Low complexity timing synchronization method based on gardner timing error detection

Abstract

The application discloses a low-complexity timing synchronization method based on a Gardner timing error detection algorithm, and belongs to the field of communication signal processing. The application optimizes the Gardner timing error detection algorithm, so that the algorithm is applicable to an open-loop feedforward timing synchronization structure. On the basis of a functional relationship between a Gardner timing error detection result and an actual timing error, a corresponding error compensation strategy of sampling point shift and fixed fractional interval interpolation is proposed, the complexity of error compensation is reduced, and a low-complexity open-loop feedforward timing synchronization method applicable to a short frame burst system is constructed. The application has the following advantages: (1) in the open-loop feedforward structure, the improved Gardner timing error detection algorithm is used, the complexity of the error detection algorithm is reduced compared with an open-loop timing synchronization method, and the real-time performance is improved compared with a traditional Gardner timing synchronization loop; (2) through sampling point shift and fixed fractional interval interpolation, the complexity of error compensation is reduced, the timing synchronization processing delay is reduced, and the system throughput is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to a low complexity timing synchronization method based on Gardner timing error detection, in particular to an open loop low complexity timing synchronization method for short frame burst system, and belongs to the field of communication signal processing. BACKGROUND

[0002] Timing synchronization technology, also known as symbol synchronization or chip synchronization, is one of the key technologies for realizing all-digital communication system. In all-digital wireless communication system, because the clock of receiver and transmitter are independent of each other, there is usually a phase deviation or a small frequency deviation between the two clocks. The data received by the receiver will have timing deviation, so that the receiver cannot sample the signal at the best sampling time, the signal-to-noise ratio of the signal is reduced, resulting in the demodulation performance of the whole system being degraded. The process of eliminating timing deviation and finding the best sampling time is timing synchronization, which mainly includes timing error detection and compensation.

[0003] In the field of communication signal processing, the current mature timing error detection methods include early-late gate algorithm, Mueller & Muller algorithm, maximum likelihood timing error detection method, absolute value nonlinear algorithm, square rate nonlinear algorithm, quartic nonlinear algorithm and logarithmic nonlinear algorithm. Among the numerous error detection algorithms, Gardner timing error detection algorithm has been widely applied because of its characteristics of not requiring auxiliary data, only requiring the signal oversampling rate to be twice or more, and being able to proceed independently of carrier synchronization. The basic principle of error compensation is to reconstruct the signal and resample it, and in all-digital communication system, this process is completed by an interpolation filter. The all-digital interpolation formula proposed by Gardner has been widely used in various timing synchronization methods because it can be approximated by a simple polynomial and has very high synchronization accuracy.

[0004] Gardner timing error detection algorithm has high synchronization performance, but since its detection result does not represent the real timing error, the algorithm usually needs the assistance of a closed-loop feedback structure to compensate for the error. The closed-loop feedback structure has higher implementation complexity than the open-loop structure, and due to poor real-time performance, it cannot be applied to systems with short frame burst characteristics. Although the open-loop structure is simple and has high real-time performance, error detection algorithms suitable for open-loop structure, such as square law non-linear algorithm, have high implementation complexity because they need to accurately detect the accurate timing error at one time. Higher complexity timing synchronization algorithm will introduce higher processing delay, which not only increases the resource consumption of hardware but also reduces the real-time performance of the system. If Gardner timing error detection algorithm can be applied to open-loop structure, the system can ensure low complexity of the algorithm while improving the real-time performance of the algorithm. Therefore, it is urgent to develop a Gardner timing error detection algorithm modification method suitable for open-loop structure and the design of corresponding open-loop error compensation strategy. SUMMARY

[0005] In order to solve the technical defects existing in the prior art as follows: (1) the timing synchronization method of the closed-loop feedback structure has a relatively complex structure and poor real-time performance; (2) the timing synchronization method of the traditional open-loop feedforward structure has high complexity of the error detection algorithm; the main purpose of the present application is to provide a low complexity timing synchronization method based on Gardner timing error detection, optimize the Gardner timing error detection algorithm, make it suitable for the timing synchronization structure of open-loop feedforward, and based on the functional relationship between the Gardner timing error detection result and the actual timing error, propose the error compensation strategy of corresponding sampling point shift and fixed fractional interval interpolation, reduce the complexity of error compensation, and thus construct a low complexity open-loop feedforward timing synchronization method suitable for short frame burst system. The present application has the following advantages: (1) in the open-loop feedforward structure, the improved Gardner timing error detection algorithm is used, which reduces the complexity of the error detection algorithm compared with the traditional open-loop timing synchronization method, and improves the real-time performance of the algorithm compared with the traditional Gardner timing synchronization loop; (2) by sampling point shift and fixed fractional interval interpolation, the complexity of error compensation is reduced, thereby further reducing the timing synchronization processing delay and improving the system throughput.

[0006] The purpose of the present application is realized by the following technical solutions.

[0007] The low complexity timing synchronization method based on Gardner timing error detection disclosed in the present application comprises the following steps:

[0008] Step one, in order to reduce the influence of the intermediate sampling values of the adjacent two symbols on the intermediate sampling value of the symbol Step two, in order to reduce the influence of the intermediate sampling values of the adjacent two symbols on the intermediate sampling value of the symbol The self-noise of the Gardner timing error detection algorithm is reduced, the detection precision of the Gardner timing error detection algorithm for small extra bandwidth signals and high order signals is improved, and the universality of the Gardner timing error detection algorithm is improved. The modified intermediate sampling value is substituted into the Gardner timing error detection formula to obtain the current symbol timing error detection result. The small extra bandwidth signal refers to a signal with an extra bandwidth less than 40%, and the high order signal refers to a DQPSK signal and an 8PSK signal with a modulation order of 8 or more.

[0009] The Gardner timing error detection algorithm is modified by reducing the influence of adjacent two symbol pairs on the intermediate sampling value The modified intermediate sampling value is:

[0010]

[0011] In the formula, β = h (T / 2) / h (0), h (t) is the impulse response of the system, T is the symbol period, x (r-1) and x (r) are the previous and next two sampling points. The modified intermediate sampling value is substituted into the Gardner timing error detection formula to calculate the current symbol timing error:

[0012]

[0013] In the formula, I (r) and I (r-1) are the I-channel sampling points of the rth and (r-1)th symbols, I' (r-1 / 2) is the modified intermediate sampling point of the two symbols, Q (r) and Q (r-1) are the Q-channel sampling points of the rth and (r-1)th symbols, and Q' (r-1 / 2) is the modified intermediate sampling point of the two symbols.

[0014] Step two, by accumulating the timing error detection results obtained in step one, the influence of useless detection results on error compensation is reduced, the single detection precision of the Gardner timing error detection algorithm is improved, and the Gardner timing error detection algorithm is applicable to the open loop control structure due to the improvement of the single detection precision, the complexity of the overall timing synchronization method is reduced; and the sampling point is shifted according to the positive and negative of the error accumulation result to compensate for the timing error, the step of accurate interpolation in the traditional timing synchronization method is omitted, the complexity of the timing synchronization method is further reduced, the signal processing delay is reduced, the real-time performance of the timing synchronization is improved, and the timing synchronization method is applicable to the communication system with short frame burst characteristics.

[0015] The L timing error detection results obtained in step one are accumulated according to the following formula:

[0016]

[0017] According to the sign of U i , the sampling point position is adjusted. If U i > 0, the current sampling point position is moved one bit backward, i.e. x(r+T / N) is substituted for x(r) as the sampling value of the rth symbol, where N is the oversampling rate of the system; if U i < 0, the current sampling point position is moved one bit forward, i.e. x(r-T / N) is substituted for x(r) as the sampling value of the rth symbol.

[0018] Step three, by using the characteristics that the S curve is monotonously increasing in the range of actual timing error -0.25 < τ < 0.25 and the relationship between the sign of the error detection result and the actual timing error, the sampling value with the largest signal-to-noise ratio in all original sampling values is accurately found out by comparing the sizes of the error accumulation results of the last two times, and the sampling point position is recorded. For a signal with a large oversampling rate, the residual timing error in the sampling value can be ignored, and the signal is down-sampled according to the recorded sampling point position, i.e. the timing synchronization in the case of a large oversampling rate is realized based on the Gardner timing error detection algorithm. The S curve is the functional relationship between the detection result of the Gardner timing error algorithm and the actual timing error.

[0019] The data selected in step two but after the sampling point is shifted are repeatedly subjected to step one and step two, a total of (N / 2-1) times, N being the oversampling rate of the signal, and the error accumulation result of the (N / 2-1)th time is saved

[0020] The error accumulation in step one and step two is repeatedly performed again, and the error accumulation result is saved The sampling point is not shifted. The error accumulation results of the last two times are compared and If , it indicates that the (N / 2-1)th sampling point shifting result cannot represent the best sampling point, and the sampling point needs to be shifted again according to the sign of U , at this time, the sampling value of the signal is the sampling value with the largest signal-to-noise ratio in the original sampling points; if , it indicates that the sampling value after the (N / 2-1)th sampling point shifting already has the largest signal-to-noise ratio, and the (N / 2)th shifting is not needed. The sampling point position after the last shifting is recorded.

[0021] Since the signal is not subjected to interpolation processing, the timing error will still be left in the system, and the maximum timing error is theoretically |τ| = T / (2*N). For a signal with a large oversampling rate N, the timing error can be ignored, and the subsequent steps are not needed, and the timing synchronization is completed by down-sampling the signal according to the recorded sampling point position.

[0022] Step four, for the signal with small over-sampling rate, the fixed fractional interval interpolation filter is used to reduce the complexity of the timing error compensation in open-loop structure, and the timing error compensation in open-loop structure is realized in parallel with the timing error detection to reduce the processing delay.

[0023] Because the residual timing error in the signal after step three is unknown, as a preferred, the fractional interval μ k =0.5 is used to reduce the residual timing error in the signal to the maximum extent.

[0024] For the signal with small over-sampling rate, the fixed fractional interval interpolation filter is used to reduce the complexity of the timing error compensation in open-loop structure, and the timing error compensation in open-loop structure is realized in parallel with the timing error detection to reduce the processing delay. k =0.5 is used to reduce the residual timing error in the signal to the maximum extent.

[0025] f1=0.5x(m)-0.5x(m-1)-0.5x(m-2)+0.5x(m-3)

[0026] f2=1.5x(m-1)-0.5x(m)-0.5x(m-2)-0.5x(m-3)

[0027] f3=x(m-2)

[0028] y(k)=f1 / 4+f2 / 2+f3

[0029] The output y(k) is the intermediate value of x(m-2) and x(m-1), i.e. Because the signal is processed in the form of data stream, the above interpolation process can simultaneously obtain

[0030] By using the fixed fractional interval μ k =0.5, the intermediate value of two signal sampling points is recovered, and the theoretically maximum timing error is reduced to T / (4*N). Meanwhile, the two interpolation of μ k =0.25 and μ k =0.75 can further reduce the residual maximum timing error to T / (8*N). Similarly, using more parallel fixed fractional interval interpolation can further reduce the timing error, and the processing delay of the timing error compensation in open-loop structure is reduced significantly.

[0031] Step five, for the signal generated by interpolation in step four and the original signal according to step one, the timing error detection is carried out, the signal with smaller timing error is selected, and the down sampling is carried out according to the sampling point position recorded in step three, and the timing synchronization in the case of smaller oversampling rate N is completed.

[0032] The sequence corresponding to the error accumulation in step two in the interpolation signal is selected, the error detection is carried out based on the best sampling point position obtained in step three, and the accumulation is carried out to obtain U i1 ,U i2 …U in The minimum value in U i1 ,U i2 …U in And is selected, and the corresponding signal is selected to carry out the down sampling according to the best sampling point position obtained in step three, the symbol sampling value with the maximum signal-to-noise ratio is recovered, that is, the timing synchronization in the case of smaller oversampling rate N is completed.

[0033] Advantages:

[0034] 1. The low complexity timing synchronization method based on Gardner timing error detection disclosed in the application reduces the self-noise of the algorithm by correcting the intermediate sampling value to 0, reduces the limitation of the Gardner timing error detection algorithm on the additional bandwidth of the signal, can be applied to more systems, accumulates the error detection results to improve the single error accuracy of the algorithm, makes the Gardner timing error detection algorithm applicable to the open loop structure, reduces the complexity of the timing error detection process in the timing synchronization method, and improves the real-time performance.

[0035] 2. The low complexity timing synchronization method based on Gardner timing error detection disclosed in the application utilizes the characteristics that the S curve of the Gardner timing error detection algorithm is monotonically increasing in the range of 0.25 < τ < 0.25 and the relationship between the positive and negative error detection results and the actual timing error, accurately finds the sampling value with the maximum signal-to-noise ratio in all original sampling values by comparing the sizes of the last two error detection results through sampling point shifting, avoids the process of accurate interpolation, and reduces the timing error compensation process.

[0036] 3. The low complexity timing synchronization method based on Gardner timing error detection disclosed in the application uses the interpolation filter with fixed fractional interval, reduces the complexity of the timing error compensation of the open loop structure, simultaneously adopts the parallel implementation structure with the error detection, obviously reduces the processing delay of the error compensation of the traditional open loop structure, and has no processing delay for the whole data, and can be applied to the system with the short frame burst characteristic. DETAILED DESCRIPTION

[0037] Figure 1is a flow chart of a low-complexity timing synchronization method based on Gardner timing error detection according to the present application;

[0038] Figure 2 is a diagram showing the relationship between the signal error detection result and the actual timing error according to an embodiment of the present application;

[0039] Figure 3 is an S-curve showing the relationship between the Gardner timing error detection output and the actual timing error under the parameter condition according to an embodiment of the present application;

[0040] Figure 4 is a diagram showing the error compensation effect of the sampling point shift combined with fixed fractional interval interpolation based on the S-curve according to an embodiment of the present application;

[0041] Figure 5 is a variance curve of the error accumulation result of the Gardner timing error detection algorithm before and after correction according to an embodiment of the present application;

[0042] Figure 6 is a variance curve of the error detection result before and after the low-complexity timing synchronization algorithm according to an embodiment of the present application and the Gardner timing synchronization loop enters the lock state. DETAILED DESCRIPTION

[0043] The present application will be described in detail below with reference to the accompanying drawings and embodiments. Meanwhile, the technical problems solved by the technical solutions of the present application and the beneficial effects are described. It should be noted that the described embodiments are only intended to facilitate the understanding of the present application and do not limit the present application in any way.

[0044] In order to make the above-mentioned purposes, features and advantages of the present application more easily understood, the following will be further described in detail in combination with the accompanying drawings and specific embodiments. The present embodiment is a low-complexity timing synchronization method based on Gardner timing error detection for a frequency hopping communication system. The system parameters in the present embodiment are shown in the following table:

[0045]

[0046]

[0047] As shown in Figure 1 , the specific implementation steps of the present embodiment are as follows:

[0048] Step one, in order to reduce the influence of the intermediate sampling values of the adjacent two symbols , the intermediate sampling values of the adjacent two symbols The self-noise of the Gardner timing error detection algorithm is reduced, the detection precision of the Gardner timing error detection algorithm for small extra bandwidth signals and high order signals is improved, and the universality of the Gardner timing error detection algorithm is improved. The modified intermediate sampling value is substituted into the Gardner timing error detection formula to obtain the current symbol timing error detection result. The small extra bandwidth signal refers to a signal with an extra bandwidth less than 40%, and the high order signal refers to a DQPSK signal and an 8PSK signal with a modulation order of 8 or more.

[0049] The Gardner error detection algorithm is modified by reducing the influence of adjacent two symbol pairs on the intermediate sampling value The modified intermediate sampling value is:

[0050]

[0051] In the formula, β = h (T / 2) / h (0), h (t) is the impulse response of the system, T is the symbol period, x (r-1) and x (r) are the previous and next two sampling points. In this embodiment, the raised cosine form of the impulse response is used, and the roll-off coefficient is α = 0.25. According to the raised cosine h (t)

[0052]

[0053] β ≈ 0.625 is calculated. The modified intermediate sampling value is substituted into the Gardner timing error detection formula to calculate the current symbol timing error:

[0054]

[0055] In the formula, I (r) and I (r-1) are the I-channel sampling points of the rth and (r-1)th symbols, I' (r-1 / 2) is the modified intermediate sampling point of the two symbols, and the Q-channel sampling points are the same.

[0056] Step two, by accumulating the timing error detection result obtained in step one, the influence of useless detection results on error compensation is reduced, the single detection precision of the Gardner timing error detection algorithm is improved, and the Gardner timing error detection algorithm is applicable to the open loop control structure due to the improvement of the single detection precision, the complexity of the overall timing synchronization method is reduced; and the sampling point is shifted according to the positive and negative of the error accumulation result to compensate the timing error, the step of accurate interpolation in the traditional timing synchronization method is omitted, the complexity of the timing synchronization method is further reduced, the signal processing delay is reduced, the real-time performance of the timing synchronization is improved, and the timing synchronization method is applicable to the communication system with short frame burst characteristics.

[0057] Accumulate the first 100 error detection results calculated in Step 1 according to the following formula:

[0058]

[0059] The schematic diagram of the relationship between the PSK signal error detection result and the actual timing error is as shown in Figure 2 Figure []. It can be seen from the figure that since the positive and negative of the error detection result correspond to the timing advance and lag, adjusting the sampling point position according to the positive and negative of U i can eliminate the timing error to a certain extent. If U i > 0, move the current sampling point position one bit backward. For this embodiment, replace x(r + T / 4) with x(r) as the sampling value of the rth symbol; if U i < 0, move the current sampling point position one bit forward, that is, replace x(r - T / 4) with x(r) as the sampling value of the rth symbol.

[0060] Step 3: Utilize the characteristic that the S curve is monotonically increasing within the range of the actual timing error -0.25 < τ < 0.25 and the relationship between the positive and negative of the error detection result and the actual timing error. By shifting the sampling point and comparing the magnitudes of the last two error accumulation results, accurately find the sampling value with the maximum signal-to-noise ratio among all the original sampling values, and record the position of this sampling point. For signals with a relatively large oversampling rate, the residual timing error in the sampling value can be ignored at this time. Downsample the signal according to the recorded sampling point position, that is, achieve timing synchronization in the case of a relatively large oversampling rate based on the Gardner timing error detection algorithm. The S curve is the functional relationship between the detection result of the Gardner timing error algorithm and the actual timing error.

[0061] Select the data that is the same as in Step 2 but after the sampling point is shifted, and repeat Step 1 and Step 2, and execute a total of 1 time, and save the result U1 of this error accumulation.

[0062] Repeat the error accumulation in Step 1 and Step 2 again, save the error accumulation result U2, and do not perform sampling point shifting. According to the characteristic that the algorithm S curve is monotonically increasing within the range of -0.25 < τ < 0.25 and the relationship between the positive and negative of the error detection result and the actual timing error, by shifting the sampling point and comparing U1 and U2, the sampling value with the maximum signal-to-noise ratio among all the original sampling values can be accurately found: if U1 > U2, it indicates that the result of the first sampling point shift does not represent the optimal sampling point, and another sampling point shift needs to be performed according to the positive and negative of U2. At this time, the signal sampling value is the sampling value with the maximum signal-to-noise ratio among the original sampling points; if U1 < U2, it indicates that the sampling value after the first sampling point shift already has the maximum signal-to-noise ratio, and there is no need to perform the second shift. Record the position of the sampling point at this time. ​​

[0063] Because the signal is not interpolated, the timing error is still left in the system, which is theoretically |τ|=T / 8. For this embodiment, the oversampling rate is only 4, and the residual timing error after the signal is shifted is large, which has a great impact on the system performance, and needs to be compensated by steps four and five.

[0064] Step four, for the signal with a small oversampling rate, the timing error compensation complexity of the open-loop structure is reduced by using the fixed fractional interval interpolation filter, and the timing error compensation processing delay of the open-loop structure is significantly reduced by using the parallel implementation structure with the timing error detection.

[0065] Because the residual timing error in the signal after step three compensation is unknown, as an optimization, the fractional interval μ k =0.5 can minimize the residual timing error in the signal. The specific implementation method of step four is as follows:

[0066] The present application uses a fixed fractional interval segmented parabolic interpolation method to reduce the residual timing error after shifting. This step is completed in parallel with steps one, two and three, and after the continuous four sampling points of the original data x(m), x(m-1), x(m-2), x(m-3) are input, the interpolation is performed according to the segmented parabolic interpolation method of polynomial approximation, and the interpolation formula of the fractional interval μ k =0.5 is as follows:

[0067] f1=0.5x(m)-0.5x(m-1)-0.5x(m-2)+0.5x(m-3)

[0068] f2=1.5x(m-1)-0.5x(m)-0.5x(m-2)-0.5x(m-3)

[0069] f3=x(m-2)

[0070] y(k)=f1 / 4+f2 / 2+f3

[0071] The output y(k) is the intermediate value of x(m-2) and x(m-1), i.e. Because the signal is processed in the form of data stream, we can also get

[0072] By one interpolation of the fixed fractional interval μ k =0.5, the present application can restore the intermediate value of two signal sampling points, and reduce the theoretically maximum timing error to T / 16. In this example, the timing error of T / 16 is already small, which has a small impact on the signal-to-noise ratio, and there is no need to perform more parallel interpolations. The relationship between shifting and interpolation is shown in the following figure:Figure 4 as shown.

[0073] Step five, for the signal generated by interpolation in step four and the original signal according to step one timing error detection, select the timing error smaller signal, and according to step three record the sampling point position for downsampling, complete the over sampling rate N smaller case timing synchronization.

[0074] Select the sequence corresponding to the error accumulation in step two in the interpolation signal, and perform error detection based on the optimal sampling point position obtained in step three, and accumulate to obtain U i1 , U i2 . Select the minimum value of U i1 , U i2 1 and U2, and select the corresponding signal according to the optimal sampling point position obtained in step three for downsampling. The symbol sampling value with the largest signal-to-noise ratio in the entire processing process is completed timing synchronization.

[0075] The error detection performance simulation of this embodiment is shown in Figure 5 and Figure 6 . As shown in Figure 5 , the variance of the error accumulation result without correction is large, and the detection accuracy is low; the error variance curve after correction is closer to the Cramer-Rao limit than the uncorrected algorithm in the entire signal-to-noise ratio range. Therefore, the correction of the algorithm ensures the detection performance after error accumulation. The comparison of the corrected algorithm and the Gardner timing synchronization with high synchronization accuracy is shown in Figure 6 . For this embodiment, when the signal-to-noise ratio is lower than 5dB, the performance of the three is not significantly different, and when the signal-to-noise ratio is higher than 5dB, the error variance curves of the three will be greatly different due to self-noise, and eventually tend to be flat. In this embodiment, the performance of the low complexity timing synchronization algorithm is better than that of the timing synchronization loop before locking due to the accumulation of the error detection result and the correction of the algorithm, but it is inferior to that after locking due to the lack of feedback process and accurate interpolation. For this embodiment, the timing synchronization loop cannot enter the locked state when the low complexity algorithm completes timing synchronization, and the low complexity timing synchronization algorithm greatly reduces the system processing delay while having high timing synchronization accuracy.

[0076] The above specific description further details the purpose, technical solution and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and does not limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A low complexity timing synchronization method based on Gardner timing error detection, characterized in that: The method comprises the following steps: Step one, in order to reduce the influence of adjacent two symbols on the intermediate sampling value , the intermediate sampling value of adjacent two symbols is corrected to zero, and the self-noise of the Gardner timing error detection algorithm is reduced; the corrected intermediate sampling value is substituted into the Gardner timing error detection formula, and the current symbol timing error detection result is obtained; The step one implementation method is, The Gardner timing error detection algorithm is modified by reducing the influence of the intermediate sample value between two adjacent symbol pairs, and the modified intermediate sample value is In the formula, β=h(T / 2) / h(0), h(t) is the impulse response of the system, T is the symbol period, x(r-1) and x(r) are the previous and next two sampling points; the modified intermediate sampling value is substituted into the Gardner timing error detection formula to calculate the current symbol timing error: In the formula, I(r) and I(r-1) are the I-channel sampling points of the rth and (r-1)th symbols, I'(r-1 / 2) is the modified intermediate sampling point of the two symbols, Q(r) and Q(r-1) are the Q-channel sampling points of the rth and (r-1)th symbols, and Q'(r-1 / 2) is the modified intermediate sampling point of the two symbols; The step two implementation method is, The step two implementation method is, The step three implementation method is, Since the signal is not interpolated, there is still a residual timing error in the system, and the theoretical maximum of the residual timing error is |τ|=T / (2*N); for the signal with a large oversampling rate N, the residual timing error can be ignored, and the subsequent steps are not needed; the timing synchronization is completed by downsampling the signal according to the recorded sampling point position.

2. The low complexity timing synchronization method based on Gardner timing error detection as claimed in claim 1, characterized by: f1=0.5x(m)-0.5x(m-1)-0.5x(m-2)+0.5x(m-3) ​ According to U i the positive and negative of the sampling point position are adjusted; if U i > 0, the current sampling point position is moved one bit backward, that is, x(r+T / N) is replaced by x(r) as the sampling value of the rth symbol, wherein N is the oversampling rate of the received signal; If U i If < 0, move the current sample position one bit forward, i.e. replace x(r-T / N) for x(r) as the sample value of the rth symbol.

3. The low complexity timing synchronization method based on Gardner timing error detection as claimed in claim 2, characterized by: ​ The steps one and two are repeated with the same data but shifted by the sampling point, totally (N / 2-1) times, N is the oversampling rate of the received signal, and the result of the error accumulation of the (N / 2-1)th time is saved Repeat the error accumulation in step one and step two, save the error accumulation result No shift of sampling point; compare the error accumulation result of the last two times and If indicates that the (N / 2-1)th sampling point shift result cannot represent the best sampling point, and needs to be shifted again according to the positive and negative of the error accumulation result, and the signal sampling value at this time is the sampling value with the maximum signal-to-noise ratio in the original sampling points; if indicates that the sampling value after the (N / 2-1)th sampling point shift already has the maximum signal-to-noise ratio, and there is no need to shift the N / 2th time; record the sampling point position after the last shift; ​ 4. The low complexity timing synchronization method based on Gardner timing error detection as claimed in claim 3, characterized by: Taking fractional interval μ k = 0.5 can minimize the residual timing error in the signal; the fourth step is implemented as follows, For the signal with small oversampling rate N of received signal, the fixed fractional interval piecewise parabolic interpolation method is used to reduce the residual timing error after shifting; this step is completed in parallel with steps one, two and three, after the input of the original data x(m), x(m-1), x(m-2), x(m-3) of the continuous four sampling points, the interpolation is carried out according to the piecewise parabolic interpolation method of polynomial approximation, the interpolation formula of fractional interval μ k = 0.5 is as follows: ​ f2 = 1.5 x (m - 1) - 0.5 x (m) - 0.5 x (m - 2) - 0.5 x (m - 3) f3 = x (m - 2) y(k) = f1 / 4 + f2 / 2 + f3 The output y(k) is the intermediate value of x(m-2) and x(m-1), i.e. Because the signal is processed in the form of data stream, in the above interpolation process, the following is simultaneously obtained By fixed fractional interval μ k = 0.5, the intermediate value of two signal sampling points is recovered, and the maximum timing error is reduced to T / (4*N); at the same time, two interpolation values of μ k = 0.25 and μ k = 0.75 are performed, and the residual maximum timing error is further reduced to T / (8*N); similarly, the timing error is further reduced by using multiple parallel fixed fractional interval interpolation, so that the delay of timing error compensation processing in the open-loop structure is significantly reduced.

5. The low complexity timing synchronization method based on Gardner timing error detection as claimed in claim 4, characterized by: Step five is implemented as, Select the sequence in the interpolation signal corresponding to the error accumulation in step two, and perform error detection based on the optimal sampling point position obtained in step three, and accumulate to obtain U i1 , i2 …U in , ; Select the minimum value of U i1 , U i2 , …U in and , and select the corresponding signal to downsample according to the optimal sampling point position obtained in step three, to restore the symbol sampling value with the maximum signal-to-noise ratio, that is, to complete timing synchronization in the case of a small oversampling rate N of the received signal.

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