
specifically, the prefix signal calculation unit comprises a complex conjugate multiplication subunit and an accumulation operation subunit; the complex conjugate multiplication subunit performs complex conjugate multiplication on the filtered prefix signal:
rN(iN)=x′(i0+iN+N)[x′(i0+iN)]*
r2N(i2N)=x′(i0+i2N+2N)[x′(i0+i2N)]*
…
rKN(iKN)=x′(i0+iKN+KN)[x′(i0+iKN)]*
wherein, L is the multiple of the sampling rate compared with the GFSK/FSK code element rate, and N is a factor of L; i.e. i0Is the starting point of the available prefix signal, ikN=0,1，...,2MKNL-1 is determined by the length of the available prefix signal, K is the system complexity and the estimation precision, the maximum precision value is obtained from 1, represents complex conjugate, and M is a correction coefficient related to the system complexity and the estimation precision;
the accumulation operation subunit pair is subjected to complex conjugate multiplicationR calculated by operator unitN(iN)，r2N(i2N)，…，rKN(iKN) And (3) performing addition operation:
the frequency estimator performs frequency estimation on the R (N), R (2N), …, R (KN) to obtain a frequency offset estimation value
In addition, the value of a factor N in the complex conjugate multiplication subunit, which is a multiple L of the sampling rate compared with the GFSK/FSK code element rate, is determined by
Is determined wherein fd maxT is the sampling time interval for the maximum possible frequency offset of the GFSK/FSK signal. And the value of N is greater at high signal-to-noise ratios than at low signal-to-noise ratios.
In addition, it should be noted that, in practical applications, the prefix signal calculating unit may implement complex conjugate multiplication and accumulation operations by combining the complex conjugate unit, the N-th order serial register, the complex multiplier, the adder, the complex register, and the like as shown in fig. 2, but the present invention is not limited thereto, and any module or device combination that can implement the above operations, obtain a set of signals that eliminates phase changes generated by '0' and '1' in the prefix signal, and only leaves phase changes generated by frequency offset for the frequency estimator to perform frequency estimation is within the protection scope of the present invention.
It should be understood that this embodiment is a system example corresponding to the first embodiment, and may be implemented in cooperation with the first embodiment. The related technical details mentioned in the first embodiment are still valid in this embodiment, and are not described herein again in order to reduce repetition. Accordingly, the related-art details mentioned in the present embodiment can also be applied to the first embodiment.
It should be noted that each module referred to in this embodiment is a logical module, and in practical applications, one logical unit may be one physical unit, may be a part of one physical unit, and may be implemented by a combination of multiple physical units. In addition, in order to highlight the innovative part of the present invention, elements that are not so closely related to solving the technical problems proposed by the present invention are not introduced in the present embodiment, but this does not indicate that other elements are not present in the present embodiment.
A fourth embodiment of the present invention relates to a frequency offset estimation system. The fourth embodiment is further improved on the basis of the third embodiment, and the improvement is mainly as follows: in a fourth embodiment of the present invention, the system further comprises a phase ambiguity elimination unit that iteratively combines the frequency estimation results of R (N), R (2N), …, R (kn):
starting from i =2 to i ═ N:
wherein,
as a result of the frequency offset estimation of step i, piFor an intermediate variable used in the estimation process of step i, a is a constant greater than 0 but less than 1.
Since the second embodiment corresponds to the present embodiment, the present embodiment can be implemented in cooperation with the second embodiment. The related technical details mentioned in the second embodiment are still valid in this embodiment, and the technical effects that can be achieved in the second embodiment can also be achieved in this embodiment, and are not described herein again in order to reduce the repetition. Accordingly, the related-art details mentioned in the present embodiment can also be applied to the second embodiment.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.
Claims (12)
1. A method of frequency offset estimation for coherent demodulation of frequency shift keyed modulated signals, the method comprising the steps of:
providing a GFSK/FSK signal;
setting the prefix of the provided GFSK/FSK signal to a code with fixed length and alternating 0 and 1 to form a prefix signal x (i);
providing an infinite response low pass filter, wherein the prefix signal x (i) passes through the infinite response low pass filter, and the signal after passing through the infinite response low pass filter is a filtered signal x' (i) = fIIR-LPF[x(i)]；
Carrying out complex conjugate multiplication and accumulation operation on the filtered prefix signals to obtain a group of signals R (N), R (2N), … and R (KN) which eliminate phase changes generated by '0' and '1' in the prefix signals and only leave phase changes generated by frequency offset;
performing frequency estimation on the R (N), R (2N), …, R (KN) to obtain a frequency offset estimation value
2. The method of frequency offset estimation for coherent demodulation of frequency shift keying modulated signals according to claim 1, characterized by: the complex conjugate multiplication operation on the filtered prefix signal is calculated as follows:
rN(iN)=x′(i0+iN+N)[x′(i0+iN)]*
r2N(i2N)=x′(i0+i2N+2N)[x′(i0+i2N)]*
…
rKN(iKN)=x′(i0+iKN+KN)[x′(i0+iKN)]*
where L is a multiple of the sampling rate compared to the GFSK/FSK symbol rate, N is a factor of L, i0Is the starting point of the available prefix signal, ikN=0,1，...,2MKNL-1 is determined by the length of the available prefix signal, K is the system complexity and the estimation precision, the maximum precision value is obtained from 1, represents complex conjugate, and M is a correction coefficient related to the system complexity and the estimation precision;
for r obtained by the above calculationN(iN)，r2N(i2N)，…，rKN(iKN) And (3) performing addition operation:
…
3. the method of frequency offset estimation for coherent demodulation of frequency shift keying modulated signals according to claim 1, characterized by: the cutoff frequency of the infinite response low-pass filter is lower than the bandwidth of the GFSK/FSK signal.
4. The method of frequency offset estimation for coherent demodulation of frequency shift keying modulated signals according to claim 2, characterized by: the value of a factor N which is a multiple L of the sampling rate compared to the GFSK/FSK symbol rate is determined by
Is determined wherein fd maxT is the sampling time interval for the maximum possible frequency offset of the GFSK/FSK signal.
5. The method of frequency offset estimation for coherent demodulation of frequency shift keying modulated signals according to claim 4, characterized by: the value of N is greater at high signal-to-noise ratios than at low signal-to-noise ratios.
6. The method of frequency offset estimation for coherent demodulation of frequency shift keying modulated signals according to claim 1, characterized by: merging frequency offset estimates of R (N), R (2N), …, R (kn) by the following iterations:
starting from i =2 to i ═ N:
wherein,
as a result of the frequency offset estimation of step i, piFor an intermediate variable used in the estimation process of step i, a is a constant greater than 0 but less than 1.
7. A frequency offset estimation system using the frequency offset estimation method of coherently demodulating a frequency shift keyed modulated signal according to claim 1, characterized in that the system comprises: the device comprises a signal generator, a signal coding unit, an infinite response low-pass filter, a prefix signal calculation unit and a frequency estimator;
the signal generator is used for providing a GFSK/FSK signal;
the signal coding unit sets the prefix of the provided GFSK/FSK signal to be 0 and 1 alternating codes with fixed length to be a prefix signal x (i);
the infinite response low-pass filter receives the prefix signal x (i) and filters the prefix signal to obtain a filtered signal x' (i) = fIIR-LPF[x(i)]；
The prefix signal calculation unit performs complex conjugate multiplication and accumulation operation on the filtered prefix signals to obtain a group of signals R (N), R (2N), … and R (KN), wherein the signals are obtained by eliminating phase changes generated by '0' and '1' in the prefix signals and only leaving the phase changes generated by frequency offset;
the frequency estimator performs frequency estimation on the R (N), R (2N), …, R (KN) to obtain a frequency offset estimation value
8. The frequency offset estimation system of claim 7, wherein: the prefix signal calculation unit comprises a complex conjugate multiplication subunit and an accumulation subunit;
the complex conjugate multiplication subunit performs complex conjugate multiplication on the filtered prefix signal:
rN(iN)=x′(i0+iN+N)[x′(i0+iN)]*
r2N(i2N)=x′(i0+i2N+2N)[x′(i0+i2N)]*
…
rKN(iKN)=x′(i0+iKN+KN)[x′(i0+iKN)]*
where L is a multiple of the sampling rate compared to the GFSK/FSK symbol rate, N is a factor of L, i0Is the starting point of the available prefix signal, ikN=0,1，...,2MKNL-1 is determined by the length of the available prefix signal, K is the system complexity and the estimation precision, the maximum precision value is obtained from 1, represents complex conjugate, and M is a correction coefficient related to the system complexity and the estimation precision;
the accumulation operation subunit is used for calculating r obtained by the complex conjugate multiplication operation subunitN(iN)，r2N(i2N)，…，rKN(iKN) And (3) performing addition operation:
…
9. the frequency offset estimation system of claim 7, wherein: the cutoff frequency of the infinite response low-pass filter is lower than the bandwidth of the GFSK/FSK signal.
10. The frequency offset estimation system of claim 8, wherein: the value of a factor N in the complex conjugate multiplication subunit, which is the multiple L of the sampling rate compared with the GFSK/FSK code element rate, is passed through
Is determined wherein fd maxT is the sampling time interval for the maximum possible frequency offset of the GFSK/FSK signal.
11. The frequency offset estimation system of claim 10, wherein: the value of N is greater at high signal-to-noise ratios than at low signal-to-noise ratios.
12. The frequency offset estimation system of claim 7, wherein: the system further comprises a cancellation phase ambiguity unit that iteratively combines frequency estimates of R (N), R (2N), …, R (kn):
starting from i =2 to i ═ N:
wherein,
as a result of the frequency offset estimation of step i, piFor an intermediate variable used in the estimation process of step i, a is a constant greater than 0 but less than 1.
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