CN1137549C - Design method for 2-D signals with low/zero correlation region - Google Patents

Abstract

The present invention discloses a signal design method with a low correlation region, which leads to the addition by bit of an optimal two-dimensional signal and a group of two-dimensional signals of which the main peak of a cross correlation function is (+/-) 1. The present invention also discloses a signal design technique with a zero correlation zone, which leads to the generation of a group of orthogonal aperiodic complementary sequence sets. Non-interference transmission can be realized within the specified range, and the present invention can be used for multiple application areas of spread spectrum communication systems, aperture imaging, encryption, positioning and alignment, image processing operation, etc. The parameters of the two-dimensional signal group can be adjusted in real time and flexibly selected according to actual factors.

Description

A kind of 2D signal method for designing with low/zero correlation block

Technical field:

The present invention relates to a kind of 2D signal designing technique, particularly have the 2D signal design of low/zero correlation block good correlation.

Background technology:

In the design of many practical communication engineering systems, all require handled set of signals to possess one of following two conditions at least or satisfy this two conditions simultaneously:

1. each signal in the set of signals all is easy to make a distinction with the delay time signal of himself, also promptly requires its autocorrelation value as far as possible little;

2. each signal in the set of signals all is easy to other signal in the set of signals therewith and their delay time signal makes a distinction, and also promptly requires their cross correlation values as far as possible little.

Above-mentioned article one character is concerning very important such as spread spectrum communication system, remote control telemetering system and radar system.And to a plurality of targets of while remote measurement, multiple-target system identification and code division multiple access system, second character is then even more important.In addition, the signal with good correlation properties also can be used for numerous applications such as aperture imaging, aerial array, tomography X.

Especially, have the 2D signal of good correlation, demonstrate the not available advantage of conventional method in following application:

1. as two-dimension code, be used for efficient spread spectrum communication, reliable communication.

2. be used for encrypting, particularly the secret transmission and the kept secure of picture intelligence or other array data.

3. be used for the performance evaluation of the encoder, decoder (or volume, decoding scheme) of two-dimension code.

4. be used for the location alignment system between the parallel plane.

In the ideal case, signal should have following correlation properties: the auto-correlation function of each signal should be an impulse function, and promptly except that zero time delay, its value should be zero everywhere; The cross-correlation function value of every pair of signal should be zero everywhere.

Unfortunately, under one-dimensional case, no matter be binary, polynary or complex signal, the verified signal with this desirable correlation properties is non-existent.That is to given sequence length N and number M, maximum auto-correlation function limit peak value and maximum cross correlation functional value can not be zero simultaneously, and they are subjected to the restriction of some theoretical limits, when requiring one to diminish, another must increase, as the Welch limit, and Sidelnikov limit etc.

At this situation, designed signal (this signal has minimum or desirable correlation function near the certain limit zero time delay) in recent years with low/zero correlation block.By means of low/zero-correlation zone sequence, can realize that anti-multipath disturbs and the quasi-synchronous CDMA system of superior performance.More existing at present relevant patents as Chinese patent PCT/CN98/00151 (CN1175828A), adopt a kind of ternary spread-spectrum signal group with zero correlation block; Japan Patent TY99002 (11-023252) adopts a kind of binary spread-spectrum signal group with zero correlation block; Or the like

Summary of the invention:

The objective of the invention is to propose a kind of novel, simple two-dimensional Design of Signal, make it have low relevant district or zero correlation block.

The designed signal definition with " low/zero correlation block " is as follows:

For having M N ₁* N ₂The set of signals S={S of the 2D signal on rank ⁽ⁱ⁾, i=1,2 ..., M}, given low correlation δ＜＜N ₁N ₂(signal energy) presses the low relevant district L of following formula definition _Cz:

L _Cz=max{ (T ₁, T ₂) || R _{S, t}(τ ₁, τ ₂) |≤δ, wherein (| τ ₁|＜T ₁, | τ ₂|＜T ₂, r ≠ t)

Or (0＜| τ ₁|＜T ₁, 0＜| τ ₂|＜T ₂, s=t) } R wherein _{S, t}(τ ₁, τ ₂) be sequence S ^(s)With S ^(t)At time delay (τ ₁, τ ₂) the periodic cross-correlation functional value.According to this definition, we claim that this set of signals S is a LCZ-((N ₁, N ₂), M, L _Cz, δ) 2D signal collection.

In general, require low correlation δ as much as possible little in the practical application.Especially, when δ=0, low relevant district L _CzBe called as zero correlation block Z _Cz, corresponding set of signals is also referred to as ZCZ-((N ₁, N ₂), M, Z _Cz) the 2D signal collection.In other words, for low/zero correlation block set of signals S, around the correlation function initial point, exist a rectangular area L _Cz/ Z _Cz, their correlation function this zone near (much smaller than the value δ of signal energy) or reach the ideal (δ=0).

At low relevant district's 2D signal collection and zero correlation block 2D signal collection, provide implementation method separately respectively below.

One. the realization of low relevant district 2D signal collection

Should low relevant district signal be that ± 1 2D signal group step-by-step addition forms by a best 2D signal and a cross-correlation function main peak.

The low relevant district 2D signal that the present invention proposes is that 1 or-1 2D signal collection C combinatorial operation forms by the 2D signal B of the best (having desirable autocorrelation performance) and cross-correlation function main peak, best 2D signal B can obtain or obtain by the recursion method structure by computer search, and 2D signal collection C can utilize some known results.The district's 2D signal set construction method of should lowly being correlated with is as follows:

1. generate a best 2D signal B, promptly the submaximum of its auto-correlation function is zero entirely, and the rank of establishing 2D signal B are N ₁* N ₂

2. generate the one-dimensional signal collection D that the signal that is N by M length constitutes, requiring the cross-correlation function main peak between the signal is 1 or-1.One-dimensional signal collection D can be made of several different methods, as: the sequence sets that all cyclic shifts of a m sequence constitute, at this moment the cross-correlation function main peak is-1; In one group of Walsh sequence, all sequences is removed the element of any one same position, at this moment the cross-correlation function main peak is 1 or-1.

3. one-dimensional signal collection D is converted to 2D signal collection C, N is decomposed into N ₃N ₄, require N ₁And N ₃, N ₂And N ₄Coprime respectively.If $D=\{D_j^{\left(i\right)},i=\mathrm{1,2},K,M,j=\mathrm{0,1},K,N-1\},$ Generate the 2D signal collection $C=\{c_{m,n}^{\left(i\right)},i=\mathrm{1,2},K,M;m=\mathrm{0,1},K,N_3-1;n=\mathrm{0,1},K,N_4-1\},$ Wherein $c_{m,n}^{\left(i\right)}=d_j^{\left(i\right)},j=m\·N_4+n$ Or $c_{m,n}^{\left(i\right)}=d_j^{\left(i\right)},j=n\·N_3+m$

4. with each signal step-by-step addition among B and the set of signals C, promptly $A=\left\{A_{m,n}^{\left(i\right)}\right\},$ Wherein $A_{m,n}^{\left(i\right)}=B_{\mathrm{<figure-callout\; id="1"\; label="m\; mod\; N"\; filenames="C0110930200101.png"\; state="\{\{state\}\}">m</figure-callout>}\mathrm{mod}{N}_{}{}_1,n\mathrm{mod}{N}_2}+C_{m\mathrm{mod}{N}_3,n\mathrm{mod}{N}_4,}^{\left(i\right)}$ M=0,1, K, N ₁N ₃-1, n=0,1, K, N ₂N ₄-1 obtains a LCZ-((N ₁N ₃, N ₂N ₄), N ₃N ₄, (N ₁, N ₂), N ₁N ₂) sets of signals A.

In fact, in step 3, utilize the one-dimensional signal collection to generate the 2D signal collection, except list two kinds, several different methods can also be arranged, as $c_{m,n}^{\left(i\right)}=d_j^{\left(i\right)},$ M=j mod N ₃, n=j mod N ₄, require N ₃And N ₄Coprime.

The set of signals A that is generated has N ₃N ₄Individual signal, the absolute value of the correlation function between these signals (removing the auto-correlation function main peak) is by (N ₁, N ₂), (N ₁, N ₂), (N ₁,-N ₂), (N ₁,-N ₂) (rectangle slightly is written as (N hereinafter in 4 definite rectangular areas ₁, N ₂)) interior less than N ₁N ₂Or rather, except cross-correlation function be ± N in zero displacement place ₁N ₂Outward, all the other are zero.Thereby, by suitable selection parameter N ₁, N ₂, N ₃, N ₄, just can obtain the LCZ 2D signal collection of actual needs.

For example, the best 2D signal on given one 2 * 2 rank $B=\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right],$ The cross-correlation function main peak for two length of-1 be 9 one- dimensional signal 1,0,0,0,1,0,0,1,1} and { 1,0,1,1,1,1,1,0,1} utilizes step 3, generates the set of signals C that the 2D signal on 3 * 3 rank constitutes according to one-dimensional signal $C=\{\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 1& 1\end{array}\right],\left[\begin{array}{ccc}1& 0& 1\\ 1& 1& 1\\ 1& 0& 1\end{array}\right]\}$ At last each signal step-by-step addition among B and the 2D signal collection C is obtained A $A=\{\left[\begin{array}{cccccc}1& 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 1& 1\\ 0& 1& 1& 0& 1& 1\\ 1& 1& 0& 0& 0& 1\\ 0& 1& 0& 0& 1& 0\\ 0& 0& 1& 1& 1& 0\end{array}\right],\left[\begin{array}{cccccc}1& 0& 1& 1& 0& 1\\ 1& 0& 1& 0& 1& 0\\ 1& 0& 1& 1& 0& 1\\ 1& 1& 1& 0& 0& 0\\ 1& 1& 1& 1& 1& 1\\ 1& 1& 1& 0& 0& 0\end{array}\right]\}$ A is a LCZ-((6,6), 15, (2,2), a 4) signal 2D signal collection, and 26 * 6 rank 2D signals are arranged, low relevant district L _Cz=(2,2), low correlation δ=4.

Two. this zero correlation block signal of the realization of zero correlation block 2D signal collection divides two step structures, at first generates one group of quadrature complementary sequence set aperiodic B, again by this aperiodic complementary sequence set form by the method construct that connects with delegation's signal sequence.

Zero correlation block 2D signal method for designing proposed by the invention is based on one group of quadrature complementary 2D signal collection aperiodic.If one group of quadrature complementary 2D signal collection aperiodic B is made of M 2D signal collection, each subclass has N L ₁* L ₂The rank 2D signal is arranged as with matrix form: $B=\left[\begin{array}{cccc}{B}_{11}& B_{12}& \mathrm{\&Lambda;}& B_{1N}\\ B_{21}& B_{22}& \mathrm{\&Lambda;}& B_{2N}\\ M& M& M& M\\ B_{M1}& B_{M2}& \mathrm{\&Lambda;}& B_{\mathrm{MN}}\end{array}\right]$ Wherein the capable j of i is listed as an element B _IjRepresent j the 2D signal that i aperiodic, complementary 2D signal was concentrated, B can constitute by recursion method or Welti (Weir ladder) sign indicating number.

Based on B, it is as follows that it is connected generation set of signals A with delegation's signal sequence $A=\left[\begin{array}{cc}\mathrm{BB}& (-B)B\\ (-B)B& \mathrm{BB}\end{array}\right]---\left(1\right)$ Or $A=\left[\begin{array}{cc}B& -B\\ B& B\\ -B& B\\ B& B\end{array}\right]---\left(2\right)$ Wherein, the matrix that forms after each element negate among the-B representing matrix B, B ₁B ₂(or (B ₁) B ₂) expression B (or-B) in each element is connected the matrix of formation afterwards with each order of elements among the B.

From textural, formula (1) has increased the number (length) of the row of 2D signal, formula (2) has increased the number (width) of the row of 2D signal, the two comes down to consistent, so we will only utilize formula (1) to construct ZCZ 2D signal collection, the gained structured approach is applicable to formula (2) too.

The 2D signal collection A of gained contains 2M L ₁* (2L ₂* 2N) the rank 2D signal is a ZCZ-((L ₁, 2L ₂* 2N), 2M, (L ₁, L ₂+ 1)) 2D signal collection, zero correlation block Z _Cz=(L ₁, L ₂+ 1).Simultaneously, constitute if A regarded as by 2M subclass, each subclass has 2N L ₁* 2L ₂The rank 2D signal, then A will be one group of quadrature complementary 2D signal collection aperiodic.

In order to provide multiple structure flexibly to select for the user, the present invention provides 3 kinds of building methods:

Method 1: select different quadrature complementary 2D signal collection aperiodic B, directly construct ZCZ-((L ₁, 2L ₂* 2N), 2M, (L ₁, L ₂+ 1)) 2D signal collection A, zero correlation block Z _Cz=(L ₁, L ₂+ 1).

Method 2: since A also is one group of quadrature complementary 2D signal collection aperiodic, in formula (1), replace B, obtain new ZCZ-((L with A ₁, 4L ₂* 4N), 4M, (L ₁, 2L ₂+ 1)) 2D signal collection A ₁, 4M 2D signal arranged, zero correlation block Z _Cz=(L ₁, 2L ₂+ 1); In like manner, utilize formula (1) as recurrence formula, with A _N-1Replace B, obtain ZCZ-((L ₁, 2 ^N+1L ₂* 2 ^N+1N), 2 ^N+1M, (L ₁, 2 ⁿL ₂+ 1)) 2D signal collection A _n, have 2 ^N+1M 2D signal, zero correlation block Z _Cz=(L ₁, (L ₁, 2 ⁿL ₂+ 1), n=2,3 ...

Method 3: if rearrange matrix A=[B _LB _R], wherein, B _LThe capable j column element of i be $\left[\begin{array}{cc}{B}_{i,j}& B_{i,j}\\ -B_{i,j}& B_{i,j}\end{array}\right],$ B _RThe capable j column element of i be $\left[\begin{array}{cc}{-B}_{i,j}& B_{i,j}\\ B_{i,j}& B_{i,j}\end{array}\right],$ Then A is a ZCZ-((2L ₁, 2L ₂* 2N), M, (2L ₁, L ₂+ 1)) 2D signal collection, its zero correlation block are Z _Cz=(2L ₁, L ₂+ 1).This quadrature complementary signal aperiodic collection A has M subclass, and each subclass has 2N 2L ₁* 2L ₂The rank 2D signal.Utilize formula (1) as recurrence formula, with A _N-1Replace B, obtain ZCZ-((2 ^N+1L ₁, 2 ^N+1N*2 ^N+1L ₂), M, (2 ^N+1L ₁, 2 ⁿL ₂+ 1)) 2D signal collection A _n

For example, select quadrature complementary 2D signal collection aperiodic $B=\left[\begin{array}{cc}{B}_{11}& B_{12}\\ B_{21}& B_{22}\end{array}\right],$ Wherein ${\mathrm{<figure-callout\; id="11"\; label="B"\; filenames="C0110930200101.png"\; state="\{\{state\}\}">B</figure-callout>}}_{11}=\left[\begin{array}{cccc}0& 0& 0& 1\\ 0& 0& 0& 1\\ 0& 1& 0& 0\\ 1& 0& 1& 1\end{array}\right]$ $B_{12}=\left[\begin{array}{cccc}0& 0& 0& 1\\ 1& 1& 1& 0\\ 0& 1& 0& 0\\ 0& 1& 0& 0\end{array}\right]$ $B_{21}=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 1& 0\\ 0& 1& 1& 1\\ 1& 0& 0& 0\end{array}\right]$ $B_{22}=\left[\begin{array}{cccc}0& 0& 1& 0\\ 1& 1& 0& 1\\ 0& 1& 1& 1\\ 0& 1& 1& 1\end{array}\right]$

Utilize formula (1) to be constructed as follows 2D signal collection A $A=\left[\begin{array}{c}{A}^{\left(1\right)}\\ A^{\left(2\right)}\\ A^{\left(3\right)}\\ A^{\left(4\right)}\end{array}\right],$ A ⁽¹⁾=[B ₁₁B ₁₁B ₁₂B ₁₂(B ₁₁) B ₁₁(B ₁₂) B ₁₂] _{4 * 32}A ⁽²⁾=[B ₂₁B ₂₁B ₂₂B ₂₂(B ₂₁) B ₂₁(B ₂₂) B ₂₂] _{4 * 32}A ⁽³⁾=[(B ₁₁) B ₁₁(B ₁₂) B ₁₂B ₁₁B ₁₁B ₁₂B ₁₂] _{4 * 32}A ⁽⁴⁾=[(B ₂₁) B ₂₁(B ₂₂) B ₂₂B ₂₁B ₂₁B ₂₂B ₂₂] _{4 * 32}(3) A is one group of ZCZ-((4,32), 4, (4,5)) 2D signal collection, 4 signals is arranged, zero correlation block Z _Cz=(4,5).

Beneficial effect of the present invention:

1. in the time of within the scope of defined, can realize noiseless transmission.

2. the parameter of 2D signal group can be adjusted in real time according to practical factor, chooses flexibly

Description of drawings

Fig. 1 be of the present invention low/the zero correlation block 2D signal is applied to aperture imaging as aperture coding.

Fig. 2 is two signal A among the low relevant district 2D signal collection LCZ-of the present invention ((24,24), 2, (8,8), 64) ⁽¹⁾, A ⁽²⁾

Fig. 3 is the periodic auto-correlation function figure (is example with signal among Fig. 1 1) of low relevant district of the present invention 2D signal.

Fig. 4 is the periodic auto-correlation function figure (is example with signal 2 with signal among Fig. 1 1) of low relevant district of the present invention 2D signal.

Fig. 5 is two signal A among the zero correlation block 2D signal collection ZCZ-of the present invention ((8,32), 2, (8,5)) ⁽¹⁾, A ⁽²⁾

Fig. 6 is the periodic auto-correlation function figure (is example with signal among Fig. 1 1) of zero correlation block 2D signal of the present invention.

Fig. 7 is the periodic auto-correlation function figure (is example with signal 2 with signal among Fig. 1 1) of zero correlation block 2D signal of the present invention.

Embodiment

Below in conjunction with description of drawings embodiment:

Referring to Fig. 1, the arrangement in aperture is according to 2D signal, and the coding image that forms behind the image via hole diameter is that image and 2D signal have been done convolution one time in essence.A plurality of coding images are delivered to receiving terminal by channel multiplexing (sum operation), utilize each signal and multiplexed signals to make related operation then, recover original image separately, and whole process is very similar to CDMA mobile communication systems.As long as the 2D signal in decision aperture has good correlation properties, just can recover better image at receiving terminal.When in certain relative displacement scope, satisfying near-synchronous between each coded image and concern, adopt the 2D signal collection with low/zero correlation zone properties of the present invention will obtain the systematic function of near ideal.Similarly, 2D signal collection that also can/zero correlation zone properties low with having be used for encrypting, location aligning, image processing and other communications field.

Referring to Fig. 2, based on best 8 * 8 rank 2D signals $B=\left[\begin{array}{cccccccc}0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 1& 1& 1\\ 0& 0& 1& 1& 0& 0& 1& 1\\ 0& 0& 1& 0& 1& 1& 0& 1\\ 0& 1& 0& 1& 0& 1& 0& 1\\ 0& 1& 0& 1& 1& 0& 1& 0\\ 0& 1& 1& 0& 0& 1& 1& 0\\ 0& 1& 1& 1& 1& 0& 0& 0\end{array}\right]$ , the cross-correlation function main peak is 9 one-dimensional signal { 1,0,0 for two length of-1,0,1,0,0,1,1} and { 1,0,1,1,1,1,1,0, LCZ-((24,24), 2 that 1} generates, (8,8), 64)) 2D signal collection A.A can use for 2 users, requires on the both direction of signal time delay all less than 4.

Described a kind of periodic auto-correlation function with arbitrary signal in the low relevant Design of Signal method set of signals of distinguishing is zero in the rectangular area around the initial point; Arbitrary periodic cross-correlation function to signal is zero in the rectangular area around initial point in the set of signals, is far smaller than its signal energy in the value of initial point.

Described a kind of Design of Signal method with zero correlation block, be zero in the rectangular area of the periodic auto-correlation function of arbitrary signal around the initial point in the set of signals, arbitrary periodic cross-correlation function to signal is zero in the rectangular area that (comprises initial point) around the initial point in the set of signals.

Referring to Fig. 3, be the periodic auto-correlation function figure of signal 1 among Fig. 2, its periodic auto-correlation function submaximum is zero in a rectangular area (4,4).

Referring to Fig. 4, be the periodic cross-correlation functional arrangement of signal 1 and signal 2 among Fig. 2, its periodic cross-correlation function submaximum is zero in a rectangular area (4,4).

Referring to Fig. 5, utilize zero correlation block 2D signal set construction method 3, ZCZ-((8,32), 2, (8,5)) can use for 2 users, and time delay is less than 8 on a direction of signal in requirement, and time delay is less than 5 on the other direction.

Referring to Fig. 6, be the periodic auto-correlation function figure of signal 1 among Fig. 5, its periodic auto-correlation function submaximum is zero in a rectangular area.

Referring to Fig. 7, be the periodic cross-correlation functional arrangement of signal 1 and signal 2 among Fig. 5, its periodic cross-correlation function is zero in a rectangular area.

Claims (2)

1. 2D signal method for designing with low relevant district is characterized in that: this low relevant district signal is zero 2D signal entirely by the width of cloth peak of an auto-correlation function and a cross-correlation function main peak is that ± 1 2D signal group step-by-step addition forms.

2. according to right 1 described a kind of 2D signal method for designing with low relevant district, it is characterized in that: the periodic auto-correlation function of arbitrary signal is zero in the rectangular area around the initial point in the described set of signals; Arbitrary periodic cross-correlation function to signal is zero in the rectangular area around initial point in the set of signals, is far smaller than its signal energy in the value of initial point.

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