Construction method and device for generating three-phase complementary triad based on kronecker product

Abstract

The application discloses a construction method and device for generating three-phase complementary triad based on Kronecker product, and belongs to the technical field of communication systems. The construction method comprises the following steps: taking a three-phase complementary triad (a, b, c) with a random length of M as a seed sequence; carrying out bit interleaving on the three-phase complementary triad (a, b, c) to generate a sequence d; taking a three-phase 3*3 complete complementary code K with a random length of N; connecting the complete complementary code K in series into three parts k1, k2 and k3; and respectively obtaining the Kronecker products of the sequence d and k1, k2 and k3. The construction device comprises a control circuit, a switch circuit, six input shift registers, three multipliers and three output shift registers. The sequence length and the zero correlation zone width of the three-phase complementary triad obtained by the application are adjustable, the three-phase aperiodic Z complementary sequence triad and the Golay complementary sequence triad with the maximum zero correlation zone width can be generated, and the application can be applied to orthogonal frequency division multiplexing transmission and channel estimation in a wireless communication process.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of communication systems, and particularly to a construction method and device for generating a three-phase complementary triad based on a Kronecker product. BACKGROUND

[0002] In 1951, the two-phase Golay complementary pair was introduced, whose aperiodic autocorrelation function is zero at all non-zero shifts, and is used for infrared spectroscopy (Golay M J E. Static multislit spectrometry and its application to the panoramic display of infrared spectra[J]. JOSA, 1951, 41(7): 468-472.). Since then, the Golay complementary pair has been widely used in engineering due to its ideal correlation characteristics. For example, it can be used in the fields of inter-symbol interference channel estimation, radar waveform design, and peak-to-average envelope power ratio control in multi-carrier communication. The main disadvantage of the two-phase Golay complementary pair is its limited availability for different lengths. In 1974, it was proved that the two-phase Golay complementary pair only exists in the case of length 2 α 10 β 26 γ (Turyn R J. Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings[J]. Journal of Combinatorial Theory, Series A, 1974, 16(3): 313-333.).

[0003] To find other length binary sequence pairs, the concept of Z-complementary pairs was proposed in 2007, whose aperiodic autocorrelation is not zero everywhere but zero within a zero correlation zone (Fan P, Yuan W, Tu Y. Z-complementary binary sequences [J]. IEEE Signal Processing Letters, 2007, 14(8): 509-512.). In recent years, aperiodic binary Z-complementary sequence pairs have established a relatively rich theory. In 2010, the existence of even-length aperiodic binary Z-complementary sequence pairs was proved (Li X, Fan P, Tang X, et al. Existence of Binary Z-Complementary Pairs [J]. IEEE Signal Processing Letters, 2010, 18(1): 63-66.). In 2014, the properties and system construction method of odd-length aperiodic binary Z-complementary sequence pairs were studied (Liu Z, Parampalli U, Guan Y L. Optimal odd-length binary Z-complementary pairs [J]. IEEE transactions on information theory, 2014, 60(9): 5768-5781.). In 2017, a construction method of aperiodic Z-complementary sequence based on generalized Boolean functions was proposed (Chen C Y. A novel construction of Z-complementary pairs based on generalized Boolean functions [J]. IEEE Signal Processing Letters, 2017, 24(7): 987-990.). In 2021, even-length Z-complementary pairs with large zero correlation zones were constructed (Yu T, Du X, Li L, et al. Constructions of even-length Z-complementary pairs with large zero correlation zones [J]. IEEE Signal Processing Letters, 2021, 28: 828-831.).

[0004] In contrast, the research on non-periodic three-phase sequence triad is relatively weak. In 1980, two-phase Golay complementary pairs were extended from a two-phase alphabet {1, -1} to a three-phase alphabet {1, ω, ω2} by using any three-phase Golay complementary triad of length N to obtain a three-phase Golay complementary triad of length 3N (Frank R. Polyphase complementary codes [J]. IEEE Transactions on Information theory, 1980, 26(6): 641-647.). The three-phase alphabet is attractive in application because fewer phases are easier to distinguish received signal levels at the receiver. In 2010, three-phase sequence triads of lengths from 2 to 22 were exhaustively searched (Avis A A. 3-phase Golay triads [D]. Science: Department of Mathematics, 2010.). In 2019, it was proved that there is no three-phase Golay sequence triad of length N≡4(mod6) (Avis A A, Jedwab J. Three-phase Golay sequence and array triads [J]. Journal of Combinatorial Theory, Series A, 2021, 180: 105422.). In 2021, Z-complementary sequence triads and almost complementary triads were constructed (Liu C, Liu S, Lei X, et al. Three-phase Z-complementary triads and almost complementary triads [J]. Cryptography and Communications, 2021, 13(5): 763-773.). In summary, there are few construction methods for non-periodic three-phase complementary sequence triads in the prior art, and all the required lengths cannot be generated, the construction process is complex, and the implementation process is difficult. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a construction method and device for generating three-phase complementary triads based on Kronecker product, which can convert known three-phase Golay complementary triads into three-phase complementary triads with longer length and larger ZCZ width, and the obtained sequence length and ZCZ width are adjustable.

[0006] To solve the above technical problems, the technical scheme adopted by the present application is:

[0007] A construction method for generating three-phase complementary triad based on Kronecker product, comprising the following steps:

[0008] Step 1, taking a three-phase complementary sequence triad (a, b, c) with length M as a seed sequence;

[0009] Step 2, performing bit interleaving on the three-phase complementary sequence triad (a, b, c) to generate a sequence d;

[0010] Step 3, taking a three-phase 3*3 complete complementary code K with length N;

[0011] Step 4, concatenating the complete complementary code K into three parts k1, k2 and k3;

[0012] Step 5, respectively obtaining the Kronecker product of the sequence d and k1, k2 and k3.

[0013] Further improvement of the technical scheme of the application is that in step 1, the three-phase complementary sequence refers to all elements in the sequence taking values from {1, ω, ω 2}, wherein ω = e 2πi / 3 .

[0014] Further improvement of the technical scheme of the application is that the sequence d is expressed as d = (d1, d2, d3,..., d 3M ); the positions of the three-phase complementary sequence triad (a, b, c) with zero autocorrelation sum are (r1, r2,..., r l ), and the autocorrelation function of the sequence d generated after bit interleaving is also zero at positions (3r1, 3r2,..., 3r l ).

[0015] Further improvement of the technical scheme of the application is that the complete complementary code

[0016] K: (k 11 , k 12 , k 13 ; k 21 , k 22 , k 23 ; k 31 , k 32 , k 33 ) has (k 11 , k 12 , k 13 ), (k 21 , k 22 , k 23 ) and (k 31 , k 32 , k 33 ) three groups of sequences, and the autocorrelation sum of each group of sequences is 0 at positions other than zero shift, and the three groups of sequences are mutually irrelevant.

[0017] Further improvement of the technical scheme of the present application is that in step 4, the completely complementary code K is connected in series into three parts, i.e.

[0018] k1=(k 11 ,k 12 ,k 13 ,k 11 ,k 12 ,k 13 ,...,k 11 ,k 12 ,k 13 );

[0019] k2=(k 21 ,k 22 ,k 23 ,k 21 ,k 22 ,k 23 ,...,k 21 ,k 22 ,k 23 );

[0020] k3=(k 31 ,k 32 ,k 33 ,k 31 ,k 32 ,k 33 ,...,k 31 ,k 32 ,k 33 )。

[0021] Further improvement of the technical scheme of the present application is that in step 5, the Kronecker product of the sequence d and the three parts is respectively obtained.

[0022]

[0023]

[0024]

[0025] Further improvement of the technical scheme of the present application is that when the seed sequence is a Golay sequence, the generated sequence is also a Golay sequence; when the seed sequence is a Z-complementary sequence, the generated sequence is also a Z-complementary sequence; and when the seed sequence is a Z-complementary sequence, the type of the generated sequence is the same as that of the seed sequence, the sequence length of the generated sequence is lengthened, the width of the zero correlation zone is lengthened, and the width ratio of the zero correlation zone is the same as that of the seed sequence.

[0026] A kind of construction device of three-phase complementary triad based on kronig product, the device includes control circuit, switch circuit, six input shift registers, three multipliers and three output shift registers;

[0027] The control circuit is used to control the state of switch, and the input order of each sequence;

[0028] The switch circuit is used to control the input of input shift register 1,2,3;

[0029] The input shift register 1,2,3 respectively realizes the temporary storage of three-phase complementary triad (a, b, c);

[0030] The input shift register 4,5,6 respectively realizes the temporary storage of three parts k1,k2,k3 connected in series by completely complementary code;

[0031] The three multipliers are used to generate the result of kronig product of input sequence;

[0032] The output shift register 1,2,3 respectively realizes the temporary storage of generated three-phase complementary sequence triad f1,f2,f3.

[0033] The further improvement of the technical scheme of the present application is that the process of the construction device generating three-phase complementary triad includes:

[0034] Firstly, switch circuit controls input shift register 1 to output a number to three multipliers, and input shift register 4,5,6 respectively outputs N numbers in turn to multiply with the number output by input shift register 1, and the results obtained by multipliers 1,2,3 are sequentially moved into output shift register 1,2,3;

[0035] Secondly, switch circuit controls input shift register 2 to output a number to three multipliers, and input shift register 4,5,6 respectively outputs N numbers in turn to multiply with the number output by input shift register 2, and the results obtained by multipliers 1,2,3 are sequentially moved into output shift register 1,2,3;

[0036] Finally, switch circuit controls input shift register 3 to output a number to three multipliers, and input shift register 4,5,6 respectively outputs N numbers in turn to multiply with the number output by input shift register 3, and the results obtained by multipliers 1,2,3 are sequentially moved into output shift register 1,2,3;

[0037] Repeat the above operation M times.

[0038] Due to the adoption of the above technical scheme, the technical progress achieved by the present application is:

[0039] The application proposes a new three-phase complementary triplet construction method and device by using a completely complementary code and a three-phase complementary sequence triplet; a three-phase complementary sequence triplet (a, b, c) with a random length M is taken as a seed sequence, and the (a, b, c) is bit-interleaved to generate a sequence d, which is expressed as d=(d1, d2, d3,..., d 3M ). A three-phase 3*3 completely complementary code K with a random length N is connected in series into three parts k1, k2, k3, i.e., k1=(k 11 , k 12 , k 13 , k 11 , k 12 , k 13 , ..., k 11 , k 12 , k 13 ), k2=(k 21 , k 22 , k 23 , k 21 , k 22 , k 23 , ..., k 21 , k 22 , k 23 ), and k3=(k 31 , k 32 , k 33 , k 31 , k 32 , k 33 , ..., k 31 , k 32 , k 33 ); and the Kronecker products f1, f2, f3 of the sequence d and k1, k2, k3 are obtained respectively. The generated sequence (f1, f2, f3) has similar characteristics to the seed sequence (a, b, c); when the seed sequence is a Golay sequence, the generated sequence is also a Golay sequence; and when the seed sequence is a Z-complementary sequence, the generated sequence is also a Z-complementary sequence. The sequence length of the generated sequence is longer than that of the seed sequence, and when the seed sequence is a Z-complementary sequence, the type of the generated sequence is the same as that of the seed sequence, the zero correlation zone width is longer, and the zero correlation zone width ratio is the same as that of the seed sequence. The application can be applied to orthogonal frequency division multiplexing transmission, channel estimation, etc. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort.

[0041] Figure 1 is the principle block diagram of the construction method of the three-phase complementary triad based on the Kronecker product provided by the application;

[0042] Figure 2 is the principle structure diagram of the construction device of the three-phase complementary triad based on the Kronecker product provided by the application;

[0043] Figure 3 is the simulation diagram of the autocorrelation function and of the sequence (a, b, c) in the embodiment of the application;

[0044] Figure 4 is the simulation diagram of the autocorrelation function of the sequence d in the embodiment of the application;

[0045] Figure 5 is the simulation diagram of the autocorrelation function and of the sequence (f1, f2, f3) in the embodiment of the application. DETAILED DESCRIPTION

[0046] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification and claims of the application and the above-mentioned drawings are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device containing a series of steps or units does not have to be limited to the clearly listed steps or units, but can include other steps or units that are not clearly listed or inherent to the process, method, product or device.

[0047] The embodiment of the application provides a construction method and device of a three-phase complementary triad based on the Kronecker product, solves the problems of "few construction methods of a three-phase complementary sequence triad, and the construction process is relatively complex and the implementation process is relatively difficult." in the prior art, and the general idea is as follows: generating a three-phase non-periodic complementary sequence triad by using the Kronecker product method, and performing the Kronecker product on the sequence obtained after the bit interleaving of the three-phase complementary sequence triad of any length and the three-phase 3*3 complete complementary code (CCC) of any length to obtain the three-phase non-periodic complementary sequence triad.

[0048] The application will be further described in detail below in combination with the drawings and embodiments:

[0049] As shown in Figure 1 a construction method of a three-phase complementary sequence triad based on the Kronecker product, comprising the following steps:

[0050] Step 1, taking a three-phase complementary sequence triad (a, b, c) with a length of M as a seed sequence;

[0051] The three-phase complementary sequence means that all elements in the sequence take values from {1, ω, ω 2}, where ω = e 2πi / 3 .

[0052] Step 2, bit interleaving the three-phase complementary sequence triplet (a, b, c) to generate sequence d;

[0053] The sequence d is expressed as d = (d1, d2, d3,..., d 3M ), the positions of the three-phase complementary sequence triplet (a, b, c) with zero autocorrelation sum are (r1, r2,..., r l ), and the autocorrelation function of the sequence d generated after bit interleaving is also zero at positions (3r1, 3r2,..., 3r l ).

[0054] Step 3, randomly take a three-phase 3*3 complete complementary code K with length N;

[0055] The complete complementary code K: (k 11 ,k 12 ,k 13 ; k 21 ,k 22 ,k 23 ; k 31 ,k 32 ,k 33 ) has (k 11 ,k 12 ,k 13 ), (k 21 ,k 22 ,k 23 ) and (k 31 ,k 32 ,k 33 ) three groups of sequences, and the autocorrelation sum of each sequence in the three groups of sequences is zero at positions other than zero shift, and the two sequences in the three groups are not correlated.

[0056] Step 4, concatenating the complete complementary code K into three parts k1, k2, k3;

[0057] That is:

[0058] k1 = (k 11 ,k 12 ,k 13 ,k 11 ,k 12 ,k 13 ,...,k 11 ,k 12 ,k 13 )

[0059] k2 = (k 21 ,k22 ,k 23 ,k 21 ,k 22 ,k 23 ,...,k 21 ,k 22 ,k 23

[0060] k3=(k 31 ,k 32 ,k 33 ,k 31 ,k 32 ,k 33 ,...,k 31 ,k 32 ,k 33

[0061] Step 5, respectively, obtain the Kronecker product of sequence d and k1, k2, k3, and three sequences obtained are as follows:

[0062]

[0063]

[0064]

[0065] When the seed sequence is Golay sequence, the generated sequence is also Golay sequence; when the seed sequence is Z complementary sequence, the generated sequence is also Z complementary sequence. The sequence length of the generated sequence is longer than that of the seed sequence, and when the seed sequence is Z complementary sequence, the type of the generated sequence is the same as that of the seed sequence, the zero correlation zone width is lengthened, and the zero correlation zone width ratio is the same as that of the seed sequence.

[0066] As shown in Figure 2 , the application further provides a construction device for generating three-phase complementary triad based on the Kronecker method, which comprises a control circuit, a switch circuit, six input shift registers, three multipliers and three output shift registers, wherein:

[0067] The control circuit is used for controlling the state of the switch and the input order of each sequence;

[0068] The switch circuit is used for controlling the input of the input shift registers 1, 2 and 3;

[0069] The input shift registers 1, 2 and 3 respectively realize the temporary storage of the three-phase complementary sequence triad (a, b, c);

[0070] The input shift registers 4, 5 and 6 respectively realize the temporary storage of the three-part body k1, k2 and k3 connected in series by the completely complementary code K; ​​

[0071] The three multipliers are used to generate the result of the input sequence Kronecker product;

[0072] The output shift registers 1, 2, and 3 respectively realize the temporary storage of the generated three-phase complementary sequence triplet f1, f2, and f3.

[0073] Further, the device generates a three-phase complementary triplet (three-phase non-periodic complementary sequence triplet) generation process, specifically comprising:

[0074] First, the switch circuit controls the input shift register 1 to output a number to the three multipliers, and the input shift registers 4, 5, and 6 respectively output N numbers to multiply with the number output by the input shift register 1, and the results obtained by the multipliers 1, 2, and 3 are sequentially shifted into the output shift registers 1, 2, and 3;

[0075] Second, the switch circuit controls the input shift register 2 to output a number to the three multipliers, and the input shift registers 4, 5, and 6 respectively output N numbers to multiply with the number output by the input shift register 2, and the results obtained by the multipliers 1, 2, and 3 are sequentially shifted into the output shift registers 1, 2, and 3;

[0076] Finally, the switch circuit controls the input shift register 3 to output a number to the three multipliers, and the input shift registers 4, 5, and 6 respectively output N numbers to multiply with the number output by the input shift register 3, and the results obtained by the multipliers 1, 2, and 3 are sequentially shifted into the output shift registers 1, 2, and 3;

[0077] Repeat the above operation M times.

[0078] Embodiment

[0079] The construction method for generating a three-phase complementary sequence triplet based on Kronecker product includes the following steps:

[0080] Step 1, take a three-phase complementary sequence triplet (a, b, c) with a length of M as a seed sequence;

[0081] Let M = 5, and the zero correlation zone length Z = 4, then the specific sequence is as follows: a = (1, 2, 1, 1, 0), b = (1, 1, 2, 1, 0), and c = (1, 1, 1, 2, 0);

[0082] Step 2, bit-interleave the three-phase complementary sequence triplet (a, b, c) to generate a sequence d;

[0083] The generated sequence d = (1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 0, 0, 0).

[0084] Step 3, take a three-phase 3*3 complete complementary code K with a length of N;

[0085] Let N=3, then the specific sequence is as follows: k 11 =(0, 1, 2), k 12 =(0, 2, 1), k 13 =(0, 0, 0); k 21 =(0, 2, 1), k 22 =(0, 0, 0), k 23 =(0, 1, 2); k 31 =(0, 0, 0), k 32 =(0, 1, 2), k 21 =(0, 2, 1).

[0086] Step 4, concatenate the completely complementary code K into three parts k1, k2, k3, which are as follows:

[0087] k1=(0, 1, 2, 0, 2, 1, 0, 0, 0,..., 0, 2, 1, 0, 0, 0)

[0088] k2=(0, 2, 1, 0, 0, 0, 0, 1, 2,..., 0, 0, 0, 0, 1, 2)

[0089] k3=(0, 0, 0, 0, 1, 2, 0, 2, 1,..., 0, 1, 2, 0, 2, 1)

[0090] Step 5, respectively, the Kronecker product of sequence d and k1, k2, k3, can get f1, f2, f3 is:

[0091] f1=(1, 2, 0, 1, 0, 2, 1, 1, 1, 2, 0, 1, 1, 0, 2, 1, 1, 1, 1, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 2, 2, 0, 1, 2, 0, 2, 1, 0, 0, 0),

[0092] f2=(1, 0, 2, 1, 1, 1, 1, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 2, 2, 1, 2, 0, 1, 0, 2, 1, 1, 1, 2, 0, 1, 0, 2, 1, 0, 0, 0, 0, 1, 2),

[0093] f3=(1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 2, 2, 1, 2, 0, 1, 0, 2, 1, 1, 1, 2, 0, 1, 1, 0, 2, 1, 1, 1, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1).

[0094] As can be seen in the embodiments, when the seed sequence triple-phase complementary sequence triplet (a, b, c) is the first type of triple-phase complementary sequence triplet, and the length M = 5 and the zero correlation zone length Z = 4, i.e. the sum of the autocorrelation function thereof is 0 at the shift (1, 2, 3) as shown in Figure 3 . The length of the sequence d generated after bit interleaving is 15, and the autocorrelation function thereof is 0 at the shift (3, 6, 9) as shown in Figure 4 . The final sequence (f1, f2, f3) is also the first type of triple-phase complementary sequence triplet, and the length is 45 and the zero correlation zone length Z = 36, thereby realizing the construction of triple-phase complementary sequence triplet with longer length and wider zero correlation zone as shown in Figure 5 .

[0095] In summary, the present application takes triple-phase complementary sequence triplet (a, b, c) with length M as a seed sequence, and performs bit interleaving on (a, b, c) to generate sequence d, which is expressed as d = (d1, d2, d3,..., d 3M ), and takes triple-phase 3*3 complete complementary code K with length N, and connects the complete complementary code in series into three parts k1, k2 and k3, i.e. k1 = (k 11 , k 12 , k 13 , k 11 , k 12 , k 13 ,..., k 11 , k 12 , k 13 ), k2 = (k 21 , k 22 , k 23 , k 21 , k 22 , k 23 ,..., k 21 , k 22 , k 23 ), and k3 = (k 31 , k 32 , k 33 , k 31 , k 32 , k 33 ,..., k 31 , k 32 , k 33); respectively obtain the Kronecker product f1, f2, f3 of the sequence d and k1, k2, k3; that is, a new three-phase complementary triad is constructed by the perfect complementary code and the three-phase complementary triad. The characteristics of the generated sequence (f1, f2, f3) are similar to the seed sequence (a, b, c), when the seed sequence is Golay sequence, the generated sequence is also Golay sequence; when the seed sequence is Z complementary sequence, the generated sequence is also Z complementary sequence. The sequence length of the generated sequence is longer than the seed sequence, and when the seed sequence is Z complementary sequence, the type of the generated sequence is the same as the seed sequence, and the width of the zero correlation zone is lengthened.

[0096] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not limited to them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method of construction of a three-phase complementary triad based on a Kronecker product, characterized in that: The method comprises the following steps: Step 1, taking a three-phase complementary sequence triplet (a, b, c) with a length of M as a seed sequence; Step 2, performing bit interleaving on the three-phase complementary sequence triplet (a, b, c) to generate a sequence d; The sequence d is expressed as d = (d1, d2, d3,..., d 3M ); the positions where the autocorrelation sum of the three-phase complementary sequence triplet (a, b, c) is zero are (r1, r2,..., r l ); the autocorrelation function of the sequence d generated after bit interleaving is also zero at positions (3r1, 3r2,..., 3r l ); Step 3, taking a three-phase 3*3 complete complementary code K with a length of N; Step 4, concatenating the complete complementary code K into three parts k1, k2, k3; that is: k1= (k 11 ,k 21 ,k 31 ,k 11 ,k 21 ,k 31 ,...,k 11 ,k 21 ,k 31 ); k2= (k 12 ,k 22 ,k 32 ,k 12 ,k 22 ,k 32 ,...,k 12 ,k 22 ,k 32 ); k3 = (k 13 ,k 23 ,k 33 ,k 13 ,k 23 ,k 33 ,...,k 13 ,k 23 ,k 33 ); Step 5, respectively calculating the Kronecker products of the sequence d and k1, k2, k3.

2. The method of claim 1, wherein the method is based on the construction of a three-phase complementary triad using the Kronecker product. In step 1, the three-phase complementary sequence means that all elements in the sequence take values from the set {1, ω, ω 2}, where ω = e 2πi / 3 .

3. The method of claim 1, wherein the method is based on the construction of a three-phase complementary triad using the Kronecker product. complementary code K: (k 11 ,k 12 ,k 13 ; k 21 ,k 22 ,k 23 ; k 31 ,k 32 ,k 33 ) (k 11 ,k 12 ,k 13 ) (k 21 ,k 22 ,k 23 ) and (k 31 ,k 32 ,k 33 ) are all three groups of sequences, the autocorrelation of each sequence in the three groups of sequences is 0 at all positions except zero shift, and the three groups of sequences are not correlated with each other in pairs.

4. The method of claim 1, wherein: In Step 5, the Kronecker products of the sequence d and the three parts are respectively calculated:

5. The method for constructing a triplet based on the Kronecker product according to claim 1, characterized in that: When the seed sequence is a Golay sequence, the generated sequence is also a Golay sequence; when the seed sequence is a Z-complementary sequence, the generated sequence is also a Z-complementary sequence; and when the seed sequence is a Z-complementary sequence, the type of the generated sequence is the same as that of the seed sequence, the sequence length of the generated sequence is lengthened, the zero correlation zone width is lengthened, and the zero correlation zone width ratio is the same as that of the seed sequence.

6. A construction apparatus for use in a method of constructing a three-phase complementary triad based on a Kronecker product according to any one of claims 1 to 5, characterized in that: The device comprises a control circuit, a switch circuit, six input shift registers, three multipliers, and three output shift registers; The control circuit is used for controlling the states of the switches and the input sequences of the sequences; The switch circuit is used for controlling the inputs of the input shift registers 1, 2, and 3; The input shift registers 1, 2, and 3 are respectively used for temporarily storing a three-phase complementary triplet (a, b, c); The input shift registers 4, 5, and 6 are respectively used for temporarily storing three parts k1, k2, and k3 obtained by concatenating a complete complementary code; The three multipliers are used for generating the results of the Kronecker products of the input sequences; The output shift registers 1, 2, and 3 are respectively used for temporarily storing generated three-phase complementary sequence triplets f1, f2, and f3.

7. The construction apparatus of claim 6, wherein: The process of constructing the device to generate a three-phase complementary triplet comprises the following steps: First, the switch circuit controls the input shift register 1 to output a number to the three multipliers, the input shift registers 4, 5, and 6 respectively output N numbers to multiply with the number output by the input shift register 1, and the results obtained by the multipliers 1, 2, and 3 are sequentially shifted into the output shift registers 1, 2, and 3; Second, the switch circuit controls the input shift register 2 to output a number to the three multipliers, the input shift registers 4, 5, and 6 respectively output N numbers to multiply with the number output by the input shift register 2, and the results obtained by the multipliers 1, 2, and 3 are sequentially shifted into the output shift registers 1, 2, and 3; Finally, the switch circuit controls the input shift register 3 to output a number to the three multipliers, the input shift registers 4, 5, and 6 respectively output N numbers to multiply with the number output by the input shift register 3, and the results obtained by the multipliers 1, 2, and 3 are sequentially shifted into the output shift registers 1, 2, and 3; The above operations are repeated M times.

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