Method for constructing code set of code division multiple access underwater acoustic communication

Abstract

The present application aims at the problem that the traditional wireless spread spectrum code set is difficult to be directly applied to the underwater acoustic CDMA communication system due to the narrow channel bandwidth and the significant Doppler effect, and proposes a code set construction method combining orthogonal transformation, random permutation and iteration optimization. The method is based on the LK sequence family with good correlation characteristics, uses the cyclic shift copies to expand the initial code set, then generates candidate sequences through Hadamard matrix orthogonal transformation and random permutation, and optimizes according to the cross-correlation threshold, and finally constructs a spread spectrum code set with large scale, high orthogonality and special adaptation to the characteristics of underwater acoustic channel through multiple iterations, which significantly improves the user capacity and anti-multiple access interference capability of the underwater acoustic CDMA system.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic communication technology, specifically relating to a method for constructing a code set for code division multiple access underwater acoustic communication. Background Technology

[0002] In CDMA underwater acoustic communication systems, all users share the same channel resources. Adding new users increases the power of multiple access interference, leading to a deterioration in the received signal-to-noise ratio (SNR), the degree of which is proportional to the user capacity. One of the core aspects of a CDMA system is the design of the spreading code set. The characteristics of the spreading code set largely determine the user capacity and multiple access resistance. Researching CDMA communication code set construction techniques, and constructing a large number of spreading code sets with good orthogonality, is the main technical approach to improving the user capacity of CDMA access and reducing multiple access interference.

[0003] Underwater acoustic CDMA communication commonly employs two communication methods: direct sequence spread spectrum and M-ary spread spectrum. The former modulates the data using PSK and then spreads it using PN codes, achieving a high frequency utilization rate. Q is the PSK modulation order. Increasing the modulation order can improve the link rate, but the decoding performance is easily affected by random phase changes in the underwater acoustic channel, and the larger the Q value, the more significant the impact. The latter maps data into a code sequence in an orthogonal PN code set, and then completes spread spectrum through carrier modulation, with a frequency utilization rate of... M represents the size of the PN code set. By increasing the code set size (generally M is much larger than Q), a considerable link rate can be obtained. The information recovery in M-ary spread spectrum communication is determined by the correlation value between the received sequence and the PN code sequence, and random changes in the channel phase have little impact on decoding performance. Therefore, M-ary underwater acoustic spread spectrum communication has advantages in frequency utilization and adaptability to underwater acoustic channels, and is widely used in underwater acoustic CDMA systems.

[0004] The wireless CDMA system employs a three-layer code structure: Walsh code (64 or 128 bytes in length) for forward link channel differentiation and reverse link quadrature modulation; and long PN code (usually an m-sequence) for data scrambling and user identification, with an extremely long period (up to 2200 MHz). 42-1), which will enhance signal randomness; short PN codes (Gold sequence family, length 32768), the Gold sequence family has good autocorrelation and cross-correlation, used for forward and reverse link orthogonal modulation, controlling the final signal transmission, and providing timing synchronization. Through the three-layer code structure design, a balance is achieved in code sequence orthogonality, noise reduction and synchronization. Compared with wireless channels, underwater acoustic channels have extremely narrow bandwidth. When designing an underwater acoustic CDMA system with a certain user capacity and a certain link rate, the spreading code design of wireless CDMA systems cannot be completely copied. First, Walsh codes are strictly orthogonal, but have strong regularity and are easily interfered with when used alone; second, excessively long PN codes are extremely sensitive to Doppler, and the Doppler effect in underwater acoustic channels is much more serious than that in radio, which brings huge challenges to frequency synchronization, and the duration of the code is much longer than the channel coherence time due to the narrow bandwidth of the channel, causing a decrease in spreading gain; third, the so-called short codes in wireless CDMA systems are still long codes for underwater acoustic communication, and they also face the problems of Doppler and channel time-varying. Summary of the Invention

[0005] The technical problem this invention aims to solve is to provide a code set construction method for code division multiple access (CDMA) underwater acoustic communication, addressing the issues of traditional wireless CDMA spreading code sets in narrow-bandwidth, Doppler-effect underwater acoustic channels, where excessively long sequences lead to difficulties in frequency synchronization, limited code set size, and an inability to simultaneously achieve large user capacity and high orthogonality. This method is based on the LK sequence family with good correlation characteristics. It uses cyclically shifted copies of these sequences to expand the initial code set, then performs orthogonal transformations and random permutations using the Hadamard matrix to generate candidate sequences. These sequences are then optimized based on a cross-correlation threshold. Through multiple iterations, a large-scale, highly orthogonal spreading code set that is particularly well-suited to the characteristics of underwater acoustic channels is finally constructed.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for constructing a code set for code division multiple access underwater acoustic communication includes the following steps:

[0008] S1: Base sequence set construction: Select an LK sequence family with good orthogonality, and generate multiple cyclically shifted copies of the sequence family. Use the set of the LK sequence family and its cyclically shifted copies as the initial base sequence set X.

[0009] S2: Candidate Sequence Set Generation: The base sequence set X is subjected to orthogonal transformation, random permutation, and inverse orthogonal transformation to generate a candidate sequence set Y, represented as:

[0010] ,

[0011] Where Q is the orthogonal transformation matrix. Let Q be a random permutation matrix. H This is the conjugate transpose of Q;

[0012] S3: Sequence optimization: Calculate the cross-correlation value between each sequence in the candidate sequence set Y and each sequence in the base sequence set X, compare the maximum cross-correlation value with a preset threshold, remove sequences whose maximum cross-correlation value exceeds the preset threshold, and retain the sequences to form an additional sequence set;

[0013] S4: Iterative amplification: Merge the selected sequence set with the current base sequence set X to form a new base sequence set. Repeat steps S2 to S4 for multiple iterations until the total number of generated sequences reaches the preset requirement.

[0014] S5: Code set output: The base sequence set obtained after the final iteration is merged with the additional sequence set generated during all iterations, and the output is the final underwater acoustic CDMA communication spread spectrum code set.

[0015] In step S1, the orthogonal transformation matrix Q is a Hadamard matrix.

[0016] In step S1, the cyclic shift is implemented using a cyclic shift matrix P, which is expressed as:

[0017] ,

[0018] The sequence family copy S after k cyclic shifts k =P k S, where S is the original LK sequence family.

[0019] In step S3, the preset threshold is set as a specific multiple of the maximum value of the off-diagonal elements in the correlation matrix of the candidate sequence set Y.

[0020] The spreading code set generated by the method is a binary sequence.

[0021] Compared with existing technologies, the present invention has the following advantages:

[0022] This invention proposes a code set construction method for code division multiple access (CDMA) underwater acoustic communication. Its advantages are: ① Based on an iterative construction mechanism using orthogonal transformation and random permutation, it effectively expands the number of available code sets while ensuring the inherent orthogonality of the generated sequences, overcoming the bottleneck of the limited size of a single pseudo-random sequence family; ② By setting a cross-correlation threshold to optimize candidate sequences, it strictly controls the level of multiple access interference introduced by new sequences, ensuring quality during code set expansion; ③ Using the LK sequence family and its cyclically shifted replicas as the base sequence set provides a starting point with excellent orthogonality and sufficient quantity for the iterative process, fundamentally guaranteeing the orthogonality and quantity of the constructed code set. Attached Figure Description

[0023] Figure 1This is a general block diagram of the code set construction of the present invention;

[0024] Figure 2 This is a correlation matrix diagram of the sequence set Y of the present invention;

[0025] Figure 3 The diagram shows the autocorrelation and cross-correlation of the present invention, wherein: (a) is the autocorrelation of the Y sequence, and (b) is the cross-correlation of the X and Y sequences. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0027] (1) Construction of orthogonal transform code set:

[0028] Figure 1 This is a general block diagram of the code set construction of the present invention. Spreading codes generally use pseudo-random sequences. According to random matrix theory, the randomness of a random sequence remains essentially unchanged after undergoing orthogonal transformation, random permutation, and inverse orthogonal transformation to generate a new sequence. The present invention employs a CDMA underwater acoustic communication code set construction method based on orthogonal transformation, such as... Figure 1 First, a family of pseudo-random sequences with good orthogonality is selected as the base sequence set. Then, each sequence in the base sequence set is subjected to orthogonal transformation, random permutation, and inverse orthogonal transformation in turn to generate a candidate sequence set. Then, sequences with good orthogonality are selected from the candidate sequence set to become the supplementary sequence set. Finally, the supplementary sequence set and the base sequence set are used as the new base sequence set. The above operation is repeated and iterated multiple times until the required number of sequences is reached. The final sequence set is the sum of the base sequence set and the supplementary sequence set obtained in each iteration.

[0029] Specifically, given a base sequence set X, let the orthogonal transformation matrix be Q, and the random permutation matrix be... , Figure 1 The generated candidate sequence set can be represented as:

[0030] (1)

[0031] In equation (1), This represents the conjugate transpose of Q.

[0032] The correlation matrix of Y is:

[0033] (2)

[0034] Substituting into equation (1), we get:

[0035] (3)

[0036] It can be seen that Y and X have consistent orthogonality. As long as the orthogonality of the base sequence set is good, the orthogonality of the candidate sequence set can be guaranteed. For CDMA communication, the pseudo-random sequence used to carry information is usually a binary sequence. Otherwise, the communication signal generated will have a large peak-to-average power ratio. The base sequence set of this invention is a binary sequence. The orthogonal transformation matrix Q is used to select the Hada code matrix. Y constructed using equation (1) is also a binary sequence, thereby avoiding the peak-to-average power ratio problem.

[0037] Figure 2 The correlation matrix of the candidate sequence set Y generated using equation (1) is given. The base sequence set X is selected as a family of pseudo-random sequences of length 255. Figure 2 It can be seen that Y has good orthogonality. Although Y generated by equation (1) has the characteristic of preserving orthogonality, the random permutation destroys the orthogonal correlation between X and Y to a certain extent, resulting in a decrease in the orthogonality of the sequences of X and Y, such as Figure 3 As shown in (a) and (b), the sequence set Y has good autocorrelation, but its cross-correlation peak with X is high, thus affecting the anti-multiple access interference capability of CDMA underwater acoustic communication. To address this problem, this invention optimizes the candidate sequence set Y by eliminating sequences with high cross-correlation peaks. Assuming the sequence set... ,sequence , sequence set ,sequence ,sequence and The cross-correlation value is,

[0038] (4)

[0039] In equation (4), k = 1-L, 2-L, ..., 0, 1, ..., L-1. The maximum cross-correlation value is found and compared with a preset threshold. If the value is greater than the threshold, it is discarded; otherwise, it is retained and used as an additional selection sequence set for the next iteration. Figure 1 As shown. The threshold value is set as a multiple of the maximum value of the off-diagonal elements of the correlation matrix of the Y sequence set. The multiple can be selected according to the size of the code set to be generated. The larger the multiple, the larger the code set, but the resistance to multiple access interference decreases. The specific selection should be determined by a compromise in actual application.

[0040] (2) Selection of base sequence set:

[0041] The orthogonality and quantity of pseudo-random sequence sets constructed through random permutations in the orthogonal transformation domain largely depend on the characteristics of the base sequence set; therefore, a suitable base sequence set needs to be selected. This invention uses the LK (large kasami) sequence family and its cyclically shifted copies as the base sequence set. Common binary pseudo-random sequence families include Gold, GL (gold-like), DBCH, SK (small kasami), and LK (large kasami). These sequence families are generally constructed from preferred m-sequences through cyclic shifting followed by modulo-2 addition, thus exhibiting good orthogonality. Among them, the SK sequence family has the best orthogonality but the fewest number, while the LK sequence family has the largest number and its orthogonality is comparable to other sequence families. The LK sequence family still maintains good orthogonality with the original sequence family after cyclic shifting; therefore, constructing multiple copies through cyclic shifting can further expand the size of the base sequence set. Assume the LK sequence family can be represented as:

[0042] (5)

[0043] In equation (5), L is the sequence length and N is the number of sequences. .

[0044] The sequence family replica after k cyclic shifts is:

[0045] (6)

[0046] In equation (6), P is a cyclic shift matrix, expressed as:

[0047] (7)

[0048] Therefore, the base sequence set used in this invention is The quantity is L×N.

[0049] In summary, the code set construction method for underwater acoustic communication proposed in this invention organically combines a candidate sequence generation mechanism based on orthogonal transformation and random permutation, a sequence selection mechanism based on a preset threshold, and a base sequence set expansion mechanism based on the LK sequence family and its cyclically shifted copies, forming a systematic iterative code set construction process. The core advantages of this method are: firstly, the mathematical transformations of formulas (1) to (3) ensure the inherent orthogonality of the candidate sequence set; secondly, the cross-correlation calculation and threshold comparison in formula (4) effectively control the potential impact of newly added sequences on the system's multiple access interference level, ensuring the quality of the code set during the expansion process; and finally, the expansion strategy of cyclically shifting numerous LK sequences with good orthogonality provides a more abundant and high-performance starting point for the iterative process. The method proposed in this invention theoretically guarantees that the generated code set possesses both large capacity and good orthogonality. In practice, the different requirements for user capacity and anti-interference capability in different underwater acoustic communication scenarios can be taken into account by adjusting parameters (such as threshold multiples), thereby effectively solving the code set design problem of CDMA communication in narrowband underwater acoustic channels.

[0050] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for constructing a code set for code division multiple access underwater acoustic communication, characterized in that, Includes the following steps: S1: Base sequence set construction: Select an LK sequence family with good orthogonality, and generate multiple cyclically shifted copies of the sequence family. Use the set of the LK sequence family and its cyclically shifted copies as the initial base sequence set X. S2: Candidate Sequence Set Generation: The base sequence set X is subjected to orthogonal transformation, random permutation, and inverse orthogonal transformation to generate a candidate sequence set Y, represented as: ， Where Q is the orthogonal transformation matrix. Let Q be a random permutation matrix. H This is the conjugate transpose of Q; S3: Sequence optimization: Calculate the cross-correlation value between each sequence in the candidate sequence set Y and each sequence in the base sequence set X, compare the maximum cross-correlation value with a preset threshold, remove sequences whose maximum cross-correlation value exceeds the preset threshold, and retain the sequences to form an additional sequence set; S4: Iterative amplification: Merge the selected sequence set with the current base sequence set X to form a new base sequence set. Repeat steps S2 to S4 for multiple iterations until the total number of generated sequences reaches the preset requirement. S5: Code set output: The base sequence set obtained after the final iteration is merged with the additional sequence set generated during all iterations, and the output is the final underwater acoustic CDMA communication spread spectrum code set.

2. The method for constructing a code set for code division multiple access underwater acoustic communication according to claim 1, characterized in that, In step S1, the orthogonal transformation matrix Q is a Hadamard matrix.

3. The method for constructing a code set for code division multiple access underwater acoustic communication according to claim 1, characterized in that, In step S1, the cyclic shift is implemented using a cyclic shift matrix P, which is expressed as: ， The sequence family copy S after k cyclic shifts k =P k S, where S is the original LK sequence family.

4. The method for constructing a code set for code division multiple access underwater acoustic communication according to claim 1, characterized in that, In step S3, the preset threshold is set as a specific multiple of the maximum value of the off-diagonal elements in the correlation matrix of the candidate sequence set Y.

5. The method for constructing a code set for code division multiple access underwater acoustic communication according to claim 1, characterized in that, The spreading code set generated by the method is a binary sequence.

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