ISAC complementary sequence generation method and device

Abstract

The invention provides an ISAC complementary sequence generation method and device, and relates to the technical field of communication perception integration, and the method comprises the steps: presetting a sequence length parameter which is a positive integer not less than 2; generating a constant modulus sequence with the length based on the length parameter; the permutation of the preset set is obtained, an initial complementary sequence is generated based on the constant modulus sequence and the permutation, and the initial complementary sequence A is composed of N subsequences {a0, a1,..., aN-1} with the length being N; presetting a sequence set size parameter which is a positive integer not less than 2, and selecting a P-order unitary matrix O; and expanding the initial complementary sequence based on the unitary matrix to generate a complementary sequence set. According to the method, the self-fuzzy function of the complementary sequence is in a drawing pin type, and zero cross-fuzzy function values exist among different complementary sequences.

Description

Technical Field

[0001] This invention relates to the field of integrated communication and sensing technology, and more specifically, to an ISAC complementary sequence generation method and apparatus. Background Technology

[0002] In Integrated Sensing and Communication (ISAC) systems, waveform design is one of the core challenges. An ideal signal waveform should possess both excellent resolution and low interference characteristics, typically requiring its self-ambiguity function to exhibit a "thumbtack" shape with a sharp central main lobe and extremely low side lobes. However, traditional single sequences (such as Barker codes and linear frequency modulated signals) have inherent limitations in autocorrelation performance, and their ambiguity functions often exhibit high range-Doppler coupling side lobes, failing to meet the requirements of high-precision sensing. To overcome this problem, existing technologies have proposed using complementary sequences, such as Golay complementary sequence pairs, which synthesize a thumbtack-shaped self-ambiguity function by adding the ambiguity functions of multiple sub-sequences. However, these traditional complementary sequence sets have significant drawbacks: firstly, the sequence set size is limited, making it difficult to support the large number of orthogonal signals required in multi-user or large-scale MIMO scenarios; secondly, the performance of the mutual ambiguity function between different complementary sequence pairs is often not optimized or controlled, leading to severe interference between sequences during simultaneous multi-target sensing or multi-user communication, thus limiting the overall system performance.

[0003] Therefore, there is an urgent need for an ISAC complementary sequence generation method and apparatus to achieve a self-fuzzy function that is pin-shaped and has zero mutual fuzzy function values ​​between different complementary sequences. Summary of the Invention

[0004] The purpose of this invention is to provide a method and apparatus for generating ISAC complementary sequences to improve the aforementioned problems. To achieve this objective, the technical solution adopted by this invention is as follows:

[0005] Firstly, this application provides a method for generating a set of complementary ISAC sequences, including:

[0006] The sequence length parameter N is preset, where N is a positive integer not less than 2;

[0007] Based on the length parameter N, a constant modulus sequence b of length N is generated, which contains elements b0, b1, ..., b N-1 ;

[0008] Obtain the permutation π of the preset set {0,1,…,N-1}, and generate an initial complementary sequence A based on the sequence b and the permutation π, wherein the initial complementary sequence A consists of N subsequences of length N {a0,a1,…,a...} N-1}constitute;

[0009] A preset sequence set size parameter P is set, where P is a positive integer not less than 2, and a P-order unitary matrix O is selected, wherein each element of the unitary matrix O... The modulus of each is 1, where the values ​​of s and t range from 0 to P-1;

[0010] Based on the unitary matrix O, the initial complementary sequence O is expanded to generate a complementary sequence set {A}. (0) A (1) ,…,A (P-1)}

[0011] Secondly, this application also provides an ISAC complementary sequence generation apparatus, comprising:

[0012] A preset unit is used to preset the sequence length parameter N, where N is a positive integer not less than 2;

[0013] The processing unit is configured to generate a constant modulus sequence b of length N based on the length parameter N, the sequence containing elements b0, b1, ..., b N-1 ;

[0014] A construction unit is used to obtain the permutation π of a preset set {0,1,…,N-1}, and generate an initial complementary sequence A based on the sequence b and the permutation π, wherein the initial complementary sequence A consists of N subsequences of length N {a0,a1,…,a...} N-1}constitute;

[0015] The selection unit is used to preset the sequence set size parameter P, where P is a positive integer not less than 2, and to select a P-order unitary matrix O, wherein each element of the unitary matrix O... The modulus of each is 1, where the values ​​of s and t range from 0 to P-1;

[0016] An extension unit is used to extend the initial complementary sequence O based on the unitary matrix O to generate a complementary sequence set {A}. (0) A (1) ,…,A (P-1)}

[0017] The beneficial effects of this invention are as follows:

[0018] This invention provides a systematic scheme for constructing complementary sequence sets by introducing specific permutation operations and a unitary matrix extension structure. This method can flexibly and efficiently generate large-scale sequence sets, where each complementary sequence can achieve a thumbtack-shaped self-ambiguity function, while ensuring low or even zero mutual ambiguity function values ​​between any different sequences within the set. This significantly improves the perception accuracy and communication reliability of the ISAC system in complex scenarios.

[0019] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of the ISAC complementary sequence generation method described in this embodiment of the invention;

[0022] Figure 2 This is a schematic diagram of the ISAC complementary sequence generation device described in an embodiment of the present invention;

[0023] Figure 3 The complementary sequence A in the ISAC complementary sequence generation method described in this embodiment of the invention. (0) The self-fuzzy function;

[0024] Figure 4 The complementary sequence A in the ISAC complementary sequence generation method described in this embodiment of the invention. (1) The self-fuzzy function;

[0025] Figure 5 The complementary sequence A in the ISAC complementary sequence generation method described in this embodiment of the invention. (0) and A (1) Mutually ambiguous functions.

[0026] In the diagram: 701, Preset unit; 702, Processing unit; 703, Construction unit; 704, Selection unit; 705, Extension unit. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present 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 the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0028] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0029] Example 1:

[0030] This embodiment provides a method for generating ISAC complementary sequences.

[0031] See Figure 1 , Figure 3 , Figure 4 and Figure 5 The figure shows that the method includes steps S1, S2, S3, S4 and S5.

[0032] Step S1: Preset the sequence length parameter N, where N is a positive integer not less than 2;

[0033] Understandably, in integrated sensing and communication systems, the parameter N directly determines the duration of the generated waveform and the bandwidth resource usage, thus affecting the system's distance resolution and processing gain. As a positive integer not less than 2, the value of N gives designers great flexibility, allowing for precise configuration based on specific sensing accuracy requirements and communication data rate requirements.

[0034] Step S2: Generate a constant modulus sequence b of length N based on the length parameter N. This sequence contains elements b0, b1, ..., b N-1 ;

[0035] Understandably, this step provides a clean and power-efficient "seed" signal for all subsequent signal processing. Its randomness introduces the potential for good autocorrelation and cross-correlation characteristics into the entire sequence set, providing initial conditions for the final realization of the thumbtack-type fuzzy function and ensuring that the signal can still maintain excellent sensing and communication performance after power amplification.

[0036] Step S3: Obtain the permutation π of the preset set {0,1,…,N-1}, and generate an initial complementary sequence A based on the sequence b and the permutation π, wherein the initial complementary sequence A consists of N subsequences of length N {a0,a1,…,a…} N-1}constitute;

[0037] Understandably, this step utilizes the permutation π to perform a nonlinear, aperiodic rearrangement of the indices of the sequence elements. This operation fundamentally alters the energy distribution characteristics of the signal in the time-frequency two-dimensional plane. In this step, step S3 includes steps S31 and S32.

[0038] Step S31: Based on the preset subsequence construction formula, the nth element b of the constant modulus sequence b is... n The value π corresponding to the nth position of the permutation π n The subsequence a is generated by processing the preset Nth-order primitive unit root. m The nth element a m,n ;

[0039] It is understandable that this step is specifically for each subsequence a m This process endows the sequences with unique "phase fingerprints," laying an indispensable mathematical foundation for achieving sidelobe cancellation and forming a sharp, thumbtack-shaped main lobe (i.e., ideal complementarity) when the fuzz functions of all subsequences are subsequently added together. It ensures that while individual subsequences may possess complex fuzz functions, as a whole, their set will exhibit the desired superior properties. The pre-defined subsequence construction formula in this step is as follows:

[0040]

[0041] Among them, 0≤m≤N-1, 0≤n≤N-1, π=(π0,π1,…,π N-1 ) is a permutation of the set {0,1,…,N-1}, a m,n For sequence a m The nth element, b n π is the nth element of the constant modulus sequence b. n Let ξ be the nth element of the permutation of the set {0,1,…,N-1}. N Let m be the Nth primitive unit root, and m be the m-th subsequence.

[0042] Step S32: Repeat the above steps to generate N subsequences, and build a set based on all the subsequences to obtain an initial complementary sequence A.

[0043] Understandably, this step systematically integrates the N sub-sequences with specific phase codes generated in the previous step, completing the construction from basic components to functional signal units. This step organizes each sub-sequence carrying a unique "phase fingerprint" into an ordered set, namely the initial complementary sequence A. Each sub-sequence is a carefully designed and indivisible component aimed at achieving the overall goal of "complementarity."

[0044] Step S4: Preset the sequence set size parameter P, where P is a positive integer not less than 2, and select a P-order unitary matrix O, wherein each element of the unitary matrix O... The modulus of each is 1, where the values ​​of s and t range from 0 to P-1;

[0045] It is understandable that this step prepares the key control dimension (P) and core mathematical tools (unitary matrix O) for achieving large-scale, high-performance signal set expansion. The technical effect of this preparatory step is to lay the foundation for generating an orthogonal waveform set with strict mathematical guarantees, ensuring that the subsequent expansion process can not only increase the number of sequences, but also maintain and optimize the cross-correlation characteristics between sequences, thereby meeting the needs of modern ISAC systems for large-scale parallel signal processing, where s,t represents the position coordinates of elements in unitary matrix O.

[0046] Step S5: Expand the initial complementary sequence O based on the unitary matrix O to generate a complementary sequence set {A}. (0) A (1) ,…,A (P-1 )}.

[0047] It is understandable that each sequence in this step inherits the potential of the thumbtack-shaped self-ambiguity function obtained by the initial sequence A through complementarity. More importantly, due to the properties of unitary transform, the mutual ambiguity function between any two different sequences in the set is effectively suppressed, achieving low or even zero mutual interference. This marks a leap in system capability from generating a single high-quality signal to providing a set of orthogonal signals that can be used simultaneously by multiple users / data streams, laying a practical signal foundation for multi-target detection and multi-user access in the ISAC system. In this step, step S5 includes step S51.

[0048] Step S51: Based on P extended complementary sequences A (k) Generate a set of complementary sequences, where k is the index of the extended complementary sequence, and each extended complementary sequence A... (k) It contains PN subsequences of length N.

[0049] It is understandable that this step not only clarifies the number of sequences (P sequences), but more importantly, establishes the internal complex structure of each sequence (PN subsequences). This concretizes an abstract mathematical construction into a dimensional signal resource pool that can be directly called by communication protocols and sensing algorithms, providing the most critical physical layer signal foundation for realizing interference-free multi-target detection and multi-user parallel communication.

[0050] In this step, step S51 includes step S511.

[0051] Step S511: Based on the element o in the k-th row and r-th column of the unitary matrix O k,r The u-th subsequence a of the initial complementary sequence A u Performing multiplication, we obtain the extended complementary sequence A. (k) The rN+uth subsequence Given that 0 ≤ r, k ≤ P-1, and 0 ≤ u ≤ N.

[0052] It is understandable that this step systematically generates the extended complementary sequence A. (k) Each subsequence in the sequence has a definite address rN+u. This operation ensures that all subsequences generated from the same row (the k-th row) logically belong to the same new complementary sequence A. (k) The corresponding self-fuzzy function is formed by summing the fuzzy functions of these subsequences, and it inherits the thumbtack-like characteristic. In this step, the formula for representing the rN+u-th subsequence is as follows:

[0053]

[0054] Where 0≤r,k≤P-1,0≤u≤N, Let r be the (rN+u)th subsequence, o k,r Let a represent the complex element located in the k-th row and r-th column of the unitary matrix O. u Let a represent the i-th subsequence in the initial complementary sequence A. u,1 Let a represent the first subsequence in the initial complementary sequence A. u,N-1 This represents the Nth subsequence in the initial complementary sequence A.

[0055] Example 2:

[0056] like Figure 2 As shown, this embodiment provides an ISAC complementary sequence generation device. See [link to previous document]. Figure 2 The device includes a preset unit 701, a processing unit 702, a construction unit 703, a selection unit 704, and an expansion unit 705.

[0057] The preset unit 701 is used to preset the sequence length parameter N, where N is a positive integer not less than 2;

[0058] Processing unit 702 is configured to generate a constant modulus sequence b of length N based on the length parameter N, the sequence containing elements b0, b1, ..., b N-1 ;

[0059] Construction unit 703 is used to obtain the permutation π of a preset set {0,1,…,N-1}, and generate an initial complementary sequence A based on the sequence b and the permutation π, wherein the initial complementary sequence A consists of N subsequences of length N {a0,a1,…,a...} N-1}constitute;

[0060] Selection unit 704 is used to preset the sequence set size parameter P, where P is a positive integer not less than 2, and select a P-order unitary matrix O, wherein each element of the unitary matrix O... The modulus of each is 1, where the values ​​of s and t range from 0 to P-1;

[0061] Extension unit 705 is used to extend the initial complementary sequence O based on the unitary matrix O to generate a complementary sequence set {A}. (0) A (1θ ,…,A (P-1 )}.

[0062] It should be noted that the specific manner in which each module performs its operation in the apparatus described in the above embodiments has been described in detail in the embodiments of the method, and will not be elaborated here.

[0063] Example 3:

[0064] Corresponding to the above method embodiments, this embodiment also provides an example of generating ISAC complementary sequences, as shown below:

[0065] First, let the sequence length N = 8. It is a constant modulus sequence with permutation π = (4, 6, 5, 0, 1, 2, 3, 7). As shown in construction method 1, a complementary sequence is generated. B is shown below:

[0066]

[0067] in, This indicates that each element in B is acted upon by ξ8, and each row of A represents a subsequence of a complementary sequence.

[0068] The presupposes a unitary matrix O as follows:

[0069]

[0070] The unitary matrix O is a 2-order unitary matrix, generating two complementary sequences. and Two complementary sequences are shown below:

[0071]

[0072]

[0073] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0074] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for generating a set of complementary ISAC sequences, characterized in that, include: The sequence length parameter N is preset, where N is a positive integer not less than 2; Based on the length parameter N, a constant modulus sequence b of length N is generated, which contains elements b0, b1, ..., b N-1 ; Obtain the permutation π of the preset set {0,1,…,N-1}, and generate an initial complementary sequence A based on the sequence b and the permutation π, wherein the initial complementary sequence A consists of N subsequences of length N {a0,a1,…,a...} N-1 }constitute; A preset sequence set size parameter P is set, where P is a positive integer not less than 2, and a P-order unitary matrix O is selected, wherein each element of the unitary matrix O... The modulus of each is 1, where the values ​​of s and t range from 0 to P-1; Based on the unitary matrix O, the initial complementary sequence O is expanded to generate a complementary sequence set {A}. (0) A (1) ,…,A (P-1) } 2. The ISAC complementary sequence generation method according to claim 1, characterized in that, And based on the sequence b and the permutation π, including: Based on the preset subsequence construction formula, the nth element b of the constant modulus sequence b is... n The value π corresponding to the nth position of the permutation π n The subsequence a is generated by processing the preset Nth-order primitive unit root. m The nth element a m,n ; Repeat the above steps to generate N subsequences, and build a set based on all the subsequences to obtain an initial complementary sequence A.

3. The ISAC complementary sequence generation method according to claim 1, characterized in that... Generate a complementary sequence set {A} (0) A (1) ,…,A (P-1) },include: Based on P extended complementary sequences A (k) Generate a set of complementary sequences, where k is the index of the extended complementary sequence, and each extended complementary sequence A... (k) It contains PN subsequences of length N.

4. The ISAC complementary sequence generation method according to claim 3, characterized in that... The complementary sequence set contains P extended complementary sequences A. (k) ,include: Based on the element o in the k-th row and r-th column of the unitary matrix O k,r The u-th subsequence a of the initial complementary sequence A u Performing multiplication, we obtain the extended complementary sequence A. (k) The rN+uth subsequence Given that 0 ≤ r, k ≤ P-1, and 0 ≤ u ≤ N.

5. The ISAC complementary sequence generation method according to claim 1, characterized in that... Generate a constant modulus sequence b of length N based on the length parameter N, including: The constant modulus sequence b is randomly generated based on the length parameter N, and the modulus value of each element in the constant modulus sequence b is equal.

6. An ISAC complementary sequence generation device, characterized in that, include: A preset unit is used to preset the sequence length parameter N, where N is a positive integer not less than 2; The processing unit is configured to generate a constant modulus sequence b of length N based on the length parameter N, the sequence containing elements b0, b1, ..., b N-1 ; A construction unit is used to obtain the permutation π of a preset set {0,1,…,N-1}, and generate an initial complementary sequence A based on the sequence b and the permutation π, wherein the initial complementary sequence A consists of N subsequences of length N {a0,a1,…,a...} N-1 }constitute; The selection unit is used to preset the sequence set size parameter P, where P is a positive integer not less than 2, and to select a P-order unitary matrix O, wherein each element of the unitary matrix O... The modulus of each is 1, where the values ​​of s and t range from 0 to P-1; An extension unit is used to extend the initial complementary sequence O based on the unitary matrix O to generate a complementary sequence set {A}. (0) A (1) ,…,A (P-1) } 7. The ISAC complementary sequence generation apparatus according to claim 6, characterized in that, The building unit includes: The first construction subunit is used to construct the nth element b of the constant modulus sequence b based on a preset subsequence construction formula. n The value π corresponding to the nth position of the permutation π n The subsequence a is generated by processing the preset Nth-order primitive unit root. m The nth element a m,n ; The second construction subunit is used to repeat the above steps to generate N subsequences, and to build a set based on all the subsequences to obtain an initial complementary sequence A.

8. The ISAC complementary sequence generation apparatus according to claim 6, characterized in that, The expansion unit includes: The first extended subunit is used to expand complementary sequences A based on P sequences. (k) Generate a set of complementary sequences, where k is the index of the extended complementary sequence, and each extended complementary sequence A... (k) It contains PN subsequences of length N.

9. The ISAC complementary sequence generation apparatus according to claim 6, characterized in that, The first extended subunit includes: The second extended subunit is used to base the element o in the k-th row and r-th column of the unitary matrix O. k,r The u-th subsequence a of the initial complementary sequence A u Performing multiplication, we obtain the extended complementary sequence A. (k) The rN+uth subsequence Given that 0 ≤ r, k ≤ P-1, and 0 ≤ u ≤ N.

10. The ISAC complementary sequence generation apparatus according to claim 6, characterized in that, The processing unit includes: The first processing subunit is used to randomly generate the constant modulus sequence b based on the length parameter N, wherein the modulus value of each element of the constant modulus sequence b is equal.

Images