A frequency offset estimation method suitable for low signal-to-noise ratio

Abstract

The application relates to burst waveform modulation and demodulation technology in the field of wireless communication, and particularly discloses a frequency offset estimation method suitable for low signal-to-noise ratio, which comprises pilot sequence design, FFT transformation of the pilot sequence, denoising and smoothing processing of frequency domain data, IFFT transformation of the denoised data, front-back cross-correlation processing of two sections of sequences, phase difference value calculation and frequency offset estimation value calculation. The application can overcome the problem that the frequency offset estimation accuracy of the traditional frequency offset estimation scheme rapidly reduces under low signal-to-noise ratio, and can obtain more accurate frequency offset estimation information by improving the signal-to-noise ratio of the pilot sequence. The application is simple to realize, low in complexity and high in practicability, and provides a relatively effective realization approach for further improving the receiving sensitivity scheme under low signal-to-noise ratio through specific format pilot design and data processing based on the transformation domain.

Description

Technical Field

[0001] This invention relates to burst waveform modulation and demodulation technology in the field of wireless communication, specifically to a frequency offset estimation method aimed at improving the accuracy of frequency offset estimation in communication systems. It is particularly suitable for scenarios where relatively accurate frequency offset estimation is required under low signal-to-noise communication conditions to support subsequent data processing. Background Technology

[0002] In wireless communication systems, the carrier frequencies of the receiver and transmitter are usually different, i.e., f0 tx ≠f rx The frequency offset is mainly caused by the inconsistency in the oscillator frequencies of the transmitting and receiving systems, as well as the Doppler effect under mobile environmental conditions. The former's impact is approximately fixed, while the latter's is time-varying; the faster the movement speed changes, the faster the frequency deviation caused by the Doppler effect changes. Frequency offset caused by high-speed movement severely affects the demodulation performance of communication systems, especially for OFDM systems. Frequency offset disrupts the orthogonality between subcarriers, leading to inter-carrier interference and significantly impacting communication performance. Many communication systems incorporate frequency offset estimation and correction modules to eliminate or reduce the impact of frequency offset. Frequency offset estimation accuracy is positively correlated with the signal-to-noise ratio (SNR). Frequency offset estimation errors at low SNRs are a significant cause of performance loss; therefore, improving the accuracy of frequency offset estimation at low SNRs is of great importance.

[0003] Traditional frequency offset estimation schemes suffer from a rapid decrease in accuracy at low signal-to-noise ratios, severely limiting the receiver sensitivity performance of communication systems and failing to meet the increasingly high reliability requirements of non-signal communication. Summary of the Invention

[0004] The purpose of this invention is to improve the accuracy of frequency offset estimation, thereby reducing the impact of inter-symbol interference caused by frequency offset and improving communication reception performance. This is achieved by providing a frequency offset estimation method that offers higher accuracy. The frequency offset estimation method described can, to a certain extent, meet the accuracy requirements of communication systems under low signal-to-noise ratio (SNR) conditions, and can also provide a reference scheme for the design of other communication systems. This invention aims to improve the accuracy of frequency offset estimation under low SNR conditions. Through specific pilot format design and transform domain-based data processing, it provides a relatively effective approach to further improve receiver sensitivity under low SNR conditions.

[0005] The technical solution adopted in this invention is as follows:

[0006] A frequency offset estimation method suitable for low signal-to-noise ratio includes the following steps:

[0007] (1) Design two pilot sequences;

[0008] (2) Perform FFT transformation on the two pilot sequences respectively to obtain two frequency domain data;

[0009] (3) Denoise and smooth the two frequency domain data segments respectively to obtain two segments of denoised and smoothed data;

[0010] (4) Perform IFFT transformation on the two denoised and smoothed data segments respectively, and transform them to the time domain;

[0011] (5) Perform cross-correlation operation on the two time-domain sequences to obtain the cross-correlation result;

[0012] (6) Calculate the phase difference between the two sequences based on the cross-correlation results;

[0013] (7) The frequency offset estimate is calculated based on the phase difference, symbol interval and symbol rate of the two sequences.

[0014] Furthermore, step (1) specifically includes the following steps:

[0015] (101) Select two identical pilot sequences l1 and l2. The selected pilot sequences are power-of-2 repeated sequences, and the length of a single sequence satisfies the power of 2.

[0016] (102) The total sequence length N = k * m is determined by combining the number of sequence segments k and the length of a single sequence segment m;

[0017] (103) Determine the number of FFT points N used in the transform domain based on the total sequence length N.

[0018] Furthermore, the specific process of step (2) is as follows:

[0019] Perform an N-point FFT transform on the two pilot sequences l1 and l2 respectively to obtain the frequency domain data, which are denoted as f1 and f2 respectively.

[0020] Furthermore, step (3) includes the following specific steps:

[0021] (301) For the frequency domain data f1 and f2 after FFT transformation, keep the n*kth data unchanged and set the other data to zero. The corresponding sequences after setting to zero are denoted as z1 and z2; where n = 1, 2, 3...m;

[0022] (302) Perform IFFT transformation on z1 and z2 respectively, and the resulting sequences are denoted as s1 and s2. s1 and s2 are the data after denoising and smoothing.

[0023] Furthermore, the specific process of step (4) is as follows:

[0024] Perform IFFT transformation on the denoised and smoothed data s1 and s2 to transform them to the time domain, and extract a sequence of length m from the first number, denoted as x1 and x2 respectively.

[0025] Furthermore, the cross-correlation operation in step (5) is specifically as follows:

[0026]

[0027] Where R represents the cross-correlation result.

[0028] Furthermore, the calculation process for the phase difference θ in step (6) is as follows:

[0029]

[0030] Furthermore, the specific process of step (7) is as follows:

[0031] By calculating the phase angle of the correlation results of two repeated training sequences, the frequency deviation f0 carried in the signal is estimated:

[0032]

[0033] In the formula, θ represents the phase difference between the two sequences, and f s N represents the clock sampling frequency. c T represents the number of sampling points between two repeating sequences. c =N c / f s Indicates the duration of the training sequence.

[0034] The advantages of this invention compared to the prior art are:

[0035] This invention is simple to implement, has low complexity, and is highly practical. Through specific format pilot design and transform domain-based data processing, it provides a relatively effective way to further improve receiver sensitivity under low signal-to-noise ratio conditions. Attached Figure Description

[0036] Figure 1 This is a graph showing the relationship between the symbol signal-to-noise ratio and the frequency offset estimation accuracy of this invention. Detailed Implementation

[0037] The invention will be further explained below with reference to the accompanying drawings.

[0038] A frequency offset estimation method suitable for low signal-to-noise ratio includes the following steps:

[0039] (1) Design two pilot sequences; the pilot sequences need to meet certain formats, and the specific steps include:

[0040] (101) Select two identical pilot sequences l1 and l2 for frequency offset estimation. The selected pilot sequences need to meet a certain format, that is, a power of 2 segment repeating sequence, such as 2 segments, 4 segments, 8 segments, 16 segments, 32 segments, 64 segments, etc.; the sequence type is not limited, and the length of a single segment needs to meet the power of 2, such as 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc.

[0041] (102) The total sequence length N = k * m is determined by combining the number of sequence segments k and the length of a single sequence segment m;

[0042] (103) Determine the number of FFT points N used in the transform domain based on the total sequence length N.

[0043] (2) Perform FFT transformation on the two pilot sequences respectively to obtain two frequency domain data segments; specifically:

[0044] Perform an N-point FFT transform on the two pilot sequences l1 and l2 respectively to obtain the frequency domain data, which are denoted as f1 and f2 respectively.

[0045] (3) Denoise and smooth the two frequency domain data segments respectively to obtain two segments of denoised and smoothed data; the specific steps include:

[0046] (201) For the frequency domain data f1 and f2 after FFT transformation, keep the n*kth data (where n = 1, 2, 3...m) unchanged, and set the other data to zero. The corresponding sequences after setting to zero are denoted as z1 and z2.

[0047] (202) Perform IFFT transformation on z1 and z2 respectively, and the resulting sequences are denoted as s1 and s2. s1 and s2 are the data after denoising and smoothing.

[0048] In AWGN channels, the normalized variance of the estimator is considered as a measure of the reliability of the estimation. The normalized variance of the estimator is as follows:

[0049] var{(f est -Δf) / f s}=1 / (4π 2 ρ)

[0050] In the formula, ρ represents the signal-to-noise ratio, and f est Let Δf represent the estimated frequency offset, and Δf represent the actual frequency offset. Clearly, the accuracy of frequency offset estimation is inversely proportional to the signal-to-noise ratio (SNR). Therefore, improving the SNR of the signal can significantly improve the accuracy of frequency offset estimation. Of course, the accuracy of frequency offset estimation is not only related to the SNR, but also to the symbol period, the length of the pilot sequence used for frequency offset estimation, and the number of symbols between the two sequences.

[0051] T sRepresented as symbol period, L0 represents the length of the pilot sequence, D in E represents the number of signs between two sequences. s / N0 represents the symbol signal-to-noise ratio, then the performance limit of the frequency offset estimation, i.e., the Cramer-Rao bound CRB(f), is:

[0052]

[0053] As can be seen from the above formula, the estimation accuracy of the cross-correlation algorithm is similar to that of D. 2 in and L 2 A positive correlation is found between the signal-to-noise ratio (SNR) and the value of the cross-correlation signal. Under the same SNR conditions, increasing the pilot length and pilot spacing can effectively improve estimation accuracy. However, this simultaneously reduces the range of frequency offset estimation. In other words, the estimation range and accuracy of the cross-correlation algorithm are contradictory. Therefore, with a fixed frame structure, improving the SNR is key to further improving the accuracy of frequency offset estimation.

[0054] Figure 1 In the symbol period T s =1 / (5.12*10 7 (seconds), pilot sequence length L0 = 256, number of symbols D between the two sequences in Under the condition of 4864, the simulation of the Cramer-Rao bound of frequency offset estimation accuracy and signal-to-noise ratio should be noted. It should be noted that since the original Cramer-Rao bound corresponds to the variance of frequency offset estimation accuracy, it has been square rooted to more significantly show the frequency offset estimation accuracy.

[0055] Simulation results show that a higher signal-to-noise ratio (SNR) leads to more accurate frequency offset estimation. As the SNR decreases, the accuracy of frequency offset estimation gradually declines, potentially impacting demodulation performance at extremely low SNR levels. At high SNR, the frequency offset estimation accuracy is less than 30Hz, but as the SNR decreases, the accuracy can reach around 150Hz, which may affect communication performance.

[0056] Therefore, denoising the frequency offset estimation sequence and improving its signal-to-noise ratio can effectively improve the frequency offset estimation accuracy and enhance communication performance.

[0057] To improve the accuracy of frequency offset estimation, increasing the signal-to-noise ratio (SNR) of the signal is one effective method. Therefore, the SNR of the sequence used for frequency offset estimation is first increased, and then the frequency offset estimation process is continued after the SNR is improved.

[0058] (4) Perform IFFT transformation on the two denoised and smoothed data segments respectively, transforming them to the time domain; the specific process is as follows:

[0059] Perform IFFT transformation on the denoised and smoothed data s1 and s2 to transform them to the time domain, and then perform truncation processing on them respectively. Starting from the first number, truncate a sequence of length m, denoted as x1 and x2.

[0060] x1 = s1(n), where n = 1, 2, ..., m

[0061] x2 = s2(n), where n = 1, 2, ..., m.

[0062] (5) Perform cross-correlation on the two time-domain sequences to obtain the cross-correlation result; specifically:

[0063] Perform a cross-correlation test on sequences x1 and x2, and denote the cross-correlation result as R:

[0064]

[0065] (6) The phase difference θ between the two sequences is calculated based on the cross-correlation results; the calculation process for the phase difference θ is as follows:

[0066]

[0067] (7) The frequency offset estimate is calculated based on the phase difference, symbol interval, and symbol rate of the two sequences; specifically:

[0068] By calculating the phase angle of the correlation results of two repeated training sequences, the frequency deviation f0 carried in the signal can be estimated:

[0069]

[0070] In the formula, θ represents the phase difference between the two sequences, and f s N represents the clock sampling frequency. c T represents the number of sampling points between two repeating sequences. c =N c / f s Indicates the duration of the training sequence.

Claims

1. A frequency offset estimation method suitable for low signal-to-noise ratio, characterized in that, Includes the following steps: (1) Design two pilot sequences; (2) Perform FFT transformation on the two pilot sequences respectively to obtain two frequency domain data segments; (3) Denoise and smooth the two frequency domain data segments respectively to obtain two segments of denoised and smoothed data; (4) Perform IFFT transformation on the two segments of denoised and smoothed data respectively, and transform them to the time domain; (5) Perform cross-correlation operation on the two time-domain sequences to obtain the cross-correlation result; (6) Calculate the phase difference between the two sequences based on the cross-correlation results; (7) The frequency offset estimate is calculated based on the phase difference, symbol interval, and symbol rate of the two sequences; The specific steps of step (3) include: (301) For the frequency domain data after FFT transformation and Keep the n*kth data unchanged, and set all other data to zero. The sequence after setting to zero is denoted as . and Where n = 1, 2, 3...m, k is the number of segments in the pilot sequence, and m is the length of a single segment. (302) respectively for and Performing an IFFT transformation, the resulting sequence is denoted as... and , and This refers to the data after denoising and smoothing.

2. The frequency offset estimation method suitable for low signal-to-noise ratio according to claim 1, characterized in that, The specific steps of step (1) include: (101) Select two identical pilot sequences and The selected pilot sequence is a power-of-2 repeating sequence, and the length of a single sequence segment satisfies a power of 2. (102) The total sequence length N = k * m is determined by combining the number of sequence segments k and the length of a single sequence segment m; (103) Determine the number of FFT points N used in the transform domain based on the total sequence length N.

3. The frequency offset estimation method suitable for low signal-to-noise ratio according to claim 2, characterized in that, The specific process of step (2) is as follows: For the two pilot sequences respectively and Perform an N-point FFT transform to obtain the frequency domain data, denoted as . and .

4. The frequency offset estimation method suitable for low signal-to-noise ratio according to claim 1, characterized in that, The specific process of step (4) is as follows: For the denoised and smoothed data and Perform an IFFT transform to the time domain, and extract a segment of length m from the first number, denoted as . and .

5. The frequency offset estimation method suitable for low signal-to-noise ratio according to claim 4, characterized in that, The cross-correlation operation in step (5) is as follows: Where R represents the cross-correlation result.

6. The frequency offset estimation method suitable for low signal-to-noise ratio according to claim 5, characterized in that, Phase difference value in step (6) The calculation process is as follows: 。

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