An adaptive iterative feedback equalization method for underwater acoustic channel delay-Doppler domain based on maximum ratio combining

Abstract

This invention relates to an adaptive iterative feedback Doppler domain equalization method for underwater acoustic channels based on maximum ratio combining. The purpose of this invention is to address the problem of low reliability and high computational complexity in underwater acoustic communication caused by the Doppler effect in the underwater acoustic channel. This 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 combining process is determined, avoiding the high computational complexity caused by excessive combining terms in equalizers based on maximum ratio combining. Simultaneously, interference between delay branches is considered during 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 itself.

Description

Technical Field

[0001] This invention relates to an adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining. Background Technology

[0002] Underwater acoustic communication is a key technology for realizing marine information exchange. Improving the transmission rate and stability of underwater moving units in highly mobile scenarios is one of the main challenges currently faced. Orthogonal Time-Frequency Space (OTFS) communication technology is considered an effective method to solve the problem of high-reliability communication in high-speed mobile scenarios. OTFS relies on two-dimensional orthogonal transformation, where each time-delay Doppler domain symbol can undergo a complete time-frequency domain channel, resulting in time-frequency diversity gain and robustness to external sudden interference, effectively enhancing communication reliability.

[0003] OTFS detection has attracted much research attention in the field of underwater communication, leading to numerous proposed solutions, such as linear minimum mean square error equalization, deep learning detectors based on convolutional neural networks, and message-passing nonlinear detection methods. However, nonlinear detectors often require higher complexity to achieve better performance. Notably, detection based on Maximum Ratio Combining (MRC) achieves a good trade-off between design complexity and performance. During OTFS modulation, 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 indices, 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 this with an iterative targeted receiver to achieve symbol detection with linear complexity.

[0004] Unlike radio communication, underwater acoustic multicarrier communication (MCC) is a broadband communication method. The severe Doppler effect in the underwater acoustic channel leads to a double spread in the delay-Doppler domain, thus giving the channel matrix in the delay-Doppler domain the characteristics of a full matrix. In the delay-Doppler, the received component of the transmitted symbol comes not only from the multipath components of the real channel but also from the delay components adjacent to the delay branches of the real channel. This interference is related to the Doppler factor; as the Doppler factor increases, the received multipath components of the transmitted symbol increase, thereby increasing the complexity of the MRC scheme. Summary of the Invention

[0005] The purpose of this invention is to address the problem of low reliability and high computational complexity in underwater acoustic communication caused by the Doppler effect in the underwater acoustic channel, 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: Receive the time-domain passband signal using an underwater acoustic communication device, and process the time-domain passband signal to obtain a coarse estimate of the Doppler factor.

[0008] based on The received time-domain passband signal is resampled, and the resampled signal is down-converted to obtain the baseband time-domain signal.

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

[0010] Step 3: Perform 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 and the channel delay τ. p Amplitude h p and Doppler factor α p ;

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

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

[0014] Step 6: Set the threshold δ;

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

[0016] When the initial value of the inter-branch interference depth D = 0 is calculated, the time delay is calculated.

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

[0018] Calculate the current inter-branch interference depth D = D+1.

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

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

[0021] When the absolute value of the difference is less than the threshold, the current inter-branch interference depth D is the optimal inter-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, repeat step 7 until the absolute value of the difference is less than the threshold, and obtain the optimal inter-branch interference depth D. Based on D, obtain the total number of delay branches to be merged Q.

[0023] Step 8: Convert the submatrix K of the time-delay Doppler domain equivalent channel. m,q In the optimal time delay inter-branch interference depth D input adaptive iterative feedback equalizer, the output mapping symbol of the adaptive iterative feedback equalizer is:

[0024] Step 9, for c m Hard decision yields an estimate of the emitted symbol vector;

[0025] Step 10: Substitute the estimated value of the emitted 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 emitted symbol vector.

[0026] The beneficial effects of this invention are as follows:

[0027] This 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 combining process is determined, avoiding the high computational complexity caused by excessive combining terms in equalizers based on maximum ratio combining. Simultaneously, interference between delay branches is considered during the equalization process, further improving the reliability of underwater acoustic communication. In summary, the equalizer achieves optimal detection performance without increasing its complexity.

[0028] Simulation results show that, compared with traditional MRC detectors, the adaptive iterative feedback equalizer based on maximum ratio combining proposed in this 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, enabling more efficient and stable communication. Attached Figure Description

[0029] Figure 1 The diagram shows the equivalent model of the underwater acoustic channel delay in the Doppler domain.

[0030] Figure 2 The figure shows how the variance of different path velocities affects the underwater acoustic channel interference as IDeI depth.

[0031] Figure 3This diagram compares the bit error rate performance of the MRC-based adaptive iterative feedback equalizer and the minimum mean square error equalizer proposed in this invention under the same channel. Detailed Implementation

[0032] Specific Implementation Method 1: The specific process of this implementation method, which is an adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining, is as follows:

[0033] Step 1: Receive the time-domain passband signal using an underwater acoustic communication device, and process the time-domain passband signal to obtain a coarse estimate of the Doppler factor.

[0034] based on The received time-domain passband signal is resampled, and the resampled signal is down-converted to obtain the baseband time-domain signal.

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

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

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

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

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

[0040] Step 6: Set the threshold δ;

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

[0042] When the initial value of the inter-branch interference depth D = 0 is calculated, the time delay is calculated.

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

[0044] Calculate the current inter-branch interference depth D = D+1.

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

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

[0047] When the absolute value of the difference is less than the threshold, the current inter-branch interference depth D is the optimal inter-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, repeat step 7 until the absolute value of the difference is less than the threshold, and obtain the optimal inter-branch interference depth D. Based on D, obtain the total number of delay branches to be merged Q.

[0049] Step 8: Convert the submatrix K of the time-delay Doppler domain equivalent channel. m,q In the optimal time delay inter-branch interference depth D input adaptive iterative feedback equalizer, the output mapping symbol of the adaptive iterative feedback equalizer is:

[0050] Step 9, for c m Hard decision yields the emission symbol vector (x) m+q-q′ The estimated value of );

[0051] Step 10: Substitute the estimated value of the emitted 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 emitted symbol vector.

[0052] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that step 2 discretizes the baseband time-domain signal, and then performs OTFS demodulation on the discretized baseband time-domain signal to obtain the time-delay Doppler domain received signal; the specific process is as follows:

[0053] Step 21: Discretize the baseband time-domain signal;

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

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

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

[0057] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that step 4 involves reconstructing the time-delay Doppler domain equivalent channel matrix based on channel state information; the specific process is as follows:

[0058] Constructing a baseband time-domain signal input-output model

[0059]

[0060] Where s represents the baseband transmitted signal vector;

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

[0062] Represents the baseband noise vector;

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

[0064]

[0065] Where G(i′,i) represents A certain element;

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

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

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

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

[0070] Other steps and parameters are the same as in specific implementation method one or two.

[0071] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the equivalent residual Doppler factor after resampling...

[0072] Where, α p This represents the residual Doppler factor after resampling. This indicates a rough estimate of the Doppler factor (known).

[0073] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0074] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the equivalent channel delay...

[0075] Where, τ p Indicates the channel delay (known).

[0076] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0077] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that, in step 5, the interference level SIR value is calculated based on the time-delay Doppler domain equivalent channel matrix. The specific process is as follows:

[0078] The input-output relationship of the time-delay Doppler domain after OTFS demodulation is expressed as follows:

[0079]

[0080] Among them, set It is the set of delay branches that contribute significantly to the transmitted symbol components in the delay-Doppler domain, and q is an element in the set. It is the set of real channel delay branches l, where D represents the depth of interference between delay branches;

[0081] x m-q This represents the mq-th transmitted symbol vector in the time-delay Doppler domain;

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

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

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

[0085]

[0086] in,

[0087] This represents the discrete time delay response; n represents the time domain index, n = 0:N-1, where 0:N-1 represents 0 to N-1, and N represents the number of Doppler domain symbols; M represents the number of subcarriers, m represents the subcarrier index, where m = 0:M-1, where 0:M-1 represents 0 to M-1, and q represents the time 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,qThe submatrix representing the time-delay Doppler domain equivalent channel, v m,q (0) represents the response of the 0th Doppler symbol, v m,q (1) represents the response to the first Doppler symbol, v m,q (2) represents the response to the second Doppler symbol, v m,q (N-1) represents the response of the (N-1)th Doppler symbol, v m,q (N-2) represents the response of the (N-2)th Doppler symbol;

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

[0091] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0092] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that, in step 52, the submatrix K based on the time-delay Doppler domain equivalent channel... m,q Calculate the signal interference ratio (SIR) value. The specific process is as follows:

[0093] Baseband transmitted symbols in Q = |Ω| received symbol vectors y m There are signal components in it;

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

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

[0096] l represents the actual channel delay branch.

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

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

[0099] Submatrix K based on the time-delay Doppler domain equivalent channel m,q Calculate the Signal Interference Ratio (SIR) value. Expressed as:

[0100]

[0101] in, The SIR (Signal Interference Ratio) value represents the level of interference; E represents the expected value. This represents the square of the Frobenius norm of the matrix.

[0102] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0103] Specific Implementation Method Eight: This implementation method differs from one of Specific Implementation Methods One to Seven in that, in step 8, the submatrix K of the time-delay Doppler domain equivalent channel is... m,q In the optimal time-delay inter-branch interference depth D input adaptive iterative feedback equalizer, the output of the adaptive iterative feedback equalizer is mapped to a symbol; the specific process is as follows:

[0104] Step 81: Submatrix K based on the time-delay Doppler domain equivalent channel m,q And the optimal delay inter-branch interference depth D, calculated to eliminate other transmitted symbol vectors After interference, the y received at the delay index m+q m+q In the vector x m Channel-damaged signal components

[0105] Step 82, based on Get the mapping symbol c m .

[0106] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0107] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that, in step 81, the submatrix K based on the time-delay Doppler domain equivalent channel... m,q And the optimal delay inter-branch interference depth D, calculated to eliminate other transmitted symbol vectors After interference, the y received at the delay index m+q m+q In the vector x m Channel-damaged signal components

[0108] The expression is:

[0109]

[0110] in,

[0111] y m+q This represents the (m+q)th received symbol vector in the delay-Doppler domain;

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

[0113] x m+q-q′ This represents the m+qq′th transmitted symbol in the time-delayed Doppler domain.

[0114] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0115] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that step 82 is based on... Get the mapping symbol c m The expression is:

[0116]

[0117] in,

[0118]

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

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

[0121] K m+q,q This represents a submatrix representing the time-delay Doppler domain equivalent channel.

[0122] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0123] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. An adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining, characterized in that: The specific process of the method is as follows: Step 1: Receive the time-domain passband signal using an underwater acoustic communication device, and process the time-domain passband signal to obtain a coarse estimate of the Doppler factor. based on The received time-domain passband signal is resampled, and the resampled signal is down-converted to obtain the baseband time-domain signal. Step 2: Discretize the baseband time domain signal, and perform OTFS demodulation on the discretized baseband time domain signal to obtain the time-delay Doppler domain received signal; Step 3: Perform channel estimation on the baseband delay Doppler domain received signal to obtain channel state information; Channel state information includes the number of paths P and the channel delay τ. p Amplitude h p and Doppler factor α p ; Step 4: Reconstruct the time-delay Doppler domain equivalent channel matrix based on channel state information; Step 5: Calculate the SIR value of interference level based on the time-delay Doppler domain equivalent channel matrix. Step 6: Set the threshold δ; Set the initial value of the interference depth between delay branches to D = 0; When the initial value of the inter-branch interference depth D = 0 is calculated, the time delay is calculated. Step 7: Set the current inter-branch interference depth D = D + 1; Calculate the current inter-branch interference depth D = D+1. Calculate the current inter-branch interference depth D and the corresponding inter-branch interference depth D of the previous time delay. The absolute value of the difference; Compare the absolute value of the difference with the threshold δ; When the absolute value of the difference is less than the threshold, the current inter-branch interference depth D is the optimal inter-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, repeat step 7 until the absolute value of the difference is less than the threshold, and obtain the optimal inter-branch interference depth D. Based on D, obtain the total number of delay branches to be merged Q. Step 8: Convert the submatrix K of the time-delay Doppler domain equivalent channel. m,q In the optimal time-delay inter-branch interference depth D input adaptive iterative feedback equalizer, the output mapping symbol of the adaptive iterative feedback equalizer is... c m ; Step 9, for c m Hard decision yields an estimate of the emitted symbol vector; Step 10: Substitute the estimated value of the emitted 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 emitted symbol vector.

2. The adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining according to claim 1, characterized 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 the time-delay Doppler domain received signal. The specific process is as follows: Step 21: Discretize the baseband time-domain signal; Step 22: Perform a one-dimensional transformation on the discretized baseband time-domain signal to obtain the time-frequency domain; Step 23: Perform a two-dimensional transformation on the time-frequency domain obtained in step 22 to obtain the baseband time-delay Doppler domain received signal.

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

4. The adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining according to claim 3, characterized in that: The resampled equivalent residual Doppler factor Where, α p This represents the residual Doppler factor after resampling. This indicates a rough estimate of the Doppler factor.

5. The adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining according to claim 4, characterized in that: The equivalent channel delay Where, τ p Indicates channel delay.

6. The adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining according to claim 5, characterized in that: In step 5, the interference level SIR value is calculated based on the time-delay Doppler domain equivalent channel matrix. The specific process is as follows: Step 51: Submatrix K of the time-domain baseband equivalent channel G and the time-delay Doppler domain equivalent channel m,q The relationship is specifically represented as follows: in, This represents the discrete time delay response; n represents the time domain index, n = 0:N-1, where 0:N-1 represents 0 to N-1, and N represents the number of Doppler domain symbols; M represents the number of subcarriers, m represents the subcarrier index, where m = 0:M-1, where 0:M-1 represents 0 to M-1, and q represents the time delay branch index; v m,q (k) represents the Doppler response, k represents the Doppler domain index, k = 0:N-1; K m,q The submatrix representing the time-delay Doppler domain equivalent channel, v m,q (0) represents the response of the 0th Doppler symbol, v m,q (1) represents the response to the first Doppler symbol, v m,q (2) represents the response to the second Doppler symbol, v m,q (N-1) represents the response of the (N-1)th Doppler symbol, v m,q (N-2) represents the response of the (N-2)th Doppler symbol; Step 52: Submatrix K based on the time-delay Doppler domain equivalent channel m,q Calculate the SIR value of interference level 7. The adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining according to claim 6, characterized in that: In step 52, the submatrix K based on the time-delay Doppler domain equivalent channel... m,q Calculate the SIR value of interference level The specific process is as follows: Baseband transmitted symbols in Q = |Ω| received symbol vectors y m There are signal components in it; |Ω| represents the number of elements in set Ω; gather It is the set of delay branches to be merged; l represents the actual channel delay branch. It is the set of actual channel delay branches l; D represents the depth of interference between delay branches; Submatrix K based on the time-delay Doppler domain equivalent channel m,q Calculate the SIR value of interference level Expressed as: in, The SIR value represents the level of interference; E represents the expected value. This represents the square of the Frobenius norm of the matrix.

8. The adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining according to claim 7, characterized in that: In step 8, the submatrix K of the time-delay Doppler domain equivalent channel is... m,q In the optimal time-delay inter-branch interference depth D input adaptive iterative feedback equalizer, the output of the adaptive iterative feedback equalizer is mapped to a symbol; the specific process is as follows: Step 81: Submatrix K based on the time-delay Doppler domain equivalent channel m,q And the optimal delay inter-branch interference depth D, calculated to eliminate other transmitted symbol vectors After interference, the y received at the delay index m+q m+q In the vector x m Channel-damaged signal components Step 82, based on Get the mapping symbol c m .

9. The adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining according to claim 8, characterized in that: In step 81, the submatrix K based on the time-delay Doppler domain equivalent channel... m,q And the optimal delay inter-branch interference depth D, calculated to eliminate other transmitted symbol vectors After interference, the y received at the delay index m+q m+q In the vector x m Channel-damaged signal components The expression is: in, y m+q This represents the (m+q)th received symbol vector in the delay-Doppler domain; K m+q,q′ The submatrix representing the time-delay Doppler domain equivalent channel; x m+q-q′ This represents the m+qq′-th transmitted symbol vector in the time-delayed Doppler domain.

10. The adaptive iterative feedback underwater acoustic channel delay Doppler domain equalization method based on maximum ratio combining 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 Represents the mapping symbol; D m Indicates an intermediate variable; g m Indicates intermediate variables; K represents m+q,q The conjugate transpose of; K m+q,q This represents a submatrix representing the time-delay Doppler domain equivalent channel.

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