Underwater acoustic spread spectrum communication Doppler estimation algorithm based on matched filtering and fuzzy function

Abstract

The invention discloses an underwater acoustic spread spectrum communication Doppler estimation algorithm based on matched filtering and a fuzzy function, and belongs to the technical field of underwater acoustic communication. The method specifically comprises the following steps of: 1, performing Doppler estimation on a signal based on matched filtering, and determining a rough frequency offset range to obtain a rough estimation Doppler factor; 2, Doppler estimation based on a fuzzy function is carried out on the signal, and a fine estimation Doppler factor is obtained; and step 3, carrying out residual Doppler differential demodulation to obtain a final estimated Doppler factor. According to the method, the defect that a large Doppler spreading factor generated during high-speed movement between underwater mobile nodes cannot be well estimated by a matched filtering-based estimation method can be overcome, and the defects that a fuzzy function estimation method with higher precision is long in consumed operation time and high in calculation complexity are overcome.

Description

Technical Field

[0001] The invention relates to an underwater acoustic spread spectrum communication Doppler estimation algorithm, in particular to an underwater acoustic spread spectrum communication Doppler estimation algorithm based on matched filtering and fuzzy function, and belongs to the technical field of underwater acoustic communication. Background Art

[0002] Compared with traditional underwater acoustic communication, spread spectrum communication has the advantages of anti-interference and high concealment. Spread spectrum communication refers to a communication technology that uses a specific spread spectrum sequence to expand the signal to be transmitted at the transmitter into a wideband signal, and then uses the same spread spectrum function as the transmitter as the local despread signal at the receiving end after passing through the channel, performs correlation despreading, compresses the widened signal, restores it to the original signal to be transmitted, and finally deciphers the original information sequence, thereby achieving the purpose of transmitting information.

[0003] The water flow disturbance in the ocean channel and the relative change of the position of the transmitter and receiver will introduce Doppler into the underwater acoustic communication system, causing signal distortion. In actual ocean communication scenarios, due to the influence of ocean currents and wind and waves, it is usually difficult to maintain absolute uniform motion between the transmitting and receiving nodes, resulting in dynamic changes in the Doppler frequency shift. Spread spectrum communication technology itself is insensitive to frequency offset, but due to the low transmission rate of underwater acoustic signals, the Doppler frequency shift rate of underwater acoustic communication is very high compared to radio electromagnetic wave communication. Therefore, how to solve carrier synchronization has become one of the key technologies in underwater acoustic spread spectrum communication. Subsequently, Doppler estimation technology for real-time systems has become a research hotspot in the field of underwater acoustic spread spectrum communication.

[0004] Spread spectrum is a common technology for underwater acoustic mobile real-time communication, but it is very sensitive to Doppler shift, and Doppler deviation will have a serious impact on underwater acoustic spread spectrum communication systems. Therefore, research on the improvement of Doppler estimation algorithms for underwater acoustic spread spectrum communication is particularly important. Summary of the invention

[0005] In order to solve the problem that Doppler deviation has a serious impact on underwater acoustic spread spectrum communication systems, the present invention further improves estimation accuracy while reducing computational complexity, and further proposes an underwater acoustic spread spectrum communication Doppler estimation algorithm based on matched filtering and fuzzy function.

[0006] The technical solution adopted by the present invention to solve the above problems is:

[0007] The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function is implemented by the following steps:

[0008] S1: Perform Doppler estimation on the signal based on matched filtering, determine the approximate frequency deviation range, and obtain a rough estimate of the Doppler factor;

[0009] S2: perform Doppler estimation on the signal based on the fuzzy function to obtain a detailed estimated Doppler factor;

[0010] S3: Residual Doppler differential demodulation to obtain the final estimated Doppler factor.

[0011] Furthermore, the Doppler estimation based on matched filtering described in S1 is achieved by the following steps:

[0012] S1.1: cross-correlate the first and last segments of the linear frequency modulation signal;

[0013] S1.2: Calculate the compression or expansion change of the length of the transmitted and received signals;

[0014] S1.3: Obtain the corresponding rough estimate of the Doppler factor.

[0015] Furthermore, in the Doppler estimation based on matched filtering of the signal, it is assumed that the time length of the transmitted signal is T r , the received signal after passing through the channel is measured to have a length of T v , then the Doppler expansion factor α can be expressed as:

[0016]

[0017] Furthermore, the estimation accuracy of the Doppler estimation method based on matched filtering is inversely proportional to the product of the bandwidth B and the pulse width T of the linear frequency modulation signal, and the expression of the estimation accuracy δ of the Doppler estimation method based on matched filtering is as follows:

[0018]

[0019] Furthermore, the product of the bandwidth B and the pulse width T of the linear frequency modulation signal is greater than or equal to 100.

[0020] Further, the Doppler estimation based on the ambiguity function described in S2 is achieved by the following steps:

[0021] S2.1: Accurately synchronize the received signal to make the signal delay zero;

[0022] S2.2: Initialize the step size of Doppler factor search;

[0023] S2.3: binary search with variable step size;

[0024] S2.4: Find the position where the fuzzy graph has the maximum energy;

[0025] S2.5: Obtain the corresponding refined estimated Doppler factor.

[0026] Furthermore, the process of performing Doppler estimation on the signal based on the ambiguity function is as follows:

[0027] For a signal s(t) with a time delay of τ and a Doppler of υ, the output response function of the matched filter can be expressed as:

[0028] χ(τ,υ)=∫s(t)s * (t-τ)e j2πυt dt=∫S(f)S * (f-υ)e j2πτt df (3)

[0029] The square value of the amplitude of equation (3) |χ(τ,υ) 2 It is called the fuzzy function, namely:

[0030] |χ(τ,υ)| 2 =|∫s(t)s * (t-τ)e j2πυt dt| 2 (4)

[0031] The delay-Doppler resolution is defined as the Q function, which is expressed as:

[0032]

[0033] The maximum value of the fuzzy function of the signal is at its origin (τ,υ), that is:

[0034]

[0035] The fuzzy function of the linear frequency modulation signal is:

[0036]

[0037] The pseudo-random sequence uses an m-sequence that is orthogonal to the spread spectrum code sequence. The signal after carrier modulation can be expressed as:

[0038]

[0039] In formula (8), T c is the chip length of the m sequence; is the phase of the pseudo-random phase modulation signal, which takes the value of 0 or π according to the m sequence;

[0040] The mutual ambiguity function expression of the received signal after passing through the channel and the original transmitted signal is:

[0041]

[0042] Furthermore, the resolution of the fuzzy function χ(τ,υ) includes time delay and frequency shift resolution, the time delay resolution is proportional to the signal bandwidth, expressed as Δτ∝1 / B; the frequency shift resolution is proportional to the signal pulse width, expressed as Δυ∝1 / T.

[0043] The beneficial effects of the present invention are:

[0044] 1. According to the characteristics of the underwater acoustic mobile spread spectrum communication system, the present invention inserts a linear frequency modulation signal at the beginning and end of the data frame respectively, so that two correlation peaks can be obtained before and after the signal through cross-correlation processing at the receiving end, so that the matched filtering method can be used for Doppler estimation. By applying the fuzzy function algorithm to the Doppler estimation of the receiving end of the mobile underwater acoustic spread spectrum communication system, the problem of splitting of the correlation peak of the linear frequency modulation signal caused by the relative motion speed exceeding the tolerance threshold is solved, so that the algorithm has higher synchronization accuracy. By combining the matching filter with the fuzzy function method, the signal is correlated and matched with a smaller search step size, which effectively reduces the complexity of the algorithm.

[0045] 2. The present invention aims at the performance balance problem of estimation accuracy and complexity of the Doppler estimation algorithm in the mobile underwater acoustic spread spectrum communication system, and can avoid the shortcoming that the estimation method based on matched filtering cannot well estimate the large Doppler expansion factor generated when underwater mobile nodes move at high speed, and make up for the shortcomings of the fuzzy function estimation method with better accuracy that takes a long time to calculate and has high computational complexity.

[0046] 3. The present invention not only has excellent synchronization accuracy, but also the algorithm requires a short running time, thus ensuring the real-time requirements of communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of the Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function of the present invention;

[0048] Figure 2 It is a schematic diagram of the transmission signal structure based on the matched filtering Doppler estimation method of the present invention;

[0049] Figure 3 It is a linear frequency modulation signal fuzzy graph of the present invention;

[0050] Figure 4 It is a schematic diagram of the transmission signal structure based on the fuzzy function Doppler estimation method of the present invention;

[0051] Figure 5 This is a schematic diagram of conventional search and variable step size search. DETAILED DESCRIPTION

[0052] Specific implementation method 1: Combination Figure 1-5 To illustrate this embodiment, Figure 1 As shown, the underwater acoustic spread spectrum communication Doppler estimation algorithm based on matched filtering and fuzzy function described in this embodiment is implemented by the following steps:

[0053] S1: Perform Doppler estimation based on matched filtering on the signal, determine the approximate frequency deviation range, and obtain a rough estimate of the Doppler factor. In the underwater acoustic spread spectrum communication system, the underwater acoustic Doppler estimation algorithm of the underwater acoustic mobile spread spectrum communication system based on linear frequency modulation signal is completed by introducing the matched filtering method. The Doppler estimation based on matched filtering is achieved by the following steps:

[0054] S1.1: cross-correlate the first and last segments of the linear frequency modulation signal;

[0055] S1.2: Calculate the compression or expansion change of the length of the transmitted and received signals;

[0056] S1.3: Obtain the corresponding rough estimate of the Doppler factor.

[0057] like Figure 2 As shown in the figure, it is a schematic diagram of the transmission signal structure based on the matched filter Doppler estimation method. By inserting a linear frequency modulation (LFM) signal at the beginning and end of the data frame, the linear frequency modulation signal is selected as the leading signal in the Doppler estimation, making the structure of the transmission signal simpler and reducing the power consumption of the signal transmitter. After the transmission signal passes through the underwater acoustic channel, the whole signal will be extended or compressed. Then, at the receiving end, two correlation peaks can be obtained before and after the signal through cross-correlation processing. Then, the corresponding Doppler factor can be obtained by calculating the compression / expansion change of the length of the transmitted and received signals.

[0058] If we assume that the time length of the transmitted signal is T r , the received signal after passing through the channel is measured to have a length of T v , then the Doppler expansion factor α can be expressed as:

[0059]

[0060] After obtaining the Doppler expansion factor, the signal can be resampled or linearly interpolated in the time domain by 1:(1+α) to compensate for the Doppler expansion.

[0061] The estimation accuracy of the Doppler estimation method based on matched filtering is related to the LFM signal bandwidth B and the pulse width T, and is inversely proportional to the product of the two. Its accuracy δ can be expressed as:

[0062]

[0063] Generally, the signal's time-bandwidth product BT is required to be ≥ 100 so that the signal sequence can be easily detected by a single correlator. Because this method estimates the Doppler expansion factor α by calculating the change in the duration of the entire data frame before and after it passes through the channel, it is more suitable for estimating the constant Doppler expansion factor α.

[0064] 1. S2: Perform Doppler estimation based on fuzzy function on the signal to obtain a fine estimated Doppler factor. Aiming at the problem that the LFM correlation peak is split due to the relative motion speed of the transmitting and receiving ends, the Doppler estimation algorithm of the underwater acoustic spread spectrum communication system is improved based on the fuzzy function model. The Doppler estimation based on fuzzy function is achieved by the following steps:

[0065] S2.1: Accurately synchronize the received signal to make the signal delay zero;

[0066] S2.2: Initialize the step size of Doppler factor search;

[0067] S2.3: binary search with variable step size;

[0068] S2.4: Find the position where the fuzzy graph has the maximum energy;

[0069] S2.5: Obtain the corresponding refined estimated Doppler factor.

[0070] Under the condition of the same relative motion speed, the estimation accuracy based on the matched filtering method will decrease as the length of the LFM signal decreases. This is because the correlation peak amplitude of the LFM signal is proportional to its time-bandwidth product. The sharper the correlation main peak, the greater the probability of being detected, and the lower the error when used for synchronous detection or Doppler estimation. In addition, as the relative motion speed of the transmitter and receiver continues to increase, the estimation accuracy of the algorithm will also decrease. Because when the relative motion speed exceeds the tolerance threshold, the LFM correlation peak will split, which will reduce the estimation accuracy of the algorithm.

[0071] The signal ambiguity function can reflect the two-dimensional joint characteristics of the signal in time and frequency. The delay-Doppler of the underwater acoustic channel can be estimated by using the mutual ambiguity function. For a signal s(t) with a delay of τ and a Doppler of υ, the output response function (time-frequency correlation function) of the matched filter can be expressed as:

[0072] χ(τ,υ)=∫s(t)s * (t-τ)e j2πυt dt=∫S(f)S * (f-υ)e j2πτt df

[0073] The square value of the amplitude of the above formula |χ(τ,υ)| 2 It is called the fuzzy function, namely:

[0074] |χ(τ,υ)| 2 =|∫s(t)s * (t-τ)e j2πυt dt| 2

[0075] The resolution of the fuzzy function χ(τ,υ) includes the time delay resolution and frequency shift resolution. The time delay resolution is proportional to the signal bandwidth, Δτ∝1 / B; the frequency shift resolution is proportional to the signal pulse width, Δυ∝1 / T.

[0076] The delay-Doppler resolution is defined as the Q function, which is expressed as:

[0077]

[0078] The Q function can be described as the integration of the square of the modulus of the cross section of the signal fuzzy function at a specific frequency (time) point over time (frequency). It can reflect the energy distribution at that point. The larger the Q, the stronger the energy at that point.

[0079] The maximum value of the fuzzy function of the signal is at its origin (τ,υ), that is:

[0080]

[0081] If the delay-Doppler parameters of the received signal and the matched filter are different, it means that there is still a time and Doppler deviation between the transmitted and received signals. Then, a complete match cannot be achieved and the correlation result will be less than the maximum value. By calculating the position of the maximum energy of the fuzzy graph, the delay-Doppler parameters of the signal can be estimated accordingly.

[0082] The fuzzy function of the LFM signal is:

[0083]

[0084] like Figure 3 As shown in Figure 1, it is a three-dimensional image of the self-blur function of the LFM signal. It can be seen that when χ(τ,υ) is at the origin, the ambiguity function reaches its maximum value.

[0085] The pseudo-random sequence uses an m-sequence (orthogonal to the spread spectrum code sequence), and the signal after carrier modulation can be expressed as:

[0086]

[0087] Where, T c is the chip length of the m sequence; is the phase of the pseudo-random phase modulation signal, which takes the value of 0 or π according to the m-sequence.

[0088] The mutual ambiguity function expression of the received signal after passing through the channel and the original transmitted signal is:

[0089]

[0090] In order to obtain a more accurate Doppler factor, it is necessary to first precisely synchronize the received signal so that its delay τ = 0, and then perform a Doppler search on the signal within a certain interval. By calculating the fuzzy function of the received signal and the local signal, the frequency deviation value corresponding to the peak of the fuzzy function is the Doppler frequency deviation introduced by the signal into the system during the transmission of the underwater acoustic channel. The signal structure emitted by the Doppler estimation method based on the fuzzy function is as follows Figure 4 shown.

[0091] This method can estimate the signal Doppler expansion factor in real time. The accuracy is mainly determined by the sensitivity of the leading signal to Doppler and the step size of the Doppler factor search at the receiving end. The use of variable step size search based on binary search can reduce the number of searches and the complexity of computational time. Figure 5 Schematic diagram of variable step search.

[0092] The time complexity of finding the peak value by the fuzzy function method with variable step size search is reduced from the original O(n) to O(logn). If the step size is set larger, the calculation time complexity of the two methods is similar; when the step size is set smaller, the time complexity of the search can be effectively reduced based on binary search.

[0093] S3: Residual Doppler differential demodulation to obtain the final estimated Doppler factor.

[0094] In the second-order differential coding modulation process at the receiving end, if the input signal phase is φ(t), the output phase after the first-order differential is θ1(t), and after another differential, the output phase of the second-order differential is θ2(t), that is:

[0095]

[0096] After simplification, we can get:

[0097] φ(t)=θ2(t)-θ2(tT)-[θ2(tT)-θ2(t-2T)]

[0098] =θ2(t)-2θ2(tT)+θ2(t-2T)

[0099] If after passing through the channel, the receiving end signal produces a frequency shift of Δw compared to the transmitting end signal s(t), then the received signal can be expressed as:

[0100]

[0101] After first-order differential detection and second-order differential detection, the output signals are:

[0102]

[0103] Therefore, the Doppler frequency deviation Δw generated during transmission is offset by the second-order differential detection.

[0104] Considering that the estimation method based on matched filtering cannot make a good estimate of the large Doppler expansion factor generated by the high-speed movement between underwater mobile nodes, it is necessary to use a fuzzy function estimation method with better estimation accuracy, but it takes a long time to calculate, has a large computational complexity, requires more hardware resources and is difficult to implement. The Doppler estimation process is divided into two parts. First, the signal is roughly estimated based on matched filtering. After determining the approximate frequency deviation range, the fuzzy logic Doppler estimation method is used to make a fine estimate of the signal. The overall process of the underwater acoustic spread spectrum communication Doppler estimation algorithm based on matched filtering and fuzzy function is shown in Table 1. Under the condition of the same amount of calculation, compared with the single fuzzy logic estimation method, this method can perform correlation matching on the signal with a smaller search step size, and the estimation accuracy is higher. By combining the Doppler rough estimation based on matched filtering and the fine estimation based on fuzzy logic, the computation time is reduced, the frequency deviation estimation accuracy is improved, and the algorithm running time is reduced.

[0105] Table 1 Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function

[0106]

[0107]

[0108] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function is characterized by: The underwater acoustic spread spectrum communication Doppler estimation algorithm based on matched filtering and fuzzy function is implemented by the following steps: S1: Perform Doppler estimation on the signal based on matched filtering, determine the approximate frequency deviation range, and obtain a rough estimate of the Doppler factor; S2: perform Doppler estimation on the signal based on the ambiguity function to obtain a detailed estimated Doppler factor; S3: Residual Doppler differential demodulation to obtain the final estimated Doppler factor.

2. The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function according to claim 1 is characterized by: The Doppler estimation based on matched filtering described in S1 is achieved by the following steps: S1.1: cross-correlate the first and last segments of the linear frequency modulation signal; S1.2: Calculate the compression or expansion change of the length of the transmitted and received signals; S1.3: Obtain the corresponding rough estimate of the Doppler factor.

3. The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function according to claim 2 is characterized by: In the Doppler estimation based on matched filtering, it is assumed that the time length of the transmitted signal is T r , the received signal after passing through the channel is measured to have a length of T v , then the Doppler expansion factor α can be expressed as:

4. The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function according to claim 3 is characterized by: The estimation accuracy of the Doppler estimation method based on matched filtering is inversely proportional to the product of the bandwidth B and the pulse width T of the linear frequency modulation signal. The estimation accuracy δ of the Doppler estimation method based on matched filtering is expressed as follows:

5. The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function according to claim 4 is characterized by: The product of the bandwidth B and the pulse width T of the linear frequency modulation signal is greater than or equal to 100.

6. The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function according to claim 1 is characterized by: The Doppler estimation based on the ambiguity function described in S2 is achieved by the following steps: S2.1: Accurately synchronize the received signal to make the signal delay zero; S2.2: Initialize the step size of Doppler factor search; S2.3: binary search with variable step size; S2.4: Find the position where the fuzzy graph has the maximum energy; S2.5: Obtain the corresponding refined estimated Doppler factor.

7. The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function according to claim 6 is characterized by: The process of performing Doppler estimation on the signal based on the ambiguity function is as follows: For a signal s(t) with a time delay of τ and a Doppler of υ, the output response function of the matched filter can be expressed as: χ(τ,υ)=∫s(t)s * (t-τ)e j2πυt dt=∫S(f)S * (f-υ)e j2πτt df (3) The square value of the amplitude of equation (3) χ(τ,υ) 2 It is called the fuzzy function, namely: |χ(τ,υ)| 2 =|∫s(t)s * (t-τ)e j2πυt dt| 2 (4) The delay-Doppler resolution is defined as the Q function, which is expressed as: The maximum value of the fuzzy function of the signal is at its origin (τ,υ), that is: The fuzzy function of the linear frequency modulation signal is: The pseudo-random sequence uses an m-sequence that is orthogonal to the spread spectrum code sequence. The signal after carrier modulation can be expressed as: In formula (8), T c is the chip length of the m sequence; is the phase of the pseudo-random phase modulation signal, which takes the value of 0 or π according to the m sequence; The mutual ambiguity function expression of the received signal after passing through the channel and the original transmitted signal is:

8. The Doppler estimation algorithm for underwater acoustic spread spectrum communication based on matched filtering and fuzzy function according to claim 7 is characterized by: The resolution of the fuzzy function χ(τ,υ) includes time delay and frequency shift resolution. The time delay resolution is proportional to the signal bandwidth, expressed as Δτ∝1 / B; the frequency shift resolution is proportional to the signal pulse width, expressed as Δυ∝1 / T.

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