CN1126307C - Multiphase orthogonal spectrum spreading code design and its spread-eliminating method - Google Patents

Abstract

The present invention discloses a multiphase spread spectrum code design method of an orthogonal synchronous CDMA communication system and a de-spread technology. A spread spectrum sequence code block based on a p element m sequence can conveniently realize the de-spread technology by two shift registers and make use of a two-stage correlator to implement the fast variation so that the system realizing complexity can be greatly reduced.

Description

A kind of multiphase orthogonal spreading code generates and despreading method

The present invention relates to a kind of direct sequence spread spectrum wireless communication technology, the orthogonal spreading sequence sign indicating number that particularly works under the method for synchronization generates and correlation technique.

Along with the arriving of information age, people are more and more stronger to the demand of communication system frequency spectrum resource.And frequency spectrum resource is very limited, and in order to improve the availability of frequency spectrum, wireless access has adopted as frequency division multiple access (FDMA), time division multiple access multiple access technologies such as (TDMA), limits but power system capacity still is subjected to the time-bandwidth product of system.

Code division multiple access (CDMA) technology then has significant advantage, it does not neither distinguish different user by time slot by frequency yet, but distinguish different user by frequency expansion sequence, its power system capacity is decided by the signal to noise ratio that allows, characteristics with big capacity and soft capacity, it also possesses characteristics such as anti-multipath, anti-interference, good confidentiality in addition.1999, in 10 kinds of candidate schemes of 3-G (Generation Three mobile communication system) that the ITU of International Telecommunications Union announces, cdma system occupy absolute leading position.

Reducing system noise, improve signal to noise ratio, is cdma communication system function admirable whether key link.The cellular wireless mobile communication system has local noise (LN), intersymbol interference (ISI), multiple access interference (MAI) and the four kinds of interference such as (ACI) of adjacent area interference usually.For cdma system, except local noise can not be eliminated, other three kinds of interference all can reduce by the spread spectrum code character that use has a good correlation or eliminate, thereby improved the capacity or the performance of system.

In the cdma system of reality, adopt two-stage spread spectrum to improve the flexibility of system usually.The first order is channelizing (Channelization), its orthogonality by user data and channelizing orthogonal sequence are multiplied each other and realize spread spectrum and guarantee all user's waveforms in the same cellular cell.The second level is for upsetting (Scrambling), and it distinguishes different cellular cells by multiply by a long pseudo random sequence.Usually each cellular cell all adopts same orthogonal sequence collection as the channelizing frequency expansion sequence, such as in IS-95 and cdma2000, having used the Walsh sequence, and Orthogonal Variable Spreading Factor OVSF (Orthogonal Variable Spreading Factor, OVSF) sequence have been adopted in the WCDMA system.

Many in recent years scholars are devoted to design and realize simple, despreading orthogonal intersection easily, more existing at present relevant patents.As United States Patent (USP) 4,460,992, directly expanding in the orthogonal CDMA system synchronously, displacement with same binary pseudo random sequence different time is distinguished the user as address code, and increases an extra bit in these address code fronts, makes in the sign indicating number 0,1 number reaches balance, makes again simultaneously to have orthogonal property between address code; Chinese patent application number 00103282.8; designed near a kind of sequence that zero time delay, has the zero correlation block of certain-length; add the supplementary protection chip at modulated spread spectrum signal; in the quasi-synchronous CDMA system, realized noiseless transmission; this sequence can be seen the generalized orthogonal sequence as; under the relatively poor situation of channel condition, preferable performance is arranged, but the number of sign indicating number is less, or the like.

The multiphase orthogonal frequency expansion sequence as 4 phases, 8 facies-suites or the like, has obtained extensive use at cdma system.P phase frequency expansion sequence correspondence p system phase keying (PSK) modulation, and generally speaking, multiphase sequence is littler to the restriction of component value, therefore as long as design is proper, just can obtain the performance multiphase sequence better than binary sequence.For example QPSK (p=4) spread spectrum mode is compared with BPSK (p=2), keeping under the relatively low condition of acceptance, can reduce interference.

The objective of the invention is to propose a kind of novel, realize simple multiphase orthogonal sign indicating number method for designing and despreading method fast, make code division multiple address communication system eliminate common-channel interference under certain condition.

This multiphase orthogonal generation method of spreading code is characterized in that: sequence can be expressed as a p in the described spread spectrum sequence code group ^kFacies-suite and the step-by-step of a p facies-suite are multiplied each other, and realize by two shift registers.This multinomial orthogonal spreading sequence code character is at first constructed the p m of unit sequence a based on the p m of unit sequence structure, utilizes the basic primitive polynomial of the proper polynomial correspondence of m sequence a to generate p again ^kThe sequence b of unit, b can construct a multiphase sequence collection E with sequence b respectively again after each cyclic shift addition of m sequence a, arbitrary same position of all multiphase sequences is added arbitrary identical element in set E, just obtains the heterogeneous spreading code of quadrature after shining upon.

Multiphase orthogonal spreading code proposed by the invention is based on maximum-length shift register sequence (the p m of unit sequence).The p m of unit sequence can be generated by shift register, sees accompanying drawing 1.

Fig. 1-shown in shift register can pass through polynomial f (x)=c ₀+ c ₁x ¹+ c ₂x ²+ Λ+c _N-1x ^N-1+ x ⁿCoefficient c _N-1..., c ₁, c ₀Characterize, this multinomial is called as the proper polynomial of shift register.Shift register can produce sequence a thus, establishes the shift register initial condition and is (a ₀, a ₁..., a _N-1), a wherein ₀ Expression 0 is state constantly, a ₁Represent i state constantly, each state correspondence [0,1 ... p-1] in a value, then n output state constantly can be expressed as: $a_n=-\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}{c}_i{a}_i\mathrm{mod}p$ [formula 1] wherein modp represents mould p computing.

According to algebraic process, it is p that n rank shift register will generate maximum length ⁿ-1 sequence, its proper polynomial f (x) is and must is galois field GF (p ⁿ) on primitive polynomial.

Now the span of shift register state by [0,1 ... p-1] expand to [and 0,1 ... p ^k-1], k is the integer greater than 1.As still adopting the above-mentioned p proper polynomial f (x) of unit, then the shift-register sequence length of Sheng Chenging will become d (p ⁿ-1), d 〉=1 here.The sequence length that makes generation is p ⁿ-1, then need change proper polynomial, establish new proper polynomial F (x)=c ₀+ c ₁' x ¹+ c ₂' x ²+ Λ+c _N-1' x ^N-1+ x " c wherein ₁' ∈ [0,1 ... p ^k-1] according to algebraic process, F (x) is Jia Luohua ring GR (p ^k, n) the basic primitive polynomial on, it has character:

F (x) mod p=f (x) [formula 2]

F (x) is called as the corresponding basic primitive polynomial of f (x).By means of new proper polynomial F (x), just can determine new shift-register sequence b fully.If the shift register initial condition is (b ₀, b ₁... b _N-1), b wherein ₀ Expression 0 is state constantly, b _iRepresent i state constantly, then n state constantly can be expressed as: $b_n=-\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}{C^{\′}}_i{b}_i\mathrm{mod}{p}^k$ [formula 3]

The defined nucleotide sequence collection

E={b, b+p ^K-1T ⁱA, i=0,1, Λ, p ⁿ-2} [formula 4] is T wherein ⁱCyclic shift i position, an expression sequence left side.

Again all sequences among the set E add an identical element 0 or arbitrary identical first α ∈ [0,1 ..., p ^k-1], must newly gather U.The definition mapping: $i\&RightArrow;\mathrm{Exp}[\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;i}/p^k]={\mathrm{\&omega;}}_{p^k}^{i}i=\mathrm{0,1},\mathrm{\&Lambda;},p^k-1$ [formula 5] wherein ${\mathrm{\&omega;}}_{p^k}=\mathrm{Exp}(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}/p^k)$ Be p ^kUnit's compound radical.

E and U be will gather and upward its correlation function of calculating of complex unit circle, any two sequence e among the set E, the zero offset cross correlation value R of e ' will be mapped to according to [formula 5] _{E, e '}(0)=-1, gathers any two sequence u among the U so, the zero offset cross correlation value R of u ' _{U, u '}(0)=0.If the reflection of U is set V, obviously, V is the orthogonal sequence collection, is designated as [p, k, n], and wherein sequence length is p ⁿ, the sequence number also is p ⁿ

With the sequence among the V by rows, the element of sequence is shown in tabulation, constitutes matrix V $V=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">V</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="V"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">V</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}& \mathrm{\&Lambda;}& {\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">V</figure-callout>}}_{1,\mathrm{<figure-callout\; id="2"\; label="N\; V"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">N</figure-callout>}}& \\ V_{}{}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="V"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">V</figure-callout>\; </figure-callout>}}_{\mathrm{2,2}}& \mathrm{\&Lambda;}& {\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">V</figure-callout>}}_{2,N}\\ M& M& M& M\\ V_{N,1}& V_{N,2}& \mathrm{\&Lambda;}& V_{N,N}\end{array}\right]---\left[6\right]$ N=p wherein ⁿ

Obviously, V is p ^kPhase Hadamard battle array, it satisfies the definition of Hadamard battle array

VV ^{* T}=NI _N[formula 7] be I wherein _NIt is N rank unit square formation.

At receiving terminal, the reply sampling number is N=p ⁿDiscrete signal Y=(Y ₁, Y ₂..., Y _N) carry out despreading, promptly obtain its broad sense Walsh and change, establish the signal after the despreading $\hat{X}=(\hat{{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">X</figure-callout>}}_1},\hat{{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">X</figure-callout>}}_2},\mathrm{\&Lambda;},\widehat{X_N}),$ It is to sending signal X=(X ₁, X ₂..., X _N) valuation, for $\widehat{X^T}=V*Y^T,Y=X+N$ [formula 8] wherein N is additive noise.

From computation complexity, generally need carry out N ²Inferior arithmetic (being accurate to the order of magnitude).The despreading method that the present invention is designed can make operation times reduce to Nlog _pN, when N was very big, this fast algorithm was very effective.

Therefore multiphase orthogonal spreading code despreading method of the present invention is characterised in that: adopt the despreading of two-stage correlator., its feature also is: during described spread spectrum sequence code group despreading, by a displacement battle array P _L, P _SAfter matrix M is converted into matrix H, utilize the recurrence relation of matrix H again, implement Fast transforms.First order correlator is directly used p ^kFacies-suite is carried out related operation, and second level correlator then need carry out carrying out related operation again after matrix M=LS decomposes, and matrix L and S generate by shift register.

Arbitrary sequence among the set E of the present invention all can be expressed as follows after [formula 5] mapping $E_n^{\left(1\right)}\&RightArrow;{{\mathrm{\&omega;}}_{p^k}}^{b_n+p^{k-1}{T}^1{a}_n}={{\mathrm{\&omega;}}_{p^k}}^{b_n}{{\mathrm{\&omega;}}_p}^{T^1{a}_n}$ [formula 9] be each sequence all by two step-by-steps formation that multiplies each other on [formula 9] the right, first is p ^kFacies-suite, it does not change with i, and is all the same to all sequences; Second changes with sequence variation, and actual is the different cyclic shifts of the same p m of unit sequence.When despreading, multiply by first p at first to received signal ^kFacies-suite is promptly directly used p ^kFacies-suite is carried out first order related operation; Because second correspondence the different m sequence of initial phase, so computation complexity mainly concentrates on second level correlator, and despreading method of the present invention is implemented Fast transforms to this just.

If the p m of unit sequence is (a ₁, a ₂... a _N-1), definition

[formula 10] can obtain p phase Hadamard battle array to the mapping that M implements [formula 5] definition.What be noted that here that spread spectrum in the practical application and despreading use all is matrix after the mapping, but matrix M is still adopted in narration for convenience below.

According to matrix theory, there is following matrix permutation:

M＝LS＝P _LBB ^TP _S＝P _LHP _S

L=P _LB S=B ^TP _S[formula 11] wherein, S constitutes by the preceding n of M is capable, is n*N rank battle arrays; B is N*n rank battle arrays, first row be 0,0 ... 0}, 0, the i of corresponding p system is capable to be the i-1 of corresponding p system, 1≤i≤p ⁿ, N is capable to be 1,1 ... 1}; L is N*n rank battle arrays, P _L, P _SBe N*N rank displacement battle array, their generation sees fast algorithm for details.During the spread spectrum sequence code group despreading, behind displacement battle array sorting data, utilize the recurrence relation of matrix H, implement Fast transforms.To matrix H, can use following recurrence formula: ${\mathrm{<figure-callout\; id="1"\; label="H\; p"\; filenames="C00124898.700121.png"\; state="\{\{state\}\}">H</figure-callout>}}_{p^{}}=\left[\begin{array}{c}0\\ 1\\ M\\ p-1\end{array}\right]\left[\begin{array}{cccc}0& 1& \mathrm{\&Lambda;}& p-1\end{array}\right]=\begin{array}{c}\left[\begin{array}{cccc}0& 0& \mathrm{\&Lambda;}& 0\\ 0& 1& \mathrm{\&Lambda;}& p-1\\ M& M& M& M\\ 0& p-1& \mathrm{\&Lambda;}& 1\end{array}\right]\end{array}$

$=H_{p^1}^{\left(1\right)}*H_{p^1}^{\left(2\right)}+H_{p^1}^{\left(3\right)}$ $H_{p^m}=\left[\begin{array}{cccc}{H}_{p^{m-1}}& H_{p^{m-1}}& \mathrm{\&Lambda;}& H_{p^{m-1}}\\ H_{p^{m-1}}& 1_{p^{m-1}}+H_{p^{m-1}}& \mathrm{\&Lambda;}& (p-1)1_{p^{m-1}}+H_{p^{m-1}}\\ M& M& M& M\\ H_{p^{m-1}}& (p-1)1_{p^{m-1}}+H_{p^{m-1}}& \mathrm{\&Lambda;}& 1_{p^{m-1}}+H_{p^{m-1}}\end{array}\right]$ $=H_{p^{m-1}}^{\left(1\right)}*H_{p^{m-1}}^{\left(2\right)}+H_{p^{m-1}}^{\left(3\right)}-----m=1,\mathrm{\&Lambda;},n$ [formula 12] here,

Be that all elements is 1 p entirely ^mThe rank square formation.

Utilize above-mentioned recurrence relation, just can obtain quick despreading algorithm, see Fig. 7 for details.

Beneficial effect of the present invention

(1) multiphase orthogonal sign indicating number of the present invention is realized simple;

(2) multiphase orthogonal sign indicating number of the present invention despreading fast;

(3) the present invention can make CDMA communication system eliminate common-channel interference under certain condition.

Description of drawings

Fig. 1 is the shift register implementation method of the p m of unit sequence.

Fig. 2 is the shift register implementation method of multiphase orthogonal sequence of the present invention.

Fig. 3 is a multiphase orthogonal spread spectrum sequence code group example of the present invention [2,3,4].

Fig. 4 is periodic cross-correlation functional arrangement of the present invention (is example with sequence 2 with sequence among Fig. 2 1).

Fig. 5 is the shift register implementation method of matrix L in the Fast transforms of the present invention.

Fig. 6 is the shift register implementation method of matrix S in the Fast transforms of the present invention.

Fig. 7 is the algorithm flow chart of Fast transforms of the present invention.

Below in conjunction with description of drawings embodiment.

Referring to Fig. 2, it provides the short-cut method of realizing the multiphase orthogonal sequence with shift register:

1. according to primitive polynomial f (x), by linear shift register, generate the p m-of a unit sequence a, length is p ⁿ-1.

2. according to primitive polynomial F (x),, generate a p by linear shift register ^kMetasequence b, length also is p ⁿ-1.

3. sequence a, b step-by-step addition obtain new sequence s.

4. sequence a ring shift left is one, and repeating step 4 is up to p ⁿ-2 times.

5. the p that newly obtains ⁿ-1 sequence S constitutes arrangement set E with sequence b.

From [0,1 ..., p ^k-1] appoints in and get a number, add the head of all multiphase sequences among the set E or arbitrary same position of all sequences to, this p ⁿIndividual sequence promptly constitutes p after mapping ^kPhase orthogonal sequence collection [p, k, n].

Referring to Fig. 3, given p=2, k=3, n=4, we can construct 8 phase orthogonal sequence collection [2,3,4], select primitive polynomial f (x)=x ⁴+ x ³+ 1, the basic primitive polynomial that f (x) is corresponding is F (x)=x ⁴+ 3x ³+ 6x ²+ 4x+1 generates the orthogonal sequence collection, it be one with 16 orthogonal spreading sequence code characters, can be for 16 users' uses.Each sequence is made up of 16 units.

Referring to Fig. 4, be the periodic cross-correlation functional arrangement of sequence 1 and sequence 2 among Fig. 1.Time delay is 0 o'clock, and its periodic cross-correlation functional value is zero.The periodic cross-correlation function of other sequences is 0 o'clock also to be zero in time delay, has verified notional result.

Referring to Fig. 5, it is the L battle array shift register implementation method of decomposing for the LS that reduces matrix M in the Fast transforms that amount of calculation takes.Because the capable vector element of i with L is the multinomial that coefficient is formed $g\left(x\right)=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{L}_{\mathrm{ij}}{x}^{j-1},$ The surplus x of delivery f (x) ^I-1So by means of shift register, we can produce matrix L easily.

Referring to Fig. 6, it is the S battle array shift register implementation method of decomposing for the LS that reduces matrix M in the Fast transforms that amount of calculation takes.S is the capable n*N rank battle array that constitutes of preceding n by M in fact.

Matrix L and S respectively with B and B ^TRelatively, be easy to obtain displacement battle array P _L, P _S, the quick variation of matrix H in addition.We just can implement the despreading of second layer correlator, referring to Fig. 7.Here we explain (6) crucial among Fig. 7, (7) two steps, when m=i, Following form is arranged $H_{p^{i-1}}^{\left(3\right)}=\left[\begin{array}{cccc}A& & & \\ & A& & \\ & & O& \\ & & & A\end{array}\right]$ $A=\left[\begin{array}{cccc}0& 0& \mathrm{\&Lambda;}& 0\\ 0& 1_{p^{i-1}}& \mathrm{\&Lambda;}& (p-1)1_{p^{i-1}}\\ M& M& M& M\\ 0& (p-1)1_{p^{i-1}}& \mathrm{\&Lambda;}& 1_{p^{i-1}}\end{array}\right]$ $H_{p^{i-1}}^{\left(2\right)}\left[\begin{array}{cccc}B& & & \\ & B& & \\ & & O& \\ & & & B\end{array}\right]$ $B=\left[\begin{array}{cccc}{I}_{p^{i-1}}& I_{p^{i-1}}& \mathrm{\&Lambda;}& I_{p^{i-1}}\\ I_{p^{i-1}}& I_{p^{i-1}}& \mathrm{\&Lambda;}& I_{p^{i-1}}\\ M& M& M& M\\ I_{p^{i-1}}& I_{p^{i-1}}& \mathrm{\&Lambda;}& I_{p^{i-1}}\end{array}\right]$ [formula 13] wherein A, B is p ⁱThe rank square formation. Remove outside complete zero row, have only (p-l) p ^N-iIndividual different row, the non-vanishing row of element p just in these row ^I-1It is individual, When multiply by row, operand is (p-1) p ^N-1≤ p ⁿ=N.The amount of calculation of two column vector additions is taken into account, operand is less than 2N again. Has only p ^N-iIndividual different row, every row has only p ⁱIndividual non-vanishing element equals N with row when multiplying each other, non-repetitive operation number of times.

Like this, get when deciding m, operation times is less than 3N, and m changes to 1 from n, and total operation times from the order of magnitude, also is Nlog less than 3N*n _pN.

Referring to Fig. 7, it provides quick despreading method, and step is:

1. according to Fig. 5,6 shift register implementation method, matrix M is decomposed into the product of two matrix L, S.

2. with matrix S and B ^TRelatively, obtain permutation matrix P _s

3. the sampling V of received signal and permutation matrix P _sMultiply each other, obtain signal Y ₁ ^T

4. the initial value that makes output signal is X ₁=0, integer m assignment is m=n.

5. according to formula 12, with matrix H _p ^mBe decomposed into $H_{p^m}={H_{p^{m-1}}}^{\left(1\right)}{H_{p^{m-1}}}^{\left(2\right)}+{H_{p^{m-1}}}^{\left(3\right)}.$

6. output signal X ₁ ^TAssignment is ${X_1}^T={X_1}^T{+H_{p^{m-1}}}^{\left(3\right)}{Y_1}^T.$

7. input signal Y ₁ ^TAssignment is ${Y_1}^T={H_{p^{m-1}}}^{\left(2\right)}{Y_1}^T.$

8. make m=m-1, repeating step 5-7 is up to m=1.

9. output signal ${Y_1}^T={H_{p^{m-1}}}^{\left(2\right)}{Y_1}^T.$

10. matrix L and B are compared, obtain permutation matrix P _L

11. permutation matrix P _LWith output signal X ₁ ^TProduct be despread signal.

Claims (2)

1. multiphase orthogonal generation method of spreading code, it is characterized in that: sequence can be expressed as a P in the described spread spectrum sequence code group ^kFacies-suite and the step-by-step of a p facies-suite are multiplied each other, and realize that by two shift registers it is as follows specifically to generate step:

(1) according to primitive polynomial f (x), by linear shift register, generate the p m-of a unit sequence a, length is p ⁿ-1; (2), generate a P by linear shift register according to primitive polynomial F (x) ^kMetasequence b, length also is p ⁿ-1; (3) sequence a, b step-by-step addition obtain new sequence s; (4) sequence a ring shift left is one, and repeating step (4) is up to p ⁿ-2 times; (5) p that newly obtains ⁿ-1 sequence s constitutes arrangement set E with sequence b; (6) from [0,1 ... p ^k-1] appoints in and get a number, add the head of all multiphase sequences among the set E or arbitrary same position of all sequences to, this p ⁿIndividual sequence promptly constitutes p after mapping ^kPhase orthogonal sequence collection [p, k, n].

2. multiphase orthogonal spreading code despreading method is characterized in that: described spread spectrum sequence code group despreading realizes that by the two-stage correlator first order correlator is directly used p ^kFacies-suite is carried out related operation, and second level correlator then need carry out carrying out related operation again after matrix M=LS decomposes, and matrix L and S generate by shift register, and concrete despreading step is as follows:

(1), matrix M is decomposed into the product of two matrix L, S according to the shift register implementation method; (2) with matrix S and B ^TRelatively, obtain permutation matrix P _s(3) the sampling V of received signal and permutation matrix P _SMultiply each other, obtain signal Y ₁ ^T(4) making the initial value of output signal is X ₁=0, integer m assignment is m=n; (5) with matrix

Be decomposed into $H_{p^m}={H_{p^{m-1}}}^{\left(1\right)}{H_{p^{m-1}}}^{\left(2\right)}{H_{p^{m-1}}}^{\left(3\right)};$ (6) output signal X ₁ ^TAssignment is ${X_1}^T={X_1}^T+{H_{p^{m-1}}}^{\left(3\right)}{Y_1}^T;$ (7) input signal Y ₁ ^TAssignment is ${Y_1}^T={H_{p^{m-1}}}^{\left(2\right)}{Y_1}^T;$ (8) make m=m-1, repeating step 5-7 is up to m=1; (9) output signal ${Y_1}^T={H_{p^{m-1}}}^{\left(2\right)}{Y_1}^T;$ (10) matrix L and B are compared, obtain permutation matrix P _L(11) permutation matrix P _LWith output signal X ₁ ^TProduct be despread signal.

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