Method for doppler frequency shift estimation in low earth orbit satellite communication system

Abstract

The invention discloses a method for estimating Doppler frequency shift in a low-orbit satellite communication system. The Doppler frequency shift is compensated by utilizing spectrum interference between subcarriers caused by Doppler frequency shift in an OFDM (Orthogonal Frequency Division Multiplexing) system. According to the method, possible maximum Doppler frequency shift and estimation resolution are set for different scenes, an interference coefficient matrix between subcarriers is constructed, the interference coefficient matrix is multiplied by a known pilot signal, the difference between a multiplication result and a received signal is used as a target function, and frequency shift is obtained by searching optimal matching. In the search process, normalized Doppler frequency shift is divided into a decimal part and an integer part, and internal correlation of spectrum change under two conditions is utilized: (1) interference caused by small-range frequency shift between different subcarriers; and (2) spectrum interference generated by more than one subcarrier interval. According to the method, Doppler frequency shift estimation in a large range can be carried out by adopting a small number of subcarriers, and the frequency shift range can reach 20 times of the subcarrier interval.

Description

Technical Field

[0001] The invention relates to a method for estimating when a large Doppler frequency shift exists in a low-orbit satellite communication system based on OFDM technology, and belongs to the field of microwave engineering and automatic control. Background Art

[0002] Low-orbit satellites have attracted widespread attention due to their low transmission delay, large communication capacity, and wide coverage. Low-orbit satellites can be used as a supplement to GNSS (Global Navigation Satellite System) to enhance PNT (positioning, navigation, and timing). However, low-orbit satellites have low orbit heights and strong dynamics. The Doppler shift of signals during transmission is large, and a method for estimating Doppler shift for high dynamic situations is needed. Most of the existing methods for estimating Doppler shift in OFDM systems are only for small-range Doppler shifts. The method proposed in this scheme can be applied to high dynamic situations. In the estimation process, this scheme uses the inter-subcarrier interference caused by the Doppler shift to perform calculations and searches to obtain the Doppler shift. At the same time, the number of subcarriers used for different situations is also studied. The Doppler shift can be estimated over a larger range by using a smaller number of subcarriers, which greatly reduces the amount of calculation and realizes the estimation of large Doppler shifts generated in high dynamic situations. Summary of the invention

[0003] Purpose of the invention: The present invention proposes a method for estimating Doppler shift for high dynamic situations. The maximum Doppler shift and estimation resolution are set for different situations, an interference matrix between subcarriers is constructed, the interference matrix is ​​multiplied with a known signal, the difference between the multiplication result and the received signal is used as the objective function, and the target value is searched. This method is aimed at estimating a large range of Doppler shift in an OFDM system.

[0004] Technical solution: The present invention provides a method for estimating Doppler frequency shift for high dynamic conditions. When the maximum Doppler frequency shift is known, the frequency shift estimation resolution is set, and the Doppler frequency shift is obtained by analyzing the spectrum interference coefficient between subcarriers caused by the Doppler frequency shift; in the estimation process, the interference coefficient matrix is ​​multiplied by the known signal, and the difference between the multiplication result and the received signal is used as the objective function. The specific solution is as follows:

[0005] A method for estimating Doppler frequency shift in a low-orbit satellite communication system can estimate Doppler frequency shift in a larger range using fewer resources, comprising the following steps:

[0006] Step 1: After obtaining the baseband signal, extract the known signal and determine the number of subcarriers L and the normalized Doppler frequency shift resolution ε involved in the estimation. r and the maximum Doppler shift ε max ;

[0007] Step 2: Considering the interference between subcarriers caused by Doppler frequency shift, a correlation coefficient matrix B is constructed;

[0008] Step 3: Define the objective function, search for the interference matrix and its Doppler frequency shift corresponding to the optimal solution of the objective function, and obtain the estimation result.

[0009] Preferably, a correlation coefficient matrix is ​​constructed. The amount of calculation required to directly calculate the correlation coefficient matrix according to the formula is extremely large. The amount of calculation can be reduced by utilizing the relationship between subcarriers: the correlation coefficient vector between all subcarriers and the second subcarrier is the correlation coefficient vector between the first subcarrier shifted one position to the right. Therefore, when constructing the corresponding correlation coefficient matrix, only the first row corresponding to the matrix needs to be calculated, and the other data of the matrix can be obtained by shifting the first row.

[0010] Preferably, the correlation coefficient matrix is ​​constructed. The amount of calculation required to directly calculate the correlation coefficient matrix according to the formula is extremely large. There is a certain relationship between the correlation coefficient matrix corresponding to the integer multiple Doppler frequency shift and the correlation coefficient matrix corresponding to the decimal multiple Doppler frequency shift: if the integer multiple normalized Doppler frequency shift is n, the corresponding correlation coefficient matrix is ​​the decimal multiple Doppler frequency shift shifted to the right by n bits. Therefore, when constructing the correlation coefficient matrix when the normalized subcarrier frequency shift integer is greater than 1, it is only necessary to translate it according to the correlation coefficient matrix of the corresponding decimal part.

[0011] Preferably, the amount of calculation required to construct the correlation coefficient matrix and consider all subcarriers is very large. After analyzing the relationship between the frequency difference and the Doppler shift, it is concluded that after experiencing the same Doppler shift, the greater the frequency difference between the signals, the greater the interference. Therefore, in order to reduce the amount of calculation, a limited number of subcarriers can be selected while considering the maximum Doppler shift. The number of selected subcarriers must be greater than an integer multiple of the maximum normalized Doppler shift.

[0012] Preferably, the objective function Defined as Where Y is the received baseband signal value, X is the baseband signal value used for frequency shift estimation, and the correlation coefficient matrix B corresponding to the optimal solution of the objective function and the estimated Doppler frequency shift are searched and obtained.

[0013] Preferably, the update method of the variables during the search process is ε k+1 =ε k +ε r , where ε r is the normalized Doppler shift resolution.

[0014] Preferably, two judgments are required during the search process, one to determine whether the current variable is within the search interval, and one to compare the current objective function value with the recorded objective function value to determine whether the recorded objective function value needs to be updated.

[0015] Beneficial effects:

[0016] The present invention proposes a method for estimating Doppler shift for high dynamic conditions. The method is to set the frequency shift estimation resolution when the maximum Doppler shift is known, use the inter-subcarrier interference caused by the Doppler shift to construct an interference matrix between subcarriers, multiply the interference matrix and the known signal, use the difference between the multiplication result and the received signal as the objective function, search for the target value, and realize the estimation of Doppler shift under high dynamic conditions. Most of the previous estimation methods focus on the estimation of Doppler shift in a small range. The present scheme can use a smaller number of subcarriers to estimate Doppler shift in a large range, which greatly reduces the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a known signal required for high dynamic situations. The signal modulation method is BPSK. If 4 subcarriers are used, there are 16 signal combination types. Figure 1 Eight of these types are shown.

[0018] Figure 2 To show Figure 1 The estimation results of 8 signals under different signal-to-noise ratios are shown. The normalized Doppler shift ε=0.25 and the number of calculations P=100 are set. The accuracy of the estimation is judged by the mean square error. When the signal-to-noise ratio is in the range of 10 to 20, the estimation accuracy of the sixth signal is the highest. The sixth signal type is 0101...

[0019] Figure 3 for Figure 3 In order to use the estimation results of different numbers of subcarriers under different Doppler shift conditions using the sixth signal type, the signal-to-noise ratio is set to 15dB and the number of calculations P = 100. The normalized Doppler shift is in the range of 0 to 30. The number of subcarriers considered is 4, 10, 16, 22, 28, 34, and 40. As can be seen from the figure, for high dynamic conditions (normalized Doppler shift ε>1), this scheme can use the known limited number of subcarrier data for Doppler shift estimation.

[0020] Figure 4 This is the flow chart of the algorithm.

[0021] Figure 5 This is the derivation diagram of the spectrum interference coefficient matrix. DETAILED DESCRIPTION

[0022] The present invention will be further described below in conjunction with the accompanying drawings:

[0023] In an OFDM system, the received signal undergoes a Doppler shift f d It can be expressed as:

[0024]

[0025] Where x[n] is the transmitted signal, n is the time domain sampling point, F s is the sampling frequency, N and F0 are the number of subcarriers and the subcarrier frequency interval in the OFDM system. Therefore, in the OFDM system, the normalized Doppler frequency ε is Most existing methods for estimating Doppler shift focus on the case of ε < 0.5, while this solution considers a wider range of cases. When the Doppler shift is ε, the interference of the nth subcarrier to the kth subcarrier is:

[0026]

[0027] Therefore, when a Doppler frequency shift of ε is experienced, the frequency domain signal of the kth subcarrier can be expressed as:

[0028]

[0029] After obtaining the frequency domain information of the received signal, the Doppler shift can be inversely calculated using the correlation between the subcarriers caused by it. For a large range of Doppler shifts, it is not enough to consider only one subcarrier. If all subcarriers are considered, the amount of calculation is very large. Therefore, in order to cope with high dynamic situations and reduce the amount of calculation, we divide the Doppler shift into a fractional part and an integer part, use their inherent relationship to reduce the amount of calculation, and use a limited number of subcarriers for calculation.

[0030] Decimal part: For the case of normalized Doppler shift ε<1, according to formula 2, it can be found that if the frequency difference is the same, the correlation coefficient is the same. Therefore, when constructing the correlation coefficient matrix, the first row and the first column represent the interference of the first subcarrier itself under this Doppler frequency shift. The second row and the second column represent the interference of the first subcarrier itself under this Doppler frequency shift, and the two values ​​are equal. The first row and the second column represent the interference of the second subcarrier to the first subcarrier under this Doppler frequency shift, and the second row and the third column represent the interference of the third subcarrier to the second subcarrier under this Doppler frequency shift. Both represent a frequency shift difference of one subcarrier interval, so the values ​​are equal. Finally, the entire correlation coefficient matrix can be obtained through a row of data.

[0031] Integer part: For the case of normalized Doppler shift ε>1, according to formula 2, it can be found that if the Doppler shift differs by an integer multiple, the correlation coefficient has a displacement relationship. Therefore, when constructing the correlation coefficient matrix, if the normalized Doppler shift integer part is 1, the value is the corresponding decimal part of the correlation coefficient matrix shifted to the right by 1 bit, and if the normalized Doppler shift integer part is 2, the value is the corresponding decimal part of the correlation coefficient matrix shifted to the right by 2 bits. Therefore, the correlation coefficient matrix in high dynamic conditions can be obtained through the decimal part of the correlation coefficient matrix.

[0032] Limited number of subcarriers: Using the correlation coefficient to inversely calculate the Doppler frequency shift requires a lot of calculations. Even if the calculations can be reduced to a certain extent through its inherent correlation, the calculations using N subcarriers in the OFDM system are still huge. Considering that as the frequency difference increases, the impact between the two decreases, a limited number of subcarriers can be used to reduce the amount of calculations.

[0033] The orbital altitude of low-orbit satellites is in the range of 500-2000km. This scheme uses an orbital altitude of 1500km, a circular orbit, and an operating speed of 7120m / s. According to the geometric relationship between the earth and the satellite, the maximum Doppler shift can be obtained to be about 211.3KHz. If the working mechanism of the OFDM system is that the number of subcarriers N is 1024, the subcarrier spacing is 15KHz, and the corresponding maximum normalized Doppler shift of the operating frequency is 11GHz, it is about 14.1, and the corresponding maximum normalized Doppler shift of the operating frequency is about 23.1.

[0034] In order to study the beneficial effects of the proposed method, in a low-orbit satellite system based on OFDM technology, the number of subcarriers N is set to 1024 and the subcarrier spacing is set to 15KHz.

[0035] Step 1: Convert the received baseband signal to the frequency domain and extract the known signal Y

[0036] Step 2: Determine the parameter normalized Doppler frequency shift resolution ε r , the maximum normalized Doppler shift ε max , the required number of subcarriers is L.

[0037] Step 3: Construct the correlation coefficient matrix and normalize the Doppler frequency ε k The corresponding correlation coefficient matrix is ​​B(ε k ), the specific process is:

[0038] Normalized Doppler frequency ε at the kth search k It can be expressed as

[0039] ε k =ε ki +εkf (4)

[0040] where ε ki is the integer part of the normalized Doppler frequency, ε kf is the fractional part of the normalized Doppler frequency. From this, the interference matrix of the inter-subcarrier interference caused by the Doppler frequency can be constructed. Considering L subcarriers and the normalized Doppler frequency ε k The first row of the corresponding interference matrix can be expressed as:

[0041] v(ε k )=cirshift(v(ε kf ),ε ki ) (5)

[0042] in

[0043]

[0044] f i ∈{f1,f2,…,f L},

[0045]

[0046] Finally, the entire interference matrix can be calculated as:

[0047] B m (ε k )=cirshift(v(ε k ),m), (7)

[0048] The subscript m represents the mth row of the matrix.

[0049] Step 4: Define the objective function as

[0050]

[0051] The result of the k-th search is recorded as Y is the received frequency domain signal, and X is the known signal.

[0052] Step 5: Use step 2 to calculate the variable ε k+1 The corresponding objective function value is where ε k+1 =ε k +ε r .

[0053] Step 6: Determine ε k+1 <ε max If it is not true, record the function value at this time and output the corresponding solution ε k This is the estimated value If it holds true, the objective function value is updated.

[0054] Step 7: Update the objective function value. If Then update the variables again to calculate without changing the objective function value. If the inequality does not hold, update And update the variables.

[0055] This method uses the mean square error to measure the accuracy of the proposed method, which is defined as:

[0056]

[0057] Where P is the number of repeated estimations.

Claims

1. A method for estimating Doppler frequency shift in a low-orbit satellite communication system, characterized in that: The following steps are involved: Step 1: After obtaining the baseband signal, extract the known signal and determine the number of subcarriers L and the normalized Doppler frequency shift resolution ε involved in the estimation. r and the maximum Doppler shift ε max ; Step 2: Considering the interference between subcarriers caused by Doppler frequency shift, a correlation coefficient matrix B is constructed; Step 3: Define the objective function, search for the interference matrix and its Doppler frequency shift corresponding to the optimal solution of the objective function, and obtain the estimation result.

2. The method for estimating Doppler frequency shift in a low-orbit satellite communication system according to claim 1, characterized in that: When constructing the correlation coefficient matrix, you only need to calculate the first row corresponding to the matrix, and the other data in the matrix are obtained by translating the first row.

3. The method for estimating Doppler frequency shift in a low-orbit satellite communication system according to claim 1, characterized in that: When constructing the correlation coefficient matrix when the normalized subcarrier frequency shift integer is greater than 1, it is obtained by performing translation according to the correlation coefficient matrix of the corresponding fractional part.

4. The method for estimating Doppler frequency shift in a low-orbit satellite communication system according to claim 1, characterized in that: When constructing the correlation coefficient matrix, a finite number of subcarriers is selected while taking into account the maximum Doppler frequency shift; the number of subcarriers selected must be greater than an integer multiple of the maximum normalized Doppler frequency shift.

5. The method for estimating Doppler frequency shift in a low-orbit satellite communication system according to claim 1, characterized in that: The objective function Defined as Where Y is the received baseband signal value, X is the baseband signal value used for frequency shift estimation, and the correlation coefficient matrix B corresponding to the optimal solution of the objective function and the estimated Doppler frequency shift ε are searched. k .

6. The method for estimating Doppler frequency shift in a low-orbit satellite communication system according to claim 1, characterized in that: The update method of variables during the search process is ε k+1 =ε k +ε r , where ε r is the normalized Doppler shift resolution, ε k is the Doppler shift.

7. The method for estimating Doppler frequency shift in a low-orbit satellite communication system according to claim 1, characterized in that: Two judgments are required during the search process: one is to determine whether the current variable is within the search interval, and the other is to compare the current objective function value with the recorded objective function value to determine whether the recorded objective function value needs to be updated.

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