Underwater sound OFDM system carrier synchronization algorithm based on gradient estimation combined with optimal solution search

Abstract

The invention discloses an underwater acoustic OFDM (Orthogonal Frequency Division Multiplexing) system carrier synchronization algorithm based on gradient estimation combined with optimal solution search, and belongs to the technical field of underwater acoustic communication. The method specifically comprises the following steps: step 1, in an underwater acoustic OFDM communication system, synchronizing underwater acoustic OFDM carriers by adopting a time domain method; and step 2, in one OFDM frame, carrying out frequency offset estimation on the first OFDM symbol by adopting a carrier synchronization algorithm based on optimal solution search. And step 3, starting from the second OFDM symbol, estimating a frequency offset value by adopting a carrier synchronization algorithm based on gradient descent, and taking a frequency offset estimation result of the first OFDM symbol as an initial value of iteration. According to the method, finer residual carrier frequency offset compensation can be carried out through pilot symbols, an Adam method is adopted to improve an underwater acoustic system carrier synchronization algorithm of a step length, the complexity is reduced while the precision is improved, and reliable and effective underwater acoustic OFDM communication is realized.

Description

Technical Field

[0001] The invention relates to an underwater acoustic OFDM system carrier synchronization algorithm, in particular to an underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and joint optimal solution search, belonging to the technical field of underwater acoustic communication. Background Art

[0002] The underwater acoustic channel is a double-selective fading channel with serious multipath effect and Doppler effect. Orthogonal Frequency Division Multiplexing (OFDM) technology is a modulation technology with high spectrum utilization and strong anti-multipath capability, and has become a common technology for underwater acoustic communication.

[0003] Generally speaking, there are two reasons for the frequency deviation of the carrier signal. One is the phase noise caused by the different fixed frequencies at the transmitting and receiving ends, and the other is the carrier frequency offset (CFO) caused by the Doppler frequency shift. The carrier frequency offset will cause the OFDM signal entering the Fast Fourier Transformation (FFT) window to no longer be a complete symbol period. At the same time, there are partial symbol periods of other subcarriers, which are multipath components and affect the judgment of the current symbol. Whether it is an integer multiple subcarrier spacing offset or a fractional frequency offset, the orthogonality between subcarriers will be lost, causing inter-channel interference (ICI).

[0004] In order to ensure the performance of the OFDM system, the receiver must use synchronization technology, that is, accurately estimate the start and end points of the OFDM symbol to smoothly perform FFT. Usually, the carrier synchronization accuracy, estimation range and algorithm complexity are used as important indicators to measure the performance of the carrier synchronization algorithm. They influence and restrict each other. Therefore, when designing a carrier synchronization algorithm, it is necessary to comprehensively consider the real-time requirements of the algorithm, the size of the allocable hardware resources and the usage scenarios, so as to better exert the best performance in practical applications.

[0005] OFDM is a common technology for realizing underwater acoustic high-speed communication, but it is very sensitive to synchronization deviation, which will have a serious impact on the OFDM communication system. Therefore, it is particularly important to study the improvement of the carrier synchronization algorithm for underwater acoustic OFDM communication. Summary of the invention

[0006] In order to solve the problem of inter-channel interference caused by carrier frequency offset caused by Doppler frequency shift of underwater acoustic OFDM channel, further improve the carrier synchronization accuracy and reduce the computational complexity, a carrier synchronization algorithm for underwater acoustic OFDM system based on gradient estimation and joint optimal solution search is proposed in the present invention.

[0007] The technical solution adopted by the present invention to solve the above problems is:

[0008] The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and optimal solution search is implemented by the following steps:

[0009] S1: In the underwater acoustic OFDM communication system, the time domain method is used to synchronize the underwater acoustic OFDM carrier;

[0010] S2: In an OFDM frame, the frequency offset is estimated for the first OFDM symbol using a carrier synchronization algorithm based on optimal solution search.

[0011] S3: Starting from the second OFDM symbol, a carrier synchronization algorithm based on gradient descent is used to estimate the frequency offset value, and the frequency offset estimation result of the first OFDM symbol is used as the initial value of the iteration.

[0012] Furthermore, the time domain method for underwater acoustic OFDM carrier synchronization described in S1 specifically includes:

[0013] According to the nature of OFDM, the signal sent by the transducer is:

[0014]

[0015] Assuming that the noise of the underwater acoustic channel is an additive white Gaussian noise channel, the noise is w, T is the OFDM symbol length, N is the number of subcarriers, and the receiving end signal is:

[0016]

[0017] Sample y(t) with a sampling period of T s but:

[0018]

[0019] There is a symbol synchronization deviation Δn in synchronization f When , it is equivalent to performing a discrete Fourier transform operation in front of the cyclic prefix, that is:

[0020]

[0021] Let Δn f (i) is the starting point τ in the orthogonal regionmax / T s The signal after phase compensation is:

[0022] Y k (i) = S k (i)+w(i) (5)

[0023] By using the properties of the orthogonal region, we can change the starting position of the discrete Fourier transform to obtain multiple S k The estimated Y k (1),Y k (2),…, for multiple Y k Difference processing can achieve diversity and smoothing effects, and the received signal with carrier frequency deviation is:

[0024]

[0025] In the formula, is the sampling frequency at the receiving end, N fft is the number of discrete Fourier transform points, T o is the OFDM symbol duration, S k is the spectrum of the subcarrier;

[0026] The baseband signal adopts rectangular wave and quadrature phase shift keying modulation, then S k is a SINC function, with a main lobe width of 2 / T o , the side lobe width is 1 / T o When:

[0027]

[0028] By taking the derivative of formula (7) with respect to m, we can obtain:

[0029]

[0030] By using high-power fast Fourier transform, in addition to the data at the subcarrier, the frequency point data adjacent to the subcarrier can also be obtained. If the adjacent frequency points are within the allowable range, the inherent inter-channel interference they bring can be treated as noise. By performing differential analysis, the effect of differential analysis can be obtained. If adjacent subcarriers are used to transmit pilot signals, the inter-channel interference they bring can be removed. Other methods using interpolation or subtraction will cause errors. The frequency domain signal at the non-orthogonal frequency point is:

[0031]

[0032] Subscript j is the non-subcarrier frequency after high-multiple Fourier transformation, which should satisfy:

[0033]

[0034] In formula (10), the frequency resolution after high-power Fourier transformation is Δf', the original transmission frequency is Δf, the orthogonality factor is λ, the interval between adjacent subcarriers is Δf, and the total phase is π. The impact of these non-orthogonal frequency points can be treated as noise.

[0035] Furthermore, all power differences are ≤0.25dB, and the sum of the maximum phase angles on the left and right sides is ≤π / 4.

[0036] Furthermore, the carrier synchronization algorithm based on optimal solution search described in S2 specifically includes:

[0037] In the underwater acoustic OFDM communication system, the number of subchannels is fixed to 1024, the signal bandwidth is B, the modulation frequency of the first subcarrier is f0, and the carrier frequency of the kth carrier is f k =f0+kΔf(k≤64), then the subchannel interval is Δf=B / K, K is the Kth subchannel (K≤1024), and the modulation method of orthogonal phase shift keying is adopted. The OFDM signal s(t) can be expressed as:

[0038]

[0039] In formula (11), T = 1 / Δf represents the symbol length, T CP represents the duration of the cyclic prefix, d k Represents the user information to be sent;

[0040] Assume that the length of the cyclic prefix is ​​greater than or equal to the delay spread length of the channel, T CP >>T DS , after passing through the channel, the impulse response h(τ,t) of the signal received by the receiver can be expressed as:

[0041]

[0042] In formula (12), h p (t) represents the amplitude of the channel, τ p (t) represents the delay of channel p, τ p (t)≈τ p -at, at is the delay caused by multipath,

[0043] Because of small-scale fading, the channel amplitude will change due to multipath effects, with h p (t)≈h p , further analysis h(τ,t) can be expressed as:

[0044]

[0045] The signal received by the receiving end after channel amplitude attenuation and delay expansion can be expressed as:

[0046]

[0047] In formula (14), n(t) represents Gaussian white noise, whose power spectrum density is N0 / 2.

[0048] After the received signal y(t) undergoes packet synchronization estimation, symbol timing synchronization, and coarse frequency offset compensation,

[0049]

[0050] In formula (15), ε is the carrier frequency deviation, H k is the frequency response of the kth subcarrier of the OFDM symbol, w(t) is the additive noise,

[0051] In the carrier synchronization algorithm based on optimal solution search, a frequency offset estimation range is assumed and the search step size is set. The frequency offset estimation value in each search interval is The signal is finely compensated in the time domain, and the compensated signal can be expressed as:

[0052]

[0053] The pilot symbols are spaced equally k , k∈κ p , and the resulting mean square error is:

[0054]

[0055] In formula (17), d k Represents the user data sent out by the transmitter after modulation. Represents the user data received by the receiving end after passing through the channel. Represents the user data after frequency offset compensation at the receiving end;

[0056] If there are multiple frequency offset results, the mean square error of each frequency offset estimate of the received signal can be calculated by the above formula. The accurate frequency offset value of the received signal can be obtained by finding the minimum mean square error.

[0057]

[0058] Furthermore, assuming that the residual frequency offset of the i-th symbol is The residual frequency offset of the next i+1 symbol in the same frame is Using the similarity of the frequency offsets of two adjacent symbols, the residual frequency offset of the current symbol in the same frame is approximately equal to the residual frequency offset of the previous symbol, so:

[0059]

[0060] Furthermore, the frequency offset estimation method is as follows: based on the known frequency offset value of the current symbol, the next symbol is compensated with the current frequency offset estimation value, so that the detection area of ​​the frequency offset estimation of the next symbol can be reduced. When the search step size remains unchanged, the number of detections of the next symbol is reduced, and the running time is also reduced accordingly.

[0061] Furthermore, the gradient descent-based carrier synchronization algorithm described in S3 specifically includes:

[0062] The error gradient can be expressed as

[0063]

[0064] In formula (20), Then we have:

[0065] y k =∫ T tv(t)e -iβt e -2πikΔft dt (21)

[0066] Through the error gradient, the frequency deviation β can be iteratively calculated as:

[0067]

[0068] In formula (22), K β is the step size of frequency deviation iteration, and the initial value of frequency deviation is set

[0069] for

[0070] Furthermore, the Adam method is used to improve the selection of step size, which can be expressed as:

[0071]

[0072] In formula (23), is the estimated exponential moving mean of the gradient.

[0073] The beneficial effects of the present invention are:

[0074] 1. According to the frame structure characteristics of the OFDM system, the present invention reduces the overall computational complexity by performing more refined residual carrier frequency offset compensation on the pilot symbols in the carrier synchronization algorithm based on the optimal solution search. By applying the stochastic gradient descent algorithm to the carrier synchronization of the receiving end of the underwater acoustic OFDM communication system, the local minimum error value is crossed, so that the algorithm has higher synchronization accuracy. By combining the gradient estimation with the optimal solution search method, the frequency offset estimation accuracy is improved, the problem that the gradient descent algorithm is easily trapped in the local error minimum is avoided, the complexity of the algorithm is effectively reduced, and the optimal mean square error performance is achieved.

[0075] 2. The present invention can perform more precise residual carrier frequency offset compensation through pilot symbols and use the Adam method to improve the step-size of the underwater acoustic system carrier synchronization algorithm, thereby improving accuracy and reducing complexity, thereby achieving reliable and effective underwater acoustic OFDM communication.

[0076] 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

[0077] Figure 1 It is a flow chart of the carrier synchronization algorithm of the underwater acoustic OFDM system based on gradient estimation and optimal solution search of the present invention;

[0078] Figure 2 It is a flow chart of a carrier synchronization algorithm based on optimal solution search of the present invention. DETAILED DESCRIPTION

[0079] Specific implementation method 1: Combination Figure 1 and Figure 2 This embodiment is described. The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and joint optimal solution search described in this embodiment is implemented by the following steps:

[0080] S1: In the underwater acoustic OFDM communication system, the time domain method is used to synchronize the underwater acoustic OFDM carrier; that is, the underwater acoustic OFDM carrier synchronization algorithm based on the time domain method specifically includes:

[0081] According to the nature of OFDM, the signal sent by the transducer is:

[0082]

[0083] Assume that the noise of the underwater acoustic channel is an additive white Gaussian noise (AWGN) channel, the noise is w, T is the OFDM symbol length, and N is the number of subcarriers. Since the signal modulation used does not require carrier modulation and demodulation, the receiving end signal is:

[0084]

[0085] Sample y(t) with a sampling period of T s but:

[0086]

[0087] There is a symbol synchronization deviation Δn in synchronization f When , it is equivalent to performing a discrete Fourier transform (DFT) operation in front of the cyclic prefix, that is:

[0088]

[0089] Symbol timing deviation only causes the rotation of the transmitted signal phase, without destroying the orthogonality. In actual communication, it is necessary to ensure that the duration of the cyclic prefix is ​​greater than the maximum delay spread of the channel. There is an orthogonal region, namely τ max <t<t CP As long as the starting point of the DFT operation falls into the orthogonal region, the orthogonality of the received signal will not be destroyed. It is just that the phase rotation caused by the different starting points is different, and data demodulation can be achieved by performing phase compensation.

[0090] Let Δn f (i) is the starting point τ in the orthogonal region max / T s The signal after phase compensation is:

[0091] Y k (i) = S k (i)+w(i)

[0092] Using the properties of the orthogonal region, we can change the starting position of the DFT to obtain multiple S k The estimated Y k (1),Y k (2),…, for multiple Y k Difference processing can achieve diversity and smoothing effects.

[0093] The received signal with carrier frequency deviation is:

[0094]

[0095] In the formula, is the sampling frequency at the receiving end, N fft is the number of DFT points, T o is the OFDM symbol duration, S k is the spectrum of the subcarrier.

[0096] The baseband signal uses a rectangular wave and QPSK modulation, then Sk is a SINC function, with a main lobe width of 2 / T o , the side lobe width is 1 / T o When:

[0097]

[0098] Taking the derivative of this formula with respect to m, we can obtain:

[0099]

[0100] Divide Except for , they are all constant terms, and the result is only related to the sampling frequency, so the sampling frequency deviation can be estimated. When using high-power FFT, in addition to the data at the subcarrier, the frequency point data adjacent to the subcarrier can also be obtained. The adjacent frequency points are within the allowable range, and the inherent ICI brought by them can be treated as noise. By differentiating them, the differential effect can be obtained. If the adjacent subcarriers are used to transmit pilot signals, the ICI brought by them can be removed. Other methods using interpolation or subtraction will bring errors. The frequency domain signal at non-orthogonal frequency points is:

[0101]

[0102] Subscript j is the non-subcarrier frequency after high-multiple DFT, which should satisfy:

[0103]

[0104] The impact of these non-orthogonal frequencies can be treated as noise.

[0105] The frequency resolution after high-power DFT is Δf', the original transmission frequency Δf, the orthogonality factor λ, the total phase is π within the adjacent subcarrier interval Δf, and the phase interval of each frequency point is π / (N fftnew / N fftold ), in order to utilize non-orthogonal subcarriers, the point that can be used for QPSK is that in the absence of noise, the maximum can only be λ=1 / 8, but there is noise in the channel. In order to ensure the effect, all power differences do not exceed 0.25dB, and the sum of the maximum phase angles on the left and right sides does not exceed π / 4.

[0106] S2: In an OFDM frame, the frequency offset is estimated by using the carrier synchronization algorithm based on the optimal solution search for the first OFDM symbol. By introducing the optimal solution search, pilot symbols are used to perform more precise residual carrier frequency offset compensation.

[0107] The carrier synchronization algorithm based on optimal solution search specifically includes:

[0108] In the underwater acoustic OFDM communication system, the number of subchannels is fixed to 1024, the signal bandwidth is B, the modulation frequency of the first subcarrier is f0, and the carrier frequency of the kth carrier is f k =f0+kΔf(k≤64), then the subchannel interval is Δf=B / K, K is the Kth subchannel (K≤1024), and the OFDM signal s(t) using QPSK modulation can be expressed as:

[0109]

[0110] Where, T = 1 / Δf represents the symbol length; T CP Represents the duration of the cyclic prefix; d k Represents the user information to be sent.

[0111] Assume that the length of the cyclic prefix is ​​greater than or equal to the delay spread length of the channel, T CP >>T DS , after passing through the channel, the impulse response h(τ,t) of the signal received by the receiver can be expressed as:

[0112]

[0113] In the formula, h p (t) represents the amplitude of the channel; τ p (t) represents the delay of channel p, τ p (t)≈τ p -at, at is the delay caused by multipath,

[0114] Because of small-scale fading, the channel amplitude will change due to multipath effects, with h p (t)≈h p . Further analysis of h(τ,t)

[0115]

[0116] The signal received by the receiving end after channel amplitude attenuation and delay expansion can be expressed as:

[0117]

[0118] Where n(t) represents Gaussian white noise, and its power spectral density is N0 / 2.

[0119] After the received signal y(t) undergoes packet synchronization estimation, symbol timing synchronization, and coarse frequency offset compensation,

[0120]

[0121] Among them, ε is the carrier frequency deviation, H kis the frequency response of the kth subcarrier of the OFDM symbol, and w(t) is the additive noise.

[0122] In the carrier synchronization algorithm based on optimal solution search, a frequency offset estimation range is assumed and the search step size is set. The frequency offset estimation value in each search interval is The signal is finely compensated in the time domain, and the compensated signal can be expressed as

[0123]

[0124] The pilot symbols are spaced equally k , k∈κ p , the mean square error (MSE) obtained

[0125]

[0126] Where, d k Represents the user data sent out by the transmitter after modulation; Represents the user data received by the receiving end after passing through the channel; Represents the user data after frequency offset compensation at the receiving end.

[0127] If there are multiple frequency offset results, the MSE of each frequency offset estimate of the received signal can be calculated by the above formula. The minimum mean square error can be found to obtain the accurate frequency offset value of the received signal.

[0128]

[0129] When estimating each symbol, according to the set frequency offset range and frequency search step, if all symbols are repeatedly calculated according to each assumed frequency offset value, it will inevitably take a lot of computing time, because in addition to estimating the frequency offset of the first symbol, the remaining symbols must be recalculated. In order to reduce the complexity of the carrier synchronization algorithm, the relationship between the frequency offset estimates of two adjacent symbols is analyzed. Assume that the residual frequency offset of the i-th symbol is The residual frequency offset of the next i+1 symbol in the same frame is Taking advantage of the similarity of the frequency offsets of two adjacent symbols, the residual frequency offset of the current symbol in the same frame is approximately equal to the residual frequency offset of the previous symbol. Therefore, the frequency offset estimation method is: based on the known frequency offset value of the current symbol, the next symbol is compensated with the current frequency offset estimation value, so that the detection area of ​​the next symbol frequency offset estimation can be reduced. When the search step size remains unchanged, the number of detections of the next symbol is reduced, and the running time is also reduced accordingly. This improved method will improve the synchronization accuracy while reducing the overall computational complexity.

[0130] According to the above method, after the received signal v(t) is processed, the frequency offset range is first set, and the received signal is compensated for the frequency offset in the time domain for each assumed frequency offset estimate according to the detection interval. Then, the pilot symbol is used to estimate the phase rotation caused by the residual frequency offset, and finally, the MSE of the signal after compensation is calculated under different initial frequency offset values ​​to find the frequency offset estimate with the minimum MSE. The specific process of the algorithm is as follows: Figure 2 shown.

[0131] S3: Starting from the second OFDM symbol, the frequency offset value is estimated by using a carrier synchronization algorithm based on gradient descent, and the frequency offset estimation result of the first OFDM symbol is used as the initial value of the iteration. The random gradient descent algorithm is applied to the carrier synchronization of the receiving end of the underwater acoustic OFDM communication system, while keeping the algorithm complexity unchanged, the algorithm has higher synchronization accuracy.

[0132] The carrier synchronization algorithm based on gradient descent specifically includes:

[0133] If the gradient of each sample is calculated in each iteration, the cost will be very high. The idea of ​​stochastic gradient descent is adopted to update the weights according to each individual training sample. By inputting a large number of samples and continuously adjusting the weights, a set of weights is obtained so that the algorithm can get infinitely close results for the newly added samples, and the amount of calculation is greatly reduced. The essence of the gradient algorithm is to use the first-order derivative information of the function to select the direction of descent, which can quickly find the minimum point, but the limitation of the gradient descent algorithm is that it cannot cross the local minimum error value. Once it falls into the local minimum error, it is difficult to reach the global minimum error.

[0134] If frequency offset estimation is performed on all sample sets, it will take a lot of time. The stochastic gradient descent method uses a single (or a small number of) samples to estimate the current gradient, which can effectively reduce the amount of computation of the synchronization algorithm.

[0135] The error gradient can be expressed as:

[0136]

[0137] In the formula, have:

[0138] y k =∫ T tv(t)e -iβt e -2πikΔft dt

[0139] Through the error gradient, the frequency deviation β can be iteratively calculated as:

[0140]

[0141] In the formula, K β is the step size of frequency deviation iteration. The initial value of frequency deviation is set to

[0142] The step size in the carrier synchronization algorithm based on gradient descent has a huge impact on the synchronization result, and is crucial to the iteration speed and operation stability of the algorithm. The iteration step size with a constant interval will make the algorithm unable to take into account the convergence speed, CFO tracking speed and steady-state misalignment. In order to take into account the running speed, frequency offset estimation accuracy and stability, the Adam method is used to improve the selection of step size. The Adam algorithm adaptively optimizes the selection of step size by calculating the first-order moment estimate and the second-order moment estimate of the gradient. Compared with the traditional algorithm, it can achieve faster convergence speed, basically only requires very few parameter adjustments, and can perform efficient calculations. The choice of step size can be expressed as:

[0143]

[0144] In the formula, is the estimated exponential moving mean of the gradient.

[0145] At the same time, when the set number of iterations ends, if the system reaches a stable state, the correct frequency deviation estimation value can be obtained. If the system does not reach a stable state, the correct frequency deviation estimation value cannot be obtained. At the same time, blindly increasing the number of iterations in pursuit of entering a stable state will increase the system's computing burden and thus increase the system's running time. In addition, according to the nature of the stochastic gradient descent algorithm itself, the wrong setting of the initial value may cause the system to fall into the problem of local minimum error.

[0146] In order to further improve the carrier synchronization accuracy and reduce the computational complexity, the carrier synchronization is completed by introducing the time domain method to further improve the carrier synchronization accuracy and reduce the computational complexity. Then, in an OFDM frame, the carrier synchronization algorithm based on the optimal solution search is used to estimate the frequency offset of the first OFDM symbol. Starting from the second OFDM symbol, the carrier synchronization algorithm based on gradient descent is used to estimate the frequency offset value, and the frequency offset estimation result of the first OFDM symbol is used as the initial value of the iteration. As a result, the joint synchronization algorithm not only has excellent synchronization accuracy, but also has a short running time, which ensures the real-time requirements of communication.

[0147] 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. An underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and optimal solution search, characterized by: The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and optimal solution search is implemented by the following steps: S1: In the underwater acoustic OFDM communication system, the time domain method is used to synchronize the underwater acoustic OFDM carrier; S2: In an OFDM frame, the frequency offset is estimated for the first OFDM symbol using a carrier synchronization algorithm based on optimal solution search. S3: Starting from the second OFDM symbol, a carrier synchronization algorithm based on gradient descent is used to estimate the frequency offset value, and the frequency offset estimation result of the first OFDM symbol is used as the initial value of the iteration.

2. The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and joint optimal solution search according to claim 1 is characterized by: The time domain method for underwater acoustic OFDM carrier synchronization described in S1 specifically includes: According to the nature of OFDM, the signal sent by the transducer is: Assuming that the noise of the underwater acoustic channel is an additive white Gaussian noise channel, the noise is w, T is the OFDM symbol length, N is the number of subcarriers, and the receiving end signal is: Sample y(t) with a sampling period of T s but: There is a symbol synchronization deviation Δn in synchronization f When , it is equivalent to performing a discrete Fourier transform operation in front of the cyclic prefix, that is: Let Δn f (i) is the starting point τ in the orthogonal region max / T s The signal after phase compensation is: Y k (i)=S k (i)+w(i) (5) By using the properties of the orthogonal region, we can change the starting position of the discrete Fourier transform to obtain multiple S k The estimated Y k (1),Y k (2),…, for multiple Y k Difference processing can achieve diversity and smoothing effects, and the received signal with carrier frequency deviation is: In the formula, is the sampling frequency at the receiving end, N fft is the number of discrete Fourier transform points, T o is the OFDM symbol duration, S k is the spectrum of the subcarrier; The baseband signal adopts rectangular wave and quadrature phase shift keying modulation, then S k is a SINC function, with a main lobe width of 2 / T o , the side lobe width is 1 / T o When: By taking the derivative of formula (7) with respect to m, we can obtain: By using high-power fast Fourier transform, in addition to the data at the subcarrier, the frequency point data adjacent to the subcarrier can also be obtained. If the adjacent frequency points are within the allowable range, the inherent inter-channel interference they bring can be treated as noise. By performing differential analysis, the effect of differential analysis can be obtained. If adjacent subcarriers are used to transmit pilot signals, the inter-channel interference they bring can be removed. Other methods using interpolation or subtraction will cause errors. The frequency domain signal at the non-orthogonal frequency point is: Subscript j is the non-subcarrier frequency after high-multiple Fourier transformation, which should satisfy: In formula (10), the frequency resolution after high-power Fourier transformation is Δf', the original transmission frequency is Δf, the orthogonality factor is λ, the interval between adjacent subcarriers is Δf, and the total phase is π. The impact of these non-orthogonal frequency points can be treated as noise.

3. The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and joint optimal solution search according to claim 2 is characterized by: The power difference is ≤0.25dB, and the sum of the maximum phase angles on the left and right sides is ≤π / 4.

4. The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and optimal solution search according to claim 2 is characterized by: The carrier synchronization algorithm based on optimal solution search described in S2 specifically includes: In the underwater acoustic OFDM communication system, the number of subchannels is fixed to 1024, the signal bandwidth is B, the modulation frequency of the first subcarrier is f0, and the carrier frequency of the kth carrier is f k =f0+kΔf(k≤64), then the subchannel interval is Δf=B / K, K is the Kth subchannel (K≤1024), and the modulation method of orthogonal phase shift keying is adopted. The OFDM signal s(t) can be expressed as: In formula (11), T = 1 / Δf represents the symbol length, T CP represents the duration of the cyclic prefix, d k Represents the user information to be sent; Assume that the length of the cyclic prefix is ​​greater than or equal to the delay spread length of the channel, T CP >>T DS , after passing through the channel, the impulse response h(τ,t) of the signal received by the receiver can be expressed as: In formula (12), h p (t) represents the amplitude of the channel, τ p (t) represents the delay of channel p, τ p (t)≈τ p -at, at is the delay caused by multipath, Because of small-scale fading, the channel amplitude will change due to multipath effects, with h p (t)≈h p , further analysis h(τ,t) can be expressed as: The signal received by the receiver after channel amplitude attenuation and delay expansion can be expressed as: In formula (14), n(t) represents Gaussian white noise, whose power spectrum density is N0 / 2. After the received signal y(t) undergoes packet synchronization estimation, symbol timing synchronization, and coarse frequency offset compensation, In formula (15), ε is the carrier frequency deviation, H k is the frequency response of the kth subcarrier of the OFDM symbol, w(t) is the additive noise, In the carrier synchronization algorithm based on optimal solution search, a frequency offset estimation range is assumed and the search step size is set. The frequency offset estimation value in each search interval is The signal is finely compensated in the time domain, and the compensated signal can be expressed as: The pilot symbols are spaced equally k , k∈κ p , and the resulting mean square error is: In formula (17), d k Represents the user data sent out by the transmitter after modulation. Represents the user data received by the receiving end after passing through the channel. Represents the user data after frequency offset compensation at the receiving end; If there are multiple frequency offset results, the mean square error of each frequency offset estimate of the received signal can be calculated by the above formula. The accurate frequency offset value of the received signal can be obtained by finding the minimum mean square error.

5. The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and optimal solution search according to claim 4 is characterized by: Assume that the residual frequency offset of the i-th symbol is The residual frequency offset of the next i+1 symbol in the same frame is Using the similarity of the frequency offsets of two adjacent symbols, the residual frequency offset of the current symbol in the same frame is approximately equal to the residual frequency offset of the previous symbol, so:

6. The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and joint optimal solution search according to claim 5 is characterized by: The frequency offset estimation method is as follows: based on the known frequency offset value of the current symbol, the next symbol is compensated with the current frequency offset estimation value, so that the detection area of ​​the frequency offset estimation of the next symbol can be reduced. When the search step size remains unchanged, the number of detections of the next symbol is reduced, and the running time is also reduced accordingly.

7. The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and joint optimal solution search according to claim 6 is characterized by: The carrier synchronization algorithm based on gradient descent described in S3 specifically includes: The error gradient can be expressed as In formula (20), Then we have: y k =∫ T tv(t)e -iβt e -2πikΔft dt (21) Through the error gradient, the frequency deviation β can be iteratively calculated as: In formula (22), K β is the step size of frequency deviation iteration, and the initial value of frequency deviation is set to 8. The underwater acoustic OFDM system carrier synchronization algorithm based on gradient estimation and joint optimal solution search according to claim 7 is characterized by: The Adam method is used to improve the selection of step size, which can be expressed as: In formula (23), is the estimated exponential moving mean of the gradient.

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