Joint estimation method of carrier frequency offset and symbol in underwater acoustic OFDM under carrier frequency offset interference

Abstract

This invention provides a joint estimation method for carrier frequency offset and symbols in underwater acoustic OFDM under carrier frequency offset interference, belonging to the field of underwater acoustic communication technology. Utilizing the memory-based linear estimation and orthogonalization characteristics of the memory approximation message passing algorithm, and employing type II maximum likelihood estimation and exponential moving average mechanisms, the CFO estimation is embedded within the same iterative process of symbol updates, allowing both to share the memory structure of the MAMP and achieving collaborative optimization of parameters and symbols. Compared with existing Turbo equalization methods based on vector approximation message passing, this invention significantly reduces computational complexity, improves carrier frequency offset estimation accuracy and system bit error rate performance without requiring special pilot design, and is insensitive to initial frequency offset, thus having a wider range of applications and superior estimation performance.

Description

Technical Field

[0001] This invention relates to a method for joint estimation of carrier frequency offset and symbol in underwater acoustic OFDM under carrier frequency offset interference, belonging to the field of underwater acoustic communication technology. Background Technology

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology is widely used in underwater acoustic communication systems due to its high spectral efficiency and strong multipath resistance. However, underwater acoustic channels are characterized by rapid time-varying and severe Doppler spread, leading to significant carrier frequency offset (CFO) at the receiver. CFO disrupts the orthogonality between subcarriers, causing inter-carrier interference (ICI) and severely degrading system performance.

[0003] Existing CFO estimation methods mainly include those based on training sequences, those based on empty subcarrier energy, and those based on the constant mode property of the signal. These methods are usually processed separately from channel equalization, failing to fully utilize the soft information in the iterative process. Regarding equalization techniques, the Linear Least Mean Square Error (LMMSE) equalizer has high complexity and limited performance; while the Vector Approximate Message Passing (VAMP) equalizer has better performance, it requires matrix inversion in each iteration, resulting in high computational complexity and making it difficult to meet real-time processing requirements.

[0004] Therefore, there is an urgent need for a joint processing method that can simultaneously achieve high-precision CFO estimation and low-complexity balance to improve the reliability of underwater acoustic OFDM systems in dynamic channels. Summary of the Invention

[0005] The purpose of this invention is to provide a joint estimation method for carrier frequency offset and symbol in underwater acoustic OFDM under carrier frequency offset interference, so as to solve the problems of performance limitation caused by the separate processing of carrier frequency offset estimation and channel equalization in existing underwater acoustic OFDM communication systems, the high computational complexity of traditional equalization algorithms, and the strong dependence on pilot structure, and to achieve high-precision, low-complexity joint parameter estimation and symbol detection without special pilots.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] A method for joint estimation of carrier frequency offset and symbol in underwater acoustic OFDM under carrier frequency offset interference includes the following steps:

[0008] S1. Establish the frequency domain received signal model of the underwater acoustic OFDM system and initialize the carrier frequency offset estimate. Equal probability with symbolic priors;

[0009] Specifically, a frequency domain signal receiving model for an underwater acoustic OFDM system is established. ,in For the frequency domain received signal vector, For normalized carrier frequency offset A given frequency domain cyclic matrix, This is the frequency domain channel impulse response. Transmit symbol vectors in the frequency domain. The noise is additive Gaussian. Initialize the carrier frequency offset estimate. Equal probability with symbolic priors;

[0010] S2. Construct an equivalent observation matrix based on the current carrier frequency offset estimate. ;

[0011] Specifically: Construct an equivalent observation matrix based on the current carrier frequency offset estimate. ;in Normalized carrier frequency offset The resulting circular matrix, The frequency domain channel impulse response vector. For the reason The constructed diagonal matrix.

[0012] S3. During the internal iteration of the memory approximation message passing algorithm, memory linear estimation, nonlinear estimation, damping operation and carrier frequency offset estimation are executed sequentially. Among them, the carrier frequency offset estimation is solved by the multi-starting point variable step size Newton iteration method based on the type II maximum likelihood criterion, and the exponential moving average mechanism is used to give the CFO estimation memory.

[0013] Specifically, in the inner iteration process of the memory approximation message passing algorithm, for the ... Within each iteration, the sub-steps are executed sequentially.

[0014] S3.1, Memory Linear Estimation:

[0015] Using the current carrier frequency offset estimation Calculate the output of the matched filter : in , For matrix Median of eigenvalues For relaxation parameters, We use weights, and then orthogonalize them to obtain: in , The orthogonalization parameter can be obtained from the MAMP state evolution.

[0016] S3.2, Nonlinear Estimation:

[0017] right Perform symbolic MMSE estimation: in for The probability distribution of the signal can be orthogonalized to obtain the estimated transmitted signal for the current iteration. : in Similarly, the orthogonalization parameters are obtained from the MAMP state evolution;

[0018] S3.3, Damping Operation

[0019] Perform a damping operation to improve convergence by weighting the current and historical estimates: ,in The damping vector;

[0020] S3.4, Carrier Frequency Offset Estimation:

[0021] Carrier frequency offset estimation is based on the asymptotic Gaussian error property of the orthogonalized output of MAMP, defining latent variables. Its posterior statistic can be approximated as .

[0022] Then assume latent variables The posterior distribution is approximately a Gaussian distribution. Therefore, the type II maximum likelihood cost function is constructed as follows: ,in This is the corrected observation signal after phase rotation compensation. . It is a diagonal matrix, and Irrelevant For noise variance, The posterior mean of the intermediate variables. The carrier frequency offset estimate can be obtained by minimizing the cost function. ;

[0023] The cost function is minimized using a multi-starting-point variable-step-size Newton iteration method. Within the Newton iteration, a variable-step-size backtracking search is employed. This involves introducing step-size control in the standard Newton direction within the iteration and using the Armijo condition to ensure that the objective function value monotonically decreases during the iteration, thus avoiding divergence due to excessively large step sizes.

[0024] The Armijo condition can be expressed as: In the formula For Newton's direction, The iteration step size is initially set to 1. When the Armijo condition is not satisfied, the iteration step size is adjusted accordingly. Reduce by controlling parameters .

[0025] Simultaneously, in the outer layer, multiple initial points are evenly set within the search range. A variable-step-size Newton iteration is run independently for each initial point to avoid the Newton iteration method getting trapped in local minima due to the initial points. Finally, the estimate with the minimum cost function value is selected as the CFO information. : And the reciprocal of the second derivative at that point is taken as the innovation variance: ;

[0026] Then, the exponential moving average method is used to give the CFO estimate memory, and historical CFO estimates are used. Considered as a priori The new information is considered likely. The posterior mean and variance are given through Bayesian sequential update: , ;

[0027] initial variance Set to a large value to represent no prior information about the CFO. This is the result. To integrate all The variance of the memory-based CFO estimate based on the next iteration information satisfies Strictly monotonically decreasing

[0028] S3.5 Repeat S3.1 to S3.4 until the iteration termination condition is met, and output the signed posterior mean. and posterior variance .

[0029] S4. Convert the symbolic posterior statistic of the memory approximate message passing output into extrinsic information: ;in, This indicates the decoder output symbol. This indicates that the decoder outputs external information. This represents the prior information of the current decoder.

[0030] External information is fed into a soft-input soft-output decoder, which updates the symbol prior probability and feeds it back to the memory approximation message passing module for external iteration.

[0031] S5. After reaching the preset number of external iterations, output the decoded information bits.

[0032] This invention also provides an underwater acoustic OFDM communication system, which uses the aforementioned method for joint estimation of carrier frequency offset and symbols under carrier frequency offset interference to perform joint estimation of carrier frequency offset and symbols. Compared with the prior art, this invention has the following advantages:

[0033] (1) Carrier frequency offset estimation does not rely on any special pilot or training sequence design. It fully utilizes the symbol soft information generated during the memory approximation message passing iteration process for adaptive estimation, and uses the exponential moving average method to give CFO estimation memory structure. This not only improves the spectrum utilization rate, but also enables the algorithm to flexibly adapt to various pilot modes and has good engineering adaptability.

[0034] (2) This invention integrates carrier frequency offset estimation and Turbo equalization into the same iterative framework. It achieves joint optimization of parameters and symbols by alternating updates of memory linear estimation and nonlinear estimation. At the same time, only matrix-vector multiplication is required, without the need for complex matrix inversion. Thus, the computational complexity is significantly reduced while ensuring high estimation accuracy, making it easy to implement in real time.

[0035] (3) Compared with traditional methods, the present invention has significant advantages in frequency offset estimation accuracy, bit error rate performance and system robustness. It is especially suitable for underwater acoustic communication environments with fast time variation and strong Doppler, and can effectively suppress inter-carrier interference and improve overall communication reliability. Attached Figure Description

[0036] Figure 1 This is a framework diagram of the method of the present invention;

[0037] Figure 2 This is a schematic diagram of the experimental deployment;

[0038] Figure 3 A bar chart showing the probability distribution of the original bit error rate;

[0039] Figure 4 A bar chart showing the probability distribution of the bit error rate.

[0040] Figure 5 The graph shows the variation of the number of floating-point calculations in the method of this invention and the comparative method. Detailed Implementation

[0041] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment takes a single-transmitter, single-receiver underwater acoustic OFDM communication system as an example for illustration, but the application scope of the present invention is not limited to this, and can be extended to multiple-input multiple-output systems and other multi-carrier communication scenarios.

[0042] like Figure 1 The steps of this invention are as follows:

[0043] S1. Establish a frequency domain signal receiving model for an underwater acoustic OFDM system. ,in For the frequency domain received signal vector, For normalized carrier frequency offset A given frequency domain cyclic matrix, This is the frequency domain channel impulse response. Transmit symbol vectors in the frequency domain. The noise is additive Gaussian. Initialize the carrier frequency offset estimate. Equal probability with symbolic priors;

[0044] S2. Construct an equivalent observation matrix based on the current carrier frequency offset estimate. ;in Normalized carrier frequency offset The resulting circular matrix, The frequency domain channel impulse response vector. For the reason The constructed diagonal matrix.

[0045] S3. During the inner iteration of the memory approximation message passing algorithm, for the first... Within each iteration, the sub-steps are executed sequentially.

[0046] S3.1, Memory Linear Estimation:

[0047] Using the current carrier frequency offset estimation Calculate the output of the matched filter : in , For matrix Median of eigenvalues For relaxation parameters, We use weights, and then orthogonalize them to obtain: in , The orthogonalization parameter can be obtained from the MAMP state evolution.

[0048] S3.2, Nonlinear Estimation:

[0049] right Perform symbolic MMSE estimation: in for The probability distribution of the signal can be orthogonalized to obtain the estimated transmitted signal for the current iteration. : in Similarly, the orthogonalization parameters are obtained from the MAMP state evolution;

[0050] S3.3, Damping Operation

[0051] Perform a damping operation to improve convergence by weighting the current and historical estimates: ,in The damping vector;

[0052] S3.4, Carrier Frequency Offset Estimation:

[0053] Carrier frequency offset estimation is based on the asymptotic Gaussian error property of the orthogonalized output of MAMP, defining latent variables. Its posterior statistic can be approximated as .

[0054] Then assume latent variables The posterior distribution is approximately a Gaussian distribution. Therefore, the type II maximum likelihood cost function is constructed as follows: ,in This is the corrected observation signal after phase rotation compensation. . It is a diagonal matrix, and Irrelevant For noise variance, The posterior mean of the intermediate variables. The carrier frequency offset estimate can be obtained by minimizing the cost function. ;

[0055] The cost function is minimized using a multi-starting-point variable-step-size Newton iteration method. Within the Newton iteration, a variable-step-size backtracking search is employed. This involves introducing step-size control in the standard Newton direction within the iteration and using the Armijo condition to ensure that the objective function value monotonically decreases during the iteration, thus avoiding divergence due to excessively large step sizes.

[0056] The Armijo condition can be expressed as: In the formula For Newton's direction, The iteration step size is initially set to 1. When the Armijo condition is not satisfied, the iteration step size is adjusted accordingly. Reduce by controlling parameters .

[0057] Simultaneously, in the outer layer, multiple initial points are evenly set within the search range. A variable-step-size Newton iteration is run independently for each initial point to avoid the Newton iteration method getting trapped in local minima due to the initial points. Finally, the estimate with the minimum cost function value is selected as the CFO information. : And the reciprocal of the second derivative at that point is taken as the innovation variance: ;

[0058] Then, the exponential moving average method is used to give the CFO estimate memory, and historical CFO estimates are used. Considered as a priori The new information is considered likely. The posterior mean and variance are given through Bayesian sequential update: , ;

[0059] initial variance Set to a large value to represent no prior information about the CFO. This is the result. To integrate all The variance of the memory-based CFO estimate based on the next iteration information satisfies Strictly monotonically decreasing

[0060] S3.5 Repeat S3.1 to S3.4 until the iteration termination condition is met, and output the signed posterior mean. and posterior variance .

[0061] S4. Convert the symbolic posterior statistic of the memory approximate message passing output into extrinsic information: ;in, This indicates the decoder output symbol. This indicates that the decoder outputs external information. This represents the prior information of the current decoder.

[0062] External information is fed into a soft-input soft-output decoder, which updates the symbol prior probability and feeds it back to the memory approximation message passing module for external iteration.

[0063] S5. After reaching the preset number of external iterations, output the decoded information bits.

[0064] Data processing for the present invention:

[0065] The proposed method was validated using data from the Songhua Lake under-ice mobile underwater acoustic communication test in March 2026. The test deployment was as follows: Figure 2 As shown in Table 1, a remotely operated underwater vehicle (ROV) was used as the mobile transmitting platform under the ice in the experiment. The transmitted signal frequency band was 2-8 kHz, the sound source depth was 15 m, and the ROV moved horizontally underwater. The receiver used a 24-element vertical array with an element spacing of 0.25 m and the uppermost element depth of 15 m. The horizontal distance between the transmitter and receiver was 200 m. The transmitted data was divided into frames of 5 packets, each packet containing 3 OFDM symbols, and each symbol contained 512 subcarriers. The channel coding used recursive systematic convolutional codes. Due to the high signal-to-noise ratio in the ice environment, band-limited Gaussian noise was manually added to reduce the signal-to-noise ratio to approximately 7.2 dB. The experimental parameters are shown in Table 1.

[0066] Table 1 Experimental parameters

[0067]

[0068] Data was received using array elements 1-15, totaling 30 OFDM data frames. Channel estimation results, using array element 6 as an example, show that the channel exhibits typical short-delay spread and strong sparsity characteristics. This invention was compared with VAMP-Turbo without CFO compensation and VAMP-Turbo with independent CFO compensation. The average bit error rate (BER) of all 450 OFDM symbols was statistically analyzed. Table 2 shows the raw BER and coded BER performance of the three methods, thus verifying the performance advantage of this invention.

[0069] Table 2 Average Bit Error Rate

[0070]

[0071] Figure 3 The bar charts show the probability distribution of the original bit error rate for the three methods at different iteration numbers. Figure 4 The corresponding code error rate probabilities are shown in bar charts for comparison. Figure 3 and Figure 4 As can be seen, the coding error rates of all three algorithms are significantly lower than the original error rate, reflecting the gain from the coding and iteration effects. This also indicates that the soft information output by the method of this invention is of higher quality and has better matching with the channel decoder, thus achieving superior coding gain and demonstrating a significant advantage in balanced performance compared to existing methods.

[0072] Other performance parameters were verified using simulations with the same parameters as the experimental data. Figure 5 A comparison of the number of floating-point operations between the VAMP-Turbo algorithm and the equalization algorithm of this invention is shown in the figure for different numbers of subcarriers. As can be seen from the figure, the computational cost of the algorithm of this invention is reduced by approximately two orders of magnitude compared to VAMP-Turbo. These results fully demonstrate the significant advantages of this invention in terms of estimation performance and computational complexity.

[0073] The above description only illustrates preferred embodiments of the present invention and should not be construed as limiting the scope of the claims. Any equivalent structural or procedural modifications made using this specification are included within the patent protection scope of the present invention.

Claims

1. A method for joint estimation of carrier frequency offset and symbol in underwater acoustic OFDM under carrier frequency offset interference, characterized in that, Includes the following steps: S1. Establish the frequency domain received signal model of the underwater acoustic OFDM system and initialize the carrier frequency offset estimate. And symbolic priors are equal; S2. Construct an equivalent observation matrix based on the current carrier frequency offset estimate. ; S3. During the internal iteration of the memory approximation message passing algorithm, memory linear estimation, nonlinear estimation, damping operation and carrier frequency offset estimation are executed sequentially. Among them, the carrier frequency offset estimation is solved by the multi-starting point variable step size Newton iteration method based on the type II maximum likelihood criterion, and the exponential moving average mechanism is used to give the CFO estimation memory. S4. Convert the symbolic posterior statistics output by the memory approximation message passing module into extrinsic information and send it to the soft-input soft-output decoder. The decoder updates the symbolic prior probability and feeds it back to the memory approximation message passing module for extrinsic iteration. S5. After reaching the preset number of external iterations, output the decoded information bits.

2. The method for joint estimation of carrier frequency offset and symbol in underwater acoustic OFDM under carrier frequency offset interference as described in claim 1, characterized in that, The specific method for S1 is as follows: Establish a frequency domain received signal model for the underwater acoustic OFDM system. ,in For the frequency domain received signal vector, For normalized carrier frequency offset A given frequency domain cyclic matrix, This is the frequency domain channel impulse response. Transmit symbol vectors in the frequency domain. Additive Gaussian noise; initialize carrier frequency offset estimate. And symbolic priors are equal.

3. The method for joint estimation of carrier frequency offset and symbol in underwater acoustic OFDM under carrier frequency offset interference as described in claim 2, characterized in that, The equivalent observation matrix is ​​constructed in step S2 as follows: ,in Normalized carrier frequency offset estimator The resulting circular matrix, The frequency domain channel impulse response vector. For the reason The constructed diagonal matrix.

4. The method for joint estimation of carrier frequency offset and symbol in underwater acoustic OFDM under carrier frequency offset interference as described in claim 1, characterized in that, In step S3, during the inner iteration of the memory approximate message passing algorithm, for the first... In each iteration, the sub-steps are executed sequentially: S3.1, Memory Linear Estimation: Using the current carrier frequency offset estimation Calculate the output of the matched filter : ， in , For matrix Median of eigenvalues For relaxation parameters, We use weights, and then orthogonalize them to obtain: ， in , The orthogonalization parameter is obtained from the MAMP state evolution; S3.2, Nonlinear Estimation: right Perform symbolic MMSE estimation: ， in for The probability distribution of the signal can be orthogonalized to obtain the estimated transmitted signal for the current iteration. : ， in , Similarly, the orthogonalization parameters are obtained from the MAMP state evolution; S3.3, Damping Operation Performing damping operations improves convergence for the current estimate. and historical estimates Perform weighted combination: ， in The damping vector; S3.4, Carrier Frequency Offset Estimation: Carrier frequency offset estimation is based on the asymptotic Gaussian error property of the orthogonalized output of MAMP, defining latent variables. Its posterior statistic can be approximated as ; Then let the hidden variable The posterior distribution is approximately a Gaussian distribution. Therefore, the type II maximum likelihood cost function is constructed as follows: ， in This is the corrected observation signal after phase rotation compensation. ; It is a diagonal matrix, and Irrelevant For noise variance, The posterior mean of the intermediate variable; Carrier frequency offset can be estimated by minimizing the cost function. ; When minimizing the cost function, a multi-starting point variable step-size Newton iteration method is used. Inside the Newton iteration, a variable step-size backtracking search is used. That is, by introducing step-size control in the standard Newton direction inside the Newton iteration, the Armijo condition is used to ensure that the objective function value decreases monotonically during the iteration, thus avoiding divergence due to excessive step size. Armijo conditions are expressed as: ， In the formula For Newton's direction, The iteration step size is initially set to 1. When the Armijo condition is not satisfied, the iteration step size is adjusted accordingly. Reduce by controlling parameters ; Simultaneously, in the outer layer, multiple initial points are evenly set within the search range. A variable-step-size Newton iteration is run independently for each initial point to avoid the Newton iteration method getting trapped in local minima due to the initial points. Finally, the estimate with the minimum cost function value is selected as the CFO information. : ， And the reciprocal of the second derivative at that point is taken as the innovation variance: ， Then, the exponential moving average method is used to give the CFO estimate memory, and historical CFO estimates are used. Considered as a priori The new information is considered likely. The posterior mean and variance are given through Bayesian sequential update: ， initial variance Set to a large value to represent no prior information about the CFO; thus, the obtained To integrate all The variance of the memory-based CFO estimate based on the next iteration information satisfies Strictly monotonically decreasing; S3.5 Repeat S3.1 to S3.4 until the iteration termination condition is met, and output the signed posterior mean. and posterior variance .

5. An underwater acoustic OFDM communication system, characterized in that, The carrier frequency offset and symbol joint estimation method under carrier frequency offset interference as described in any one of claims 1 to 4 is used to perform the joint estimation of carrier frequency offset and symbol.

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