CN110971558B - CAZAC sequence-based low-complexity anti-frequency offset synchronization method - Google Patents
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Abstract
The invention discloses a low-complexity anti-frequency offset synchronization method based on a CAZAC sequence in a multi-carrier OFDM system, which mainly solves the problems of poor synchronization performance and high complexity of the existing algorithm, and the implementation scheme is as follows: constructing a training sequence based on a CAZAC sequence at a transmitting end; constructing a timing measurement function at a receiving end, searching the maximum value of the timing measurement function, and completing timing synchronization; and by utilizing the result of timing synchronization, estimating rough decimal frequency offset, then estimating fine decimal frequency offset, and finally estimating integral multiple frequency offset to finish frequency synchronization. The invention improves the synchronization performance of the OFDM system, simplifies the timing measurement function, reduces the calculation complexity and can be used for the wireless communication scene of burst transmission or continuous transmission.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a multi-carrier-oriented OFDM system synchronization method which can be used in a wireless communication scene of burst transmission or continuous transmission.
Background
Orthogonal Frequency Division Multiplexing (OFDM) is used as a multi-carrier modulation mode, has the advantages of high spectrum efficiency, frequency selective fading resistance, easiness in modulation and demodulation and the like, and is widely applied to a plurality of wireless communication scenes, such as Long Term Evolution (LTE), Digital Video Broadcasting (DVB), Wireless Local Area Network (WLAN) and the like. Although OFDM has the above advantages, the signal modulation mechanism thereof also makes OFDM signals have some disadvantages in transmission, such as being very sensitive to timing offset and frequency offset caused by doppler shift or instability of an oscillator, once synchronization error occurs, orthogonality between subcarriers is destroyed, inter-subcarrier interference ICI and inter-symbol interference ISI are introduced, and OFDM signal demodulation fails, so that OFDM systems have high requirements for synchronization, and in recent years, many synchronization algorithms are proposed for jointly or separately estimating timing offset and frequency offset.
In the OFDM system, the synchronization method is roughly classified into two types according to whether data assistance is required: non-data aided blind estimation algorithms and data aided estimation algorithms. Wherein the content of the first and second substances,
the non-data-aided blind estimation algorithm is generally used in a continuous system, mainly utilizes the structural characteristics of an OFDM system to carry out synchronization, the representative algorithm is a maximum likelihood ML estimation algorithm based on a cyclic prefix, and the algorithm does not need to additionally design a synchronization sequence, so that the system bandwidth is saved, the bandwidth utilization rate is improved, but the synchronization performance is poorer than that of a data-aided algorithm.
Data-aided estimation algorithms are generally used in burst systems, and mainly utilize some random sequences to complete timing synchronization by capturing the peak value of a timing metric function, thereby completing frequency synchronization. The random sequence is mainly composed of PN sequence or CAZAC sequence and other sequences with good self-correlation and cross-correlation performance. The representative algorithm for synchronization based on the PN sequence is: SC in its published paper "Robust Frequency and Timing Synchronization for OFDM" (IEEE Transactions on Communications,1997,45: 1613-; an article published by Minn, namely 'On Timing Estimation for OFDM Systems' (IEEE Communications Letters,2000,4: 242-; park designs a training sequence structure with conjugate symmetry property in a published paper "A Novel Timing Estimation Method for OFDM Systems" (IEEE Communications Letters,2003,7:53-55), and compared with SC algorithm and Minn algorithm, the algorithm has a larger peak value at the correct starting point position, so that the accuracy of Timing measurement is improved, but smaller side lobes still exist; in the published paper "An effective Symbol Timing Scheme for OFDM Systems Using Optimal Correlation-Based cyclic-Shifted Preamble" (IEEE Wireless Communications Letters,2019), Yang proposes a coarse Symbol Timing algorithm Based on An optimally correlated cyclic shift Preamble sequence CSP, which has good performance in a multipath fading channel, but has high computational complexity.
The peak flat top effect or the existing larger side lobe of the algorithms has certain influence on timing synchronization, and when a PN sequence is adopted for symbol timing synchronization, the problems of high peak-to-average ratio exist, and the good correlation characteristic and the low peak-to-average ratio characteristic of the CAZAC sequence can be exactly solved, so that the CAZAC sequence is widely applied to the OFDM system for synchronization.
The existing CAZAC sequence-based synchronization representative algorithm includes: fang in its published paper "A Novel Synchronization Algorithm Based on CAZAC sequences for OFDM Systems" (IEEE International Conference on Wireless Networks and Mobile Communications,2012:1-4) uses a random index Sequence to weight CAZAC sequences to achieve Timing Synchronization, Shao in its published paper "Robust Timing and Frequency Synchronization Based on Constant Amplitude Zero Autocorrelation Sequence for OFDM Systems" (IEEE International Conference Communication processing, bl: 14-17) uses a training Sequence structure similar to the Park Algorithm, the new weighting factor is used at the receiving end to carry out weighting processing on the CAZAC sequence to complete timing synchronization, the Fang algorithm and the Shao algorithm have good performance under a multipath fading channel, however, when the receiving end performs synchronization, an additional weighting sequence needs to be used, which wastes some storage space and increases the computational complexity; a new training Sequence structure is designed in a paper "A Novel Timing Synchronization Method Based on CAZAC Sequence for OFDM Systems" (IEEE International Conference on Signal Processing, Communications and Computing,2018:10-15) published by Jian, and the calculation complexity can be reduced when Timing Synchronization is carried out by using the structure, but the Timing Synchronization performance is obviously reduced when frequency offset exists.
Disclosure of Invention
The invention aims to provide a low-complexity frequency offset resistant synchronization method based on a CAZAC sequence aiming at the defects of the existing algorithm so as to improve the synchronization performance and reduce the calculation complexity.
The technical key points of the invention are as follows: generating a training symbol constructed by a CAZAC sequence at a transmitting end, simplifying a timing measurement function at a receiving end, and realizing accurate and stable synchronization by using characteristics of delay correlation and symmetric correlation, wherein the method comprises the following implementation steps:
(1) at the transmitting end, a training sequence based on a CAZAC sequence is constructed: t ═ A (n), B (n), C (n) D (n)]Wherein A (N) is a first partial sequence of the training sequence of the transmitting end, which is composed of a CAZAC sequence with a length of N/4, and is represented as
J is an imaginary unit, N is 0,1, …, N/4-1, and N is the number of subcarriers in the OFDM system;
b (n) is a second partial sequence of the training sequence of the transmitting end, which is a conjugate symmetric sequence of the A (n) sequence, i.e.
C (n) is a third part of the sequence of the training sequence of the transmitting end, which is obtained by inverting the even number of the sequence A (n), that is
D (n) is a fourth part of the transmitting end training sequence, which is obtained by inverting the even number of the B (n) sequence, i.e.
(2) Set the length to NgAdding the cyclic prefix to the front end of the training sequence T of the transmitting end to obtain the cyclic prefix P with the length of N + NgTraining symbol S ═ P T]And transmitting the training symbol;
(3) at the receiving end, setting the length of a receiving window as N, and constructing a timing metric function M (d) in the window length:
wherein the content of the first and second substances,
the correlation function is represented by a function of the correlation,
representing energy functions, wherein m and k are respectively intermediate variables of functions P (d) and R (d), d is a sampling point serial number,
and
respectively receiving samples with different values;
(4) searching the maximum value of the timing metric function M (d) to obtain a timing synchronization estimated value:
completing timing synchronization;
(5) based on timing synchronization estimates
Determining the starting position of the training sequence in the received sample to obtain the training sequence of the receiving end:
wherein the content of the first and second substances,
to receive a sample, n1N-1, and using the symmetric property of the two sequences before and after the training sequence T', calculating to obtain a rough decimal frequency offset estimation value
(6) Based on timing synchronization estimates
Determining the starting position of the training symbol in the received sample to obtain the training symbol of the receiving end:
wherein the content of the first and second substances,
to receive a sample, n3＝-Ng,-Ng+ 1.. ang.N-1, and based on a coarse fractional frequency offset estimate
Carrying out rough decimal frequency offset compensation on the training symbol S' to obtain the training symbol S after the first frequency offset compensation1Further performing fine decimal frequency offset estimation based on the cyclic prefix, and calculating to obtain a fine decimal frequency offset estimation value
(7) According to fine decimal frequency deviation estimated value
Training symbol S after compensating for first frequency offset1Fine decimal frequency deviation compensation is carried out to obtain a training symbol S after the second frequency deviation compensation2Then, using the property of integral multiple frequency offset causing shift to the CAZAC sequence, constructing an integral multiple frequency offset decision function F (g):
wherein g is an argument of the function F (), g is 0,1,2,., N-1, p, q are intermediate variables of the function F (g), respectively,
and
respectively taking two receiving samples with different values after secondary frequency offset compensation, and marking the upper marks to represent that conjugation is taken;
(8) searching the maximum value of an integral multiple frequency offset decision function F (g) to obtain an integral multiple frequency offset estimation value:
(9) using rough fractional frequency offset estimation
Fine fractional frequency offset estimation
And integer multiple frequency offset estimation
Obtaining a frequency offset estimation value:
frequency synchronization is completed.
Compared with the existing algorithm, the invention has the following advantages:
firstly, the invention constructs the training sequence structure based on the CAZAC sequence at the transmitting end, thereby eliminating the timing measurement peak platform or larger side lobe phenomenon introduced by the symmetrical structure of the cyclic prefix and the synchronous sequence at the receiving end, improving the timing synchronization performance in the environment of Gaussian channel and multipath fading channel, and solving the problems of poor timing synchronization performance and sensitivity to frequency offset of the existing algorithm.
Secondly, the invention firstly carries out rough decimal frequency offset estimation and further carries out fine decimal frequency offset estimation at the receiving end, and the scheme of correcting decimal frequency offset by two stages enables the frequency offset estimation precision to be higher, and solves the problem of low frequency offset estimation precision of the existing algorithm.
Thirdly, all the operations are carried out in the time domain, FFT processing is not needed, and an additional weighting sequence is not needed, so that the storage space is saved, the realization complexity of a synchronization module is reduced, and the system synchronization speed is improved.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram of a training sequence architecture in the present invention;
FIG. 3 is a graph comparing the timing detection probability of the present invention and the prior synchronization algorithm under the condition of Gaussian channel without adding frequency offset;
FIG. 4 is a graph comparing the timing detection probability of the present invention and the prior synchronization algorithm under the condition of Gaussian channel and frequency offset;
FIG. 5 is a graph comparing the timing detection probability of the present invention and the prior synchronization algorithm under the condition of multipath fading channel and no frequency offset;
FIG. 6 is a graph comparing the mean square error performance of the frequency offset estimation under Gaussian channel in the present invention and the existing synchronization algorithm;
fig. 7 is a graph comparing the mean square error performance of frequency offset estimation under multipath fading channel in the present invention and the existing synchronization algorithm.
Detailed Description
Embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the specific implementation steps of this embodiment are as follows:
1a) The first part of the training sequence A (N) at the transmitting end is constructed from an N/4 long CAZAC sequence, denoted as
J is an imaginary unit, N is 0,1, and N/4-1, and N is the number of subcarriers in the OFDM system;
wherein, CAZAC sequenceThe columns are represented as:
wherein N is1Is the period of CAZAC sequence, takes an even number, and r is N1Is a reciprocal prime number, v is 0,11-1, for the a (N) sequence, r ═ 1, N1＝N；
1b) Constructing a second part of the training sequence B (n) of the transmitting end, which is a conjugate symmetric sequence of the sequence A (n), i.e.
1c) Constructing a third part C (n) of the training sequence at the transmitting end, which is obtained by inverting the even number of the A (n) sequence, i.e. by using the inverted sequence
1d) Constructing a fourth part sequence D (n) of the transmitting end training sequence, which is obtained by inverting the even number of the B (n) sequence, i.e.
1e) Obtaining a transmitting end training sequence with the length of N from the sequence A (N), the sequence B (N), the sequence C (N) and the sequence D (N): t ═ a (n) b (n) c (n) d (n), as shown in fig. 2.
And 2, constructing a training symbol S.
By N at the tail of the training sequence T at the sending endgEach data signal constitutes a cyclic prefix P;
adding the cyclic prefix P to the front end of the training sequence T of the transmitting end to obtain the training sequence T with the length of N + NgTraining symbol S ═ P T]And transmitting the training symbol.
And 3, constructing a timing metric function M (d).
At the receiving end, the length of a receiving window is set to be the same as the length of a training sequence T at the sending end, the length is N, and a timing measurement function M (d) is constructed in the length of the receiving window:
wherein the content of the first and second substances,
the correlation function is represented by a function of the correlation,
representing energy functions, wherein m and k are respectively intermediate variables of functions P (d) and R (d), d is a sampling point serial number,
and
respectively, are received samples of different values.
And 4, finishing timing synchronization.
Searching the maximum value of the timing metric function M (d) to obtain a timing synchronization estimated value:
the timing synchronization is completed.
5a) Based on timing synchronization estimates
Determining the starting position of the training sequence in the received sample to obtain the training sequence of the receiving end:
wherein the content of the first and second substances,
to receive a sample, n1＝0,1,...,N-1；
5b) Calculating to obtain a rough decimal frequency offset estimation value by utilizing the symmetric property of the sequences of the front part and the rear part of the training sequence T
Wherein, angle () represents taking the phase,
and
two received samples, n, of different values 20,1, N/2-1, superscript denotes taking the conjugate.
Step 6, estimating fine decimal frequency deviation
6a) Based on timing synchronization estimates
Determining the starting position of the training symbol in the received sample to obtain the training symbol of the receiving end:
wherein the content of the first and second substances,
to receive a sample, n3＝-Ng,-Ng+1,...,N-1；
6b) Estimating the frequency offset according to the rough decimal multiple
Performing coarse fractional frequency offset compensation on the training symbol S ', i.e. multiplying the training symbol S' byA compensation term
Obtaining a training symbol after the first frequency offset compensation:
i＝0,1,...,N+Ng-1；
6c) training symbol S compensated by first frequency offset1Further carrying out fine decimal frequency offset estimation based on the cyclic prefix, and calculating to obtain a fine decimal frequency offset estimation value
Wherein the content of the first and second substances,
and
two received samples, n, of different values, respectively, after a first frequency offset compensation4＝0,1,...,Ng-1。
And 7, constructing an integer multiple frequency offset decision function F (g).
7a) According to fine decimal frequency deviation estimated value
Training symbol S after compensating for first frequency offset1Performing fine fractional frequency offset compensation, i.e. on the training symbol S1By a compensation term
Obtaining a training symbol after the second frequency offset compensation:
l＝0,1,...,N+Ng-1；
7b) using the training symbol S after the second frequency offset compensation2According to the property that the integer multiple frequency offset causes the displacement to the CAZAC sequence, an integer multiple frequency offset decision function F (g) is constructed:
wherein g is an argument of the function F (), g is 0,1,2,., N-1, p, q are intermediate variables of the function F (g), respectively,
and
two different values of the received samples after the second frequency offset compensation are respectively marked with a symbol to represent the conjugate.
Step 8, estimating integral multiple frequency deviation
Searching the maximum value of an integral multiple frequency offset decision function F (g) to obtain an integral multiple frequency offset estimation value:
and 9, completing frequency synchronization.
Using rough fractional frequency offset estimation
Fine fractional frequency offset estimation
And integer multiple frequency offset estimation
Obtaining a frequency offset estimation value:
frequency synchronization is completed.
The effect of the present invention will be further explained with the simulation experiment.
1. Simulation conditions are as follows:
the simulation experiment of the invention is carried out under MATLAB 2016B software, and the number N of subcarriers in the OFDM system is set to be 256, and the length N of cyclic prefix is set to begThe introduced normalized frequency offset epsilon is 5.65, and the channels used for simulation are additive white gaussian noise channel and multipath fading channel (ITU 3GIBx channel in ITU standard), respectively, and the simulation times of a single signal-to-noise ratio are set to be 2000.
The existing synchronization algorithm includes: SC algorithm, Minn algorithm, Park algorithm, Yang algorithm, Fan algorithm, Shao algorithm, and Jianan algorithm. The existing synchronization algorithms for performing timing synchronization comparison include a Minn algorithm, a Park algorithm, a Yang algorithm, a Fang algorithm, a Shao algorithm and a Jian algorithm, and the existing synchronization algorithms for performing frequency synchronization comparison include an SC algorithm, a Fang algorithm and a Shao algorithm.
2. Simulation content and result analysis:
As can be seen from FIG. 3, the detection probability of the invention, the Fan algorithm, the Shao algorithm and the Jianan algorithm reaches 1 when the signal-to-noise ratio is about 0dB, the detection probability of the Park algorithm reaches 1 when the signal-to-noise ratio is about 5dB, and the detection probability of the Minn algorithm and the Yang algorithm reaches 1 when the signal-to-noise ratio is about 20dB, which shows that the invention has good timing synchronization performance under the conditions of Gaussian channel and no frequency offset.
Simulation 2 shows the result of performing timing synchronization under the gaussian channel and frequency offset conditions using the present invention and the conventional synchronization algorithm under the above conditions, as shown in fig. 4. In fig. 4, the horizontal axis represents the signal-to-noise ratio of the OFDM system in dB, and the vertical axis represents the timing detection probability.
It can be seen from fig. 4 that when there is frequency offset, the timing detection probability of Jian algorithm is significantly reduced, and other existing algorithms have stable performance, and the present invention still has good detection performance, which indicates that the timing synchronization performance of the present invention is good under the conditions of gaussian channel and frequency offset.
Simulation 3 shows that the timing synchronization is performed in the multipath fading channel without adding frequency offset under the above conditions by using the present invention and the above conventional synchronization algorithm, and the result is shown in fig. 5. In fig. 5, the horizontal axis represents the signal-to-noise ratio of the OFDM system in dB, and the vertical axis represents the timing detection probability.
It can be seen from fig. 5 that, under the condition of multipath fading channel and no frequency offset, the timing detection probability of Minn algorithm, Park algorithm and Jian algorithm is obviously reduced, and other existing algorithms have stable performance, and the present invention still has good detection performance, which indicates that the present invention has good timing synchronization performance under the condition of multipath fading channel and no frequency offset.
Simulation 4, which performed frequency synchronization under the gaussian channel using the present invention and the conventional synchronization algorithm under the above conditions, is shown in fig. 6. In fig. 6, the horizontal axis represents the signal-to-noise ratio of the OFDM system in dB, and the vertical axis represents the mean square error of the frequency offset estimation.
As can be seen from fig. 6, the mean square error performance of the frequency offset estimation of the present invention is equivalent to that of the Fang algorithm, but better than that of the shano algorithm and the SC algorithm, and as the signal-to-noise ratio increases, the frequency offset estimation performance approaches the cralmelo boundary, which indicates that the frequency synchronization performance of the present invention is good under the gaussian channel.
As can be seen from fig. 7, the mean square error performance of the frequency offset estimation of the present invention is equivalent to that of the Fang algorithm, but better than that of the shano algorithm and the SC algorithm, and the frequency offset estimation performance approaches the cramer-pero boundary with the increase of the signal-to-noise ratio, which indicates that the frequency synchronization performance of the present invention is good in the multipath fading channel.
In order to compare the computation complexity of the present invention and the above conventional synchronization algorithm, the computation amount of the present invention and the above conventional synchronization algorithm in the timing synchronization stage is counted, and the result is shown in table 1.
Table 1 statistics table of calculated amount of each synchronization algorithm in timing synchronization stage
As can be seen from table 1, in the timing synchronization stage, the number of conjugation used in the present invention is 0, the total number of complex multiplications is N +2, and the total number of additions is N-4, which is lower in computational complexity than other algorithms.
Claims (5)
1. The low-complexity anti-frequency offset synchronization method based on the CAZAC sequence is characterized by comprising the following steps:
(1) at the transmitting end, a training sequence based on a CAZAC sequence is constructed: t ═ A (n), B (n), C (n) D (n)]Wherein A (N) is a first partial sequence of the training sequence of the transmitting end, which is composed of a CAZAC sequence with a length of N/4, and is represented as
J is an imaginary unit, N is 0,1, and N/4-1, and N is the number of subcarriers in the OFDM system;
b (n) is a second partial sequence of the training sequence of the transmitting end, which is a conjugate symmetric sequence of the A (n) sequence, i.e.
C (n) is a third part of the sequence of the training sequence of the transmitting end, which is obtained by inverting the even number of the sequence A (n), that is
D (n) is a fourth part of the transmitting end training sequence, which is obtained by inverting the even number of the B (n) sequence, i.e.
(2) Set the length to NgAdding the cyclic prefix to the front end of the training sequence T of the transmitting end to obtain the cyclic prefix P with the length of N + NgTraining symbol S ═ P T]And transmitting the training symbol;
(3) at the receiving end, setting the length of a receiving window as N, and constructing a timing metric function M (d) in the window length:
wherein the content of the first and second substances,
the correlation function is represented by a function of the correlation,
representing energy functions, wherein m and k are respectively intermediate variables of functions P (d) and R (d), d is a sampling point serial number,
respectively receiving samples with different values;
(4) searching the maximum value of the timing metric function M (d) to obtain a timing synchronization estimated value:
completing timing synchronization;
(5) based on timing synchronization estimates
Determining the starting position of the training sequence in the received sample to obtain the training sequence of the receiving end:
wherein the content of the first and second substances,
to receive a sample, n1N-1, and using the symmetric property of the two sequences before and after the training sequence T', calculating to obtain a rough decimal frequency offset estimation value
By the following formula:
wherein, angle () represents taking the phase,
and
two received samples, n, of different values20,1, N/2-1, superscript denotes taking the conjugate;
(6) based on timing synchronization estimates
Determining the starting position of the training symbol in the received sample to obtain the training symbol of the receiving end:
wherein the content of the first and second substances,
to receive a sample, n3＝-Ng,-Ng+ 1.. ang.N-1, and based on a coarse fractional frequency offset estimate
Carrying out rough decimal frequency offset compensation on the training symbol S' to obtain the training symbol S after the first frequency offset compensation1Further performing fine decimal frequency offset estimation based on the cyclic prefix, and calculating to obtain a fine decimal frequency offset estimation value
By the following formula:
wherein the content of the first and second substances,
and
two received samples, n, of different values, respectively, after a first frequency offset compensation4＝0,1,...,Ng-1；
(7) According to fine decimal frequency deviation estimated value
Training symbol S after compensating for first frequency offset1Fine decimal frequency deviation compensation is carried out to obtain a training symbol S after the second frequency deviation compensation2Then, using the property of integral multiple frequency offset causing shift to the CAZAC sequence, constructing an integral multiple frequency offset decision function F (g):
wherein g is an argument of the function F (), g is 0,1,2,., N-1, p, q are intermediate variables of the function F (g), respectively,
and
respectively taking two receiving samples with different values after secondary frequency offset compensation, and marking the upper marks to represent that conjugation is taken;
(8) searching the maximum value of an integral multiple frequency offset decision function F (g) to obtain an integral multiple frequency offset estimation value:
(9) using rough fractional frequency offset estimation
Fine fractional frequency offset estimation
And integer multiple frequency offset estimation
Obtaining a frequency offset estimation value:
frequency synchronization is completed.
2. The method according to claim 1, wherein the CAZAC sequence in (1) is represented as follows:
wherein N is1Is the period of CAZAC sequence, takes an even number, and r is N1Is a reciprocal prime number, v is 0,11-1。
3. The method of claim 1, wherein the cyclic prefix P in (2) is N at the tail of training sequence T from the transmitting endgA data signal.
4. The method of claim 1, wherein the coarse fractional frequency offset compensation of the training symbol S 'in (6) is performed by multiplying the training symbol S' by a compensation term
Obtaining a training symbol after the first frequency offset compensation:
5. the method of claim 1, wherein the training symbol S compensated for the first frequency offset in (7)1Fine fractional frequency offset compensation is performed on the training symbol S1By a compensation term
Obtaining a training symbol after the second frequency offset compensation:
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