A burst communication carrier frequency offset estimation method in a low signal-to-noise ratio environment

Abstract

This invention discloses a method for estimating the carrier frequency offset in burst communication under low signal-to-noise ratio (SNR) environments, relating to the field of wireless communication technology. It addresses the technical problem that while existing technologies can simultaneously estimate frequency offset and its rate of change, high FFT points and computational complexity are required to ensure high estimation accuracy. The invention includes: converting the Doppler frequency offset in the received signal into a signal phase model; calculating the frequency offset rate of change compensation signal model of the signal phase model; estimating the compensation signal model from the coarse frequency offset compensation step to obtain a secondary compensation signal model; estimating the frequency offset of the secondary compensation model as a fine-estimated frequency offset; and summing the coarse and fine-estimated frequency offsets to obtain the received signal carrier frequency offset. Considering the frequency offset rate of change, this invention can accurately estimate the Doppler information in the received signal even when there is motion acceleration between communication terminals or when communication terminals undergo trajectory changes, ensuring normal communication.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and specifically to a method for estimating the frequency offset of burst communication carriers in low signal-to-noise ratio environments. Background Technology

[0002] Burst communication is a key technology in modern communication and has wide applications in wireless communication. The most significant characteristic of burst communication is its short transmission time, during which the channel state changes frequently. The communication between the two terminals is influenced not only by Doppler frequency offset and the rate of frequency offset change due to relative motion speed and acceleration, but also by frequency offset introduced by errors in the terminal hardware circuitry. These frequency offsets alter the position of the received symbols in the constellation diagram, leading to an increase in the demodulation bit error rate.

[0003] In addition, communication terminal equipment is limited by transmit power and antenna gain, resulting in significant propagation loss during long-distance communication, as well as noise and interference introduced during transmission, leading to a low signal-to-noise ratio (SNR) at the receiving end. A low SNR increases the estimation error of the received signal frequency offset. Therefore, achieving rapid and accurate carrier frequency offset estimation is of great significance in environments with low SNR, large carrier frequency offset, and varying carrier frequency offset.

[0004] Current carrier frequency offset estimation methods can be classified into three types according to the auxiliary means: non-data-assisted, coding-assisted, and data-assisted.

[0005] Non-data-assisted carrier frequency offset estimation methods do not require pilot signals and utilize the demodulated soft information after linear demodulation of data for carrier parameter estimation. They offer high bandwidth utilization and good synchronization performance, but fail to function properly in low signal-to-noise ratio (SNR) environments. Code-assisted carrier frequency offset estimation methods leverage soft information from the channel decoder, making them suitable for low SNR environments, but their frequency offset estimation range is limited. Data-assisted carrier frequency offset estimation methods estimate carrier parameters using pilot sequences, resulting in relatively low computational complexity; however, their estimation performance depends on the length of the pilot sequence.

[0006] Among commonly used data-assisted carrier frequency offset estimation methods, Fits, L&R, and Kay algorithms can achieve the corrected Cramer-Rao bound under certain signal-to-noise ratio (SNR) conditions, but they struggle to balance estimation accuracy and range. The M&M algorithm achieves a balance between estimation accuracy and range, but requires a high SNR. These four algorithms can only estimate fixed frequency offsets. While a series of frequency-domain frequency offset estimation algorithms based on FFT can simultaneously estimate frequency offset and its rate of change, they require a high number of FFT points to ensure high estimation accuracy, resulting in high computational complexity.

[0007] Therefore, a carrier frequency offset estimation method that takes into account low signal-to-noise ratio, large estimation range, high estimation accuracy, estimation frequency offset change rate, and low computational complexity is needed to adapt to complex communication environments. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides a method for estimating the frequency offset of burst communication carriers in low signal-to-noise ratio environments. This method solves the technical problem that while the prior art can simultaneously estimate the frequency offset and the rate of change of the frequency offset, it requires a high number of FFT points and has high computational complexity in order to ensure high estimation accuracy.

[0009] A method for estimating carrier frequency offset in burst communication under low signal-to-noise ratio environments includes:

[0010] Step 1: Perform Taylor expansion on the Doppler frequency offset in the received signal to obtain the discrete pilot signal model after optimal sampling;

[0011] Step 2: Demodulate and recover the discrete pilot signal model to obtain the demodulated signal model, including demodulation and low-pass filtering;

[0012] Step 3: Use signal differential to convert the nonlinear relationship between the frequency offset change rate and the phase of the demodulated signal model into a linear relationship, and then estimate the frequency offset change rate;

[0013] Step 4: Use the frequency offset rate of change estimated in Step 3 to compensate for the demodulated signal model to obtain the compensated signal model;

[0014] Step 5: Calculate the coarse frequency offset of the compensated signal model, and then use the coarse frequency offset to compensate the compensated signal model to obtain the secondary compensated signal model;

[0015] Step 6: Perform smoothing filtering on the secondary compensation signal model to obtain a smoothed signal model;

[0016] Step 7: Use the mean phase of the autocorrelation signal to estimate the frequency offset of the smoothed signal model as a fine-grained frequency offset estimate;

[0017] Step 8: Summing the coarse and fine frequency offsets yields the received signal carrier frequency offset.

[0018] Further, step 1 includes: when there is relative motion between communication terminals, the received signal at the receiving end has a Doppler frequency offset, the Doppler frequency offset is expanded by a Taylor series, and the second-order and higher frequency offset change rates are ignored to obtain a discrete pilot signal model with optimal sampling.

[0019] Furthermore, the demodulation in step 2 includes: receiving pilot symbols and multiplying them by the conjugate of modulation symbols to eliminate the phase of modulation symbols; the low-pass filtering includes: using a low-pass filter to reduce the bandwidth of the noise signal after demodulation and reduce the impact of noise on the useful signal.

[0020] Furthermore, step 3 includes:

[0021] Step 3.1: Downsample the demodulated signal model;

[0022] Step 3.2: The nonlinear relationship between the frequency offset rate of change and the phase of the demodulated signal model is converted into a linear relationship using a first-order differential processing method;

[0023] Step 3.3: Calculate the mean phase of the second-order differential signal, including: based on the first-order differential signal, divide it into two equal segments with the midpoint as the dividing line; multiply the second segment differential signal by the conjugate of the first segment differential signal according to the time sequence to obtain the second-order differential signal; first sum all the second-order differential signals, and then calculate the angle of the summed signal to obtain the mean phase of the second-order differential signal;

[0024] Step 3.4: Calculate the frequency offset rate directly using the mean phase of the second-order differential signal.

[0025] Furthermore, step 5 includes:

[0026] Step 5.1: Ignore the residual frequency offset rate of change in the compensated signal model;

[0027] Step 5.2: Use the mean phase estimation after differential analysis of adjacent signals to coarsely estimate the frequency offset;

[0028] Step 5.3: Finally, the secondary compensation signal model is obtained by using the coarse estimation frequency offset compensation signal model.

[0029] Furthermore, the smoothing filtering in step 6 includes: performing coherent accumulation by using smoothing filtering to increase the signal-to-noise power ratio and obtain signal-to-noise ratio gain.

[0030] Further, step 7 includes: calculating the autocorrelation signal based on the smoothed signal model, and using the mean phase of the autocorrelation signal to estimate the frequency offset of the smoothed signal model as a fine estimate of the frequency offset.

[0031] The beneficial effects of this invention include:

[0032] 1) Reduced the signal-to-noise ratio threshold required for frequency offset estimation

[0033] This invention incorporates FIR low-pass filtering, smoothing filtering, and mean calculation during the processing. All signal processing steps result in signal-to-noise ratio (SNR) gain, thus improving the SNR. Given a fixed SNR threshold required by the frequency offset estimation algorithm, the preprocessing provides SNR gain, effectively lowering the overall SNR threshold required by the scheme. Furthermore, performing frequency offset estimation in two steps further reduces the required SNR threshold.

[0034] 2) It balances both estimation accuracy and estimation range performance indicators.

[0035] This invention first uses a large estimation range algorithm for coarse frequency offset estimation to obtain a large frequency offset estimation range. Then, the coarsely estimated frequency offset is used to compensate for the frequency offset of the received signal, reducing the frequency offset value. Finally, a small estimation range algorithm is used for fine frequency offset estimation to obtain high frequency offset estimation accuracy.

[0036] 3) Calculate the frequency offset rate of change to expand the applicability of the algorithm.

[0037] This invention employs a two-stage differential signal method to convert the nonlinear phase change of the demodulation pilot signal over time into a linear change over time, thereby estimating the frequency offset rate. Even considering the frequency offset rate, and when there is motion acceleration between communication terminals or when the communication terminals undergo trajectory changes, the Doppler information within the received signal can still be accurately estimated, ensuring normal communication.

[0038] 4) Reduced computational complexity

[0039] Compared with frequency-domain-based frequency offset rate estimation algorithms, this invention has a significant advantage in computational complexity when estimating the frequency offset rate. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating a method for estimating the frequency offset of a burst communication carrier in a low signal-to-noise ratio environment, as described in an embodiment of this application.

[0041] Figure 2 In this embodiment, the normalized frequency offset is 0.001, and the frequency offset change rate is... The curves show the comparison of estimation accuracy performance between the method in this embodiment and other methods.

[0042] Figure 3 In this embodiment, the normalized frequency offset is 0.001, and the frequency offset change rate is... The curves show the comparison of estimation accuracy performance between the method in this embodiment and other methods.

[0043] Figure 4 In this embodiment, the signal-to-noise ratio is -4dB and the frequency offset variation rate is... The comparison curves show the estimation range performance of the method in this embodiment compared with those of the Kay, L&W, and M&M algorithms.

[0044] Figure 5 In this embodiment, the signal-to-noise ratio is -4dB and the frequency offset variation rate is... The comparison curves show the estimation range performance of the method in this embodiment compared with those of the Kay, L&W, and M&M algorithms. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0046] Example 1

[0047] The following is in conjunction with the appendix Figure 1 Specific embodiments of the present invention will be described in detail;

[0048] A method for estimating carrier frequency offset in burst communication under low signal-to-noise ratio environments includes:

[0049] Step 1: Perform Taylor expansion on the Doppler frequency offset in the received signal to obtain the discrete pilot signal model after optimal sampling.

[0050] When there is relative motion between communication terminals, the received signal at the receiving end has a Doppler frequency offset. Performing a Taylor series expansion on the Doppler frequency offset and ignoring second-order and higher-order frequency offset rates, the optimally sampled discrete pilot signal model is obtained as follows:

[0051]

[0052] in, To receive pilot symbols, For modulation symbols, For frequency offset, For symbol period, The frequency deviation rate, For the sake of bias, It is noise.

[0053] As shown above, in the discrete pilot signal model, the signal phase consists of the modulation symbol phase, the frequency offset integral phase, the frequency offset rate of change integral phase, the phase offset phase, and the noise phase. To accurately estimate the frequency offset and frequency offset rate of change information, it is necessary to minimize the modulation symbol phase, phase offset phase, and noise phase in the received pilot signal model. The modulation symbol phase is completely eliminated through demodulation processing using local pilot symbols; the phase offset phase is eliminated through subsequent differential operations; and the noise phase is reduced through filtering.

[0054] Step 2: Demodulate and recover the discrete pilot signal model to obtain the demodulated signal model, including demodulation and low-pass filtering.

[0055] The demodulation includes:

[0056] The phase of the received pilot symbol is eliminated by multiplying it by the conjugate of the modulation symbol, as shown in the following formula:

[0057]

[0058]

[0059]

[0060]

[0061] in, To demodulate the pilot symbols, For pilot symbol conjugate, To demodulate the symbol, To demodulate the noise in the pilot symbols.

[0062] The low-pass filter includes:

[0063] Low-pass filtering can reduce Bandwidth is increased to reduce the impact of noise on the useful signal. An FIR filter is used as the low-pass filter. For Gaussian white noise, the signal-to-noise ratio gain after passing through the low-pass filter is:

[0064]

[0065] in, For signal-to-noise ratio gain, To demodulate the pilot symbol bandwidth, This represents the bandwidth after low-pass filtering.

[0066] The formula for the demodulation pilot symbol after low-pass filtering is:

[0067]

[0068] in, This is noise that reduces bandwidth.

[0069] Step 3: Use signal differential to convert the nonlinear relationship between the frequency offset change rate and the phase of the demodulated signal model into a linear relationship, and then estimate the frequency offset change rate.

[0070] Step 3.1: Downsample the demodulated signal model. The calculation formula is as follows:

[0071]

[0072]

[0073]

[0074]

[0075] in, The extracted low-pass filter is used to demodulate the pilot symbols. These are the demodulated pilot symbols after low-pass filtering. The sampling time of the discrete signal after extraction. To draw numbers, To extract multiples, For the first pilot symbol time, To reduce noise in order to increase bandwidth, This indicates the integer division operation.

[0076] Step 3.2: The frequency offset change rate and the phase of the demodulated pilot symbol exhibit a nonlinear relationship, making direct estimation of the frequency offset change rate computationally complex. A first-order differential method is used to transform the nonlinear relationship into a linear one. The calculation formula is as follows:

[0077]

[0078]

[0079]

[0080] in, This is the extracted first-order differential signal. for conjugate, The amplitude of the extracted first-order differential signal. This is the noise of the extracted first-order differential signal.

[0081] Step 3.3: Calculate the mean phase of the second-order differential signal, including:

[0082] Based on the first-level differential signal, it is divided into two equal segments with the midpoint as the dividing line. The second segment of the differential signal is then multiplied sequentially by the conjugate of the first segment according to the time sequence to obtain the second-level differential signal. The calculation formula is as follows:

[0083]

[0084]

[0085]

[0086]

[0087] in, It is a second-order differential signal. for Conjugate, It is a second-order differential signal interval. The amplitude of the second-order differential signal. It is a second-order differential signal noise. This is used for frequency offset estimation of pilot symbol length.

[0088] First, sum all the second-order differential signals, then calculate the angle of the summed signals to obtain the mean phase of the second-order differential signals. The calculation formula is as follows:

[0089]

[0090] in, The mean phase of the second differential signal. To estimate the rate of change of frequency offset.

[0091] Step 3.4: Calculate the frequency offset rate directly using the mean phase of the second-order differential signal. The calculation formula is as follows:

[0092]

[0093] Step 4: Use the frequency offset rate of change estimated in Step 3 to compensate for the demodulated signal model to obtain the compensated signal model.

[0094] The compensation signal model is as follows:

[0095]

[0096]

[0097] in, This is the compensated signal after frequency offset rate compensation. This refers to the noise in the compensated signal after frequency offset rate compensation.

[0098] Step 5: Calculate the coarse frequency offset of the compensated signal model, and then use the coarse frequency offset to compensate the compensated signal model to obtain the secondary compensated signal model.

[0099] The coarse estimate of frequency offset for calculating the compensated signal model includes:

[0100] First, ignore the residual frequency offset rate of change of the compensated signal model:

[0101]

[0102] The frequency offset is then estimated using the mean phase of the smoothed adjacent differential signals, calculated as follows:

[0103]

[0104]

[0105] in, To roughly estimate the frequency offset, These are the smoothing coefficients for adjacent differential signals. for Conjugate.

[0106] The secondary compensation signal model is as follows:

[0107]

[0108]

[0109] in, To roughly estimate the secondary compensation signal after frequency offset compensation, This is to roughly estimate the noise in the secondary compensated signal after frequency offset compensation.

[0110] Step 6: Perform smoothing filtering on the secondary compensation signal model to obtain a smoothed signal model.

[0111] The smoothing filter includes:

[0112] Coherent accumulation is performed using a smoothing filter to increase the signal-to-noise power ratio and obtain the signal-to-noise ratio gain. The calculation formula is as follows:

[0113]

[0114] in, To smooth the filtering and demodulate the pilot symbols, This is the length of the smoothing filter window.

[0115] Step 7: Use the mean phase of the autocorrelation signal to estimate the frequency offset of the smoothed signal model as a fine-grained frequency offset estimate.

[0116] The calculation of the fine-estimated frequency offset includes:

[0117] The autocorrelation signal is calculated based on the smoothed signal model, using the following formula:

[0118]

[0119]

[0120] in, For smoothing the signal model of autocorrelation signal, The length of the autocorrelation signal.

[0121] The frequency offset of the smoothed signal model is estimated using the mean phase of the autocorrelation signal as a fine-grained frequency offset. The calculation formula is as follows:

[0122]

[0123] in, To estimate frequency offset more precisely.

[0124] Step 8: Summing the coarse and fine frequency offsets yields the received signal carrier frequency offset.

[0125] The received signal carrier frequency offset is the sum of the coarsely estimated frequency offset and the finely estimated frequency offset, that is:

[0126]

[0127] in, To estimate carrier frequency offset.

[0128] In the simulation of this application's implementation examples, multiple metrics were used to analyze the estimation performance of the present invention, and a comparison was made with a partial data-assisted frequency offset estimation algorithm. The received signal was a QPSK modulated signal under an AWGN channel with a symbol rate of 76.8. The shaping filter uses a raised cosine filter with a roll-off factor of 0.3, and the pilot symbol length used for frequency offset estimation is 1024.

[0129] The theoretical parameters used in the simulation are explained as follows: the normalized frequency offset MCRB (Cramer-Rao bound) is used as the theoretical lower bound of the frequency offset estimation accuracy; the mean square error (MSE) of the normalized frequency offset is used as the measurement of estimation accuracy; the smaller the MSE, the higher the estimation accuracy; the theoretical boundary of the frequency offset estimation range is determined according to the Nyquist sampling theorem. The specific effects are as follows: Figure 2-5 As shown:

[0130] Figure 2 The method in this embodiment has a normalized frequency offset of 0.001 and a frequency offset change rate of 0. The graph compares the estimation accuracy performance of the method in this embodiment with other methods. The horizontal axis represents the signal-to-noise ratio (SNR), and the vertical axis represents the normalized frequency offset (MSE). Due to the limitation of the estimation range, the Fitz algorithm fails. The MSE of the other algorithms decreases as the SNR increases. Among them, the MSE of the algorithm in this embodiment and the M&M algorithm are second only to the L&R algorithm, indicating high estimation accuracy. Specifically, the smaller the MSE, the higher the estimation accuracy. In the legend, *- represents the L&R algorithm, whose MSE is close to CRB, indicating the highest estimation accuracy. The MSE of the algorithm in this embodiment is slightly higher than that of the L&R algorithm, but the accuracy is slightly worse.

[0131] Figure 3 The method in this embodiment has a normalized frequency offset of 0.001 and a frequency offset change rate of -50. The curves show a comparison of the estimation accuracy performance of the method in this embodiment with other methods. The horizontal axis represents the signal-to-noise ratio, and the vertical axis represents the normalized frequency offset (MSE). Figure 2In contrast, due to the existence of frequency offset change rate, in addition to the Fitz algorithm, the L&R, Kay, L&W and M&M algorithms also fail to estimate. The estimation accuracy of the algorithm of this invention is not affected when the signal-to-noise ratio is greater than -6dB.

[0132] Figure 4 The method in this embodiment operates at a signal-to-noise ratio of -4dB and a frequency offset rate of 0. The curves compare the estimation range performance of the method in this embodiment with that of the Kay, L&W, and M&M algorithms. The horizontal axis represents the theoretical value of the normalized frequency offset, and the vertical axis represents the estimated value of the normalized frequency offset. At this time, the signal-to-noise ratio is low, the Kay algorithm fails to estimate, but the estimation ranges of L&W, M&M, and the algorithm of this invention are close to the theoretical values.

[0133] Figure 5 The method in this embodiment operates at a signal-to-noise ratio of -4dB and a frequency offset rate of -50%. The curves compare the estimation range performance of the method in this embodiment with that of the Kay, L&W, and M&M algorithms. The horizontal axis represents the theoretical value of the normalized frequency offset, and the vertical axis represents the estimated value of the normalized frequency offset. Figure 4 In contrast, due to the existence of the frequency offset rate of change, the M&M algorithm also fails to estimate the value except for the Kay algorithm. Only the L&W algorithm and the algorithm of this invention have estimation ranges close to the theoretical value.

[0134] The embodiments described above merely illustrate specific implementation methods of this application, and while the descriptions are detailed and specific, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the technical solution of this application, and these modifications and improvements all fall within the scope of protection of this application.

Claims

1. A method for estimating carrier frequency offset in burst communication under low signal-to-noise ratio environments, comprising: Step 1: Perform Taylor expansion on the Doppler frequency offset in the received signal to obtain the discrete pilot signal model; Step 2: Demodulate and recover the discrete pilot signal model to obtain the demodulated signal model. The demodulation and recovery include demodulation and low-pass filtering. Step 3: Use signal differential to convert the nonlinear relationship between the frequency offset change rate and the phase of the demodulated signal model into a linear relationship, and then estimate the frequency offset change rate; Step 4: Use the frequency offset rate of change estimated in Step 3 to compensate for the demodulated signal model to obtain the compensated signal model; Step 5: Calculate the coarse frequency offset of the compensated signal model, and then use the coarse frequency offset to compensate the compensated signal model obtained in Step 4 to obtain the secondary compensated signal model; Step 6: Perform smoothing filtering on the secondary compensation signal model to obtain a smoothed signal model; Step 7: Use the mean phase of the autocorrelation signal to estimate the frequency offset of the smoothed signal model as a fine-grained frequency offset estimate; Step 8: Sum the coarse and fine frequency offset estimates to obtain the received signal carrier frequency offset; Step 3 includes: Step 3.1: Downsample the demodulated signal model; Step 3.2: The nonlinear relationship between the frequency offset change rate and the phase of the demodulated signal model processed in Step 3.1 is converted into a linear relationship using a first-order differential processing method; Step 3.3: Calculate the mean phase of the second-order differential signal, including: based on the first-order differential signal, divide it into two segments with the midpoint as the dividing line, and multiply the second segment differential signal by the conjugate of the first segment differential signal according to the time series to obtain the second-order differential signal; first sum all the second-order differential signals, and then calculate the angle of the summed signal to obtain the mean phase of the second-order differential signal; Step 3.4: Calculate the frequency offset rate directly using the mean phase of the second-order differential signal.

2. The method according to claim 1, wherein, Step 1 includes: when there is relative motion between communication terminals, the received signal has a Doppler frequency offset. The Doppler frequency offset is expanded by a Taylor series, and the second-order and higher frequency offset change rates are ignored to obtain a sampled discrete pilot signal model.

3. The method of claim 1, wherein, The demodulation in step 2 includes: receiving pilot symbols and multiplying them by the conjugate of modulation symbols to eliminate the phase of modulation symbols; the low-pass filtering includes: using a low-pass filter to reduce the bandwidth of the noise signal after demodulation and reduce the impact of noise on the useful signal.

4. The method of claim 1, wherein, Step 5 includes: Step 5.1: Ignore the residual frequency offset rate of change in the compensated signal model; Step 5.2: Use the mean phase estimation after differential analysis of adjacent signals to coarsely estimate the frequency offset; Step 5.3: Finally, the secondary compensation signal model is obtained by using the coarse estimation frequency offset compensation signal model.

5. The method for estimating the frequency offset of burst communication carriers in a low signal-to-noise ratio environment according to claim 1, characterized in that, The smoothing filtering in step 6 includes: using smoothing filtering to perform coherent accumulation, increasing the signal-to-noise power ratio, and obtaining signal-to-noise ratio gain.

6. The method for estimating the frequency offset of a burst communication carrier in a low signal-to-noise ratio environment according to claim 1, characterized in that, Step 7 includes: calculating the autocorrelation signal based on the smoothed signal model, and using the mean phase of the autocorrelation signal to estimate the frequency offset of the smoothed signal model as a fine estimate of the frequency offset.

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