阅读说明：本技术 一种5gnr系统中zc序列dft运算的方法 (Method for DFT operation of ZC sequence in 5GNR system ) 是由 卜智勇 王炜 王江 于 2020-06-18 设计创作，主要内容包括：本发明公开了一种5GNR系统中ZC序列DFT运算的方法,通过对ZC序列DFT运算共轭表示进行解算,然后令<Image he="117" wi="419" file="DDA0002545602080000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>C＝X<Sub>u</Sub>[0]并存储为查找表,所述循环移位的ZC序列的频域表示为：<Image he="78" wi="277" file="DDA0002545602080000012.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image><Image he="101" wi="674" file="DDA0002545602080000013.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>其中,查找表A和C使用u作为索引,查找表B使用k作为索引。本发明的循环移位的ZC序列的频域表示中,仅需要5个实数乘法运算和1个复数乘法运算,就能完成循环移位和DFT运算,大大降低了大素数点PRACH基带算法复杂度和处理时延,利于终端实现。(The invention discloses a method for ZC sequence DFT operation in a 5GNR system, which comprises the steps of resolving conjugate representation of the DFT operation of the ZC sequence, and enabling C＝X u [0]And stored as a look-up table, the frequency domain of the cyclically shifted ZC sequence is represented as: where lookup tables a and C use u as an index and lookup table B uses k as an index. In the frequency domain representation of the cyclically shifted ZC sequence of the invention, only 5 are requiredThe real number multiplication and 1 complex number multiplication can complete the cyclic shift and DFT operation, greatly reduces the complexity and processing time delay of the PRACH baseband algorithm with large prime number points, and is beneficial to the realization of the terminal.)

1. A method for DFT operation of ZC sequence in 5GNR system is characterized in that the ZC sequence has a root u and a length P, u < P; the method comprises the following steps:

s1, conjugate of ZC sequence DFT computation:

wherein i is an imaginary unit, k is 0,1,2, … P-1, u^-1Is u is the modulo inverse with respect to P;

s2, solving equation (2), obtaining:

wherein the content of the first and second substances,

s3, substituting equation (10) into equation (1) to obtain a frequency domain representation of the ZC sequence:

s4, introducing cyclic shift C in formula (11)_vObtaining a frequency domain representation of the cyclically shifted ZC sequence:

s5, the exponential part of the formula (12) is proposed to be 2 pi, and the expression is as follows:

s6, orderC＝X_u[0]And stored as a look-up table, the frequency domain of the cyclically shifted ZC sequence is represented as:

where lookup tables a and C use u as an index and lookup table B uses k as an index.

2. The method of DFT calculation of ZC sequence in 5GNR system as claimed in claim 1, wherein u is^-1And u satisfies:

uu^-1＝mP+1,m＝1,2,3..... (3)。

3. the method for DFT calculation of ZC sequence in 5GNR system as claimed in claim 2, wherein the process of solving equation (2) in step S2 is:

s21, expanding the step (2) as follows:

s22, substituting equation (3) into equation (4) includes:

s23, when k is equal to 1, combining equation (1) and equation (5), there is:

wherein n is an integer;

s24, making:

substituting equation (7) into equation (6) results in:

substituting equation (8) into equation (5) results in:

s25, n is,k. m is an integer, respectively, so 2nk²And mk (k-1) is an even number, so the last two terms of the exponential portion in equation (9) are eliminated, yielding:

4. a method for DFT computation of ZC sequence in a 5GNR system as claimed in claim 3, wherein in step S4 a cyclic shift C is introduced in equation (11)_vIs that the index part in the formula (11)

5. The method of claim 4, wherein the ZC sequence DFT operation is defined as:

wherein k is 0,1,2, … P-1, X_u[n]Indicating a ZC sequence.

6. The method of DFT operation on ZC sequences in a 5GNR system according to claim 5, wherein the ZC sequences are defined as:

where n is 0,1,2, … P-1, and indicates the nth point of the ZC sequence.

7. A method for DFT calculation of ZC sequences in a 5GNR system according to any one of claims 1 to 6, wherein P is a prime number.

Technical Field

The invention relates to the technical field of communication, in particular to a method for DFT operation of a ZC sequence in a 5GNR system.

Background

The Zadoff-chu (zc) sequence is widely used in the synchronization process of wireless communication due to its good correlation characteristics and low peak-to-average ratio. The LTE downlink synchronization channel (PSS) and uplink random access channel (PRACH) use ZC sequences as baseband signals and their use on PRACH is continued in 5 GNR. However, the generation of the PRACH baseband signal requires DFT and IDFT operations on the ZC sequence of the maximum 1151 point, and the computational complexity thereof poses a great challenge to algorithm implementation and real-time performance. Therefore, how to efficiently generate PRACH baseband signals under limited resources becomes a hot spot of research.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: in view of the above existing problems, a method for performing DFT operation on ZC sequences in a 5GNR system is provided.

The technical scheme adopted by the invention is as follows:

a method for DFT operation of ZC sequence in 5GNR system, the ZC sequence has root u and length P, u < P; the method comprises the following steps:

s1, conjugate of ZC sequence DFT computation:

wherein i is an imaginary unit, k is 0,1,2, … P-1, u^-1Is u is the modulo inverse with respect to P;

s2, solving equation (2), obtaining:

wherein the content of the first and second substances,

s3, substituting equation (10) into equation (1) to obtain a frequency domain representation of the ZC sequence:

s4, introducing cyclic shift C in formula (11)_vObtaining a frequency domain representation of the cyclically shifted ZC sequence:

s5, the exponential part of the formula (12) is proposed to be 2 pi, and the expression is as follows:

s6, order

C＝X_u[0]And stored as a look-up table, the frequency domain of the cyclically shifted ZC sequence is represented as:

where lookup tables a and C use u as an index and lookup table B uses k as an index.

Further, u^-1And u satisfies:

uu^-1＝mP+1,m＝1,2,3…… (3)。

further, the process of solving equation (2) in step S2 is:

s21, expanding the step (2) as follows:

s22, substituting equation (3) into equation (4) includes:

s23, when k is equal to 1, combining equation (1) and equation (5), there is:

wherein n is an integer;

s24, making:

substituting equation (7) into equation (6) results in:

substituting equation (8) into equation (5) results in:

s25, n, k and m are integers, so 2nk²And mk (k-1) is an even number, so the last two terms of the exponential portion in equation (9) are eliminated, yielding:

further, in step S4, cyclic shift C is introduced in equation (11)_vIs that the index part in the formula (11)And cyclic shift C_vGenerated phase deflection factor

And (6) merging.

Further, the ZC sequence DFT operation is defined as:

wherein k is 1,2, … P-1, X_u[n]Indicating a ZC sequence.

Further, the ZC sequence is defined as:

where n is 1,2, … P-1, and indicates the nth point of the ZC sequence.

Further, P is a prime number.

In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:

in the frequency domain representation of the ZC sequence of the cyclic shift, only 5 real number multiplication operations and 1 complex number multiplication operation are needed to complete the cyclic shift and DFT operation, thereby greatly reducing the complexity of the PRACH baseband algorithm of large prime number points and the processing time delay and being beneficial to the realization of a terminal.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.

FIG. 1 is a schematic diagram of a method for DFT operation of ZC sequences in a 5GNR system according to the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.

The features and properties of the present invention are described in further detail below with reference to examples.

According to the invention, a given ZC sequence has a root u and a length P, u < P, said ZC sequence being defined as:

wherein i is an imaginary unit, n is 0,1,2, … P-1, and represents an nth point of the ZC sequence;

the ZC sequence DFT operation is defined as:

wherein k is 0,1,2, … P-1.

Then, the method for calculating the DFT of the ZC sequence in the 5GNR system of the invention comprises the following steps:

s1, available from the paper efficiency calculation of DFT of Zadoff-Chussequences, the conjugate of the DFT operation of the ZC sequence is expressed as:

wherein i is an imaginary unit, u^-1Is u is the modulo inverse with respect to P; u. of^-1And u satisfies:

uu^-1＝mP+1,m＝1,2,3…… (3)

s2, direct calculation by formula (2)It is difficult to find the value of m and the formula is not beneficial to fixed-point realization, therefore, the invention solves the formula (2):

s21, expanding the step (2) as follows:

s22, due to u^-1If u is a modulo inverse of P, substituting equation (3) into equation (4) yields:

s23, when k is equal to 1, combining equation (1) and equation (5), there is:

wherein n is an integer;

s24, making:

substituting equation (7) into equation (6) results in:

substituting equation (8) into equation (5) results in:

s25, n, k and m are integers, so 2nk²And mk (k-1) is an even number, so the last two terms of the exponential portion in equation (9) are eliminated, yielding:

s3, substituting equation (10) into equation (1) to obtain a frequency domain representation of the ZC sequence:

s4, introducing cyclic shift C in formula (11)_vObtaining a frequency domain representation of the cyclically shifted ZC sequence:

wherein a cyclic shift C is introduced in the formula (11)_vIs that the index part in the formula (11)And cyclic shift C_vGenerated phase deflection factor

Combining to obtain

S5, the exponential part of the formula (12) is proposed to be 2 pi, and the expression is as follows:

s6, orderC＝X_u[0]And stored as a look-up table, the frequency domain of the cyclically shifted ZC sequence is represented as:

where lookup tables a and C use u as an index and lookup table B uses k as an index. The lookup tables A and B are both decimal numbers, the integer bit is 0 during quantization, and after 2 pi is extracted, only decimal bits and integer bits can be reserved after A and B are multiplied each time, and the fixed point can reach higher precision when the bit width is limited. As shown in fig. 1, it can be seen that, in the frequency domain representation of the ZC sequence of the cyclic shift of the present invention, only 5 real number multiplications and 1 complex number multiplications are required to complete the cyclic shift and DFT operations, thereby greatly reducing the complexity and processing delay of the PRACH baseband algorithm with large prime number points, and facilitating the implementation of the terminal.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.