CN1290274C - A method for composing optimum optical orthogonal code - Google Patents

Abstract

The present invention provides a method for forming optimum (v, k, 1) optical orthogonal codes. The optical orthogonal codes form a preferred spread spectrum sequence used in an optical fiber CDMA system and form a two-element (0, 1) sequence group having excellent correlation properties. The construction of the optical orthogonal codes and the combined design have intimate association, namely that one optimum (v, k, 1) optical orthogonal code is equivalent to one optimum circulation difference set group CDF (V, k, 1); according to the elementary theory of number, the finite field and the basic theory of the combined design, when the code length v is a prime number, some circulation differential set groups CDF (v, k, 1) can be designed and obtained by the computer-aided design. Thus, a series of optimum (v, k, 1) optical orthogonal codes are formed. The present invention provides the optimum spread spectrum sequence design in the optical fiber CDMA system with an effective path.

Description

A kind of method for composing of optimum optical orthogonal code

Technical field

The invention belongs to technical field of optical fiber communication, it is particularly related to the structure of light orthogonal code in the optical fiber cdma system and makes method.

Background technology

Optical fiber CDMA is a kind of novel communication mode that the CDMA communication technology is combined with Fibre Optical Communication Technology, the characteristics of two kinds of communication modes have been made full use of, have very strong technical advantage and wide application prospect and (see document Svetislav V.Maric, Oscar Moreno.Multimedia transmission in Fiber-Optic LAN ' s usingoptical CDMA.J.Lightwave Technol., 1996,14 (10): 2149-2153 and document Jawad A.Salehi.Emerging optical code-division multiple access communications systems.IEEE Network, 1989, (3): 31-39).The optical fiber CDMA technology mainly is by using a series of frequency expansion sequences (address code) with good correlation to come identifying user, different access users is multiplexed on the identical frequency band and time slot synchronously or asynchronously, thereby realizes that a plurality of users share the total capacity of same fiber channel and raising system.Therefore, to do method research be very important to the frequency expansion sequence structure with good correlation.

In the non-coherent optical fiber cdma system, (see document Jawad A.Salehi.Code division multiple-accesstechniques in optical fiber networks-Part I:fundamental principles.IEEE Trans.Comm., 1989,37 (8): 824-833 and document Jawad A.Salehi, Charles A.Brackett.Code divisionmultiple-access techniques in optical fiber networks-Part II:systems performance analysis.IEEE Trans.Comm., 1989,37 (8): 834-842), generally adopt light intensity modulation and direct detection technology respectively at transmitter terminal and receiver end, frequency expansion sequence in this system can only be selected the unipolarity sequence with non-negative element for use, light orthogonal code a kind of sequence that comes to this, can show good correlation properties, as a kind of preferred frequency expansion sequence, be generally used in the non-coherent optical fiber cdma system.Length is that v, weight are that the light orthogonal code C of k uses four-tuple Φ (v, k, λ usually ₁, λ ₂) expression, wherein λ ₁, λ ₂The upper bound of representing auto-correlation function and cross-correlation function respectively, Φ represents the maximum of code word number that C comprises.At present, λ is mainly discussed in the research of light orthogonal code ₁=λ ₂The situation of=λ, at this moment, its characteristic can be used tlv triple Φ (v, k, λ) expression.Based on the relation that waits heavy error correcting code and light orthogonal code, and famous Johnson circle as can be known, if (v, k, a 1) light orthogonal code contains Code word just is called optimum optical orthogonal code.

The research of relevant light orthogonal code mainly concentrates on three aspects, i.e. the Existence problems of length-specific and weight light orthogonal code; The theoretical calculation problems of the accurate number of code word (is seen document Ryoh Fuji-hara, Ying Miao.Optical orthogonalcodes:their bounds and new optimal constructions.IEEE Trans.Inform.Theory, 2000,46 (11): 2396-2406 and document Yang Yi are earlier. light orthogonal code. and electronic letters, vol, 1991,19 (1): 25-31); The structure of light orthogonal code is made the method problem and (is seen document Fan R.K.Chung, J.A.Salehi.Optical orthogonal codes:design, analysis, and applications.IEEE Trans.Inform.Theory, 1998,35 (5): 595-604, document Gennian Ge, Jianxing Yin.Constructions for optimal (v, 4,1) optical orthogonal codes.IEEE Trans.Inform.Theory, 2001,47 (11): 2998-3004, and document Ryoh Fuji-hara, Ying Miao.Optical orthogonalcodes:their bounds and new optimal constructions.IEEE Trans.Inform.Theory, 2000,46 (11): 2396-2406).With regard to the Existence problems of sign indicating number, Bose, people such as Buratti have done number of research projects in this respect and (have seen document Marco Buratti.Constructions of (q, k, 1) difference families with q a prime powerand k=4,5.Discrete Mathematics, 1995, (138): 169-175), and with the correlation theory of Combination Design and Elementary Number Theory, proved that the light orthogonal code that code length satisfies specified conditions exists, still, they do not provide the concrete structure of these light orthogonal codes and make method.The present invention is based on Bose, people's such as Buratti theoretical work, the structure that proposes a kind of optimum optical orthogonal code is made method, by computer-aided design, has constructed a series of the bests (v, k, 1) light orthogonal code.

Summary of the invention

The objective of the invention is to propose the method for composing of a kind of the best (v, k, 1) light orthogonal code, this method can construct a series of the best (v, k, 1) light orthogonal codes with good correlation, and wherein, code length v is a prime number, code weight k=4,5 and 6.

The structure of light orthogonal code and Combination Design have closely gets in touch (seeing M.Hall.Combinatorial Theory.2ndedition, New York:Wiley, 1986), especially, the best (v, a k, 1) light orthogonal code is equivalent to an optimum cycle difference set CDF of family (v, k, 1).As seen, in fact the design problem of best (v, k, 1) light orthogonal code is exactly the design problem of best CDF (v, k, 1).Principle of the present invention is (to see Underwood Dudley.Elementary NumberTheory.2nd edition according to Elementary Number Theory, San Francisco:W.H.Freeman and Company, 1978) basic theories, at the research Cycle Difference CDF (v of collection of sets, k, 1) on the basis of design problem, further studies best (v, k, 1) the building method problem of light orthogonal code.

According to the basic theories of finite field, the feature of finite field must be prime number, and its rank must be the power of prime number.A finite field that is characterized as prime number p if its exponent number also is p, claims that then it is the sub-prime territory of p property field, the i.e. territory that can not decompose again.Suppose that v is a prime number, t, k are positive integer, and satisfy relational expression v=tk (k-1)+1, and then the set of the residue integer of mould v constitutes the sub-prime territory of a v feature finite field, can be expressed as F _v=0,1 ..., v-1} according to the definition of Fermat theorem and primitive root, necessarily can obtain F _vPrimitive root α (α ∈ F _v), i.e. α ^V-1(mod v) for ≡ 1.Make the set F of v-1 unit _v ^*={ α ⁰, α ¹, α ²..., α ^V-2(mod v), it constitutes a v-1 rank cyclic group, and its element is F _vIn an equivalent replacement of all nonzero elements.

Based on the Lagrange theorem of finite group, the exponent number of subgroup must be the factor of group's exponent number.Make s=k (k-1)/2, β=α ^s, with β primitive element then, can generate rank is the cyclic subgroup C of s for the 2t index ₀ ^s, C ₀ ^sAnd all cosets are as follows:

C ₀ ^s＝{1，β，β ²，β ³，...，β ^(2t-1)}＝{1，α ^s，α ^2s，α ^3s，...，α ^(2t-1)s}

C ₁ ^s＝αC ₀ ^s＝{α，α ^s+1，α ^2s+1，α ^3s+1，...，α ^(2t-1)s+1}

C ₂ ^s＝α ²C ₀ ^s＝{α ²，α ^s+2，α ^2s+2，α ^3s+2，...，α ^(2t-1)s+2}

………………………

C _s-1 ^s＝α ^s-1C ₀ ^s＝{α ^s-1，α ^2s-1，α ^3s-1，α ^4s-1，...，α ^2ts-1}

By top relational expression as can be known, subgroup C ₀ ^sAll cosets be to v-1 rank cyclic group F _v ^*An equivalent partition of middle all elements, the element between promptly any two different cosets is different.

Suppose that having one is defined in F _vOn k unit set B ₀={ b ₁, b ₂, b ₃..., b _k(modv), define two set Δs ⁺B ₀={ b _i-b _j| 1≤j≤i≤k} (mod v) with Δ B ₀={ b _i-b _j| 1≤i, j≤k} is (mod v), if the set Δ ⁺B ₀In all s element belong to C respectively ₀ ^s, C ₁ ^s..., C _S-1 ^s, promptly different, then gather Δ B ₀In all 2s element also different.

If make the set Ω of the family={ B of k unit _i=α ^IsB ₀(1≤i≤t) }, difference set Δ then ⁺B _iAll s element still belong to C respectively ₀ ^s, C ₁ ^s..., C _S-1 ^s, and with the difference set Δ ⁺B ₀Mutually disjoint.Therefore, difference set

All 2ts element also different, equal F respectively _vIn all nonzero elements, the k unit set Ω of family has just constituted a CDF (v, k, 1) Cycle Difference collection of sets, thereby just can determine the best (v, k, 1) light orthogonal code.

The method for composing of optimum optical orthogonal code provided by the present invention is characterized in that adopting following step:

The first step, program begins, and gives the initializaing variable assignment, promptly under the given situation of code weight amount k, gives code word number t assignment, calculate code length v, and v is necessary for prime number.If v is not a prime number, change the value of t, till v is prime number;

In second step, calculate and obtain finite field F _vPrimitive element α;

In the 3rd step, generate v-1 rank cyclic group F by primitive element α _v ^*And its all elements stored;

In the 4th step, make β=α ^s(wherein s=k (k-1)/2), for the generator structural index is s, rank are the cyclic subgroup C of 2t with β ₀ ^s, calculate C simultaneously ₀ ^sAll cosets, the storage C ₀ ^sAnd all elements of coset;

The 5th step, structure k unit set B ₀=0, a, a ²..., a ^K-1(modv), wherein, a ∈ F _v, calculate the difference set Δ ⁺B ₀All elements;

In the 6th step, judge the set Δ ⁺B ₀In all elements whether belong to s different coset respectively.If this condition satisfies, carried out for the 7th step; If this condition does not satisfy, carried out for the 5th step; If construction set B ₀All situations all comprise, this condition does not still satisfy, and carries out for the 8th step;

In the 7th step, utilize relational expression B _i=α ^IsB ₀(1≤i≤t) determines the set of t k unit, gathers all code words of determining to obtain the best (v, k, 1) light orthogonal code by this t, and result data is stored EP (end of program);

The 8th goes on foot, and can not construct the optimum optical orthogonal code of this length, EP (end of program).

Need to prove: addition and multiplyings all in the program all are at finite field F _vOn carry out.

Computer Simulation flow process of the present invention as shown in Figure 1.

The invention has the beneficial effects as follows: adopt building method provided by the invention, can construct the best (v, k, 1) light orthogonal code, for the design that has the good correlation frequency expansion sequence in the optical fiber cdma system provides a kind of valid approach.

Description of drawings:

Fig. 1 is the Computer Design flow chart of best (v, k, 1) light orthogonal code

Fig. 2 is the structured approach that proposes according to the present invention, (v=12t+1, k=4) result data that calculate

Fig. 3 is the structured approach that proposes according to the present invention, (v=20t+1, k=5) result data that calculate

Fig. 4 is the structured approach that proposes according to the present invention, (v=30t+1, k=6) result data that calculate

In Fig. 2,3 and 4, v represents the length of light orthogonal code, and t represents the number of code word, and a represents set B ₀The generator of element, α represent finite field gf (primitive element v), ε represent a about primitive element α at the finite field gf (index v).

Fig. 5 is the autocorrelation performance analysis of best (541,5,1) light orthogonal code

Fig. 6 is the their cross correlation analysis of best (541,5,1) light orthogonal code

Can find out that from Fig. 5,6 the zero displacement autocorrelation value of light orthogonal code (541,5,1) is 5, non-zero displacement autocorrelation value λ≤1, displacement cross correlation value λ≤1 between different sign indicating number sequences, the correlation properties of satisfied best (v, 5,1) light orthogonal code.

Embodiment:

In the actual light cdma system, the spreading gain of frequency expansion sequence (address code) is generally about 1000, and therefore, we have only discussed the situation of code length v＜1200, and certainly, when code length v 〉=1200, this method for composing still is suitable for.

The example that is configured to best (661,5,1) light orthogonal code illustrates how to obtain its all code words.Based on the data in the accompanying drawing 3, when code length v=661, code weight k=5, as can be known, code word number t=33, primitive element α=2 of finite field gf (541), set B ₀The generator a=531=2 of all elements ³⁴²(mod 661), thus can determine B ₀{ 0,531,375,164,493} utilizes relational expression B _i=2 ¹⁰ⁱB ₀(1≤i≤33) can obtain 33 5 yuan of set:

{0，402，620，42，489} {0，506，320，43，359} {0，581，485，406，100}

{0，44，229，636，606} {0，108，502，179，526} {0，205，451，199，570}

{0，383，446，188，17} {0，219，614，161，222} {0，177，125，275，605}

{0，134，427，14，163} {0，389，327，455，340} {0，414，382，576，474}

{0，235，517，212，202} {0，36，608，280，616} {0，509，591，507，190}

{0，348，369，283，226} {0，73，425，274，74} {0，59，262，312，422}

{0，265，583，225，495} {0，350，109，372，554} {0，138，568，192，158}

{0，519，613，291，508} {0，12，423，534，646} {0，390，197，169，504}

{0，116，123，535，516} {0，465，362，532，245} {0，240，528，104，361}

{0，529，635，75，165} {0，337，477，124，405} {0，46，630，64，273}

{0，173，645，97，610} {0，4，141，178，656} {0，130，286，497，168}

By top these 5 yuan of set, just can determine a binary (0,1) sequence family, this is all code words of the best (661,5,1) light orthogonal code.According to the definition of light orthogonal code correlation properties, by Computer Simulation, can analyze the correlation properties of (661,5,1) light orthogonal code, accompanying drawing 5,6 is the result of Computer Simulation.

Be part computer source program of the present invention (matlab language) below, this program mainly solves and satisfies particular constraints set of circumstances B ₀Construction problem.

Element_Search=0;Parameter_Condition=1;for r=1:Index_Generator_Subgroup       for s=1:Order_Subgroup           Index_Element_Find(1)=mod(Index_Element_Coset(r,s),(Number_Element_CDF-1));           Element_Find(1)=Element_Coset(r,s);           for t=2:Number_Element_CDS-1               Index_Element_Find(t)=mod(t*Index_Element_Find(1),(Number_Element_CDF-1));               Element_Find(t)=Element_Coset(Index_Element_Find(t)+1);           end           Base_Block_Find=[0 Element_Find];           Number_Difference=0;           for i=1:Number_Element_CDS                for j=i+1:Number_Element_CDS                      Number_Difference=Number_Difference+1;                      Difference(Number_Difference)=                         mod((Base_Block_Find(j)-Base_Block_Find(i)),Number_Element_CDF);                end           end           c=ismember(0,Difference);           if c~=0        <!-- SIPO <DP n="5"> -->        <dp n="d5"/>           continue;       end       for k=1:Number_Difierence           Index_Difference(k)=find(Element_Coset==Difference(k))-1;           Order_Difference(k)=mod(Index_Difference(k),Index_Generator_Subgroup);       end       Order_Difference=sort(Order_Difierence);       Set_Give=0:Index_Generator_Subgroup-1;       if Order_Difference==Set_Give           Parameter_Condition=0;       end       if Parameter_Condition==0           break;       end   end   if Parameter_Condition==0        Element_Search=Element_Find(1);        Index_Element_Search=Index_Element_Find(1);        break;    endend

Claims (1)

1, a kind of method for composing of optimum optical orthogonal code is characterized in that adopting following step:

The first step, program begins, and gives the initializaing variable assignment, promptly under the given situation of code weight amount k, gives code word number t assignment, calculate code length v, and v is necessary for prime number; If v is not a prime number, change the value of t, till v is prime number;

In second step, calculate and obtain finite field F _vPrimitive element α;

In the 3rd step, generate v-1 rank cyclic group F by primitive element α _v ^*And its all elements stored;

In the 4th step, make β=α ^s, s=k (k-1)/2 wherein, for the generator structural index is s, rank are the cyclic subgroup C of 2t with β ₀ ^s, calculate C simultaneously ₀ ^sAll cosets, the storage C ₀ ^sAnd all elements of coset;

The 5th step, structure k unit set B ₀=0, α, α ²..., α ^K-1(modv), wherein, a ∈ F _v, calculate the difference set Δ ⁺B ₀All elements;

In the 6th step, judge the set Δ ⁺B ₀In all elements whether belong to s different coset respectively; If this condition satisfies, carried out for the 7th step; If this condition does not satisfy, carried out for the 5th step; If construction set B ₀All situations all comprise, this condition does not still satisfy, and carries out for the 8th step;

In the 7th step, utilize relational expression B _i=α ^IsB ₀, 1≤i≤t determines the set of t k unit, gathers all code words of determining to obtain the best (v, k, 1) light orthogonal code by this t, and result data is stored EP (end of program);

The 8th goes on foot, and can not construct the optimum optical orthogonal code of this length, EP (end of program).

Images