CN107846272A - A kind of Golden sequences quickly generate device and method - Google Patents

A kind of Golden sequences quickly generate device and method Download PDF

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Publication number
CN107846272A
CN107846272A CN201711146923.8A CN201711146923A CN107846272A CN 107846272 A CN107846272 A CN 107846272A CN 201711146923 A CN201711146923 A CN 201711146923A CN 107846272 A CN107846272 A CN 107846272A
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lfsr
models
register
sequence
galois field
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CN107846272B (en
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陈庆禄
刘坤
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Dongguan Anpu Sichuan Automation Technology Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2602—Signal structure
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2602—Signal structure
    • H04L27/261—Details of reference signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/003—Arrangements for allocating sub-channels of the transmission path
    • H04L5/0048—Allocation of pilot signals, i.e. of signals known to the receiver

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  • Engineering & Computer Science (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Power Engineering (AREA)
  • Mobile Radio Communication Systems (AREA)
  • Error Detection And Correction (AREA)

Abstract

The present invention relates to communication of algorithms technical field, and disclose a kind of Golden sequences quickly generates device and method, comprises the following steps：Generate m-sequence LFSR models；The buffer status S (n) of m-sequence LFSR models is mapped to galois field i.e. f (S (n))；Calculate Golden sequences S (n+Nc)=f‑1(f(S(n))*λNc).The present invention to the Fast Generation of Golden sequences by being improved, reference signal for wireless communication system generates, reference signal does channel estimation, demodulation in receiving terminal, to realize the recovery of original unknown signaling, as the necessary link in wireless communication system, reference signal quickly generates；Meanwhile reduction amount of calculation, reduction terminal cost are higher, energy consumption is small, especially applies in Internet of Things based on application scenarios NB IoT, LTE M etc. high to energy consumption and cost requirement.

Description

A kind of Golden sequences quickly generate device and method
Technical field
The present invention relates to communication of algorithms technical field, more particularly to a kind of Golden sequences quickly generate device and side Method.
Background technology
The randomness and orthogonal letter that Golden sequences have, the generation for pilot frequency sequence in a communications system, to realize Channel estimation based on interpolation model.But existing method, which directly calculates, needs a large amount of recurrence, belong to because traditional circulation is embedding Set, it is less efficient and need to largely consume process resource.
The content of the invention
The present invention for it is less efficient in the prior art, cost is higher the shortcomings that, there is provided a kind of Golden sequences it is fast Fast-growing is into device and method.
In order to solve the above-mentioned technical problem, the present invention is addressed by following technical proposals.
A kind of rapid generation of Golden sequences, including：
Generate m-sequence LFSR models；
The buffer status S (n) of m-sequence LFSR models is mapped to galois field i.e. f (S (n))；
Calculate Golden sequences S (n+Nc)=f-1(f(S(n))*λNc),
Wherein：Nc is known initial value, and Nc=1600, n are random natural number, and λ is primitive element.
Preferably, generation m-sequence LFSR model steps include：The generation model of Golden sequences, can be equivalent to down The superposition of the LFSR models of 2 m-sequences shown in figure, every group of m-sequence is by 30 shift registers and a modulo 2 adder group Into the generating algorithm of corresponding Golden sequences is as follows：
X1(n+31)=X1(n)⊕X1(n+3)；
X2(n+31)=X2(n)⊕X2(n+1)⊕X2(n+2)⊕X2(n+3)；
C (n)=X1(n+Nc)⊕X2(n+Nc)；
Wherein, Nc, X1、X2For known initial value, Nc=1600, X1Original state is 0x40000000, X2Original state by CinitProvide, CinitFor random natural number, n is random natural number, and C (n) is the Golden sequences of output.
Preferably, the buffer status S (n) of m-sequence LFSR models is mapped to galois field i.e. f (S (n)) step bag Include；
Generate the LFSR models of galois field；
To the register cycle displacement in LFSR models：By the second last register and the number of last 3rd register Enter last register according to XOR；The data XOR of last 3rd register is entered into the second last register, obtains m sequences LFSR buffer status S (n) is arranged to a mapping of galois field, is denoted by f (S (n)), then f (S (n))=λt+n。
A kind of Golden sequences quickly generate device, including：
LFSR model generation modules, for generating m-sequence LFSR models；
Galois field mapping block, for the buffer status S (n) of the m-sequence LFSR models to be mapped into Jia Luohua Domain is f (S (n))；
Golden sequence computing modules, for calculating Golden sequences S (n+Nc)=f-1(f(S(n))*λNc)。
Preferably, galois field mapping block includes：
Galois field LFSR model generation modules, for generating the LFSR models of galois field；
Cyclic shift module, for the register cycle displacement in LFSR models：By the second last register and most The data XOR of the 3rd register enters last register afterwards；The data XOR of last 3rd register is entered last Two registers, the buffer status S (n) for obtaining m-sequence LFSR map to one of galois field, are denoted by f (S (n)), Then f (S (n))=λt+n。
A kind of readable storage medium storing program for executing, readable storage medium storing program for executing are used to store software program, and program file is above-mentioned for performing Method.
The present invention has significant technique effect as a result of above technical scheme：The present invention is by Golden sequences The Fast Generation of row is improved, and the reference signal for wireless communication system generates, and reference signal makees letter in receiving terminal Road estimation, demodulation, to realize the recovery of original unknown signaling, as the necessary link in wireless communication system, reference signal Quickly generate；Meanwhile reduce amount of calculation, reduce terminal cost it is higher, energy consumption is small, especially apply Internet of Things be based on NB-IoT, Application scenarios high to energy consumption and cost requirement LTE-M etc..
Brief description of the drawings
Fig. 1 is a kind of operational flow diagram of the rapid generation of Golden sequences of the present invention；
Fig. 2 is the solution schematic diagram of cyclotomic polynomial in primitive polynomial equation in the present invention；
Fig. 3 is a kind of structural representation for quickly generating device of Golden sequences of the present invention；
Fig. 4 is the solution schematic diagram of cyclotomic polynomial in primitive polynomial equation in the present invention；
Fig. 5 is GF (2 in the present invention31) field element generation LFSR model schematics；
Fig. 6 is one of register rotation schematic diagram in the present invention；
Fig. 7 is two of register rotation schematic diagram in the present invention；
Fig. 8 is three of register rotation schematic diagram in the present invention；
Fig. 9 is four of register rotation schematic diagram in the present invention.
Embodiment
The present invention is described in further detail with embodiment below in conjunction with the accompanying drawings.
Embodiment 1
As shown in Figures 1 to 9, a kind of rapid generation of Golden sequences, including：
Generate m-sequence LFSR models；
The buffer status S (n) of m-sequence LFSR models is mapped to galois field i.e. f (S (n))；
Calculate Golden sequences S (n+Nc)=f-1(f(S(n))*λNc),
Wherein：Nc is known initial value, and Nc=1600, n are random natural number, and λ is primitive element.
Generation m-sequence LFSR model steps include：The generation model of Golden sequences, 2 shown in figure below can be equivalent to The superposition of the LFSR models of individual m-sequence, every group of m-sequence are made up of 30 shift registers and a modulo 2 adder, accordingly The generating algorithm of Golden sequences is as follows：
X1(n+31)=X1(n)⊕X1(n+3)；
X2(n+31)=X2(n)⊕X2(n+1)⊕X2(n+2)⊕X2(n+3)；
C (n)=X1(n+Nc)⊕X2(n+Nc)；
Wherein, Nc, X1、X2For known initial value, Nc=1600, X1Original state is 0x40000000, X2Original state by CinitProvide, CinitFor random natural number, n is random natural number, and C (n) is the Golden sequences of output.
The buffer status S (n) of m-sequence LFSR models is mapped into galois field i.e. f (S (n)) step includes；
Generate the LFSR models of galois field；
To the register cycle displacement in LFSR models：By the second last register and the number of last 3rd register Enter last register according to XOR；The data XOR of last 3rd register is entered into the second last register, obtains m sequences LFSR buffer status S (n) is arranged to a mapping of galois field, is denoted by f (S (n)), then f (S (n))=λt+n。
A kind of Golden sequences quickly generate device, including：
LFSR model generation modules, for generating m-sequence LFSR models；
Galois field mapping block, for the buffer status S (n) of the m-sequence LFSR models to be mapped into Jia Luohua Domain is f (S (n))；
Golden sequence computing modules, for calculating Golden sequences S (n+Nc)=f-1(f(S(n))*λNc)。
Preferably, galois field mapping block includes：
Galois field LFSR model generation modules, for generating the LFSR models of galois field；
Cyclic shift module, for the register cycle displacement in LFSR models：By the second last register and most The data XOR of the 3rd register enters last register afterwards；The data XOR of last 3rd register is entered last Two registers, the buffer status S (n) for obtaining m-sequence LFSR map to one of galois field, are denoted by f (S (n)), Then f (S (n))=λt+n。
GF (λ m) represents the galois field for including λ m elements, and it is a kind of Baikal group of finite element.
In galois field, in addition to 0 element, other field elements are defined below by primitive element λ and primitive polynomial P (x)：
Xp- 1=0, p=λm- 1=15 (wherein λ=2, m=4)；
It is a cyclotomic polynomial on the left of equation, in complex field, the solution of observation equation is as shown in Fig. 2 work as x1∈ P= {ej2πk/15|0<k<15, and k and 15 is coprime }, the set of non trivial solution is represented by, { x1 1, x1 2, x1 3..., x1 14, 1 }, this is One λmThe cyclic group of -1 rank.
I.e. for the either element (necessarily 8 elements herein) in set P, its integer power can travel through the λ of equationm-1 Individual solution.
In GF (2m) on, to x15- 1 factorization, it is impossible to radical is resolved into as infinite field, can prove most to terminate Fruit is necessarily：
x1 5- 1=x1 5+ 1=(x+1) ... (x4+x3+1)(x4+x+1)；
A series of not subdivisible multinomials (i.e. about multinomial) are obtained, wherein most high order is m several multinomials It is exactly xp- 1 in GF (2m) on primitive polynomial.Such as multinomial x15- 1 has two primitive polynomials：
P (x)=x4+x3+ 1 and P (x)=x4+x+1；
It can prove, non trivial solution has one-to-one relationship with non trivial solution in infinite field in finite field, and between element Operation relation keep constant (two group isomorphisms).Wherein, the element in set P and the solution of primitive polynomial P (x)=0 are also Correspondingly.That is, when λ meets x4+ x+1=0 or x4+x3+ 1=0, λ all powers necessarily travel through GF (24) in All 24- 1 element.
Such as λ4+ λ+1=0, i.e. λ4=λ+1.If GF (2 is generated with this4) all non-zero elements：
λ1=0h0010, λ2=0h0100, λ3=0h1000,
λ4=λ+1=0h0011, λ5=λ2+ λ=0h0110, λ6=λ3+λ2=0h1100,
λ7=λ4+λ3=0h1011, λ8=λ5+λ4=0h0101, λ9=λ6+λ5=0h1010,
λ10=λ7+λ6=0h0111, λ11=λ8+λ7=0h1110, λ12=λ9+λ8=0h1111,
λ13=λ10+λ9=0h0111, λ14=λ11+λ10=0h1001, λ15=λ12+λ11=0h0001=λ0；
Given λ=2, origin multinomial：P (x)=x3+x+1；
It then can obtain a GF (23), its field element is as shown in the table：
Table 1GF (23) in field element, P (x)=x3+x+1
GF(λm) in, addition is defined as step-by-step mould λ and added, and subtraction is defined as step-by-step mould λ and subtracted, and the multiplication of non-zero element is defined as λa*λb=λ(a+b)。
For λ=2, addition is identical with subtraction, i.e. step-by-step XOR.
Defined from multiplication and the definition of primitive polynomial, LFSR models generation GF (λ can be usedm) in non-zero domain Element.For example, Fig. 3 show 2 GF (231) in field element generation model.
With X2(n+31)=X2(n)⊕X2(n+1)⊕X2(n+2)⊕X2(n+3) illustrate exemplified by：
1) by X2LFSR in 31 register rotations, then can obtain the LFSR models shown in Fig. 4；
2) the data XOR of register 29 is entered into register 30, then it is as shown in Figure 5 can obtain equivalent LFSR models；
3) the data XOR of register 28 is entered into register 30, then it is as shown in Figure 6 can obtain equivalent LFSR；
4) the data XOR of register 28 is entered into register 29, then it is as shown in Figure 7 can obtain equivalent LFSR.
It can be seen that after above-mentioned logical operation, the LFSR of X2 sequences has been converted into corresponding GF (231) LFSR. I.e. this operation is equivalent to m-sequence LFSR buffer status S (n) to a mapping of galois field, is denoted as f (S (n)), then
F (S (n))=λt+n；
Wherein λ t are corresponding GF (231) a certain field element.
If its inverse mapping is present, f is denoted as-1(G), then
f-1(λt+n)=S (n)；
Therefore, S (n+Nc)=f-1(λt+n+Nc)=f-1(λt+n*λNc)=f-1(f(S(n))*λNc)；
Above formula explanation, it is desirable to which going out S (n+Nc) only needs current state S (n) being mapped to corresponding galois field, Ran Houjin Galois Field multiplication of row, then result is mapped back.
Avoided by the embodiment of the present invention due to the Golden sequence methods such as traditional loop nesting, recurrence, efficiency compared with The technical problem of low a large amount of consumption process resources, efficient, the inexpensive generation of Golden sequences.The Golden sequences generated, Reference signal for wireless communication system generates, and reference signal does channel estimation, demodulation in receiving terminal, original unknown to realize Signaling protein14-3-3, as the necessary link in wireless communication system, reference signal quickly generates；Meanwhile reduce amount of calculation, drop Low terminal cost is higher, and energy consumption is small, especially applies high to energy consumption and cost requirement based on NB-IoT, LTE-M etc. in Internet of Things Application scenarios.
In the present embodiment, the above method can be used as program storage to include in storage medium, the storage medium But it is not limited to：USB flash disk, read-only storage (ROM, Read-OnlyMemory), random access memory (RAM, RandomAccessMemory), mobile hard disk, magnetic disc or CD etc. are various can be with the medium of store program codes.
Specific example in the present embodiment may be referred to the example described in above-described embodiment and optional embodiment, this Embodiment will not be repeated here.
Obviously, those skilled in the art should be understood that above-mentioned each module of the invention or each step can be with general Computing device realize that they can be concentrated on single computing device, or be distributed in multiple computing devices and formed Network on, alternatively, they can be realized with the program code that computing device can perform, it is thus possible to they are stored Performed in the storage device by computing device, and in some cases, can be with different from shown in order execution herein The step of going out or describing, they are either fabricated to each integrated circuit modules respectively or by multiple modules in them or Step is fabricated to single integrated circuit module to realize.So, the present invention is not restricted to any specific hardware and software combination.
In a word, presently preferred embodiments of the present invention, all equalizations made according to scope of the present invention patent be the foregoing is only Change and modification, it should all belong to the covering scope of patent of the present invention.

Claims (6)

  1. A kind of 1. rapid generation of Golden sequences, it is characterised in that：Including：
    Generate m-sequence LFSR models；
    The buffer status S (n) of m-sequence LFSR models is mapped to galois field i.e. f (S (n))；
    Calculate Golden sequences S (n+Nc)=f-1(f(S(n))*λNc),
    Wherein：Nc is known initial value, and Nc=1600, n are random natural number, and λ is primitive element.
  2. 2. according to the method for claim 1, it is characterised in that：Generation m-sequence LFSR model steps include：Golden sequences Generation model, the superposition of the LFSR models for 2 m-sequences that can be equivalent to shown in figure below, every group of m-sequence posted by 30 displacements Storage and a modulo 2 adder composition, the generating algorithm of corresponding Golden sequences are as follows：
    X1(n+31)=X1(n)⊕X1(n+3)；
    X2(n+31)=X2(n)⊕X2(n+1)⊕X2(n+2)⊕X2(n+3)；
    C (n)=X1(n+Nc)⊕X2(n+Nc)；
    Wherein, Nc, X1、X2For known initial value, Nc=1600, X1Original state is 0x40000000, X2Original state is by Cinit Provide, CinitFor random natural number, n is random natural number, and C (n) is the Golden sequences of output.
  3. 3. according to the method for claim 1, it is characterised in that：The buffer status S (n) of m-sequence LFSR models is mapped It is that f (S (n)) step includes to galois field；
    Generate the LFSR models of galois field；
    To the register cycle displacement in LFSR models：The data of the second last register and last 3rd register are different Or enter last register；The data XOR of last 3rd register is entered into the second last register, obtains m-sequence LFSR buffer status S (n) is denoted by f (S (n)), then f (S (n))=λ to a mapping of galois fieldt+n。
  4. 4. a kind of Golden sequences quickly generate device, it is characterised in that：Including：
    LFSR model generation modules, for generating m-sequence LFSR models；
    Galois field mapping block, for the buffer status S (n) of the m-sequence LFSR models to be mapped into galois field i.e. f (S(n))；
    Golden sequence computing modules, for calculating Golden sequences S (n+Nc)=f-1(f(S(n))*λNc)。
  5. 5. device according to claim 4, it is characterised in that：Galois field mapping block includes：
    Galois field LFSR model generation modules, for generating the LFSR models of galois field；
    Cyclic shift module, for the register cycle displacement in LFSR models：By the second last register and last The data XOR of three registers enters last register；The data XOR of last 3rd register is entered into the second last Register, m-sequence LFSR buffer status S (n) is obtained to a mapping of galois field, is denoted by f (S (n)), then f (S (n))=λt+n。
  6. A kind of 6. readable storage medium storing program for executing, it is characterised in that：Readable storage medium storing program for executing is used to store software program, and program file is used to hold Method described in row claim 4 or claim 5.
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