CN101753247B - Construction method of multi-dimensional similar-orthogonal pseudo-random extended matrix - Google Patents

Abstract

The invention discloses a construction method of a multi-dimensional similar-orthogonal pseudo-random extended matrix, which comprises the steps of screening and combining primitive polynomials of f1(x), f2(x), ..., fn(x), then carrying out group transformation and numerical conversion, constructing a similar-orthogonal pseudo-random matrix M, then passing through a comb filter with the threshold of sigma 1, selecting a code group with good relevance and constructing a matrix PN; and then selecting another group of f1'(x), f2'(x), ..., fn'(x), screening, combining, carrying out the group transformation for obtaining a matrix M', then passing through the comb filter with the threshold of sigma 2 which is equal to 0, selecting the completely orthogonal code group, constructing a PN' matrix, finally carrying out direct product operation on the previously produced PN matrix and the completely orthogonal PN' matrix, and obtaining an MSPE matrix PN-PN' after extension. The MSPE matrix PN-PN' after extension through the method has the orthogonal property which is similar to the Walsh matrix, when the MSPE matrix PN-PN' after extension is applied in a CDMA system, the MSPE matrix PN-PN' can obtain the effects which are similar to those of the Walsh matrix. Meanwhile, the size of the matrix is different with the Walsh matrix which is limited by the order of 2, and can be arbitrary value.

Description

The constructive method of multi-dimensional similar-orthogonal pseudo-random extended matrix

Technical field

The present invention relates to a kind of constructive method of multi-dimensional similar-orthogonal pseudo-random extended matrix, multidimensional class similar-orthogonal pseudo-random extended matrix (Multi-dimensional Similar-orthogonal Pseudo-random Expansion) matrix (being called for short the MSPE matrix) is a kind of spreading code that can be applicable in the cdma communication system, belongs to the technical field of mobile communication.

Background technology

For cdma system, it mainly exists local interference, intersymbol interference, multiple access to disturb, lead the way and disturb four kinds of interference.In general, the frequency expansion sequence correlation properties in cdma system are better, and namely the autocorrelation of sequence is stronger, and cross correlation is more weak, and the interference that is subject to of system is just fewer so.In the various interference that cdma system is subject to, except disturbed this locality, remaining interference can be by selecting the reasonable frequency expansion sequence of correlation properties to reduce even eliminating.Simultaneously, cdma system and traditional wireless multiple access technology TDMA FDMA different, its capacity also mainly is subject to interference, therefore selects the frequency expansion sequence with good correlation properties, except can reducing interference, can also realize the cdma system of heap(ed) capacity.Simultaneously, frequency expansion sequence also be widely used in radar, sonar, synchronously, the various fields such as channel estimating and equilibrium, communication security, system identification.

Generally, we adopt Hadamard (Hadamard) matrix of quadrature as the chnnel coding of cdma system.Hadamard (Hadamard) matrix is a very important matrix, and its every delegation (or row) all is orthogonal code sets.Hadamard (Hadamard) matrix is referred to as the H matrix.

Because each row in Hadamard (Hadamard) matrix (or row) is mutually orthogonal, whole H matrix be exactly a kind of length be the orthogonal coding of n, it comprises n code character, the code length of each code character is n.At present, remove outside n=4 * 47=188, the H matrix of all n≤200 all finds.Because big or small limited (n≤200) of H matrix, therefore in multiple access technology, user's quantity will be very restricted, and namely number of users can not surpass 200.The number of channel and the number of users of system have been limited so to a great extent.

Multi-dimension quasi-orthogonal pseudo-random expansion (MSPE) matrix be multi-dimension quasi-orthogonal pseudo-random (MSP) matrix through screening after, pick out preferably matrix of class orthogonality, it is expanded forming again.So the MSPE matrix is compared with the MSP matrix, its class orthogonality is better, and namely matrix has more class orthogonality good capable vector or column vector, that is to say that more orthogonality can be arranged good sequence is applied to actual communication system.When MSPE matrix and MSP matrix were applied to the communication systems such as CDMA simultaneously, the error rate of MSPE matrix had had very large improvement compared to the MSP matrix.

Simultaneously, for the Walsh matrix, because its Hadamard matrix of expanding usefulness is one 2 * 2 orthogonal matrix, the matrix size after the expansion is 2 ⁿ* 2 ⁿ(n for expansion number of times), and the matrix that can not have an index power size of 6,10 etc. non-2 occurs.And the novel MSPE matrix that proposes by this patent, their matrix size can be arbitrary value, namely unlike the H matrix, can only get 2 index power size, so it no longer is restricted on matrix size.

For a DS-CDMA system, its address code adopts different sequencers with scrambler, so more complicated is loaded down with trivial details on Project Realization.The MSPE square matrix code namely can be used as again scrambler as address code among the present invention, and this will simplify the realization on the engineering greatly.

Summary of the invention

Goal of the invention of the present invention, be to overcome the technological deficiency that prior art exists, a kind of constructive method of multi-dimensional similar-orthogonal pseudo-random extended matrix has been proposed, the method can easily construct larger MSPE matrix (multi-dimensional similar-orthogonal pseudo-random extended matrix), and has good class orthogonality (namely both had stronger autocorrelation, and had again weak cross correlation) between the capable vector of these matrixes or the column vector.If the MSPE matrix that chnnel coding adopts the MSPE extended method to obtain, its channel quantity can reach more than 230,400.The MSPE matrix that is made of above extended method simultaneously satisfies the requirement of Welch circle, has well pseudo-random characteristics, can be used as spreading code and uses and cdma system.For the MSPE matrix that obtains by expansion, it can also be applied to distinguish the base station with the MSPE matrix among the AD Hoc, respectively the row, column vector in the matrix is applied to simultaneously the chnnel coding of each base station and subscriber-coded.

The constructive method of multi-dimensional similar-orthogonal pseudo-random extended matrix of the present invention, its step is as follows:

1, as required, select primitive polynomial f ₁(x), f ₂(x) ..., f _n(x) screen combination, obtain f (x) sequence.F (x) sequence is consisted of quadrature pseudo-random matrix (MSP matrix) M by group translating in buffer memory.

The screening combination of above-described primitive polynomial: can select the primitive polynomial of any number, make up in any order.Namely $f\left(x\right)=F[f_1^{n_1}\left(x\right),f_2^{n_2}\left(x\right),......,f_n^{n_j}\left(x\right)],$ Wherein $n=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_i.$

F (x) after the screening combination is carried out group translating, and the process of group translating is as follows:

1). at first with the sequence a of initial condition _na _N-1A ₀Move to right one;

2). the highest order to the sequence after moving to right is judged, if highest order is 1, then this sequence and initial order is carried out exporting a ' behind the XOR _N-1A ' _N-2A ₀', if highest order is-1, then directly export a _N-1a _N-2A ₀, 0;

3). continued to forward to the 1st step and do cycling, until duplicate sequence;

4). with all series arrangement matrix N, then output;

5). matrix N is inverted and rotation.

A kind of error correcting code by the code in the N matrix that obtains after the above group translating step, and the N matrix that uses the mode of group translating to obtain, during as error correcting code, the number of error correction what with the number of the primitive polynomial that makes up how much be one to one.And when generator polynomial can only remedy a mistake, the capable vector in the position of making a mistake and the N matrix was one to one; When generator polynomial can be corrected a plurality of mistake, the position that a plurality of mistakes occur be with the N matrix in the combination of a plurality of row vectors be one to one, after utilizing group translating, this corresponding relation between matrix and the errors present, we can carry out easily error correction and recover correct information.

Simultaneously, be a matrix that is combined by Metzler matrix and I unit matrix through the N square that obtains behind the group translating, namely $N=\left[\begin{array}{c}P\\ I\end{array}\right],$

Wherein the P matrix is the binary matrix that only contains " 1 ", " 1 ", and here, we carry out a numerical value conversion to the P matrix, obtain matrix M, namely

$m_i=\left\{\begin{array}{cc}1& (P_i=1)\\ -1& (P_i=0)\end{array}\right.$

The Metzler matrix of this moment is a multi-dimension quasi-orthogonal pseudo-random matrix.

For set E={1 ,-1}, wherein the number of sequence is M, a certain sequence x=(x ₁, x ₂..., x _L) ∈ E ^LThe length that is called as on the E is the sequence of L, for any two sequence x=(x ₁, x ₂..., x _L) and y=(y ₁, y ₂..., y _L), their aperiodic correlation function A (x, y; L) be defined as

$A(x,y;L)=\underset{i=1}{\overset{L-1}{\mathrm{\Σ}}}{x}_i{y}_{i+l}$ l＝0，1，…，L-1

If only consider positive time delay, for arbitrary sequence collection C ∈ E ^L, maximum aperiodic of the auto-correlation limit peak value δ of C _a(C)=max{|A (x, x; L|:0＜l≤L-1},

Maximum cross correlation value δ aperiodic _c(C)=max{|A (x, y; L|:x ≠ y, 0≤l≤L-1}.

According to the requirement of cdma communication system sequence, must seek the function P (L, M) and the D (L, M) that depend on parameter L and M, it is satisfied with lower inequality:

$P(L,M){{\mathrm{\δ}}_a}^2\left(C\right)+D(L,M){{\mathrm{\δ}}_c}^2\left(C\right)\≥1---\left(1\right)$

Here, make δ (C)=max{ δ _a(C), δ _c(C) }, inequality (1) can be reduced to

δ ²(C)≥H(L，M) (2)

General Requirements H (L, M) is the bigger the better.Inequality (2) is at first studied by Welch.In 1974, Welch utilized the character of inner product of vectors to derive following boundary:

${\mathrm{\δ}}^2\left(C\right)\≥\frac{(M-1)L^2}{2\mathrm{ML}-M-1}---\left(3\right)$

Below namely be called as Welch circle.

The sequence that satisfies Welch circle has good correlation.The maximum non-periodic autocorrelation function of the MSP matrix M that is produced by above method or the peak value of cross-correlation function just satisfy Welch circle.Therefore, the Metzler matrix of structure has good correlation here.

2, setting threshold σ ₁Then will have the MSP matrix M of good correlation by one-level row comb filter or row comb filter, pick out the outstanding row vector of good relationship or column vector as code character allowable, its complement vector is then as the forbidding code character, and code character allowable combined, consist of a PN matrix with good class orthogonality;

Matrix M has the class orthogonality, and the cross-correlation coefficient figure between its row vector, the column vector respectively as shown in Figure 3.As seen from Figure 3, existing class quadrature closes the very weak vector of property in the matrix, also exists the class orthogonality relatively good, i.e. smaller capable vector or the column vector of cross-correlation coefficient is so we set a threshold value σ ₁(0＜σ ₁＜1) (or σ ₁' (0＜σ ₁'＜1)), by one-level row comb filter or row comb filter, will be less than threshold value σ ₁(or σ ₁') capable vector or column vector pick out, as code character allowable, combine and consist of the PN matrix with good class orthogonality, remaining vector is then rejected as the forbidding code character.

3, setting threshold σ ₂, then with the MSP matrix M by one-level row comb filter or row comb filter, pick out completely orthogonal code character, consist of PN ' matrix;

With described in 2, set again a threshold value σ here ₂=0 (or σ ₂'=0), with quadrature pseudo-random matrix M by one-level row comb filter or row comb filter, because σ ₂=0 (or σ ₂'=0), thus by select after the one-level comb filter be completely orthogonal code character, these code characters combined just consisted of completely orthogonal PN ' matrix.

Perhaps, reselect one group of multinomial f of basis ₁' (x), f ₂' (x) ..., f _n' (x), by screening (x) sequence of the f ' that obtains after the combination, ', then with matrix M ' is σ by setting threshold by consisting of the MSP matrix M behind group translating and the numerical transformation in buffer memory with this sequence ₂=0 (or σ ₂'=0) one-level row comb filter or row comb filter are picked out completely orthogonal code character, thereby consist of completely orthogonal PN ' matrix.

4, PN matrix and completely orthogonal PN ' matrix are carried out operation of direct product, the MSPE matrix PN_PN ' after being expanded.

Similar with the Hadamard orthogonal matrix, we can obtain the complete quadrature of row or be listed as completely orthogonal matrix PN ' the passing threshold screening, for example

${\mathrm{PN}}^{\′}=\left[\begin{array}{cccccc}+1& +1& +1& +1& +1& +1\\ +1& -1& -1& -1& +1& +1\end{array}\right]$

If with the class orthogonality that obtains in 2 preferably PN matrix and PN ' matrix carry out direct computing, namely

$\mathrm{PN}\_{\mathrm{PN}}^{\′}=\mathrm{PN}\⊗{\mathrm{PN}}^{\′}=\left[\mathrm{PN}\right]\⊗\left[\begin{array}{cccccc}+1& +1& +1& +1& +1& +1\\ +1& -1& -1& -1& +1& +1\end{array}\right]$

$=\left[\begin{array}{cccccc}+\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}\\ +\mathrm{PN}& -\mathrm{PN}& -\mathrm{PN}& -\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}\end{array}\right]$

The like, PN matrix and line number and the more completely orthogonal matrix PN ' of columns can be carried out operation of direct product equally, can obtain more massive MSPE matrix after the expansion like this.

All satisfy the requirement of Welch circle by the MSPE matrix of extended method formation of the present invention, so the MSPE matrix after the expansion has better class orthogonal property (stronger autocorrelation and weak cross correlation) and pseudo-random characteristics.

Adopt the constructive method of multi-dimensional similar-orthogonal pseudo-random extended matrix of the present invention, its constructive method letter is worked as, and circuit structure is easy.The matrix of structure has good orthogonal property, pseudo-random characteristics and ultra-large characteristic.Because primitive polynomial f ₁(x), f ₂(x) ..., f _n(x) through the screening combination, by group translating, the MSP machine matrix M of formation can reach 10 again ⁶Even larger, pass through again PN ' direct product mode and expand, can obtain the MSPE matrix of larger scale.Being of wide application of MSPE machine matrix after the expansion, in cdma communication system, can be with PN_PN ' the matrix column vector after the expansion as chnnel coding (walsh), the row vector is as subscriber-coded (single PN code).Application in AdHoc is distinguished the base station with extended matrix, and simultaneously the ranks vector in the matrix is applied to the chnnel coding of each base station and subscriber-coded.

Description of drawings

Fig. 1 multi-dimension quasi-orthogonal pseudo-random matrix (MSP matrix) PN production process schematic block diagram;

The expansion schematic block diagram of Fig. 2 multi-dimension quasi-orthogonal pseudo-random matrix (MSPE matrix);

The graphics of the capable vector of the multi-dimension quasi-orthogonal pseudo-random matrix of Fig. 3 (a) 223 * 32 cross correlation;

The statistic histogram of the capable vector of the multi-dimension quasi-orthogonal pseudo-random matrix of Fig. 3 (b) 223 * 32 cross correlation;

The graphics of the multi-dimension quasi-orthogonal pseudo-random matrix column vector cross correlation of Fig. 3 (c) 223 * 32;

The statistic histogram of the multi-dimension quasi-orthogonal pseudo-random matrix column vector cross correlation of Fig. 3 (d) 223 * 32;

The graphics of the capable vector of the multi-dimension quasi-orthogonal pseudo-random matrix of Fig. 4 (a) 127 * 128 cross correlation;

The statistic histogram of the capable vector of the multi-dimension quasi-orthogonal pseudo-random matrix of Fig. 4 (b) 127 * 128 cross correlation;

The graphics of the multi-dimension quasi-orthogonal pseudo-random matrix column vector cross correlation of Fig. 4 (c) 127 * 128;

The statistic histogram of the multi-dimension quasi-orthogonal pseudo-random matrix column vector cross correlation of Fig. 4 (d) 127 * 128;

The graphics of the capable vector of the multi-dimensional similar-orthogonal pseudo-random extended matrix of Fig. 5 (a) 128 * 128 cross correlation;

The statistic histogram of the capable vector of the multi-dimensional similar-orthogonal pseudo-random extended matrix of Fig. 5 (b) 128 * 128 cross correlation;

The graphics of the multi-dimensional similar-orthogonal pseudo-random extended matrix column vector cross correlation of Fig. 5 (c) 128 * 128;

The statistic histogram of the multi-dimensional similar-orthogonal pseudo-random extended matrix column vector cross correlation of Fig. 5 (d) 128 * 128;

Fig. 6 multi-dimension quasi-orthogonal pseudo-random matrix, multi-dimensional similar-orthogonal pseudo-random extended matrix and the error rate of Walsh matrix application when cdma system.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further details.

The inventive method is that primitive polynomial is screened combination, has just obtained Metzler matrix after the multinomial after the combination is changed by group translating and numerical value.

In the Metzler matrix that produces with upper type, the reasonable vector of existing class orthogonality also has the poor vector of class orthogonality.So according to the actual requirement that engineering is used, we want the method for passing threshold filtering, pick out that wherein the class orthogonality is vectorial preferably.

According to above requirement, the present invention proposes the independently one-level comb filter of setting threshold, find out cross-correlation coefficient less than the capable vector of threshold value or the set of column vector with this, and consist of preferably PN matrix of class orthogonality.

When a plurality of primitive polynomials make up, the number n of primitive polynomial is not simultaneously, the NSP matrix M that we can obtain varying in size, and the size of Metzler matrix can be along with the change of the increase of the number n of primitive polynomial, namely along with the increase of n, the line number of Metzler matrix can reduce, and columns can increase, and matrix M is close toward square formation gradually.

Take the primitive polynomial of top step number as 8 as example, as required, after screening, with f ₁(x)=101110001, f ₂(x)=111011101, f ₃(x)=110011111, f ₄(x)=100101101 these four primitive polynomials make up.Obtain after the combination:

f(x)＝101111110100001011011010011101111；

By can obtaining one 32 * 255 matrix behind the group translating, matrix is rotated conversion by converter, and to obtain a latter half be one 32 * 32 unit matrix I, with the unit matrix amputation, just obtained size and be 223 * 32 MSP matrix M.

After the above primitive polynomial combination by 48 rank, front four capable sequence vectors of the Metzler matrix that the method by group translating produces are respectively:

The first row: 111111-11-1-1-1-11-111-111-11-1-1111-11111-1

The second row: 1-1-1-1-11-1-11-1-11-1-111-111-1-1111-11-11-1-111

The third line :-1111-11111-11-1-1-111-11111-11-1-11-1-11-1-11

Fourth line: 111-11111-11-1-1-111-11111-11-1-11-1-11-1-11-1

Front four column vector sequences of consequent Metzler matrix are respectively:

The first row: 11-111-1-111-11111111111-1-11-1-1111111-1-1-1-11-11111-1-1-11111-111-1-111-11-11-1-1-111-111-1-11-11-111-111-1-1-11-111-1-111-1-1-1111-11-1111-11-1-1-1-11111-1111-11-111 1111-111-1-1-1-11111-1-1-1-111-1-11111-11-1-11-1-11-1-11-11-11-11-1-11-1-1-111111-1-1-111-1-111111-1-1111-1-1-1-1 1-11-11-11-1-11-11111-1-1-1-11-11-1-111-1

The second row: 1-111-1-111-11111111111-1-11-1-1111111-1-1-1-11-11111-1-1-11111-111-1-111-11-11-1-1-111-111-1-11-11-111-111-1-1-11-111-1-111-1-1-1111-11-1111-11-1-1-1-11111-1111-11-111 1111-111-1-1-1-11111-1-1-1-111-1-11111-11-1-11-1-11-1-11-11-11-11-1-11-1-1-111111-1-1-111-1-111111-1-1111-1-1-1-1 1-11-11-11-1-11-11111-1-1-1-11-11-1-1111-11

The third line: 1-1111111-11-1-1-1-1-1-1-1-1111-1111-1-1-1-111-1-11-1-11-1-111-111-1-11-1111111-1-1-1-11-1111-11111-1-1-1-111-111 1-11-1-11111111-111-11-1-1-11-11-1-11-1-111-1-11-11-11-1-1-11-1-1-1-11-1111-1-111-1-111-1-1111111-1-11-1-111-111-111-1-1-1-1-1-1-111-11-111-1-1-111-1111111-1-1-11111-111-1-11-1-1-1-1-1-1-111-1-11-1-111-1-11-1-1111111

Fourth line: 1-11-1-1111-1-11111111-1-1-1-11-11-1111-1-11-11-1-1-1-11-1-1111-11-11-11-1-11111-11111111-11-1-1-1-11-1-111-11-11 1-1-1-11-1-111-1111-1-111-1-1-1-11111-111-11-11-1-1-111-1-1-1111-11-11-11-111-11-1-11-1111-1-11-11-1111-1-11-1-1 1-1-1-11-11-111-1-11111-111-1-11111-1-11-11-1-1-11-1-1-1 1-11-1-11-11-111-1-1-1-1-11-1-11-11-1-111-111-111

The matrix M that is produced by above multinomial is one 223 * 32 matrix, and the cross-correlation function figure between its row or the row and their histogram are as shown in Figure 3.We as can be seen from Figure 3, no matter be row vector or column vector, their cross-correlation coefficient concentrates near 0 substantially.

Along with the increase of primitive polynomial number n, the size of the MSP matrix M that obtains behind the group translating also can change thereupon, and its row vector can reduce along with the increase of n, and column vector can increase along with the increase of n, thereby makes Metzler matrix close to a square formation.So for the primitive polynomial that belongs to 8 rank, when the number n=16 of combination, sequence after the combination multi-dimension quasi-orthogonal pseudo-random matrix M through producing behind the group translating ₁₆Size be 127 * 128, this moment matrix M ₁₆Close to a square formation.Matrix M ₁₆Row or row between cross-correlation function figure and their histogram as shown in Figure 4.We as can be seen from Figure 4, the cross-correlation coefficient of its row and column concentrates near 0 substantially, and as a whole, near the value of the cross-correlation coefficient among Fig. 40 be than much more among Fig. 3, the matrix M of this explanation 127 * 128 ₁₆The class orthogonality better than the class orthogonality of 223 * 32 Metzler matrix.

The MSP matrix M that the sequence that still obtains take the combination of the primitive polynomial on 48 rank consists of is as example, by setting the threshold value σ of one-level comb filter ₁, we filter out the 32 every trades vector that cross correlation is lower in the Metzler matrix, and this 32 every trade Vector Groups is synthesized a matrix, are referred to as the PN matrix.

Leave in the memory through the PN matrix after group translating and the one-level comb filter above, then select the primitive polynomial of other one group of different rank, to obtain the MSP matrix M after the steps such as its process group translating again ', again by setting the threshold value σ of one-level comb filter ₂=0, just can from M ' matrix, filter out completely orthogonal row vector or column vector, and these completely orthogonal row vectors or column vector are combined into a matrix, be referred to as PN ' matrix.

Perhaps the PN matrix that produces before can also be left in the memory, then the Threshold with the one-level comb filter is σ ₂=0, be σ with the MSP matrix M that produces through threshold value again ₂=0 one-level comb filter, thus completely orthogonal matrix PN ' obtained.

Take the primitive polynomial of 1 top step number as 4 as example, f (x)=11001, the M ' matrix that is produced by this primitive polynomial is through threshold value σ ₂After=0 the one-level comb filter, the completely orthogonal matrix PN ' that obtains is:

${\mathrm{PN}}^{\′}=\left[\begin{array}{cccc}+1& +1& +1& -1\\ +1& +1& -1& -1\\ +1& -1& +1& +1\\ -1& +1& +1& +1\end{array}\right]$

The PN matrix and the completely orthogonal PN ' matrix that produce are before carried out operation of direct product, be about to Metzler matrix and expand through the PN matrix after the combed filter device, the MSPE matrix after its expansion is PN_PN '.

The result of its computing:

$\mathrm{PN}\_{\mathrm{PN}}^{\′}=\mathrm{PN}\⊗{\mathrm{PN}}^{\′}=\left[\mathrm{PN}\right]\⊗\left[\begin{array}{cccc}+1& +1& +1& -1\\ +1& +1& -1& +1\\ +1& -1& +1& +1\\ -1& +1& +1& +1\end{array}\right]=\left[\begin{array}{cccc}+\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}\\ +\mathrm{PN}& +\mathrm{PN}& -\mathrm{PN}& +\mathrm{PN}\\ +\mathrm{PN}& -\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}\\ -\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}& +\mathrm{PN}\end{array}\right]$

Front four capable sequence vectors of consequent PN_PN ' matrix are respectively:

The first row: 111111-11-1-1-1-11-111-111-11-1-1111-11111-1-1-1-1-1-1-1 1-11111-11-1-11-1-11-111-1-1-11-1-1-1-11111111-11-1-1-1-11-111-111-11-1-1111-11111-1111111-11-1-1-1-11-111-111-1 1-1-1111-11111-1

The second row: 1-1-1-1-11-1-11-1-11-1-111-111-1-1111-11-111-111-11111-1 11-111-111-1-11-1-111-1-1-11-11-111-1-11-1-1-1-11-1-11-1-11-1-111-111-1-1111-11-11-1-1111-1-1-1-11-1-11-1-11-1-11 1-111-1-1111-11-11-1-111

The third line :-1111-11111-11-1-1-111-11111-11-1-11-1-11-1-111-1-1-11-1-1-1-11-1111-1-11-1-1-1-11-111-111-111-1-1111-11111-11-1-1-111-11111-11-1-11-1-11-1-11-1111-11111-11-1-1-111-1111 1-11-1-11-1-11-1-11

Fourth line: 111-11111-11-1-1-111-11111-11-1-11-1-11-1-11-1-1-1-11-1-1-1-11-1111-1-11-1-1-1-11-111-111-111-11111-11111-11-1-1-111-11111-11-1-11-1-11-1-11-1111-11111-11-1-1-111-11111-11-1-11-1-11-1-11-1

Front four column vector sequences of consequent PN_PN ' matrix are respectively:

The--OK: 11-111-1-111-11111111111-1-11-1-1111111-1-1-11-1-111-1-1 1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1111-111-1-111-111 11111111-1-11-1-1111111-111-111-1-111-11111111111-1-11-1-1111111-1

The second row: 1-111-1-111-11111111111-1-11-1-1111111-1-1-11-1-111-1-11-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1111-111-1-111-11111 111111-1-11-1-1111111-1-11-11-1-111-11111111111-1-11-1-1 111111-1-1

The third line: 1-1111111-11-1-1-1-1-1-1-1-1111-1111-1-1-1-111-1-11-1-1-1-1-1-11-111111111-1-1-11-1-1-11111-1-111-1111111-11-1-1-1-1-1-1-1-1111-1111-1-1-1-111-11-1111111-11-1-1-1-1-1-1-1-1111-1111-1-1-1-111-1

Fourth line: 1-11-1-1111-1-11111111-1-1-1-11-11-1111-1-11-1-11-111-1-1-111-1-11-1-1-1-11111-11-11-1-1-111-111-11-1-1111-1-111 11111-1-1-1-11-11-1111-1-11-11-11-1-1111-1-11111111-1-1-1-11-11-1111-1-11-1

It also is one 128 * 128 matrix that PN and completely orthogonal PN ' matrix carry out MSPE matrix PN_PN ' after the direct product expansion, and the sequence in this matrix satisfies Welch circle.For this row matrix or row between cross-correlation function figure and their histogram as shown in Figure 5.As can be seen from Figure 5, no matter be row vector or column vector, their cross-correlation coefficient concentrates near 0 substantially, and the cross correlation of Fig. 5 obviously will be good than the cross correlation among Fig. 4 many, and in the PN_PN ' matrix cross-correlation coefficient near 0 capable vector or the quantity of column vector, also how a lot than near the row quantity of vector sum column vector 0 in the Metzler matrix.Equally, at last MSPE matrix PN_PN ' just can be leached completely orthogonal row vector or column vector by second-stage comb filter again, and they are used for cdma system, respectively as chnnel coding and subscriber-coded.

Fig. 6 is to be 127 * 128 MSP matrix M with matrix size, matrix size is 128 * 128 MSPE matrix PN_PN ', matrix size is that the mutually column vector of colleague's capable vector sum same column in 128 * 128 the Walsh matrix is used separately as chnnel coding and subscriber-coded during for cdma system, the error rate figure that obtains.As can be seen from the figure, for the similar matrix of size, capable vector sum column vector among the MSPE matrix PN_PN ' that obtains by extended method is used separately as chnnel coding and when subscriber-coded, the error rate of whole system with the expansion before with the MSP matrix M time the error rate compared good improvement, and along with the increase of signal to noise ratio, the effect that the error rate is improved is better, and when signal to noise ratio is 27 when above, the error rate can reduce more than the 10dB.From figure, also can find out, the error rate that vector in MSPE matrix PN_PN ' and the Walsh matrix is applied in the cdma system is basic identical, that is to say, MSPE matrix PN_PN ' is the same with effect in the Walsh matrix application cdma system, so PN_PN ' matrix can replace the Walsh matrix as in the systems such as chnnel coding and the subscriber-coded CDMA of being applied to and AD Hoc fully.

In actual applications, for the quantity that extends one's service as much as possible, just need more available good capable vector or the column vector of orthogonality.Therefore, the PN_PN ' after the one extension can be carried out the secondary expansion, three expansions ..., to obtain more massive MSPE matrix.

In engineering was used, in order to reduce the factor such as intersymbol interference to the impact of communication system, normally used encoder matrix all was completely orthogonal matrix.Therefore, before expanding, can be by the screening to the MSP matrix M, filter out completely orthogonal matrix PN, and no longer be the class orthogonal matrix, so after carrying out direct product expansion by two completely orthogonal matrix PN and PN ', the extended matrix PN_PN ' that obtains also is a completely orthogonal matrix, so just the institute's directed quantity in the matrix all can be used for coding, and not need again to screen by second-stage comb filter.Equally, we also can carry out orthogonal matrix PN_PN ' the secondary expansion, three expansions ... thereby, obtain more massive orthogonal matrix.

For PN_PN ' matrix, because the size of its PN matrix and PN ' matrix is unfixed, so the PN_PN ' matrix size that obtains after expansion also is unfixed.If the size of multi-dimension quasi-orthogonal pseudo-random matrix PN is p * q, the size of completely orthogonal PN ' matrix is m * n, and so through after the 1 subdirect product computing, the size of the MSPE matrix PN_PN ' that obtains is pm * qn, advanced after the 2 subdirect product computings, the size of the MSPE matrix that obtains is pm ²* qn ², the rest may be inferred, supposes that the size of the MSPE matrix PN_PN ' that then obtains is pm through the computing of k subdirect product ^k* qn ^kBecause p, q, m, n, k can get arbitrary value, so the size of matrix PN_PN ' is pm ^k* qn ^kAlso be arbitrary value, namely the number of its row vector sum column vector can be arbitrary value.

And for traditional Walsh matrix, because its Hadamard matrix of expanding usefulness is one 2 * 2 orthogonal matrix, so the matrix size after the expansion is 2 ⁿ* 2 ⁿ(n for expansion number of times), i.e. the number of its row vector or column vector 2 index power always, the number that can not have 6,10 etc. non-2 index power occurs.And the MSPE matrix PN_H and the PN_PN ' that obtain by two kinds of methods that this patent proposes, the size of their matrixes can arbitrary value, and unlike the walsh matrix, is subject to the restriction of 2 index power in matrix size.

By above analysis as can be known, MSPE matrix PN_PN ' and Walsh matrix have the essentially identical error rate in actual applications, and the effect that namely is applied to communication system is basic identical.Simultaneously the size of MSPE matrix PN_PN ' can be got arbitrary value, and is subject to the restriction of 2 index power unlike the Walsh matrix in matrix size.And because the Metzler matrix maximum of a plurality of primitive polynomials formation MSP of structure extended matrix PN_PN ' can reach 553 * 470, even after the passing threshold filtering, still can obtain a larger orthogonal matrix PN, so utilize this larger PN matrix, again by expansion, can obtain easily large-scale MSPE matrix, this has just expanded user's quantity in the communication system greatly.So MSPE matrix PN_PN ' will obtain using more widely than Walsh matrix.

Claims (2)

1. the constructive method of a multi-dimensional similar-orthogonal pseudo-random extended matrix, its step is as follows:

Step 1, selection primitive polynomial f ₁(x), f ₂(x) ..., f _n(x) screen combination, obtain f (x) sequence; F (x) sequence is consisted of quadrature pseudo-random matrix M by group translating in buffer memory;

F (x) after the screening combination is carried out group translating, and the process of group translating is as follows:

1), at first with the sequence a of initial condition _na _N-1A ₀Move to right one;

2), the highest order of the sequence after moving to right is judged, if highest order is 1, then this sequence and initial order are carried out exporting a ' behind the XOR _N-1A ' _N-2A ₀', if highest order is-1, then directly export a _N-1a _N-2 ... a ₀, 0;

3), continue to forward to step 1) do cycling, until duplicate sequence;

4), with all series arrangement matrix N, then output;

5), matrix N is inverted and rotation;

The N square that obtains behind the process group translating is a matrix that is combined by P matrix and I unit matrix, namely $N=\left[\begin{array}{c}P\\ I\end{array}\right],$

Wherein the P matrix is the binary matrix that only contains " 0 ", " 1 ", and here, we carry out a numerical value conversion to the P matrix, obtain matrix M, namely

$m_i=\left\{\begin{array}{cc}1& (P_i=1)\\ -1& (P_i=0)\end{array}\right.$

The Metzler matrix of this moment is a multi-dimension quasi-orthogonal pseudo-random matrix;

Step 2, setting threshold σ ₁Then will have the multi-dimension quasi-orthogonal pseudo-random matrix M of good correlation by one-level row comb filter or row comb filter, pick out the outstanding row vector of good relationship or column vector as code character allowable, its complement vector is then as the forbidding code character, and code character allowable combined, consist of a PN matrix with class orthogonality; That is:

Set a threshold value σ ₁(0＜σ ₁＜1) or σ ₁' (0＜σ ₁'＜1), by one-level row comb filter or row comb filter, will be less than threshold value σ ₁Or σ ₁' capable vector or column vector pick out, as code character allowable, combine and consist of the PN matrix with class orthogonality, remaining vector is then rejected as the forbidding code character;

Step 3, setting threshold σ ₂, then with multi-dimension quasi-orthogonal pseudo-random matrix M by one-level row comb filter or row comb filter, pick out completely orthogonal code character, consist of PN ' matrix; That is:

Set the threshold value σ of a capable comb filter ₂=0 and the threshold value σ of row comb filter ₂'=0, with quadrature pseudo-random matrix M by one-level row comb filter or row comb filter, because σ ₂=0 or σ ₂'=0, thus by select after the one-level comb filter be completely orthogonal code character, these code characters combined just consisted of completely orthogonal PN ' matrix;

Perhaps, reselect one group of multinomial f of basis ₁' (x), f ₂' (x) ..., f _n' (x), by screening (x) sequence of the f ' that obtains after the combination, with this sequence in buffer memory by consisting of multi-dimension quasi-orthogonal pseudo-random matrix M ' behind group translating and the numerical transformation, then with matrix M ' be σ by setting threshold ₂=0 or σ ₂'=0 one-level row comb filter or row comb filter are picked out completely orthogonal code character, thereby consist of completely orthogonal PN ' matrix;

Step 4, PN matrix and completely orthogonal PN ' matrix are carried out operation of direct product, the multi-dimensional similar-orthogonal pseudo-random extended matrix PN_PN ' after being expanded.

2. the constructive method of described a kind of multi-dimensional similar-orthogonal pseudo-random extended matrix according to claim 1 is characterized in that: described selection primitive polynomial f ₁(x), f ₂(x) ..., f _n(x) screening combination is, selects the primitive polynomial of any number, makes up in any order, namely $f\left(x\right)=F[f_1^{n_1}\left(x\right),f_2^{n_2}\left(x\right),......,f_n^{n_j}\left(x\right)],$ Wherein

Images