Adaptive iterative feedback underwater acoustic channel time delay Doppler domain equalization method based on maximum ratio combination

Abstract

The invention discloses an adaptive iterative feedback underwater acoustic channel time delay Doppler domain equalization method based on maximum ratio combination, and relates to the adaptive iterative feedback underwater acoustic channel time delay Doppler domain equalization method based on maximum ratio combination. The objective of the invention is to solve the problems of low reliability and high calculation complexity of underwater acoustic communication caused by the Doppler effect of an underwater acoustic channel. The invention provides a low-complexity linear equalizer suitable for underwater OTFS modulation. By adaptively adjusting the interference depth between the delay branches, the total number of the delay branches in the maximum-ratio merging process is determined, and the problem of high calculation complexity caused by excessive merging items of an equalizer based on maximum-ratio merging is avoided. Meanwhile, interference between time delay branches is considered in the balancing process, and the reliability of underwater acoustic communication is further improved. In conclusion, the equalizer realizes the optimal detection performance on the premise of not increasing the complexity of the equalizer.

Description

Technical Field

[0001] The invention relates to a time delay Doppler domain equalization method of an underwater acoustic channel based on a maximum ratio combining adaptive iterative feedback. Background Art

[0002] Underwater acoustic communication is a key technology for realizing ocean information interaction. Improving the transmission rate and stability of underwater motion units in high-mobility scenarios is one of the main challenges currently faced. Orthogonal Time-Frequency Space (OTFS) communication technology is considered to be an effective way to solve high-reliability communication in high-speed mobile scenarios. OTFS relies on two-dimensional orthogonal transformation. Each delay-Doppler domain symbol can experience the complete time-frequency domain channel, bringing time-frequency diversity gain, which is robust to external burst interference and effectively enhances communication reliability.

[0003] OTFS detection has attracted much research attention in the field of underwater communications, and many solutions have been proposed, such as linear minimum mean square error equalization, deep learning detector based on convolutional neural network, and message passing nonlinear detection method. However, nonlinear detectors often require higher complexity in pursuit of better performance. It is worth mentioning that detection based on Maximum Ratio Combining (MRC) achieves a good compromise between design complexity and performance. In the OTFS modulation process, for any information symbol, the received components in all delay-Doppler domain diversity branches can be separated and coherently combined. The basic principle of the MRC detector is to first group the delay-Doppler domain grid symbols into vectors according to their delay indexes, then extract the received multipath components of the transmitted symbols in the delay-Doppler grid, perform maximum ratio combining on the extracted components, and combine the iterative targeted receiver to achieve linear complexity symbol detection.

[0004] Unlike radio communication, underwater acoustic multi-carrier communication is a broadband communication. The severe Doppler effect of the underwater acoustic channel will lead to double expansion of the delay Doppler domain. Therefore, the delay Doppler domain channel matrix has the characteristics of a full matrix. The received components of the transmitted symbols in the delay Doppler are not only the multipath components from the real channel, but also the delay components adjacent to the delay branch of the real channel. This interference is related to the Doppler factor. As the Doppler factor increases, the received multipath components of the transmitted symbols increase, which leads to a higher complexity of the MRC scheme. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the Doppler effect in the underwater acoustic channel leads to low reliability of underwater acoustic communication and high computational complexity, and to propose an adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining.

[0006] The specific process of an adaptive iterative feedback underwater acoustic channel delay-Doppler domain equalization method based on maximum ratio combining is as follows:

[0007] Step 1: The time domain passband signal is received by the underwater acoustic communication device, and the time domain passband signal is processed to obtain a rough estimate of the Doppler factor.

[0008] based on Resampling the received time domain passband signal, and performing a down-conversion operation on the resampled signal to obtain a baseband time domain signal;

[0009] Step 2: discretize the baseband time domain signal, perform OTFS demodulation on the discretized baseband time domain signal, and obtain a delay Doppler domain received signal;

[0010] Step 3: performing channel estimation on the baseband delay-Doppler domain received signal to obtain channel state information;

[0011] Channel state information includes the number of paths P, channel delay τ p , amplitude h p and Doppler factor α p ;

[0012] Step 4: reconstruct the delay-Doppler domain equivalent channel matrix based on the channel state information;

[0013] Step 5: Calculate the interference level SIR value based on the delay-Doppler domain equivalent channel matrix

[0014] Step 6: Set the threshold δ;

[0015] Let the initial value of the interference depth between delay branches be D=0;

[0016] Calculate the initial value of the delay branch interference depth when D = 0

[0017] Step 7: Set the current delay branch interference depth D=D+1;

[0018] Calculate the current delay branch interference depth D = D + 1

[0019] Calculate the current delay branch interference depth D and the previous delay branch interference depth D corresponding to The absolute value of the difference;

[0020] Compare the absolute value of the difference with a threshold δ;

[0021] When the absolute value of the difference is less than the threshold, the current delay branch interference depth D is the optimal delay branch interference depth D, and the total number of delay branches to be merged Q is obtained based on D;

[0022] When the absolute value of the difference is greater than or equal to the threshold, step 7 is repeated until the absolute value of the difference is less than the threshold, and the optimal delay branch interference depth D is obtained, and the total number of delay branches to be merged Q is obtained based on D;

[0023] Step 8: Substituting the submatrix K of the delay-Doppler domain equivalent channel m,q , the optimal delay inter-branch interference depth D is input into the adaptive iterative feedback equalizer, and the adaptive iterative feedback equalizer outputs mapping symbols;

[0024] Step 9: m The hard decision obtains the estimated value of the transmitted symbol vector;

[0025] Step 10: Substitute the estimated value of the transmitted symbol vector into step 8, and repeat steps 8 and 9 until the maximum number of iterations is reached to obtain the estimated value of the optimal transmitted symbol vector.

[0026] The beneficial effects of the present invention are:

[0027] The present invention proposes a low-complexity linear equalizer suitable for underwater OTFS modulation. By adaptively adjusting the interference depth between delay branches, the total number of delay branches in the maximum ratio merging process is determined, thereby avoiding the problem of high computational complexity of the equalizer based on maximum ratio merging due to too many merging items. At the same time, the interference between delay branches is taken into account in the equalization process, further improving the reliability of underwater acoustic communication. In summary, the equalizer achieves optimal detection performance without increasing the complexity of the equalizer.

[0028] The simulation results show that compared with the traditional MRC detector, the adaptive iterative feedback equalizer based on maximum ratio combining proposed in the present invention achieves higher estimation accuracy and lower computational complexity under the same channel. This achievement is of great significance to the development of underwater mobile communication field, and the present invention can achieve more efficient and stable communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is the equivalent model diagram of the underwater acoustic channel in the delay-Doppler domain;

[0030] Figure 2 This is a diagram showing the variation of the interference of different path velocity variances on the underwater acoustic channel with the depth of IDeI;

[0031] Figure 3This is a comparison chart of the bit error rate performance of the MRC-based adaptive iterative feedback equalizer and the minimum mean square error equalizer proposed in the present invention, and the MRC-based iterative feedback equalizer under the same channel. DETAILED DESCRIPTION

[0032] Specific implementation method 1: This implementation method is an adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining. The specific process is as follows:

[0033] Step 1: The time domain passband signal is received by the underwater acoustic communication device, and the time domain passband signal is processed to obtain a rough estimate of the Doppler factor.

[0034] based on Resampling the received time domain passband signal, and performing a down-conversion operation on the resampled signal to obtain a baseband time domain signal;

[0035] Step 2: discretize the baseband time domain signal, perform OTFS demodulation on the discretized baseband time domain signal, and obtain a delay Doppler domain received signal;

[0036] Step 3: Perform channel estimation (minimum linear error) on the baseband delay-Doppler domain received signal to obtain channel state information;

[0037] Channel state information includes the number of paths P, channel delay τ p , amplitude h p and Doppler factor α p ;

[0038] Step 4: reconstruct the delay-Doppler domain equivalent channel matrix based on the channel state information;

[0039] Step 5: Calculate the interference level SIR value based on the delay-Doppler domain equivalent channel matrix

[0040] Step 6: Set the threshold δ;

[0041] Let the initial value of the interference depth between delay branches be D=0;

[0042] Calculate the initial value of the delay branch interference depth when D = 0

[0043] Step 7: Set the current delay branch interference depth D=D+1;

[0044] Calculate the current delay branch interference depth D = D + 1

[0045] Calculate the current delay branch interference depth D and the previous delay branch interference depth D corresponding to The absolute value of the difference;

[0046] Compare the absolute value of the difference with a threshold δ;

[0047] When the absolute value of the difference is less than the threshold, the current delay branch interference depth D is the optimal delay branch interference depth D, and the total number of delay branches to be merged Q is obtained based on D;

[0048] When the absolute value of the difference is greater than or equal to the threshold, step 7 is repeated until the absolute value of the difference is less than the threshold, and the optimal delay branch interference depth D is obtained, and the total number of delay branches to be merged Q is obtained based on D;

[0049] Step 8: Substituting the submatrix K of the delay-Doppler domain equivalent channel m,q , the optimal delay inter-branch interference depth D is input into the adaptive iterative feedback equalizer, and the adaptive iterative feedback equalizer outputs mapping symbols;

[0050] Step 9: m The hard decision gets the transmitted symbol vector (x m+q-q′ )

[0051] Step 10: Substitute the estimated value of the transmitted symbol vector into step 8, and repeat steps 8 and 9 until the maximum number of iterations is reached to obtain the estimated value of the optimal transmitted symbol vector.

[0052] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that in step 2, the baseband time domain signal is discretized, and the discretized baseband time domain signal is demodulated by OTFS to obtain a delay Doppler domain received signal; the specific process is:

[0053] Step 21, discretizing the baseband time domain signal;

[0054] Step 22, performing a one-dimensional transformation on the discretized baseband time domain signal to obtain a time-frequency domain;

[0055] Step 23: Perform a two-dimensional transformation on the time-frequency domain obtained in step 21 to obtain a baseband delay-Doppler domain received signal.

[0056] The other steps and parameters are the same as those in the first embodiment.

[0057] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that in step 4, the delay-Doppler domain equivalent channel matrix is ​​reconstructed based on the channel state information; the specific process is:

[0058] Constructing baseband time domain signal input and output model

[0059]

[0060] Where, s represents the baseband transmission signal vector;

[0061] r represents the baseband delay-Doppler domain received signal vector obtained in step 2;

[0062] represents the baseband noise vector;

[0063] represents the delay-Doppler domain equivalent channel matrix;

[0064]

[0065] Among them, G(i′,i) represents An element in

[0066] Discrete time series i′=0,1,....,L-1,L=[MN+Bτ max ] is the maximum number of samples of the delay scale channel output signal; i represents the discrete time index of the baseband transmission signal, M represents the number of subcarriers, N represents the number of Doppler domain symbols, B represents the communication bandwidth, τ max Indicates the maximum delay spread of the channel; represents a plural set;

[0067] fc represents the center frequency of the transmitted signal, h p represents the amplitude, P represents the number of paths, p represents the number of the pth path, c represents the underwater sound propagation speed, j represents the imaginary unit, j 2 = -1;

[0068] b p is the equivalent residual Doppler factor after resampling;

[0069] τ′ p is the equivalent channel delay.

[0070] The other steps and parameters are the same as those in the first or second embodiment.

[0071] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the equivalent residual Doppler factor after resampling is

[0072] Among them, α p represents the residual Doppler factor after resampling, Represents a rough estimate of the Doppler factor (known).

[0073] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0074] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the equivalent channel delay

[0075] Among them, τ p represents the channel delay (known).

[0076] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0077] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the interference level SIR value is calculated based on the delay-Doppler domain equivalent channel matrix in step 5. The specific process is:

[0078] The relationship between the input and output of the delay-Doppler domain after OTFS demodulation is expressed as

[0079]

[0080] Among them, the collection is the set of delayed branches with large contribution from the transmitted symbol component in the delay Doppler domain, q is an element in the set, is the set of real channel delay branches l, and D represents the depth of interference between delay branches;

[0081] x m-q represents the mqth transmitted symbol vector in the delay-Doppler domain;

[0082] y m represents the mth received symbol vector in the delay-Doppler domain;

[0083] K m,q The submatrix representing the delay-Doppler domain equivalent channel (unknown);

[0084] Step 51: Submatrix K of time domain baseband equivalent channel G and delay Doppler domain equivalent channel m,q The relationship is specifically expressed as:

[0085]

[0086] in,

[0087] Represents a discrete time delay response; n represents a time domain index, n=0:N-1, 0:N-1 represents 0 to N-1, N represents the number of Doppler domain symbols; M represents the number of subcarriers, m represents the subcarrier index, m=0:M-1, 0:M-1 represents 0 to M-1, q represents a delay branch index;

[0088] v m,q (k) represents the Doppler response, k represents the Doppler domain index, k=0:N-1;

[0089] K m,qrepresents the submatrix of the delay-Doppler domain equivalent channel, v m,q (0) represents the response of the 0th Doppler symbol, v m,q (1) represents the response of the first Doppler symbol, v m,q (2) represents the response of the second Doppler symbol, v m,q (N-1) represents the response of the N-1th Doppler symbol, v m,q (N-2) represents the response of the N-2th Doppler symbol;

[0090] Step 52: Submatrix K based on the delay-Doppler domain equivalent channel m,q Calculate the interference level SIR (Signal Interference Ratio, SIR) value

[0091] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0092] Specific implementation method 7: This implementation method is different from any one of the specific implementation methods 1 to 6 in that the submatrix K based on the delay-Doppler domain equivalent channel in step 52 m,q Calculate the interference level SIR (Signal Interference Ratio, SIR) value The specific process is:

[0093] Baseband transmit symbol in Q = |Ω| received symbol vector y m There is a signal component in

[0094] |Ω| represents the number of elements in the set Ω;

[0095] gather is the set of delayed branches to be merged;

[0096] l represents the real channel delay branch

[0097] is the set of real channel delay branches l;

[0098] D represents the depth of interference between delay branches;

[0099] Submatrix K based on the equivalent channel in delay-Doppler domain m,q Calculate the interference level SIR (Signal Interference Ratio, SIR) value It is expressed as:

[0100]

[0101] in, Indicates the interference level SIR (Signal Interference Ratio, SIR) value; E means expectation; Represents the square of the matrix Frobenius norm.

[0102] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0103] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that in step 8, the submatrix K of the delay-Doppler domain equivalent channel is m,q , the optimal delay branch interference depth D is input into the adaptive iterative feedback equalizer, and the adaptive iterative feedback equalizer outputs the mapping symbol; the specific process is:

[0104] Step 81: Submatrix K based on the delay-Doppler domain equivalent channel m,q and the optimal delay branch interference depth D, calculated by eliminating other transmission symbol vectors After the interference, the received y at the delay index m+q m+q x in vector m The channel-impaired signal component

[0105] Step 82: Based on Get the mapping symbol c m .

[0106] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0107] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that the submatrix K based on the delay-Doppler domain equivalent channel in step 81 m,q and the optimal delay branch interference depth D, calculated by eliminating other transmission symbol vectors After the interference, the received y at the delay index m+q m+q x in vector m The channel-impaired signal component

[0108] The expression is:

[0109]

[0110] in,

[0111] y m+q represents the m+qth received symbol vector in the delay-Doppler domain;

[0112] K m+q,q′ The submatrix representing the delay-Doppler domain equivalent channel;

[0113] x m+q-q′ Represents the direction of the m+qq′th transmitted symbol in the delay-Doppler domain.

[0114] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0115] Specific implementation method 10: This implementation method is different from the specific implementation methods 1 to 9 in that the step 82 is based on Get the mapping symbol c m ; The expression is:

[0116]

[0117] in,

[0118]

[0119] Among them, c m Indicates mapping symbol; D m represents an intermediate variable; g m represents an intermediate variable;

[0120] K m+q,q The conjugate transpose of ;

[0121] K m+q,q The submatrix representing the delay-Doppler domain equivalent channel.

[0122] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0123] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for delay-Doppler domain equalization of underwater acoustic channels based on adaptive iterative feedback based on maximum ratio combining, characterized in that: The specific process of the method is: Step 1: The time domain passband signal is received by the underwater acoustic communication device, and the time domain passband signal is processed to obtain a rough estimate of the Doppler factor. based on Resampling the received time domain passband signal, and performing a down-conversion operation on the resampled signal to obtain a baseband time domain signal; Step 2: discretize the baseband time domain signal, perform OTFS demodulation on the discretized baseband time domain signal, and obtain a delay Doppler domain received signal; Step 3: performing channel estimation on the baseband delay-Doppler domain received signal to obtain channel state information; Channel state information includes the number of paths P, channel delay τ p , amplitude h p and Doppler factor α p ; Step 4: reconstruct the delay-Doppler domain equivalent channel matrix based on the channel state information; Step 5: Calculate the interference level SIR value based on the delay-Doppler domain equivalent channel matrix Step 6: Set the threshold δ; Let the initial value of the interference depth between delay branches be D=0; Calculate the initial value of the delay branch interference depth when D = 0 Step 7: Set the current delay branch interference depth D=D+1; Calculate the current delay branch interference depth D = D + 1 Calculate the current delay branch interference depth D and the previous delay branch interference depth D corresponding to The absolute value of the difference; Compare the absolute value of the difference with a threshold δ; When the absolute value of the difference is less than the threshold, the current delay branch interference depth D is the optimal delay branch interference depth D, and the total number of delay branches to be merged Q is obtained based on D; When the absolute value of the difference is greater than or equal to the threshold, step 7 is repeated until the absolute value of the difference is less than the threshold, and the optimal delay branch interference depth D is obtained, and the total number of delay branches to be merged Q is obtained based on D; Step 8: Substituting the submatrix K of the delay-Doppler domain equivalent channel m,q , the optimal delay inter-branch interference depth D is input into the adaptive iterative feedback equalizer, and the adaptive iterative feedback equalizer outputs mapping symbols; Step 9: m The hard decision obtains the estimated value of the transmitted symbol vector; Step 10: Substitute the estimated value of the transmitted symbol vector into step 8, and repeat steps 8 and 9 until the maximum number of iterations is reached to obtain the estimated value of the optimal transmitted symbol vector.

2. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 1 is characterized in that: In the step 2, the baseband time domain signal is discretized, and the discretized baseband time domain signal is demodulated by OTFS to obtain a delay Doppler domain received signal; The specific process is: Step 21, discretizing the baseband time domain signal; Step 22, performing a one-dimensional transformation on the discretized baseband time domain signal to obtain a time-frequency domain; Step 23: Perform a two-dimensional transformation on the time-frequency domain obtained in step 21 to obtain a baseband delay-Doppler domain received signal.

3. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 2 is characterized in that: In step 4, the delay-Doppler domain equivalent channel matrix is ​​reconstructed based on the channel state information; the specific process is: Among them, G(i′,i) represents An element in Discrete time series i′=0,1,....,L-1,L=[MN+Bτ max ] is the maximum number of samples of the delay scale channel output signal; i represents the discrete time index of the baseband transmission signal, M represents the number of subcarriers, N represents the number of Doppler domain symbols, B represents the communication bandwidth, τ max Indicates the maximum delay spread of the channel; represents a plural set; f c Indicates the center frequency of the transmitted signal, h p represents the amplitude, P represents the number of paths, p represents the number of the pth path, c represents the underwater sound propagation speed, j represents the imaginary unit, j 2 = -1; b p is the equivalent residual Doppler factor after resampling; τ′ p is the equivalent channel delay.

4. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 3 is characterized in that: The equivalent residual Doppler factor after resampling Among them, α p represents the residual Doppler factor after resampling, Represents a rough estimate of the Doppler factor.

5. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 4 is characterized in that: The equivalent channel delay Among them, τ p Indicates the channel delay.

6. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 5 is characterized by: In step 5, the interference level SIR value is calculated based on the delay-Doppler domain equivalent channel matrix The specific process is: Step 51: Submatrix K of time domain baseband equivalent channel G and delay Doppler domain equivalent channel m,q The relationship is specifically expressed as: in, Represents a discrete time delay response; n represents a time domain index, n=0:N-1, 0:N-1 represents 0 to N-1, N represents the number of Doppler domain symbols; M represents the number of subcarriers, m represents the subcarrier index, m=0:M-1, 0:M-1 represents 0 to M-1, q represents a delay branch index; v m,q (k) represents the Doppler response, k represents the Doppler domain index, k=0:N-1; K m,q represents the submatrix of the delay-Doppler domain equivalent channel, v m,q (0) represents the response of the 0th Doppler symbol, v m,q (1) represents the response of the first Doppler symbol, v m,q (2) represents the response of the second Doppler symbol, v m,q (N-1) represents the response of the N-1th Doppler symbol, v m,q (N-2) represents the response of the N-2th Doppler symbol; Step 52: Submatrix K based on the delay-Doppler domain equivalent channel m,q Calculate the interference level SIR value 7. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 6 is characterized in that: The sub-matrix K based on the delay-Doppler domain equivalent channel in step 52 m,q Calculate the interference level SIR value The specific process is: Baseband transmit symbol in Q = |Ω| received symbol vector y m There is a signal component in Ω| represents the number of elements in the set Ω; gather is the set of delayed branches to be merged; l represents the real channel delay branch is the set of real channel delay branches l; D represents the depth of interference between delay branches; Submatrix K based on the equivalent channel in delay-Doppler domain m,q Calculate the interference level SIR value It is expressed as: in, Indicates the SIR value of interference degree; E indicates expectation; Represents the square of the matrix Frobenius norm.

8. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 7 is characterized in that: In step 8, the submatrix K of the delay-Doppler domain equivalent channel is m,q , the optimal delay branch interference depth D is input into the adaptive iterative feedback equalizer, and the adaptive iterative feedback equalizer outputs the mapping symbol; the specific process is: Step 81: Submatrix K based on the delay-Doppler domain equivalent channel m,q and the optimal delay branch interference depth D, calculated by eliminating other transmission symbol vectors After the interference of k≠m, y received at the delay index m+q m+q x in vector m The channel-impaired signal component Step 82: Based on Get the mapping symbol c m .

9. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 8 is characterized in that: The submatrix K based on the delay-Doppler domain equivalent channel in step 81 is m,q and the optimal delay branch interference depth D, calculated by eliminating other transmission symbol vectors After the interference of k≠m, y received at the delay index m+q m+q x in vector m The channel-impaired signal component The expression is: in, y m+q represents the m+qth received symbol vector in the delay-Doppler domain; K m+q,q′ The submatrix representing the delay-Doppler domain equivalent channel; x m+q-q′ represents the m+qq′th transmitted symbol vector in the delay-Doppler domain.

10. The method for delay-Doppler domain equalization of underwater acoustic channels based on maximum ratio combining and adaptive iterative feedback according to claim 9, characterized in that: In step 82, based on Get the mapping symbol c m ; The expression is: in, Among them, c m Indicates mapping symbol; D m represents an intermediate variable; g m represents an intermediate variable; K m+q,q The conjugate transpose of ; K m+q,q The submatrix representing the delay-Doppler domain equivalent channel.

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