Underwater IDMA iterative multi-user detection method and system based on polarization coding

Abstract

The invention discloses an underwater IDMA iterative multi-user detection method and system based on polarization coding. The method comprises the following steps: a transmitting end performs polarization coding, repeated spread spectrum coding and interleaving processing on a bit sequence of each user, and transmits the bit sequence to a receiving end; a receiving end carries out initial channel estimation based on the training sequence and a continuous interference elimination algorithm, inputs an estimated channel and an original received signal into a basic signal estimator, and carries out chip-by-chip multi-user detection to obtain log-likelihood ratio information of each user; the external information is subjected to de-interleaving and de-spread spectrum processing and then serves as prior information to be input into a polarization code decoder for channel decoding, a decoding result and decoding soft information are output, and the decoding result is used for reconstructing and eliminating multi-access interference so as to update channel estimation. The polarization code and the IDMA structure are combined, and channel estimation and user detection are iteratively optimized, so that the anti-interference capability and the multi-user detection performance are effectively improved, the communication reliability is enhanced, and meanwhile, a higher data rate can be supported.

Description

Technical Field

[0001] The present invention relates to an underwater IDMA iterative multi-user detection method and system based on polarization coding with high communication rate and robust communication performance, belonging to the technical field of underwater acoustic communication. Background Art

[0002] Reliable and efficient multi-user underwater acoustic communication is a key supporting technology for underwater acoustic sensor networks. However, the limited bandwidth, severe multipath delay, and strong multi-access interference of underwater acoustic channels pose significant challenges to multi-user underwater acoustic communication systems. Code Division Multiple Access (CDMA) technology is widely used in multi-user underwater acoustic communication because it can mitigate inter-code interference and multiple access interference to a certain extent by utilizing direct sequence spread spectrum gain. However, due to the limitation of spread spectrum gain, CDMA systems generally suffer from low data rates, and the system complexity increases exponentially with the number of users.

[0003] As a new multiple access scheme, interleave division multiple access (IDMA) offers higher spectral efficiency, stronger resistance to multiple access interference (MAI), and computational complexity that is independent of the number of users. Therefore, it has gradually become a hot research topic in underwater communications. However, existing underwater IDMA methods are mostly based on ideal channel assumptions, such as high signal-to-noise ratio or uniform channels between users. When faced with strong interference, traditional IDMA systems typically rely on long repetitive spreading codes to maintain decoding performance, resulting in a significant decrease in communication rate and limiting their practicality. Previous studies have proposed interference suppression methods based on successive interference cancellation in single-carrier multi-user communication systems. Their main goal is to obtain the desired user's signal through interference reconstruction and cancellation for subsequent detection. However, because IDMA requires simultaneous utilization of information from all users for joint multi-user detection, these methods are difficult to directly apply to IDMA systems. In IDMA, iterative interference cancellation is only used to improve channel estimation accuracy and is not a means of user separation and detection.

[0004] In order to achieve robust decoding performance in harsh environments such as low signal-to-noise ratios, introducing advanced channel coding technologies into underwater acoustic communication systems has become a new research direction. Polar codes are currently the only channel coding method that can theoretically reach the Shannon limit and have been widely used in wireless communications. However, their research in underwater acoustic communications is still in its infancy. Related studies have shown that polar codes exhibit better performance in underwater acoustic channels than traditional convolutional codes, Turbo codes, and LDPC codes, demonstrating high application potential. However, existing polar code designs often rely on Bhattacharyya parameters or Monte Carlo simulation to construct subchannels. These methods are difficult to adapt to complex and changing underwater acoustic channels and rely on a large number of channel measurements, which limits their practical application. Summary of the Invention

[0005] The present invention proposes an underwater IDMA iterative multi-user detection method and system based on polarization coding. This method introduces polarization coding into the underwater IDMA communication structure for the first time. Combined with the continuous interference cancellation algorithm, it achieves accurate estimation of each user channel under the soft RAKE receiving structure, thereby realizing robust multi-user information detection in complex multiple access interference and low signal-to-noise ratio environments.

[0006] In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical solutions:

[0007] In a first aspect, an underwater IDMA iterative multi-user detection method based on polarization coding is performed at a receiving end, comprising the following steps:

[0008] (1) Channel estimation initialization: Based on the training sequence and the successive interference cancellation algorithm, the initial channel of each user is estimated. The training sequence is a known signal used for channel estimation.

[0009] (2) Multi-user detection: The channel estimation result and the original received signal r are input into the basic signal estimator, and chip-level detection is performed on each user to obtain the log-likelihood ratio of each user;

[0010] (3) External information update and polarization code decoding: The detection results are deinterleaved and despread to serve as prior information for the polarization decoder; the polarization decoder performs channel decoding and outputs the decoding results for each user. and external information; re-spread the external information, remove the prior information and then interleave it again;

[0011] (4) Channel update based on interference reconstruction and cancellation: Based on the per-user decoding result obtained in the current iteration Reconstruct the multi-access interference signal and update the channel estimate based on successive interference cancellation Among them, the received signal of the kth user after interference cancellation is: Where α is the interference elimination factor, represents the channel estimation result obtained by the k'th interfering user in the previous iteration; the channel parameters are updated using the least squares algorithm: Among them U k represents the decoded symbol matrix of the kth user;

[0012] (5) Iterative update: Update the estimated channel The external information is used as the prior information for the next iteration;

[0013] (6) Determine whether the number of iterations reaches the preset maximum number of iterations. If so, output the decoding results of all users and end the detection; otherwise, return to step (2) to continue iteration.

[0014] Furthermore, based on the training sequence and the successive interference cancellation algorithm, the initial channel of each user is estimated, including:

[0015] Users are sorted by received signal power, and single-user detection and decoding are performed on the user with the highest power to obtain its hard decision value; subsequent users use the decision results of the previously decoded users to reconstruct and eliminate interference and update the current user channel estimate.

[0016] Furthermore, the basic signal estimator detection process specifically includes:

[0017] Assume that the number of channel paths is L, and the real and imaginary detection extrinsic information of user k’s l-th path at the j-th bit are:

[0018]

[0019] Where E(·) and Var(·) represent the mean and variance respectively. The final basic signal estimator output information of the k-th user is the path superposition result: The superposition result is the log-likelihood ratio of user k.

[0020] Furthermore, in the extrinsic information updating and polar code decoding steps, the extrinsic information output by multi-user detection is deinterleaved and despread: l S (s k (j)) is the j-th bit of extrinsic information after deinterleaving of the k-th user, where π k is the interleaving sequence of the kth user; l DEC (c k (n)) is the external information after despreading the nth symbol of the kth user; l DEC (c k (n)) as the prior information of the polar decoder; the polar code decoder is based on l DEC (c k (n)) performs channel decoding and obtains the decoding result under the current number of iterations and decoded external information e DEC (c k (n)); re-spread the external information output by the decoder to obtain e S (s k (j))=e DEC (c k (j / S)), remove the prior information l S (s k (j)), get new external information l(s k (j))=e S (s k (j))-l S (s k (j)), after re-interleaving, we get l ESE (x k (j))=l(s k (π k (j))).

[0021] In a second aspect, an underwater acoustic communication receiver includes:

[0022] Channel estimation initialization module: This module estimates the initial channel for each user based on a training sequence and a continuous interference cancellation algorithm. The training sequence is the signal superimposed at the receiving end after the original transmitted signal undergoes polarization coding, repeated spread spectrum coding, and interleaving modulation and is transmitted through the underwater acoustic channel.

[0023] Multi-user detection module: The channel estimation result and the original received signal r are input into the basic signal estimator, and chip-level detection is performed on each user to obtain the log-likelihood ratio of each user;

[0024] External information update and polarization code decoding module: deinterleaves and despreads the detection results as prior information for the polarization decoder; the polarization decoder performs channel decoding and outputs the decoding results for each user and external information; re-spread the external information, remove the prior information and then interleave it again;

[0025] Channel update module based on interference reconstruction and cancellation: based on the per-user decoding result obtained in the current iteration Reconstruct the multi-access interference signal and update the channel estimate based on successive interference cancellation Among them, the received signal of the kth user after interference cancellation is: Where α is the interference elimination factor, represents the channel estimation result obtained by the k'th interfering user in the previous iteration; the channel parameters are updated using the least squares algorithm: Among them U k represents the decoded symbol matrix of the kth user;

[0026] Iterative update control module: the updated estimated channel The external information is used as the prior information for the next iteration to determine whether the number of iterations has reached the preset maximum number of iterations. If so, the decoding results of all users are output and the detection ends; otherwise, the iteration continues.

[0027] In a third aspect, an electronic device comprises: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the underwater IDMA iterative multi-user detection method based on polarization coding as described in the first aspect are implemented.

[0028] In a fourth aspect, a computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the underwater IDMA iterative multi-user detection method based on polarization coding as described in the first aspect.

[0029] In a fifth aspect, an underwater acoustic communication system includes:

[0030] At the transmitting end, polarization coding, repetition spread spectrum coding, and interleaving are performed on each user's bit sequence, and the modulated signal is transmitted to the receiving end via the underwater acoustic channel;

[0031] The receiving end is configured to execute the underwater IDMA iterative multi-user detection method based on polarization coding as described in the first aspect to achieve multi-user detection.

[0032] Beneficial effects: The present invention has significant advantages in decoding performance: (1) The present invention applies the combination of polarization codes and IDMA in underwater scenarios, and uses the superior error correction capability of polarization codes to ensure communication reliability, thereby enabling the underwater acoustic communication system to adopt shorter repeated spread spectrum codes and achieve higher data transmission rates without reducing performance. (2) The present invention proposes a continuous interference cancellation algorithm adapted to the IDMA system, and uses continuous interference cancellation only to update channel estimation. Therefore, the received signal used for user detection in the IDMA system is the original signal without any interference cancellation. In this way, the accuracy of channel estimation under multiple access interference can be effectively improved without losing user information. (3) The present invention can achieve robust multi-user communication in low signal-to-noise ratio and strong multiple access interference environments, significantly enhancing the system's anti-interference capability and communication reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without inventive work, including:

[0034] Figure 1 It is an algorithm flow chart of the method of the present invention;

[0035] Figure 2 It is the channel impulse response generated based on the simulation of experimental data;

[0036] Figure 3 It is a performance comparison of different detection methods as the number of iterations and signal-to-noise ratio change;

[0037] Figure 4 It is a performance comparison of different detection methods as the signal-to-interference ratio and signal-to-noise ratio change;

[0038] Figure 5 It is the experimental bit error rate result of different detection methods as the number of iterations and signal-to-noise ratio change. DETAILED DESCRIPTION

[0039] To facilitate understanding by those skilled in the art, the present invention is further described below with reference to specific embodiments and accompanying drawings.

[0040] Example 1

[0041] This embodiment provides an underwater IDMA iterative multi-user detection method based on polarization coding. The method is executed at a receiving end of an underwater acoustic communication system and includes the following steps:

[0042] (1) Channel estimation initialization: The receiver estimates the initial channel for each user based on the training sequence and the continuous interference cancellation algorithm. Users are sorted by received signal power, and single-user detection and decoding are performed on the user with the highest power to obtain its hard decision value. Subsequent users use the decision results of the previously decoded users to reconstruct and cancel interference, update the current user's channel estimate, and gradually improve the channel estimation accuracy under multiple access interference conditions.

[0043] A training sequence (TS) is a set of known, pre-designed signal sequences used for synchronization, frequency offset estimation, and channel estimation in communication systems. The first part of the signal sent by the transmitter is the training sequence, a known signal that can be used for channel estimation. The remaining unknown signal is the signal that needs to be decoded.

[0044] (2) Multi-user detection: The channel estimation result and the original received signal r are input into the basic signal estimator, and chip-level detection is performed on each user to obtain the log-likelihood ratio of each user;

[0045] Basic Signal Estimator (ESE) detection: The channel estimation results of each user are The received signal is input into the basic signal estimator, and chip-level detection is performed on each user to obtain the log-likelihood ratio e of each user.ESE (x k (j)); Assume that the number of channel paths is L, and the real and imaginary extrinsic information of the l-th path of user k at the j-th bit is:

[0046] The final ESE output information of the kth user is the path superposition result: where E(·) and Var(·) represent the mean and variance, respectively.

[0047] (3) External information update and polarization code decoding: The detection results are deinterleaved and despread to serve as prior information for the polarization decoder; the polarization decoder performs channel decoding and outputs the decoding results for each user. and external information; re-spread the external information, remove the prior information and then interleave it again;

[0048] Specifically, the extrinsic information output by multi-user detection is deinterleaved: the extrinsic information of the jth bit after deinterleaving of the kth user can be written as: where π k is the interleaving sequence of the kth user; then the external information of the kth user after despreading the nth symbol is Will l DEC (c k (n)) as the prior information of the polar decoder; the polar code decoder is based on l DEC (c k (n)) performs channel decoding and obtains the decoding result under the current number of iterations and decoded external information e DEC (c k (n)); re-spread the external information output by the decoder to obtain e S (s k (j))=e DEC (c k (j / S)), remove the prior information l S (s k (j)), get new external information l(s k (j))=e S (s k (j))-l S (s k (j)), after re-interleaving, we get l ESE (x k (j))=l(s k (π k (j)));

[0049] (4) Channel update based on interference reconstruction and cancellation: Based on the per-user decoding result obtained in the current iteration Reconstruct the multi-access interference signal and update the channel estimate based on successive interference cancellation Among them, the received signal of the kth user after interference cancellation is: Where α is the interference elimination factor, represents the channel estimation result obtained by the k'th interfering user in the previous iteration. The channel parameters are updated using the least squares algorithm (LS): Among them U k represents the decoded symbol matrix of the kth user;

[0050] (5) Iterative update: Update the estimated channel External information ESE (x k (j)) as the prior information for the next iteration;

[0051] (6) Determine whether the number of iterations reaches the preset maximum number of iterations. If so, output the decoding results of all users and end the detection; otherwise, return to step (2) to continue iteration.

[0052] Example 2

[0053] This embodiment provides an underwater acoustic communication receiver, including:

[0054] Channel estimation initialization module: estimates the initial channel for each user based on the training sequence and the successive interference cancellation algorithm. The training sequence is a known signal used for channel estimation.

[0055] Multi-user detection module: The channel estimation result and the original received signal r are input into the basic signal estimator (ESE), which performs chip-level detection on each user and obtains the log-likelihood ratio of each user;

[0056] External information update and polarization code decoding module: deinterleaves and despreads the detection results as prior information for the polarization decoder; the polarization decoder performs channel decoding and outputs the decoding results for each user and external information; re-spread the external information, remove the prior information and then interleave it again;

[0057] Channel update module based on interference reconstruction and cancellation: based on the per-user decoding result obtained in the current iteration Reconstruct the multi-access interference signal and update the channel estimate based on successive interference cancellation Among them, the received signal of the kth user after interference cancellation is: Where α is the interference elimination factor, represents the channel estimation result obtained by the k'th interfering user in the previous iteration; the channel parameters are updated using the least squares algorithm: Among them U krepresents the decoded symbol matrix of the kth user;

[0058] Iterative update control module: the updated estimated channel The external information is used as the prior information for the next iteration to determine whether the number of iterations has reached the preset maximum number of iterations. If so, the decoding results of all users are output and the detection ends; otherwise, the iteration continues.

[0059] The specific processes of basic signal estimator (ESE) detection, external information update, and polar code decoding refer to the description of embodiment 1 and are not repeated here.

[0060] Example 3

[0061] This embodiment provides an electronic device, including: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors. When the programs are executed by the processors, the steps of the underwater IDMA iterative multi-user detection method based on polarization coding are implemented as described above.

[0062] Example 4

[0063] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the polarization-coded underwater IDMA iterative multi-user detection method described above are implemented.

[0064] Example 5

[0065] This embodiment provides an underwater acoustic communication system, including a transmitter and a receiver. The transmitter is used to perform polarization coding, repeated spread spectrum coding, and interleaving processing on the bit sequence of each user. The modulated signal is transmitted to the receiver via an underwater acoustic channel.

[0066] Specifically, the transmitter processing flow includes:

[0067] Polarization coding: The code rate of the polarization code is defined as R = K / N, where N = 2 n is the polarization channel length, and the index of the i-th subchannel can be expressed in its binary form i=(B n-1 ,B n-2 ,...,B0), the polarization weight PW of the i-th subchannel is According to the reliability of sub-channels, information bits are allocated to K W i On the largest subchannel, the remaining subchannels transmit frozen bits (set to 0). The sending sequence of the kth user is u k =[u k (1),u k (2),...,u k (N)]T , the polarization coding result is: Among them B N is the bit permutation matrix, for The nth Kronecker product of .

[0068] Spread spectrum and interleaving: the coded sequence c k Spread spectrum to get s k =[s k (1),s k (2),...,s k (J)] T , where the frame length after spread is J=N×S, S is the spreading code length of the repeated coding. Each user uses a different interleaving sequence x k , for s k Perform interleaving.

[0069] The specific processing flow at the receiving end is the same as that in Example 1 and will not be repeated here.

[0070] In order to verify the performance of the method of the present invention, the applicant conducted the following simulation experiments and field experiments.

[0071] Figure 1 This is the algorithm flow chart of the underwater IDMA multi-user detection method based on polarization coding described in the present invention. Figure 1 The process simulates a four-user communication scenario with the following system parameters: bandwidth 4 kHz, carrier frequency 6 kHz, sampling rate 48 kHz, information sequence length 256 bits, polarization code rate 1 / 2, spread spectrum code length 16, and simulation frame number 100 frames. Figure 2 This is the BELLHOP underwater acoustic channel impulse response result generated based on the sound velocity profile of Songhua Lake. All user channels have obvious multipath effects, with the maximum delay reaching 100ms.

[0072] Figure 3 The performance of the four-user average bit error rate of the traditional IDMA detection method and the proposed method under different signal-to-noise ratios (SNRs) and iteration times was compared. The results showed that after 3 iterations, when the bit error rate was 10 -3 When compared to traditional methods, the proposed method achieves a performance gain of approximately 2dB. Traditional methods are prone to error accumulation and difficulty improving performance at low signal-to-noise ratios. However, the proposed method effectively enhances the system's robustness and anti-interference capabilities through iterative interference reconstruction and channel updates, validating the practicality and superiority of the proposed method.

[0073] In order to analyze the system performance as the signal-to-interference ratio (SIR) and signal-to-noise ratio (SNR) change, a two-user communication scenario is constructed. The SIR change represents the received power ratio between the target user 1 and the interfering user 2. Figure 4The data shows that as the difference in received power between User 1 and User 2 increases, the decoding performance of the low-power user degrades. However, when the power levels are close, the bit error performance of the two users converges. Furthermore, the improved signal-to-noise ratio enhances the system's tolerance to power imbalance. When the signal-to-noise ratio is -7dB, User 1 requires approximately 3dB higher received power than User 2 to achieve a bit error rate of 10⁻³. When the signal-to-noise ratio is increased to -3dB, even if User 1's power is approximately 2dB lower than User 2's, the same performance is achieved. Figure 4 The results show that the proposed method has good multi-access interference suppression capability and has practical application potential in complex underwater acoustic multi-user communication scenarios.

[0074] The advantages of the present invention will be further explained below in conjunction with the experimental data processing results.

[0075] Test data verification:

[0076] In 2025, a four-user underwater communication experiment was conducted in Songhua Lake. The average water depth of the experimental waters was about 20 meters. Due to the limitations of the experimental conditions, the transmitter used a single transducer to simultaneously send multi-user signals. The receiver superimposed the different user signals according to the amplitude weights in the post-processing stage to simulate a multi-access communication environment. The experiment used a BPSK modulated signal with a center frequency of 5kHz and a bandwidth range of 2-8kHz. The channel coding method was a polar code with a code rate of 1 / 2 and a code length of 512. The spread spectrum length was set to 8, and the bit rate after single-user coding was 187.5bps. The receiver was a vertical array consisting of 24 array elements with an array element spacing of 0.25m. During the experiment, the transmitter moved with the ship, and four communication distances of 500m, 2km, 3.5km and 5km were set respectively. The receiver position was fixed.

[0077] First, the performance of the methods at the same distance was verified. Under the original reception conditions, both the traditional detection method and the proposed method achieved zero-error decoding across 24 array elements. To further test robustness, Gaussian white noise was added to the received signal until the received signal-to-noise ratio reached 2dB. Table 1 shows the average bit error rate (BER) across 24 array elements for the two methods at different iteration numbers and communication distances. Without iteration, the proposed method outperformed the traditional method at all distances; after two iterations, both methods achieved good BER performance.

[0078] Table 1 Average bit error rate of 24 array elements under different iteration times and communication distances

[0079]

[0080] Furthermore, the received data of different users were extracted from the signals of the first element of the receiving array at distances of 500 m, 2 km, 3.5 km, and 5 km. These signals were used as the received signals of users 1 to 4. After normalization, they were weighted and superimposed using amplitude coefficients of 1, 0.95, 0.85, and 0.8, respectively. Figure 5 Panel (a) shows a comparison of logarithmic bit error rates at different iteration numbers. The traditional detection method stabilizes its bit error rate at approximately 0.082 after two iterations and does not continue to decrease with each iteration. This is primarily due to a lack of effective multiple access interference suppression, which leads to accumulated channel estimation errors. The proposed method achieves error-free decoding with only one iteration. Figure 5 Panel (b) further compares the performance of the two methods after two iterations at different signal-to-noise ratios. At a signal-to-noise ratio of -2dB, the proposed method achieves zero bit errors, while the traditional method still has a bit error rate of 10⁻², requiring the signal-to-noise ratio to be increased to above 0dB to achieve zero bit errors.

[0081] The above analysis shows that the method and system proposed in this embodiment have robust multi-user decoding performance and high communication rate in low signal-to-noise ratio and strong multi-access interference environments, further demonstrating its effectiveness and engineering application value in underwater acoustic communication systems.

Claims

1. An underwater IDMA iterative multi-user detection method based on polarization coding, executed at the receiving end, characterized in that: The following steps are involved: (1) Channel estimation initialization: Based on the training sequence and the successive interference cancellation algorithm, the initial channel of each user is estimated. The training sequence is a known signal used for channel estimation. (2) Multi-user detection: The channel estimation result and the original received signal r are input into the basic signal estimator, and chip-level detection is performed on each user to obtain the log-likelihood ratio of each user; (3) External information update and polar code decoding: The detection results are deinterleaved and despread as prior information for the polar decoder; The polarization decoder performs channel decoding and outputs the decoding results for each user. and external information; re-spread the external information, remove the prior information and then interleave it again; (4) Channel update based on interference reconstruction and cancellation: Based on the per-user decoding result obtained in the current iteration Reconstruct the multi-access interference signal and update the channel estimate based on successive interference cancellation Among them, the received signal of the kth user after interference cancellation is: Where α is the interference elimination factor, represents the channel estimation result obtained by the k'th interfering user in the previous iteration; the channel parameters are updated using the least squares algorithm: Among them U k represents the decoded symbol matrix of the kth user; (5) Iterative update: Update the estimated channel The external information is used as the prior information for the next iteration; (6) Determine whether the number of iterations reaches the preset maximum number of iterations. If so, output the decoding results of all users and end the detection; otherwise, return to step (2) to continue iteration.

2. The method according to claim 1, characterized in that Based on the training sequence and the successive interference cancellation algorithm, the initial channel of each user is estimated, including: Users are sorted by received signal power, and single-user detection and decoding are performed on the user with the highest power to obtain its hard decision value; subsequent users use the decision results of the previously decoded users to reconstruct and eliminate interference and update the current user channel estimate.

3. The method according to claim 1, characterized in that The basic signal estimator detection process specifically includes: Assume that the number of channel paths is L, and the real and imaginary detection extrinsic information of user k’s l-th path at the j-th bit are: Where E(·) and Var(·) represent the mean and variance respectively. The final basic signal estimator output information of the k-th user is the path superposition result: The superposition result is the log-likelihood ratio of user k.

4. The method according to claim 2, characterized in that In the extrinsic information updating and polar code decoding steps, the extrinsic information output by multi-user detection is deinterleaved and despread: l S (s k (j)) is the j-th bit of extrinsic information after deinterleaving of the k-th user, where π k is the interleaving sequence of the kth user; l DEC (c k (n)) is the external information after despreading the nth symbol of the kth user; l DEC (c k (n)) as the prior information of the polar decoder; the polar code decoder is based on l DEC (c k (n)) performs channel decoding and obtains the decoding result under the current number of iterations and decoded external information e DEC (c k (n)); re-spread the external information output by the decoder to obtain e S (s k (j))=e DEC (c k (j / S)), remove the prior information l S (s k (j)), get new external information l(s k (j))=e S (s k (j))-l S (s k (j)), after re-interleaving, we get l ESE (x k (j))=l(s k (π k (j))).

5. An underwater acoustic communication receiver, characterized in that: include: Channel estimation initialization module: estimates the initial channel of each user based on the training sequence and the successive interference cancellation algorithm. The training sequence is a signal known to the transmitter. Multi-user detection module: The channel estimation result and the original received signal r are input into the basic signal estimator, and chip-level detection is performed on each user to obtain the log-likelihood ratio of each user; External information update and polarization code decoding module: deinterleaves and despreads the detection results as prior information for the polarization decoder; the polarization decoder performs channel decoding and outputs the decoding results for each user and external information; re-spread the external information, remove the prior information and then interleave it again; Channel update module based on interference reconstruction and cancellation: based on the per-user decoding result obtained in the current iteration Reconstruct the multi-access interference signal and update the channel estimate based on successive interference cancellation Among them, the received signal of the kth user after interference cancellation is: Where α is the interference elimination factor, represents the channel estimation result obtained by the k'th interfering user in the previous iteration; the channel parameters are updated using the least squares algorithm: Among them U k represents the decoded symbol matrix of the kth user; Iterative update control module: the updated estimated channel The external information is used as the prior information for the next iteration to determine whether the number of iterations has reached the preset maximum number of iterations. If so, the decoding results of all users are output and the detection ends; otherwise, the iteration continues.

6. An electronic device, characterized in that: include: one or more processors; Memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the underwater IDMA iterative multi-user detection method based on polarization coding are implemented as described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the underwater IDMA iterative multi-user detection method based on polarization coding are implemented according to any one of claims 1 to 4.

8. An underwater acoustic communication system, characterized in that: include: At the transmitting end, polarization coding, repetition spread spectrum coding, and interleaving are performed on each user's bit sequence, and the modulated signal is transmitted to the receiving end via the underwater acoustic channel; The receiving end is configured to execute the underwater IDMA iterative multi-user detection method based on polarization coding according to any one of claims 1 to 4 to realize multi-user detection.

9. The system according to claim 8, characterized in that Polarization coding includes: defining the transmission sequence of the kth user at the transmitting end as u k =[u k (1),u k (2),...,u k (N)] T , after polarization coding, the coding sequence c is obtained k ; Spread spectrum and interleaving include: the coding sequence c k Spread spectrum to get s k =[s k (1),s k (2),...,s k (J)] T , where the frame length after spread is J = N × S, S is the spreading code length of the repeated code; each user uses a different interleaving sequence x k , for s k Perform interleaving.

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