CN1767420A - Generalized duplicated complementary code generating method - Google Patents

Abstract

This invention discloses a method for generating generalized paired mutual-complementing codes, in which, a complete orthogonal mutual-complementing code expands to generate an even shift orthogonal sequence to be expanded to get the generalized paired mutual-complementing codes having the property of ideal self-correlation and mutual-correlation, the functions of the self-correlation and that of the mutual-correlation in the group have zero correlation regions, only small amount of non-zero minor lobes are scattered out of the zero correlation regions and the mutual-correlation functions among groups are all zero.

Description

The production method of the paired mutual-complementing code of a kind of broad sense

Technical field

The present invention relates to the production method and the single carrier DS-CDMA communication system of mutual-complementing code, especially, relate to the paired mutual-complementing code production method of a kind of broad sense.

Background technology

In order to improve the spectrum efficiency and the power system capacity of existing cdma system, must reduce as much as possible because the multiple access that imperfect cross-correlation of spreading code and autocorrelation performance cause inserts and disturb (MAI) and multipath to disturb (MI).If the cross-correlation of any two spreading codes is zero, then there is not MAI.Same, if the auto-correlation function secondary lobe of any one spreading code is zero, then there is not MI.If above-mentioned desirable correlation properties can realize noiseless in up link and down link all setting up synchronously and under the asynchronous condition so.Yet, have rare progress aspect the CDMA spreading code set (particularly solid size or to sign indicating number) of above-mentioned ideal characterisitics in generation.

Mainly contain two classes at present and be used for the spreading code of cdma system.One class is solid size (unitary codes), and promptly a user distributes a sign indicating number.Nearly all CDMA spreading code that is used for present 2G, 3G system all is a solid size, as the m sequence, and Gold sign indicating number, Kasami sign indicating number, Walsh sequence, ovsf code etc.The advantage of solid size is that spread spectrum is simple, only needs a spread spectrum and carrier modulator, and shortcoming is that cross-correlation and autocorrelation performance are all undesirable.

Another kind of spreading code is a mutual-complementing code, as complete complementary code etc.Golay and Truyn are respectively at " Complementary series " (M.J.E.Golay, IRE Trans.Inform.Theory, vol.IT-7, pp.82-87,1961) and " Ambiguity function of complementary sequences " (R.Turyn, IEEE Trans.Inform.Theory, vol.IT-9, pp.46-47,1963) propose in to use complete complementary code in radar system.When code division multiple access was used, a user distributed a mutual-complementing code (containing a plurality of subcodes).Paper " Amulti-carrier CDMA architecture based on orthogonal complementary codes for newgenerations of wideband wireless communications " (HH Chen, et al.IEEECommunications Magazine, vol.39, no.10, pp.126-135,2001) point out to use complete complementary code and skew stack (Offset-stacked in, OS) spread spectrum can realize not having MAI, support the variable rate transmission of burst service flexibly, effectively improve the spectrum efficiency of cdma system.Mutual-complementing code has desirable correlation properties, thereby improves power system capacity greatly.But the mutual-complementing code number is limited, and promptly the number of users that can support of cdma system is limited.In addition, a plurality of subcodes of mutual-complementing code need transmissions that walk abreast of a multi-carrier modulator, and realization is complexity comparatively; CDMA multiple carrier is comparatively responsive to frequency selective fading, the different decline of different subcode experience, and the correlation function that receiving terminal is tried to achieve no longer has ideal characterisitics.

In order to compromise between the number of sign indicating number and antijamming capability, existing many designs and application have the report of the sign indicating number of zero correlation block (ZCZ).Wherein the most noticeable is the TD-LAS system that company of Linkair (LinkAir) proposes, and this system is received as 3GPP2 by ITU and strengthens version.The spreading code LS sign indicating number that uses in the TD-LAS system is a pair of sign indicating number, is called C sign indicating number and S sign indicating number, and the number of LS sign indicating number and the length of ZCZ are inversely proportional to.At " Designfor communications applications " (Fan PZ, Darnell M John Wiley﹠amp; Sons, Ltd.:RSP, London, 1996) and " Generalized orthogonal sequences and their applications insynchronous CDMA systems " (Fan PZ, Hao L.IEICE Transactions Fundamentals, E83-A (11): 1-16,2000) zero correlation block that the ZCZ sign indicating number of mentioning in can provide is less, and great majority are not binary codes, and this makes and is difficult to realize in real system.In addition, the auto-correlation function of all these ZCZ sign indicating numbers and cross-correlation function are uncontrollable outside zero correlation block, if multipath component or interference signal drop on outside the zero correlation block, detection efficiency will be subjected to considerable influence.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, provide a kind of broad sense in pairs complementary (Generalized Pairwise Complementary, GPC) Ma production method has the advantage that the solid size spread spectrum is realized simple advantage and mutual-complementing code opposing MAI and MI concurrently.

The present invention seeks to realize by following technical solution: the production method of the paired mutual-complementing code of a kind of broad sense, this method may further comprise the steps:

(1) get the set of complete complementary code, set contains 2 sign indicating numbers, and each yard longly constitutes for the subcode of N by 2;

(2) expansion of 2 subcodes, the polyphone of described 2 complete complementary codes obtained 2 and longly be the even displacement orthogonal sequence of 4N;

(3) described 2 even displacement orthogonal sequences are obtained two matrix H through the Hadamard expansion respectively _1,2And H _2,2

(4) size of extended code set is to described matrix H _1,2And H _2,2The Hadamard expansion of carrying out recurrence obtains matrix H _{1, K}And H _{2, K}

(5) with H _{1, K}And H _{2, K}Get the paired mutual-complementing code of broad sense with one 2 * 2 Hadamard matrix operation respectively.Further, the set of the paired mutual-complementing code of the broad sense that is produced comprises 2 groups, comprises K yard in every group, and each yard contains the subcode that a pair of length is 4NK.

Further, the auto-correlation function of the paired mutual-complementing code of broad sense that is produced has one longly to be the zero correlation block of 8N-1 in zero displacement both sides, distinguish outer non-zero secondary lobe sparse distribution; The cross-correlation function of any two yards has one longly to be the zero correlation block of 8N-1 in the group, distinguishes outer non-zero secondary lobe sparse distribution; The cross-correlation function that belongs to not any two yards on the same group is complementary fully, and promptly the zero correlation head of district is 4NK-1.

The present invention has following technique effect:

The auto-correlation function of GPC sign indicating number and cross-correlation function have only a spot of non-zero secondary lobe, sparsely are distributed in outside the ZCZ, even show that auto-correlation function and cross-correlation function also are controlled outside ZCZ.The ZCZ length of GPC sign indicating number can reach 8N-1, and N is the subcode length that is used to produce the complete complementary code of GPC sign indicating number.Therefore, use different N can change the ZCZ length of GPC sign indicating number set.By the producing method decision, sign indicating numbers all in the set of GPC sign indicating number adhere to two groups separately.From on the same group the cross-correlation function of two GPC sign indicating numbers is not complementary fully, promptly ZCZ can expand to whole subcode code length.

Description of drawings

Fig. 1 is the correlation properties schematic diagram of the paired mutual-complementing code of broad sense of the present invention's generation; Wherein, (a) be autocorrelation performance figure, (b) be their cross correlation figure in the group, (c) be their cross correlation figure between group;

Fig. 2 expands schematic diagram for the set of the paired mutual-complementing code of broad sense that the present invention produces;

Fig. 3 uses the single carrier DS-CDMA system transreceiver block diagram of the paired mutual-complementing code of broad sense for the present invention.

Embodiment

Be described in detail the production process of the paired mutual-complementing code of broad sense below in conjunction with embodiment.Two steps of main branch.The first step: produce even displacement orthogonal sequence by complete complementary code

(Complete Complementary, CC) sign indicating number set comprises two complete complementary codes to choose a complementation fully.c ₁₁With c ₁₂Be two subcodes of a complete complementary code, c ₂₁With c ₂₂Be two subcodes of another complete complementary code, subcode length is N,

$c_{11}=\left[\begin{array}{cccc}{c}_{11}^{\left(1\right)}& c_{11}^{\left(2\right)}& \·\·\·& c_{11}^{\left(N\right)}\end{array}\right],c_{12}=\left[\begin{array}{cccc}{c}_{12}^{\left(1\right)}& c_{12}^{\left(2\right)}& \·\·\·& c_{12}^{\left(N\right)}\end{array}\right]$

$c_{21}=\left[\begin{array}{cccc}{c}_{21}^{\left(1\right)}& c_{21}^{\left(2\right)}& \·\·\·& c_{21}^{\left(N\right)}\end{array}\right],c_{22}=\left[\begin{array}{cccc}{c}_{22}^{\left(1\right)}& c_{22}^{\left(2\right)}& \·\·\·& c_{22}^{\left(N\right)}\end{array}\right]$

With c ₁₁Each chip with [1 1] expansion, c ₁₂Each chip with [1-1] expansion,

$c_{11}^{[++]}=\left[\begin{array}{ccccccc}{c}_{11}^{\left(1\right)}& c_{11}^{\left(1\right)}& c_{11}^{\left(2\right)}& c_{11}^{\left(2\right)}& \·\·\·& c_{11}^{\left(N\right)}& c_{11}^{\left(}\end{array}\right]$

$=\left[\begin{array}{cccc}{c}_{11}^{\left(1\right)}& c_{11}^{\left(2\right)}& \·\·\·& c_{11}^{\left(N\right)}\end{array}\right]$

$c_{12}^{[+-]}=\left[\begin{array}{ccccccc}{c}_{12}^{\left(1\right)}& {-c}_{12}^{\left(1\right)}& c_{12}^{\left(2\right)}& {-c}_{12}^{\left(2\right)}& \·\·\·& c_{12}^{\left(N\right)}& {-c}_{12}^{\left(}\end{array}\right]$

$=\left[\begin{array}{cccc}{c}_{12}^{\left(1\right)}& c_{12}^{\left(2\right)}& \·\·\·& c_{12}^{\left(N\right)}\end{array}\right]$

With these two sequences sequence c that to be merged into a length be 4N ₁,

$c_1=\left[\begin{array}{cc}{c}_{11}^{[++]}& c_{12}^{[+-]}\end{array}\right]$

$=\left[\begin{array}{cccccccc}{c}_{11}^{\left(1\right)}& c_{11}^{\left(2\right)}& \·\·\·& c_{11}^{\left(N\right)}& c_{12}^{\left(1\right)}& c_{12}^{\left(2\right)}& \·\·\·& c_{12}^{\left(N\right)}\end{array}\right]$

c ₁Relevant when even displacement is zero.Same step, can construct an even displacement more relevant is zero sequence:

${\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">c</figure-callout>}}_2=\left[\begin{array}{cc}{c}_{21}^{[++]}& c_{22}^{[+-]}\end{array}\right]$

$=\left[\begin{array}{cccccccc}{c}_{21}^{\left(1\right)}& c_{21}^{\left(2\right)}& \&CenterDot;\&CenterDot;\&CenterDot;& c_{21}^{\left(N\right)}& c_{22}^{\left(1\right)}& c_{22}^{\left(2\right)}& \&CenterDot;\&CenterDot;\&CenterDot;& c_{22}^{\left(N\right)}\end{array}\right]$

Second step: produce the set of GPC sign indicating number by even displacement orthogonal sequence

With Hadamard matrix expansion c ₁With c ₂, obtain the matrix H of 2 * 8N _1,2And H _2,2:

$H_{\mathrm{1,2}}=\left[\begin{array}{cc}{c}_1& c_1\\ c_1& -{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20051006064100101.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\end{array}\right]$

$H_{\mathrm{2,2}}=\left[\begin{array}{cc}{c}_2& c_2\\ c_2& -{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">c</figure-callout>}}_2\end{array}\right]$

In like manner, matrix H _{1, K}Can be by H _{1, K/2}By the Hadamard matrix expand, matrix H _{2, K}Can be by H _{2, K/2}Expand by the Hadamard matrix.The matrix of 2K * KP (P=4N) then

$H_K=\left[\begin{array}{c}{H}_{1,K}\\ H_{2,K}\end{array}\right]=\left[\begin{array}{cc}{H}_{1,K/2}& H_{1,K/2}\\ H_{1,K/2}& {-H}_{1,K/2}\\ H_{2,K/2}& H_{2,K/2}\\ H_{2,K/2}& -H_{2,K/2}\end{array}\right]=\left[\begin{array}{c}{h}_1\\ {\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">h</figure-callout>}}_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ h_{2K}\end{array}\right]$

With H _KMatrix is regarded two groups up and down as.Wantonly two row that belong to are not on the same group done cross-correlation, are zero in even displacement place; Wantonly two row in same group are done cross-correlation, are removing xP (x=± 1, ± 2 ... even displacement place of ∞) all is zero.

Produce one 2 * 2 Hadamard matrix D again,

$D=\left[\begin{array}{cc}{d}_{11}& d_{12}\\ d_{21}& d_{22}\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]=\left[\begin{array}{c}{d}_1\\ {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\end{array}\right]$

Matrix H _KComputing obtains a matrix with D,

$U=U_I+j{U}_Q=\left[\begin{array}{c}{u}_{I,1}\\ u_{I,2}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ u_{I,2K}\end{array}\right]+j\left[\begin{array}{c}{u}_{Q,1}\\ u_{Q,2}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ u_{Q,2K}\end{array}\right]=\left[\begin{array}{c}{u}_1\\ u_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ u_{2K}\end{array}\right]=\left[\begin{array}{c}{U}_{G1}\\ {\mathrm{<figure-callout\; id="2"\; label="U\; G"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">U</figure-callout>}}_G\end{array}\right]$

U is the set of GPC sign indicating number, contains 2K GPC sign indicating number u _k, each GPC sign indicating number contains the subcode u that a pair of length is KP _{I, k}And u _{Q, k}(k=1,2 ... 2K).In the following formula,

U _I(p，q)＝H _K(p，q)D(1，ζ)ζ＝-mod(q，2)+2，

U _Q(p，q)＝H _K(p，q)D(2，ζ)p＝1，2…2K，q＝1，2…PK

U can regard two groups up and down as, is respectively U _G1And U _G2, respectively contain K GPC sign indicating number,

$U_{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="A20051006064100101.png"\; state="\{\{state\}\}">G</figure-callout>}1}=\left[\begin{array}{c}{u}_1\\ u_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ u_K\end{array}\right],{\mathrm{<figure-callout\; id="2"\; label="U\; G"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">U</figure-callout>}}_G=\left[\begin{array}{c}{u}_{K+1}\\ u_{K+2}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ u_{2K}\end{array}\right]$

Provide the generative process of the GPC sign indicating number set that contains 4 sign indicating numbers, subcode long 32 below.Here, K=2, KP=32, thus P=16, N=4.At first, choosing a sub-code length is the set of 4 complete complementary code

$\left[\begin{array}{c}{c}_{11}\\ c_{12}\end{array}\right]=\left[\begin{array}{c}+++-\\ +-++\end{array}\right],\left[\begin{array}{c}{c}_{21}\\ c_{22}\end{array}\right]=\left[\begin{array}{c}++-+\\ +---\end{array}\right]$

Then, by expansion c ₁₁, c ₁₂, c ₂₁With c ₂₂

$c_{11}^{[++]}=[++++++--]$

$c_{12}^{[+-]}=[+--++-+-]$

$c_{21}^{[++]}=[++++--++]$

$c_{22}^{[+-]}=[+--+-+-+]$

These sequence c of long 8 contact ₁₁ ^[++]And c ₁₂ ^[+-], c ₂₁ ^[++]And c ₂₂ ^[+-], obtain long 16 even displacement orthogonal sequence c ₁And c ₂,

$c_1=\left[c_{11}^{[++]}{c}_{12}^{[+-]}\right]=[++++++--+--++-+-]$

$c_2=\left[c_{21}^{[++]}{c}_{22}^{[+-]}\right]=[++++--+++--+-+-+]$

Utilize Hadamard matrix expansion c ₁And c ₂Obtain 4 * 32 matrix H ₂

${\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">H</figure-callout>}}_2=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20051006064100101.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{1,2}}\\ {\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="H"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">H</figure-callout>\; </figure-callout>}}_{\mathrm{2,2}}\end{array}\right]=\left[\begin{array}{cc}{c}_1& c_1\\ c_1& {-c}_1\\ c_2& c_2\\ c_2& {-\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">c</figure-callout>}}_2\end{array}\right]=\left[\begin{array}{c}{h}_1\\ h_2\\ h_3\\ {\mathrm{<figure-callout\; id="4"\; label="h"\; filenames="A20051006064100111.png"\; state="\{\{state\}\}">h</figure-callout>}}_4\end{array}\right]$

By matrix H ₂Can get with 2 * 2 Hadamard matrix D computing

U _I(p，q)＝H ₂(p，q)D(1，ζ)ζ＝-mod(q，2)+2，

U _Q(p，q)＝H ₂(p，q)D(2，ζ)p＝1，2，3，4，q＝1，2…32

Final GPC sign indicating number set can be expressed as

$U_I=\left[\begin{array}{c}{u}_{I,1}\\ u_{I,2}\\ u_{I,3}\\ u_{I,4}\end{array}\right]=\left[\begin{array}{c}++++++--+--++-+-++++++--+--++-+-\\ ++++++--+--++-+-------++-++--+-+\\ ++++--+++--+-+-+++++--+++--+-+-+\\ ++++--+++--+-+-+----++---++-+-+-\end{array}\right]$

$U_Q=\left[\begin{array}{c}{u}_{Q,1}\\ u_{Q,2}\\ u_{Q,3}\\ u_{Q,4}\end{array}\right]=\left[\begin{array}{c}+-+-+--+++--+++++-+-+--+++--++++\\ +-+-+--+++--++++-+-+-++---++----\\ +-+--++-++------+-+--++-++------\\ +-+--++-++-------+-++--+--++++++\end{array}\right]$

The subcode u of a pair of length 32 _{I, k}And u _{Q, k}(k=1 ... 4) constitute a GPC sign indicating number u _kContain 4 GPC sign indicating numbers in the set, u ₁And u ₂Constitute first group, u ₃And u ₄Constitute second group.

Fig. 1 has shown the correlation properties of the GPC sign indicating number among the embodiment.Autocorrelation performance is seen (a), except displacement is nP (n=± 1, ± 2 ..., ∞ P=4N=16) locates, and the auto-correlation secondary lobe is zero.Their cross correlation is seen (b) in the group, except displacement nP (n=± 1, ± 2 ..., ∞ P=4N=16) locates, and the cross-correlation function of any two yards is zero in the group.Their cross correlation is not on the same group seen (c), and the cross-correlation function of on the same group any two yard is not zero everywhere.

Fig. 2 has shown the set expansion schematic diagram that produces the paired mutual-complementing code of broad sense.Initial complete complementary code with 2 * 4 is a starting point, by selecting the Hadamard matrix of different size for use, can produce the paired mutual-complementing code set of the broad sense with different subcode length and different sets size.

Fig. 3 has shown that the paired mutual-complementing code of application broad sense is in the transreceiver block diagram of single carrier cdma system.Respectively at I, Q two branch roads send data simultaneously behind a pair of subcode spread spectrum of GPC sign indicating number.The I that receives, addition after the data difference despreading of Q two branch roads, judgement.Because two same channel fadings of subcode experience, the correlation function that receiving terminal is tried to achieve has ideal characterisitics, has improved the availability of frequency spectrum, has reduced the hardware complexity of transmitter and receiver.

Claims (3)

1. the production method of the paired mutual-complementing code of broad sense is characterized in that, this method may further comprise the steps:

(1) choose the set of complete complementary code, set contains 2 sign indicating numbers, and each yard longly constitutes for the subcode of N by 2.

(2) expansion of 2 subcodes, the polyphone of described 2 complete complementary codes obtained 2 and longly be the even displacement orthogonal sequence of 4N.

(3) described 2 even displacement orthogonal sequences are obtained two matrix H through the Hadamard expansion respectively _1,2And H _2,2

(4) size of extended code set is to described matrix H _1,2And H _2,2The Hadamard expansion of carrying out recurrence obtains matrix H _{1, K}And H _{2, K}

(5) with H _{1, K}And H _{2, K}Get the paired mutual-complementing code of broad sense with one 2 * 2 Hadamard matrix operation respectively.

2. the production method of the paired mutual-complementing code of a kind of broad sense according to claim 1 is characterized in that, the set of the paired mutual-complementing code of the broad sense that is produced comprises 2 groups, comprises K yard in every group, and each yard contains the subcode that a pair of length is 4NK.

3. the production method of the paired mutual-complementing code of a kind of broad sense according to claim 1 is characterized in that, the auto-correlation function of the paired mutual-complementing code of broad sense that is produced has one longly to be the zero correlation block of 8N-1 in zero displacement both sides, distinguish outer non-zero secondary lobe sparse distribution; The cross-correlation function of any two yards has one longly to be the zero correlation block of 8N-1 in the group, distinguishes outer non-zero secondary lobe sparse distribution; The cross-correlation function that belongs to not any two yards on the same group is complementary fully, and promptly the zero correlation head of district is 4NK-1.

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