阅读说明：本技术 广义成对复数互补码gpcc码本构造方法及其扩展方法 (Generalized paired complex complementary code GPCC codebook construction method and expansion method thereof ) 是由 刘喜庆 彭木根 王志峰 于 2020-11-25 设计创作，主要内容包括：本发明公开一种广义成对复数互补码GPCC码本构造方法及其扩展方法,所述构造方法包括：步骤1.1,设第一矩阵A-M为一个M维正交哈达玛矩阵；步骤1.2,利用向量[+1,+1]和[+1,-1]分别扩展正交矩阵A-M的维度,获得扩展正交矩阵和步骤1.3,设第二矩阵D-N为一个N×N的正交哈达玛矩阵,令N＝2M,根据第二矩阵D获得配对矩阵E-N；步骤1.4,根据矩阵和E-N,构造GPCC码本。所述扩展方法包括将GPCC码族进行扩展。本发明所述构造方法构造的GPCC码能够实现完美的自相关特性、能够实现完美的对内相关特性、表现为完美的互相关性；所述扩展方法使码本容量得到扩展,且具备完美相关特性。(The invention discloses a construction method and an extension method of a generalized paired complex complementary code GPCC codebook, wherein the construction method comprises the following steps: step 1.1, set the first matrix A M An M-dimensional orthogonal Hadamard matrix is formed; step 1.2, use vector [ +1, +1]And [ +1, -1]Separately spreading orthogonal matrices A M Dimension of (2), obtaining an extended orthogonal matrix And step 1.3, set the second matrix D N An N × N orthogonal Hadamard matrix is formed, N is 2M, and a pairing matrix E is obtained according to a second matrix D N (ii) a Step 1.4, rootingAccording to the matrix And E N And constructing a GPCC codebook. The extension method comprises the step of extending the GPCC code family. The GPCC code constructed by the construction method can realize perfect autocorrelation property, perfect intra-correlation property and perfect cross correlation; the expansion method expands the capacity of the codebook and has perfect correlation characteristics.)

1. A method for constructing a GPCC codebook of generalized paired complex complementary codes comprises the following steps:

step 1.1, set the first matrix A_MAn M-dimensional orthogonal Hadamard matrix is formed;

step 1.2, use vector [ +1, +1]And [ +1, +1]Separately spreading orthogonal matrices A_MDimension of (2), obtaining an extended orthogonal matrixAnd

step 1.3, set the second matrix D_NAn N × N orthogonal Hadamard matrix is formed, N is 2M, and a pairing matrix E is obtained according to a second matrix D_N；

Step 1.4, according to the matrix And E_NAnd constructing a GPCC codebook.

2. The method of claim 1, wherein in step 1.1, the first matrix A is a first matrix_MAs shown in the following formula:

wherein, in the formula (1), a_m，nE { +1, -1}, M, n { +1, 2, …, M, and any two rows and two columns of the first matrix a are orthogonal, i.e., two columns and two rows are orthogonalAndwhen i ≠ j.

3. The method of claim 2, wherein in step 1.2, the extended orthogonal matrix is expressed as:

wherein, in the formulas (2) and (3),representing the kronecker product operator,a co-directional branch-circuit spreading matrix is represented,representing an orthogonal branch spreading matrix.

4. The method of claim 3, wherein in step 1.3, the second matrix D is a first matrix D_NIs divided intoTwo sub-matrices, e.g.Andthen D is_NExpressed as:

in the above formula (4), each sub-matrix is composed of M row vectors, wherein the v-th row vector is represented asAnd v E {1, 2, …, M }, pairing matrix E_NBy reconstructing the second matrix D_NObtaining, namely:

in equation (5), K denotes the number of GPCC codes, K denotes a GPCC code number, and K {1, 2, …, K }.

5. The method of claim 4, wherein in step 1.4, the GPCC codebook is expressed as:

the first pair of GPCC codes is:

the second pair of GPCC codes is:

the v-th pair of GPCC codes is:

the Mth pair of GPCC codes is:

where i denotes the imaginary unit, for C^(k)Wherein k represents the constructed GPCC code group number, k is 2v, v represents the code logarithm coding in the GPCC codebook set,representing an N by N diagonal matrix having major diagonal elements ofNamely, it isIndicating the in-phase branch and Q the quadrature branch.

6. A GPCC codebook cyclic shift codebook extension method comprises the following steps:

step 2.1, setting an address code expansion matrix psi^(j)Represented by the formula:

step 2.2, setting C^(k)An initial code of GPCC code C (K, M, N), then C^(k)The extended jth (j ═ 1, …, N) cpccs code is expressed as:

C^(j)＝C^(k)Ψ^(j)……(7)；

assume initial code C^(k)The code length of (2) is N, and the capacity of the signature code is expanded by N times after cyclic shift.

Technical Field

The invention relates to the technical field of communication, in particular to a generalized paired Complex complementary code GPCC (generalized Pairwise Complex) codebook construction method and an expansion method thereof.

Background

In order to improve the service quality and meet the demand of exponentially-increased terminals to new services and new applications in the future, a code-domain Non-orthogonal multiple access (NOMA) technology is considered as one of the most potential multiple access schemes for future wireless communication, and NOMA allows multiple users to share the same resource block for transmission, so that the spectrum efficiency and the user capacity of the system can be remarkably improved. However, the poor direct correlation of the conventional NOMA signature code can generate complex multiple access interference at the receiving end, so that designing a large number of signature codes with ideal and quasi-ideal correlation becomes the most promising and challenging subject in the CD-NOMA research field.

For example, in "Correlation and set size bases of complementary sequences with low Correlation zone" (z.liu, et al ieee trans. com., vol.59, No.12, pp.3285-3289,2011), a complementary code family construction method based on low Correlation region and a complementary code family construction method based on low Correlation are proposed, which relax the soft constraint of Correlation in code groups, only require that there is ideal Correlation between signature codes in a certain region or exhibit low Correlation in the whole code group region, so that compared with the traditional complete complementary codes, the quasi-complementary code codebook capacity of the paper structure is significantly increased, and can support multiple access of more users. For another example, chinese patent application No. 200510060641.7 discloses a method for constructing generalized paired complementary codes, which generates a Zero Correlation Zone (ZCZ) in the intra-pair cross correlation function of the generalized paired complementary codes, and has only a few non-Zero side lobes and sparse distribution outside the ZCZ. In summary, although the inner generalized complementary code has a ZCZ region to eliminate multiple access interference to some extent, if the interference signal falls outside the ZCZ, a complex multiple access interference problem is still introduced.

Based on the technical problems in the prior art, the invention provides a generalized paired complex complementary code GPCC codebook construction method and an expansion method thereof.

Disclosure of Invention

The invention provides a generalized paired complex complementary code GPCC codebook construction method and an expansion method thereof.

In order to achieve the purpose, the invention adopts the following technical scheme:

in one aspect, the present invention provides a method for constructing a GPCC codebook of generalized paired complex complementary codes, including:

step 1.1, set the first matrix A_MAn M-dimensional orthogonal Hadamard matrix is formed;

step 1.2, use vector [ +1, +1]And [ +1, -1]Separately spreading orthogonal matrices A_MDimension of (2), obtaining an extended orthogonal matrixAnd

step 1.3, set the second matrix D_NAn N × N orthogonal Hadamard matrix is formed, N is 2M, and a pairing matrix E is obtained according to a second matrix D_N；

Step 1.4, according to the matrixAnd E_NAnd constructing a GPCC codebook.

Further, in step 1.1, the first matrix A_MAs shown in the following formula:

wherein, in the formula (1), a_m，nE { +1, -1}, M, n { +1, 2, …, M, and any two rows and two columns of the first matrix a are orthogonal, i.e., two columns and two rows are orthogonalAndwhen i ≠ j.

Further, in step 1.2, the extended orthogonal matrix is represented as:

wherein, in the formulas (2) and (3),representing the kronecker product operator,a co-directional branch-circuit spreading matrix is represented,representing an orthogonal branch spreading matrix.

Further, in step 1.3, a second matrix D_NDivided into two sub-matrices, e.g.Andthen D is_NExpressed as:

in the above formula (4), each sub-matrix is composed of M row vectors, wherein the v-th row vector is represented asAnd v ∈ {1, 2, …, M }, andfor matrix E_NBy reconstructing the second matrix D_NObtaining, namely:

in equation (5), K denotes the number of GPCC codes, K denotes a GPCC code number, and K {1, 2, …, K }.

Further, in step 1.4, the GPCC codebook is expressed as:

the first pair of GPCC codes is:

the second pair of GPCC codes is:

the v-th pair of GPCC codes is:

the Mth pair of GPCC codes is:

where i denotes the imaginary unit, for C^(k)Wherein k represents the constructed GPCC code group number, k is 2v, v represents the code logarithm coding in the GPCC codebook set,representing an N by N diagonal matrix having major diagonal elements ofNamely, it isIndicating the in-phase branch and Q the quadrature branch.

In another aspect, the present invention further provides a method for extending a GPCC codebook by cyclic shift, including:

step 2.1, setting an address code expansion matrix psi^(j)Represented by the formula:

step 2.2, let C (k) be GPCC codeAn initial code of, then, from C^(k)The extended jth (j ═ 1, …, N) cpccs code is expressed as:

C^(j)＝C^(k)Ψ^(j)……(7)；

assume initial code C^(k)The code length of (2) is N, and the capacity of the signature code is expanded by N times after cyclic shift.

Compared with the prior art, the invention has the following advantages:

according to the generalized paired complex complementary code GPCC codebook construction method, the autocorrelation function of any GPCC code is represented as the characteristic of a zero correlation area on an equidirectional branch and an orthogonal branch, the length of the zero correlation area is M, M is the number of GPCC code subcodes, and the autocorrelation functions of the equidirectional branch and the orthogonal branch are perfectly complementary, so that the GPCC code can also realize the perfect autocorrelation characteristic;

according to the generalized paired complex complementary code GPCC codebook construction method, the intra-pair cross correlation function of any GPCC code set shows the characteristics of a zero correlation area in the homodromous branch and the orthogonal branch, the length of the zero correlation area is M, and similarly, the intra-pair cross correlation functions of the homodromous branch and the orthogonal branch are perfectly complementary, so that the GPCC code can also realize the perfect intra-pair correlation characteristics;

according to the generalized paired complex complementary code GPCC codebook construction method, the cross-correlation function of any two outside GPCC codes is expressed as perfect cross-correlation;

the generalized paired complex complementary code GPCC codebook construction method can realize the conversion between zero-correlation non-orthogonal codes and perfect orthogonal codes as required, the capacity of the non-orthogonal code family can be expanded, if interference signals fall outside the ZCZ, the perfect correlation codebook formed by the perfect complementary characteristics of the homodromous branch and the orthogonal branch is utilized, the multi-address interference is overcome, and the interference regulation and control of CD-NOMA are realized;

according to the GPCC codebook cyclic shift codebook expansion method, the codebook capacity is expanded, and perfect correlation characteristics are achieved.

Detailed Description

In order that the above objects, features and advantages of the present invention may be more clearly understood, the present invention is described in further detail below with reference to specific embodiments, it should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.

Examples

In this embodiment, the GPCC code is constructed by multiple sets of paired complementary codes, and each complex code is divided into two parts, namely a co-directional branch and an orthogonal branch; the autocorrelation function of any GPCC code shows zero correlation zone characteristics in the same-direction branch and the orthogonal branch, and the length of the zero correlation zone is W_minThe number of the sub-codes of the GPCC code is M, and the autocorrelation function of the homodromous branch and the orthogonal branch is perfectly complementary (y-axis symmetry), so the GPCC code can also realize perfect autocorrelation property; the intra-pair cross correlation function of any pair of GPCC codes shows the characteristics of a zero correlation zone in the same branch and an orthogonal branch, and the length of the zero correlation zone shows W_minSimilarly, because the intra-pair cross-correlation functions of the co-directional branch and the orthogonal branch are perfectly complementary (y-axis symmetry), the GPCC code can also realize the intra-pair correlation characteristic; the cross-correlation function of any two external GPCC codes is expressed as cross-correlation; the GPCC code family in this embodiment is extended to obtain a cyclic shifted Generalized paired complex complementary (GPCCCS) code, where the codebook is constructed by circularly shifting an ideal correlated GPCC codebook, and the extended GPCCCS code set can provide an ideal aperiodic cross-correlation characteristic in a synchronization channel.

The generalized paired complex complementary code GPCC codebook construction method comprises the following steps:

step (ii) of1.1, let first matrix A_MAn M-dimensional hadamard matrix, wherein the first matrix a is represented by the following formula:

wherein, in the formula (1), a_m，nE { +1, -1}, M, n { +1, 2, …, M, first matrix a_MAny two rows and columns of are orthogonal, i.e.Andwhen i is not equal to j;

step 1.2, use vector [ +1, +1]And [ +1, -1]Respectively expanding the first matrix A_MDimension of (2), obtaining an extended orthogonal matrixAndthe extended orthogonal matrix is represented as:

wherein, in the formulas (2) and (3),representing the kronecker product operator,a co-directional branch-circuit spreading matrix is represented,representing an orthogonal branch spreading matrix;

step 1.3, set the second matrix D_NIs another N × N orthogonal Hadamard matrix, N ═ 2M, according to a second matrix D_NObtaining a pairing matrix E_NSecond matrix D_NDivided into two sub-matrices, e.g.Andthen D is_NExpressed as:

in the above formula (4), each sub-matrix is composed of M row vectors, wherein the v-th row vector is represented asAnd v ∈ {1, 2, …, M }, pairing matrix E_NBy means of a second matrix D_NObtaining, namely:

in the formula (5), K represents the number of the GPCC codes, K represents the GPCC code number, and K is {1, 2, …, K };

step 1.4, according to the matrixAnd E, constructing a GPCC codebook, wherein the GPCC codebook is expressed as:

the first pair of GPCC codes is:

the second pair of GPCC codes is:

the v-th pair of GPCC codes is:

the Mth pair of GPCC codes is:

wherein I represents the imaginary part, I represents the in-phase branch, Q represents the quadrature branch, C^(k)Wherein k represents GPCC code group number, k is 2v, v represents GPCC codebook set code logarithm code, and its main diagonal element is Representing an N by N diagonal matrix, i.e.

The GPCC codebook cyclic shift codebook extension method comprises the following steps:

step 2.1, setting an address code expansion matrix psi^(j)Represented by the formula:

step 2.2, setting C^(k)Is a GPPCC codeAn initial code of, then, from C^(k)The jth (j ═ 1, …, N) GPCCS code of the extension is expressed as:

C^(j)＝C^(k)Ψ^(j)……(7)；

assume initial code C^(k)By expanding the number of codes after cyclic shift by a factor of N, G is obtained in synchronization or plesiochronousThe PCCS codes still have ideal cross correlation.

GPCC code is used belowThe number of codebooks constructed by the method is 8, the number of subcarriers is 4, the code length is 8, and the specific codebook construction process is as follows:

let a first matrix A₄Is a 4 x 4 dimensional Hadamard matrix, a first matrix A₄As shown in the following formula:

a first matrix A₄Respectively with the vector [ +1, +1]And [ +1, -1]Performing a kronecker product operation, the extended orthogonal matrix can be represented as:

setting a second matrix D₈An 8 × 8 orthogonal Hadamard matrix as another, orthogonal matrix D₈Divided into two sub-matrices, e.g.Andthe D expression can be expressed as:

each submatrix is composed of 4 row vectors, and then the pairing matrix E can be obtained by interleaving the matrix D, that is:

according to a matrixAnd E, constructing a GPCC codebook, namely:

a first pair:

the second pair:

and a third pair:

a fourth pair:

the present invention is not limited to the above-described embodiments, which are described in the specification and illustrated only for illustrating the principle of the present invention, but various changes and modifications may be made within the scope of the present invention as claimed without departing from the spirit and scope of the present invention. The scope of the invention is defined by the appended claims.