A synchronization method for OFDM system based on ZC sequence

Abstract

The application provides a synchronization method of an OFDM system based on a ZC sequence, which comprises the following steps: firstly, constructing two ZC sequences ZC1 and ZC2 with different roots; then, taking values of the ZC1 sequence and the ZC2 sequence and arranging them to obtain a training sequence; transforming the training sequence through IFFT; adding a cyclic prefix to a data frame; then, sending the training sequence out from a sending end and transmitting the training sequence through a channel; calculating the cross-correlation of data of a receiving end and a local training sequence; finally, selecting a symbol synchronization position according to the cross-correlation calculation value; and after the synchronization position is determined, estimating a carrier frequency offset. The application scheme can satisfy accurate symbol synchronization and frequency offset estimation in a large-fading and low-signal-to-noise-ratio wired channel environment, enhances the reliability of synchronization and reduces the operation amount.

Description

Technical Field

[0001] This invention relates to the field of OFDM symbol timing synchronization technology, and in particular to an OFDM system synchronization method based on ZC sequence. Background Technology

[0002] In wired twisted-pair channels, due to various adverse factors during signal transmission, including channel fading and noise interference, severe symbol desynchronization occurs between the receiver and transmitter.

[0003] In traditional symbol synchronization algorithms, the Schmidl algorithm may not accurately determine the start position of OFDM symbols due to the peak plateau problem in the timing metric function; the Minn algorithm is prone to start position detection errors due to the side peak phenomenon; and the Park algorithm's main peak is not obvious enough. Therefore, the traditional carrier estimation method based on cyclic prefix is ​​not very accurate, and the frequency offset estimation is inaccurate when the signal-to-noise ratio is low. Summary of the Invention

[0004] This invention addresses the challenge of symbol synchronization in traditional OFDM communication systems under high noise conditions by proposing a synchronization method for OFDM systems based on ZC sequences. This method redesigns the training sequence as an equal-amplitude zero-autocorrelation sequence and devises a novel training sequence construction method. Through additive white Gaussian noise (AWGN) and a twisted-pair channel, the carrier frequency offset can be determined by cross-correlation calculation with the local sequence and based on the characteristics of its own training sequence, thereby improving the accuracy of symbol synchronization and carrier frequency offset estimation.

[0005] A synchronization method for OFDM systems based on ZC sequences includes the following steps:

[0006] Step S1: Construct two ZC sequences ZC1 and ZC2 with different roots. The ZC1 and ZC2 sequences are represented as follows:

[0007]

[0008] Where N represents the number of bits carried by the subcarrier, M1 and M2 represent different prime numbers of N, and M2 = N - M1;

[0009] Step S2: Take values ​​from and arrange the ZC1 and ZC2 sequences. Name the first N / 2 elements of the ZC1 sequence A and the first N / 2 elements of the ZC2 sequence B. Then take the conjugate of B to form [AB]. * The sequence is ultimately formed into a training sequence X of total length N. n ;

[0010] Step S3, for the training sequence X nPerform IFFT transformation;

[0011] Step S4: Add a cyclic prefix of length Ng to the transmission symbol;

[0012] Step S5: The transmitting end sends out the training sequence after IFFT transformation and transmits it through the channel.

[0013] Step S6: Perform cross-correlation calculation between the received data and the local reference sequence;

[0014] Step S7: Select the symbol synchronization position based on the cross-correlation calculation value;

[0015] Step S8, based on the maximum value m after symbol synchronization sync Position truncation sequence to obtain r sync Then, carrier frequency offset estimation is performed.

[0016] Furthermore, the autocorrelation expressions for the two ZC sequences are as follows:

[0017]

[0018] Where k represents the position of a symbol in the sequence, and m represents the time shift between two ZC sequences;

[0019] When M1 and M2 are equal, let M1 = M2 = M, then we have:

[0020]

[0021] When m = 0, the autocorrelation function is R. 11 (0): R 11 (0) = N;

[0022] When m≠0, the autocorrelation function R 11 (m) = 0.

[0023] Furthermore, due to In the second training sequence, k 2 If the parity of k is equal to that of k, then we have The training sequence X n The expression for the first half of x[n], i.e., the first N / 2, obtained by IFFT transformation is:

[0024]

[0025] The expression for the second half of x[n] is:

[0026]

[0027] Furthermore, in step S5, let the transmitted training sequence be represented in the time domain as x(n), the channel impulse response as h(n), the data obtained by the receiver as r(n), and the Gaussian white noise as ω(n), then we have: r(n) = x(n) * h(n) + ω(n).

[0028] Furthermore, in step S6, let y[n] be the local reference sequence, then the cross-correlation function R xy (m) is:

[0029] Furthermore, in step S7, the delay of the symbol synchronization time is determined by determining the maximum value of the cross-correlation, and let the offset m corresponding to the maximum value be... sync For: m sync =arg max m |R xy (m)|, where || represents modulo.

[0030] Furthermore, the carrier frequency offset estimation in step S8 specifically involves:

[0031]

[0032] f CFO This is the value of the carrier frequency offset, where Ng represents the length of the cyclic prefix, N represents the length of the subcarrier, and ∠(·) represents the complex phase angle.

[0033] The beneficial technical effects of this invention are as follows:

[0034] This invention proposes a synchronization method for OFDM systems based on ZC sequences. This method significantly improves the accuracy and robustness of symbol timing synchronization by innovatively designing a composite training sequence based on multiple Zadoff-Chu sequences. Due to the excellent autocorrelation and cross-correlation characteristics of Zadoff-Chu sequences, the proposed training sequence can still achieve efficient and reliable symbol synchronization under heavy fading conditions.

[0035] Compared with the existing symbol synchronization algorithm Schmidl, the method of this invention effectively solves the peak plateau problem of the timing metric function, significantly improves timing accuracy, has no secondary peak problem compared with the Minn algorithm, and improves the main peak value compared with the Park algorithm, further enhancing the reliability of synchronization.

[0036] The method of the present invention only requires one IFFT operation. The sequence is arranged first, and then the overall IFFT transformation is performed, instead of performing IFFT transformation on multiple predetermined sequences first and then sorting the sequences, thus reducing the amount of computation.

[0037] In summary, the novel ZC sequence symbol synchronization method proposed in this invention can not only clearly capture the effective peak value through cross-correlation with the local sequence, but also significantly reduce the computational load at the receiver, thereby improving synchronization accuracy and system efficiency. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a flowchart illustrating a symbol synchronization method for an OFDM system based on ZC sequences provided in an embodiment of the present invention.

[0040] Figure 2 This is a schematic diagram of the training sequence construction provided in an embodiment of the present invention;

[0041] Figure 3 This is an autocorrelation function graph of the ZC combination sequence proposed in this invention, provided in an embodiment of the invention;

[0042] Figure 4 This is an autocorrelation function graph of sequences obtained from the traditional Schmidl algorithm, Minn algorithm, and Park algorithm provided in this embodiment of the invention;

[0043] Figure 5 This is a cross-correlation diagram of the ZC sequence and the local sequence of an OFDM system using a twisted-pair channel under a 0dB noise environment, provided by an embodiment of the present invention.

[0044] Figure 6 This is a cross-correlation graph of the sequence and the local sequence obtained by the Schmidl algorithm, Minn algorithm, and Park algorithm of an OFDM system using a twisted-pair channel in a 0dB noise environment, provided by an embodiment of the present invention.

[0045] Figure 7 This is a comparison chart of the accuracy of the training sequence provided by the method of the present invention and the traditional carrier frequency offset estimation method based on cyclic prefix. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] A synchronization method for OFDM systems based on ZC sequences, such as Figure 1 As shown, it includes the following steps:

[0048] Step S1: Construct two ZC sequences ZC1 and ZC2 with different roots. The ZC1 and ZC2 sequences are represented as follows:

[0049]

[0050] Where N represents the number of bits carried by the subcarrier, M1 and M2 represent different prime numbers of N, and M2 = N - M1. The following combination of two ZC sequences with different roots still results in good autocorrelation: The autocorrelation formula is as follows:

[0051]

[0052] Where k represents the position of the symbol in the sequence, and m represents the time shift between the two ZC sequences, substituting the two ZC sequences into the autocorrelation expression yields:

[0053]

[0054] By rearranging the exponent terms, we can obtain:

[0055]

[0056] When M1 and M2 are equal, let M1 = M2 = M, then we have:

[0057]

[0058] When m = 0, the autocorrelation function is R. 11 (0): R 11 (0) = N;

[0059] When m≠0, the autocorrelation function R 11 (m) = 0;

[0060] When M1 and M2 are not equal, the exponential term in the autocorrelation expression contains different frequency terms, which means that the spectra of the two sequences are different. This is because the spectrum of the ZC sequence is determined by the root parameter. Therefore, when the two root parameters are not equal, the spectra of the two ZC sequences will not overlap, which means they can be considered orthogonal. The autocorrelation under all delays is zero, so the combination of two sequences with different roots will not affect the correlation.

[0061] In this invention, the ZC sequence M1 and M2 are chosen as arbitrary prime numbers of N. In the embodiment, it is assumed that N = 512, M1 and M2 are 3 and 509 respectively, and it is obvious that R 12 Since (m) is not 0, combining ZC sequences with different ends will not produce correlation between the sequences.

[0062] Step S2: Take values ​​from and arrange the ZC1 and ZC2 sequences.

[0063] Take the first N / 2 elements of the ZC1 sequence and name them A, and take the first N / 2 elements of the ZC2 sequence and name them B. That is, select the first 256 items of ZC1 and ZC2, and then take the conjugate of B to form [AB]. * Sequence, such as Figure 2 As shown, the final training sequence X is formed with a total length of N. n .

[0064] Step S3: Transfer the training sequence X n Obtained through IFFT transformation:

[0065]

[0066] because In the second training sequence k 2 Since k has the same parity as k, therefore Now, the X[n] sequence is transformed by IFFT to obtain x[n]. The expression for the first half of x[n], i.e. the first N / 2, is as follows:

[0067]

[0068] The second half of x[n], that is, the expression for obtaining x[n+N / 2], is:

[0069]

[0070] Comparing the first and second halves of the expression, we can see that after the training sequence undergoes IFFT, the difference between the first and second halves is (-1). k Multiply the second half by (-1) kThis makes the first half and the second half equal, which can be used for subsequent carrier frequency offset estimation. Furthermore, based on the characteristics of the ZC sequence, the autocorrelation and cross-correlation characteristics of the sequence will not be affected after the IFFT transformation, thus not interfering with its own orthogonality and ideal correlation performance.

[0071] The first one is (-1). k The (-1) is introduced after conjugation of the sequence with root N-r1, defined from the second half of the frequency domain sequence. k ), the second (-1) k The index of the time-domain sequence is shifted N / 2 points backward (i.e., e) jπk The IFFT property naturally introduces (-1). k .

[0072] Step S4: Add a cyclic prefix of length Ng to the transmission symbol;

[0073] Step S5: The transmitting end sends out the training sequence after IFFT transformation and transmits it through the channel;

[0074] Let the transmitted training sequence be represented in the time domain as x(n), the channel impulse response as h(n), the data obtained at the receiver as n(n), and the Gaussian white noise as ω(n), then we have: r(n) = x(n) * h(n) + ω(n);

[0075] Step S6: Perform cross-correlation calculation between the received data and the local reference sequence.

[0076] Cross-correlation function R xy (m) is used to measure the similarity of two signals r[n] and y[n] at different time offsets m. The cross-correlation function gives the "degree of overlap" of the signals within a time window. If the signals r[n] and y[n] are aligned at a certain time, the cross-correlation value of the two signals will reach the maximum value, indicating that the matching degree of the two signals is the best.

[0077] Let y[n] be the local reference sequence, and the cross-correlation function R be... xy (m) is:

[0078] Step S7: Select symbol synchronization position based on cross-correlation calculation value

[0079] The received sequence and the local reference sequence are cross-correlated. The delay of symbol synchronization is determined by determining the maximum cross-correlation value R. xy (m) gives the similarity between the received signal and the local reference sequence at different time offsets, so the offset m corresponding to the maximum value is... sync The most suitable synchronization position: m sync =arg maxm |R xy (m)|, where || represents modulo.

[0080] Step S8: Based on the maximum value m after symbol synchronization sync Position truncation sequence to obtain r sync Then, carrier frequency offset estimation is performed, specifically as follows:

[0081]

[0082] Where Ng represents the length of the cyclic prefix, N represents the length of the subcarrier, and r sync This represents the sequence after symbolic synchronization, and ∠(·) represents the phase angle (in radians) of the complex number.

[0083] The autocorrelation functions of the ZC sequence proposed in this invention and the sequence obtained by the traditional method are as follows: Figure 3 and Figure 4 As shown in the figure, when the signal-to-noise ratio of the signal decreases after introducing Gaussian white noise, the training sequence proposed in this invention can effectively maintain the autocorrelation performance. Compared with the traditional method, the peak value of the main peak is less affected by the decrease in the signal-to-noise ratio.

[0084] The cross-correlation functions of the ZC sequence proposed in this invention and the sequence obtained by traditional methods in the OFDM system are as follows: Figure 5 and Figure 6 As shown, the subcarrier length is N=512, M1 and M2 are set to 3 and 5 respectively, the carrier frequency is 10MHz, the sampling frequency is 80MHz, the signal-to-noise ratio S / N=0dB, and the signal is transmitted through a twisted-pair channel. As can be seen from the figure, the method of the present invention is significantly better than the traditional method in terms of peak performance.

[0085] Figure 7 This is a comparison chart of the accuracy of the training sequence provided by the method of this invention and the traditional carrier frequency offset estimation method based on cyclic prefix. As can be seen from the chart, after symbol synchronization, when the signal-to-noise ratio is low, the accuracy of carrier frequency offset estimation by the method of this invention is improved. Compared with the traditional method, the frequency offset estimation accuracy of the method of this invention is less affected by the decrease in signal-to-noise ratio.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A synchronization method for an OFDM system based on ZC sequences, characterized in that, The method includes: Step S1: Construct two ZC sequences with different roots. and , and The sequence is represented as: ； ； in, Indicates the number of bits carried by the subcarrier. and Representing distinct prime numbers of N, ; Step S2, for and The sequence is sorted and its values ​​are selected. The first N / 2 elements of the sequence are named A, and then... The first N / 2 elements of the sequence are named B, and then... Take conjugate, form The sequence is ultimately formed into a training sequence of total length N. ; Step S3, for the training sequence Perform IFFT transformation; Step S4: Add a cyclic prefix of length Ng to the transmission symbol; Step S5: The transmitting end sends out the training sequence after IFFT transformation and transmits it through the channel. Step S6: Perform cross-correlation calculation between the received data and the local reference sequence; Step S7: Select the symbol synchronization position based on the cross-correlation calculation value; Step S8, based on the maximum value after symbol synchronization Position truncation sequence obtained Then, carrier frequency offset estimation is performed; Among them, due to In the second training sequence, , and If the parity of the two elements is equal, then we have: , training sequence Obtained through IFFT transformation , The first half, that is, the first half The expression is: The expression for the second half is: ； In step S5, let the transmitted training sequence be represented in the time domain as follows: The channel impulse response is The data received by the receiving end is Gaussian white noise is Then we have: ; In step S6, let If the local reference sequence is used, then the cross-correlation function is... for: ; In step S7, the delay of symbol synchronization is determined by determining the maximum value of the cross-correlation, and the offset corresponding to the maximum value is set as follows. for: ,in, Indicates modulo; The carrier frequency offset estimation in step S8 is specifically as follows: That is, the value of the carrier frequency offset, where, represents the length of the cyclic prefix, N represents the length of the subcarrier, and ∠(⋅) represents the phase angle of the complex number.

2. The method according to claim 1, characterized in that, The autocorrelation expressions for the two ZC sequences are as follows: in, Indicates the position of a symbol in the sequence. This represents the time shift between two ZC sequences; when and When they are equal, set Then we have: When m=0, the autocorrelation function is : ; When m At 0, the autocorrelation function .

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