CN101959289A - Method for generating periodic polyphase complementary sequence sets - Google Patents

Abstract

The invention discloses a method for generating periodic polyphase complementary sequence sets, which comprises the following steps of: continuously sampling perfect sequences at an equal interval to obtain a group of subsequences; and combining the subsequences in the group to obtain the periodic polyphase complementary sequence sets, wherein the summation of periodic autocorrelation functions of all the subsequences has impulse characteristics; the number of the obtained complementary sets is the same as that of the adopted perfect sequences; and the lengths and number of the subsequences can be regulated in real time and selected flexibly according to the needs of actual factors. The method can be used for realizing the application of multi-access interference-free transmission of communication systems, channel estimation, the synchronization of the communication systems, reduction in a peak-to-average power ratio (PAPR), the design of other signals (such as quasi-barker codes, low/zero-correlation zone sequences and the like), and the like.

Description

The generation method of heterogeneous complementary sequence set of cycle

Technical field

The present invention relates to a kind of communication sequence, the no multiple access that particularly can realize communication system disturb transmission, channel estimating, communication system synchronously, the reduction of peak-to-average power ratio (PAPR) and the generation method that designs the cycle complementary sequence set with impulse cycle autocorrelation performance of other signal.

Background technology

In many practical communication engineering system designs, must consider multi-access interference suppression, channel estimating, synchronous, peak-to-average power ratio factors such as (PAPR).In addition, also need to design signal with special characteristics for improving communication system performance.

(1) multi-access interference suppression

Exactly because adopted multiple access technique, communication system is just held more user, but has also brought the multiple access interference thus, has seriously reduced the performance of communication system, the capacity and the transmission rate of system.Especially in the 4th generation (4G) mobile communication, the target that realizes multimedia communication needs than the transmission rate of high tens of times of 2G and 3G, the higher power system capacity and the availability of frequency spectrum, and multiple access disturbs in must restriction certain scope.If can eliminate fully, communication system can be moved under near the theoretical limit state so.Suppressing one of dried implementation method of multiple access fully is to use the orthogonal complement sequence to be aided with " offset stacked " modulation technique (H.H.Chen, et al.Design of next-generation CDMA usingorthogonal complementary codes and offset stacked spreading, IEEE WirelessCommunicatiohs, 2007, pp.61-69).

(2) channel estimating

Channel estimating is exactly the impulse response that will estimate the signal of communication transmission medium, understanding the propagation characteristic of signal in transmission medium, for receiving end provides call parameter to the optimum reception of signal of communication.The method of carrying out channel estimating is a lot, wherein, can use complementary series to realize the accurate estimation (P. of channel estimating (Chinese patent CN1345124A) and ISI channel

, et al.Complementary sequences for ISI channel estimation, IEEETrans.On Inf.Theory, Vol.47, No.3,2001, pp.1145-1152).

(3) peak-to-average power ratio

OFDM (OFDM) has the high characteristics of the availability of frequency spectrum, has brought hope for the not enough problem of frequency spectrum resource of properly settling global growing tension, and in addition, OFDM also has the ability of very strong inhibition multipath fading.These advantages make OFDM become one of transmission technology that next generation mobile communication is hopeful to adopt most.But,, therefore, higher peak-to-average power ratio (PAPR) is arranged than carrier wave communication system because the transmission signals of OFDM has adopted the linear combination of a plurality of subcarrier transmission symbols.If high PAPR is not effectively suppressed, can cause transmitter amplifier to produce severe nonlinear so and damage.The PAPR that studies show that the ofdm communication system of using complementary series is 2 (J.A.Davis at the most, et al.Peak-to-Mean Power Control in OFDM, Golay complementary sequences, andReed-Muller Codes, IEEE Trans.on Inf.Theory, Vol.45, No.7,1999, pp.2397-2417), solved the high problem of ofdm communication system PAPR well.

(4) synchronous

In communication system, has considerable status synchronously.Can communication system effectively, work reliably, depends on to a great extent to have or not good synchro system.The synchronous method of communication system is a lot, wherein, studies show that and in the UWBMB-OFDM standard, use complementary series realizing all good (D.Lowe of system synchronization performance and precision of channel estimation, etal.Complementary channel estimation and synchronization for OFDM, in Proc.ofthe 2 ^NdIht.Conf.on Wireless Broadband and Ultra Wideband Commun., 2007).

(5) other signal

In actual applications, also need to produce signal with various special characteristics, for example, the sequence with impulse autocorrelation performance is desirable communication system synchronizing signal, and the AS-CDMA that no multiple access disturbs, LAS-CDMA communication system adopt the signal with zero correlation block.In the generation of these known signals, use the 2D signal (Chinese patent CN1303178A) that complementary series can design quasi-barker (Chinese patent CN101001087A) and have low/zero correlation block.

Be provided with the multiphase sequence that length is M

${\underset{\‾}{s}}^{\left(i\right)}=(s_0^{\left(i\right)},s_1^{\left(i\right)},s_2^{\left(i\right)},\·\·\·,s_{M-1}^{\left(i\right)})---\left(1\right)$

Wherein, code element

Sequence s ⁽ⁱ⁾Periodic auto-correlation function be defined as

$R_{s^{\left(i\right)},s^{\left(i\right)}}\left(u\right)=\underset{k=0}{\overset{M-1}{\mathrm{\Σ}}}{s}_k^{\left(i\right)}{\left(s_{k+u}^{\left(i\right)}\right)}^{*}\left(\right|u|\≤M-1)---\left(2\right)$

Wherein, symbol (x) ^*Expression is asked complex conjugate to x, and the subscript of code element is pressed mould M computing in the formula (2).

If sequence cConstitute by N subsequence, promptly

c＝( s ⁽⁰⁾， s ⁽¹⁾， s ⁽²⁾，…， s ^(N-1)) (3)

Wherein, sequence cIn each subsequence s ⁽ⁱ⁾(0≤i≤N-1) by formula (1) expression.

As infructescence cIn all subsequence periodic auto-correlation functions and satisfy

$R_{c,c}\left(\mathrm{\τ}\right)=\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}{R}_{s^{\left(i\right)},s^{\left(i\right)}}\mathrm{\τ}=\left\{\begin{array}{cc}\mathrm{NM}& \mathrm{\τ}=0\\ 0& \mathrm{\τ}\≠0\end{array}\right.,\left(\right|\mathrm{\τ}|\≤M-1)---\left(4\right)$

So, claim sequence cBe heterogeneous complementary sequence set of cycle.

Complementary sequence set is made up of a plurality of subsequences, the auto-correlation function of all subsequences and have an impulse characteristic.In actual applications, the subsequence quantity of complementary sequence set and the length of subsequence need and can change on request, and for example, variable rate transmission communication just need reach this requirement.Complementary sequence set be divided into again the cycle complementary sequence set and aperiodic complementary sequence set two classes.Can construct its complementary series companion (mate) and recursion with complementary sequence set and construct the orthogonal complement sequence, etc.

B.M.

Method (the B.M. of a kind of perfect sequence of use (perfect sequences) heterogeneous complementary sequence set design aperiodic is proposed Complementary sets based on sequences with idealperiodic autocorrelation.Electronics Letters, Vol.26, No.18,1990, pp.1428-1430), with length be the perfect sequence of L and its L-1 left circulation equivalent sequence combine form one aperiodic heterogeneous complementary sequence set, subsequence quantity and sub-sequence length all are L.The design of another kind of heterogeneous complementary sequence set of cycle is based on perfect array (perfect array) (P.H.Fan, et al.Sequence design forcommunicatiohs applications.New York:John Wiley ﹠amp; Sons Inc., 1996, pp.331-334), a L ₁Row, L ₂Each row of the perfect array of row is as a subsequence, and can obtain a strip sequence quantity is L ₁, sub-sequence length is L ₂Heterogeneous complementary sequence set of cycle.The common drawback of these two kinds of methods is that the subsequence quantity and the sub-sequence length of the heterogeneous complementary sequence set that obtained cannot be provided with arbitrarily.

Summary of the invention

The purpose of this invention is to provide a kind of simple, easily realize, the generation method of heterogeneous complementary sequence set of cycle that subsequence quantity and sub-sequence length can be adjusted arbitrarily.

According to first aspect, the generation method of heterogeneous complementary sequence set of cycle of the present invention comprises:

By the continuous systematic sampling of perfect sequence is obtained one group of subsequence;

Obtain heterogeneous complementary sequence set of cycle by making up described one group of subsequence then.

According to first aspect, the generation method of heterogeneous complementary sequence set of cycle of the present invention may further comprise the steps:

A) according to the communication system demand, determine the subsequence quantity N and the sub-sequence length M of the needed cycle complementary sequence set of communication system, wherein N and M are respectively the positive integer more than or equal to 2;

B) selecting length from database is the perfect sequence of L=MN;

C) the perfect sequence of having selected is carried out continuously uniformly-spaced N-1 sample process, obtaining N bar length is the subsequence of M;

D) acquired N bar subsequence is carried out combined treatment in any order, thus heterogeneous complementary sequence set of the cycle that obtains.

Wherein, step C) comprising:

C-1) in perfect sequence one-period, select code element of perfect sequence as first start element arbitrarily;

C-2) to described first start element sampling, every N-1 perfect sequence code element described perfect sequence code element is sampled then, thereby obtain M code element that obtains by sampling;

C-3) more described M code element that obtains by sampling formed article one subsequence in proper order by sampling;

C-4) then with the N continuous-1 perfect sequence code element after described first start element respectively as second start element to the N start element, repeat above-mentioned steps C-1 respectively) to C-3), obtain second to N bar subsequence.

Wherein, the every strip sequence period in the described N bar subsequence all is M.

Wherein, the periodic auto-correlation function of described all subsequences and have an impulse characteristic.

Wherein, described perfect sequence be with any positive integer N and arbitrarily the long-pending of positive integer M be the perfect sequence of length.

According to three aspects, the method that generates heterogeneous complementary sequence set of cycle based on perfect sequence of the present invention may further comprise the steps:

1) in the perfect sequence one-period of length L=MN, select code element of perfect sequence as first start element arbitrarily, wherein N and M are respectively the positive integer more than or equal to 2;

2) to described first start element sampling, every N-1 perfect sequence code element described perfect sequence code element is sampled then, thereby obtain M code element that obtains by sampling;

3) more described M code element that obtains by sampling formed article one subsequence in proper order by sampling;

4) then with the N continuous-1 perfect sequence code element after described first start element respectively as second start element to the N start element, repeat above-mentioned steps 1 respectively) to 3), obtain second to N bar subsequence; And

Resulting N bar subsequence is carried out combined treatment in any order, thus heterogeneous complementary sequence set of the cycle that obtains.

Wherein, the every strip sequence period in the described N bar subsequence all is M.

Wherein, the periodic auto-correlation function of described all subsequences and have an impulse characteristic.

Wherein, described perfect sequence be with any positive integer N and arbitrarily the long-pending of positive integer M be the perfect sequence of length.

Said method of the present invention can be for the multi-access interference suppression of communication system, channel estimating, synchronously, peak-to-average power ratio (PAPR) reduces and the signal generation provides required complementary series.

The present invention is described in detail below in conjunction with accompanying drawing.

Description of drawings

Fig. 1 is the present invention's N-1 sampling schematic diagram uniformly-spaced continuously;

Fig. 2 is the schematic diagram of device that generates heterogeneous complementary series of cycle according to perfect sequence of the present invention;

Fig. 3 is the circuit diagram of the concrete structure of displayed map 2 shown devices;

Fig. 4 is the schematic diagram that generates heterogeneous complementary series of cycle according to the communication system demand of the present invention;

Fig. 5 be the heterogeneous complementary sequence set of cycle that in example 1, produces of the present invention all subsequence periodic auto-correlation functions and absolute value figure, periodic auto-correlation function and have an impulse characteristic;

Fig. 6 be the heterogeneous complementary sequence set of cycle that in example 2, produces of the present invention all subsequence periodic auto-correlation functions and absolute value figure, periodic auto-correlation function and have an impulse characteristic, shown on example 1 basis, kept sub-sequence length constant and change the situation of subsequence quantity;

Fig. 7 be all subsequence periodic auto-correlation functions of heterogeneous complementary sequence set of cycle that in example 3, produce of the present invention and absolute value figure, periodic auto-correlation function and have an impulse characteristic, shown on example 1 basis, kept subsequence quantity constant and change the situation of sub-sequence length;

Fig. 8 be all subsequence periodic auto-correlation functions of heterogeneous complementary sequence set of cycle that in example 4, produce of the present invention and absolute value figure, periodic auto-correlation function and have an impulse characteristic, shown on example 1 basis the situation that sub-sequence length and subsequence quantity all change.

Embodiment

The core of the generation method of heterogeneous complementary sequence set of cycle of the present invention is by the continuous systematic sampling of perfect sequence is obtained one group of subsequence, to obtain heterogeneous complementary sequence set of cycle by making up described one group of subsequence then.

Fig. 1 has shown that the present invention obtains the principle of heterogeneous complementary sequence set of cycle by the continuous uniformly-spaced N-1 of perfect sequence is sampled.As shown in Figure 1, the length L of perfect sequence to be sampled is a NM code element, and complementary series has N subsequence, and its each sub-sequence length is a M code element.Be convenient expression, suppose the code element a of selected perfect sequence _λ(0≤λ≤L-1) is a start element, and subsequence number is designated as (λ+i) _N(0≤i≤N-1), symbol (x) here _NExpression is asked residue about mould N to x, and the notation of the subsequence here number only is to express conveniently in order to illustrate, and actual subsequence number can mark arbitrarily.

Fig. 2 has shown that can be realized a N sub-sequential sampling, thereby generates the device based on the heterogeneous complementary sequence set of cycle of perfect sequence.This device comprises that a continuous uniformly-spaced N-1 sampling of the code element to perfect sequence is to form the systematic sampling unit 1 of N subsequence, this unit 1 at first extracts a subsequence from perfect sequence, and then extract another subsequence, until extracting whole N bar subsequences; And N bar subsequence made up assembled unit 2 with heterogeneous complementary sequence set of formation cycle.

Fig. 3 shown one can be in communication equipment performance period heterogeneous complementary sequence set concrete device, wherein systematic sampling unit 1 is made of sampling unit 11 and temporary storage location 12.Sampling unit 11 temporarily is stored in temporary storage location to every the subsequence that extracts respectively In the respective shift register in 12 in N shift register, form N bar subsequence thus, and then it is made up by assembled unit 2, form heterogeneous complementary sequence set of cycle thus.

Utilize said apparatus, the present invention just can be by following steps Cheng Sheng based on heterogeneous complementary sequence set of the cycle of perfect sequence:

1) in the perfect sequence one-period of length L=MN, select code element of perfect sequence as first start element arbitrarily, wherein N and M are respectively the positive integer more than or equal to 2;

2) to described first start element sampling, every N-1 perfect sequence code element described perfect sequence code element is sampled then, thereby obtain M code element that obtains by sampling;

3) more described M code element that obtains by sampling formed article one subsequence in proper order by sampling;

4) then with the N continuous-1 perfect sequence code element after described first start element respectively as second start element to the N start element, repeat above-mentioned steps 1 respectively) to 3), obtain second to N bar subsequence; And

Resulting N bar subsequence is carried out combined treatment in any order, thus heterogeneous complementary sequence set of the cycle that obtains.

In the wherein above-mentioned N bar subsequence, its every strip sequence period all is M.

In addition, the periodic auto-correlation function of described all subsequences and have the impulse characteristic, will be elaborated below.

Fig. 4 shown one can be according to the communication system demand, promptly according to no multiple access disturb transmission, channel estimating, communication system synchronously, the requirement of the reduction of peak-to-average power ratio (PAPR) and other signal (as, quasi-barker and low/zero-correlation zone sequence etc.) etc. numerous application generate the method for heterogeneous complementary sequence sets of cycle.This device comprises sub-sequence quantity and length input unit 3, is used for input has been determined according to the communication system demand subsequence quantity and length parameter; The database 5 of the perfect sequence of storage different length; Selected cell 4 is used for according to subsequence quantity and length parameter to determine, selects its length to equal the perfect sequence of sub-sequence length * subsequence quantity from database 5; The perfect sequence of having selected is carried out systematic sampling to form the systematic sampling unit 1 of a plurality of subsequences; And the assembled unit 2 that makes up a plurality of subsequences.Wherein systematic sampling unit 1 can adopt structure shown in Figure 3.

Utilize the device of Fig. 4, the present invention can generate the heterogeneous complementary sequence set of cycle that is adapted to communication system by following steps:

A) according to the communication system demand, determine the subsequence quantity N and the sub-sequence length M of the needed cycle complementary sequence set of communication system, wherein N and M are respectively the positive integer more than or equal to 2;

B) selecting length from database is the perfect sequence of L=MN;

C) the perfect sequence of having selected is carried out continuously uniformly-spaced N-1 sample process, obtaining N bar length is the subsequence of M;

D) acquired N bar subsequence is carried out combined treatment in any order, thereby to heterogeneous complementary sequence set of cycle.

Step C wherein) comprising:

C-1) in perfect sequence one-period, select code element of perfect sequence as first start element arbitrarily;

C-2) to described first start element sampling, every N-1 perfect sequence code element described perfect sequence code element is sampled then, thereby obtain M code element that obtains by sampling;

C-3) more described M code element that obtains by sampling formed article one subsequence in proper order by sampling;

C-4) then with the N continuous-1 perfect sequence code element after described first start element respectively as second start element to the N start element, repeat above-mentioned steps C-1 respectively) to C-3), obtain second to N bar subsequence.

Every strip sequence period in the wherein said N bar subsequence all is M.And the periodic auto-correlation function of described all subsequences and have an impulse characteristic.

The used perfect sequence of the present invention preferably is the perfect sequence of Chu of length with any positive integer N.

As everyone knows, existence is perfect sequence (the D.Chu.Polyphase codeswith good periodic correlation properties of Chu of length with any positive integer N, IEEE Trans.On Inf.Theory, vol.18, No.4,1972, pp.531-532), there is square (N with any positive integer N ²) be perfect sequence (the R.Frank.Phase shift pulse codes with good periodic correlation properties of Frank of length, IRE Trans.on Inf.Theory, vol.IT-8,1962, pp.381-382), and exist unlimited many, with square (N of any positive integer N ²) be modulation orthogonal sequence (in the perfect sequence a kind of) (N.Suehiro of length, et al.Modulatable orthogonal sequences and their application to SSMA systems, IEEE Trans.On Inf.Theory, vol.34, no.1,1988, pp.93-100), etc.To any perfect sequence, the inventive method produces a heterogeneous complementary sequence set of cycle.Therefore, can draw to draw a conclusion.

(1) perfect sequence required for the present invention has abundant source, to arbitrarily given M and N all exist needs, length is the perfect sequence of MN;

(2) subsequence quantity of the present invention and sub-sequence length can be adjusted on demand; Can produce subsequence to fixing subsequence quantity greater than 1 positive count length; Can produce subsequence to fixing sub-sequence length greater than any positive integer quantity of 1; Can produce the heterogeneous complementary sequence set of cycle of any given sub-sequence length (greater than 1) and norator sequence quantity (greater than 1).

(3) quantity of the heterogeneous complementary sequence set of cycle of the inventive method generation is identical with the quantity of the perfect sequence of selecting for use.

(4) same perfect sequence is implemented the inventive method, the circulation that moves to left of two subsequences of the integral multiple that is spaced apart N-1 of start element is of equal value.

Prove that below all subsequences that the present invention obtains constitute heterogeneous complementary sequence set of cycle.

By the representation of figure l, get perfect sequence one-period

a＝(a _λ，a _λ+1，…，a _λ+N-1，a _λ+N，a _λ+N+1，…，a _λ+2N-1，…，a _λ+(M-1)N，a _λ+(M-1)N+1，…，a _{λ+(M-1)N+N-1}) (5)

So, according to the definition of perfect sequence, sequence aPeriodic auto-correlation function be:

$R_{a,a}\left(u\right)=\underset{k=0}{\overset{L-1}{\mathrm{\Σ}}}{a}_{k+\mathrm{\λ}}{\left(a_{k+\mathrm{\λ}+u}\right)}^{*}=\left\{\begin{array}{cc}L& u=0\\ 0& u\≠0\end{array}\right.,\left(\right|u|\≤L-1)---\left(6\right)$

Wherein, L=MN.

Press the uniformly-spaced N-1 sampling continuously of Fig. 1, the M that an obtains sequence is:

${\underset{\‾}{b}}^{{\left(\mathrm{\λ}\right)}_N}=(b_0^{{\left(\mathrm{\λ}\right)}_N},b_1^{{\left(\mathrm{\λ}\right)}_N},b_2^{{\left(\mathrm{\λ}\right)}_N},\·\·\·,b_{M-1}^{{\left(\mathrm{\λ}\right)}_N})$

${\underset{\‾}{b}}^{{(\mathrm{\λ}+1)}_N}=(b_0^{{(\mathrm{\λ}+1)}_N},b_1^{{(\mathrm{\λ}+1)}_N},b_2^{{(\mathrm{\λ}+1)}_N},\·\·\·,b_{M-1}^{{(\mathrm{\λ}+1)}_N})---\left(7\right)$ $\begin{array}{c}\·\\ \·\\ \·\end{array}$ ${\underset{\‾}{b}}^{{(\mathrm{\λ}+N-1)}_N}=(b_0^{{(\mathrm{\λ}+N-1)}_N},b_1^{{(\mathrm{\λ}+N-1)}_N},b_2^{{(\mathrm{\λ}+N-1)}_N},\·\·\·,b_{M-1}^{{(\mathrm{\λ}+N-1)}_N})$

Wherein, $b_k^{{(\mathrm{\λ}+i)}_N}=a_{\mathrm{\λ}+\mathrm{kN}+i}(i=\mathrm{0,1,2},\·\·\·,N-1;k=\mathrm{0,1,2},\·\·\·,M-1).$

So, sequence

All subsequences periodic auto-correlation function and be:

$R_{c,c}\left(\mathrm{\τ}\right)=\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}{R}_{b^{{(\mathrm{\λ}+i)}_N},b^{{(\mathrm{\λ}+i)}_N}}\left(\mathrm{\τ}\right)\left(\right|\mathrm{\τ}|\≤M-1)$

$=\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{d=0}{\overset{M-1}{\mathrm{\Σ}}}{b}_d^{{(\mathrm{\λ}+i)}_N}{\left[b_{d+\mathrm{\τ}}^{{(\mathrm{\λ}+i)}_N}\right]}^{*}$

$=\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{d=0}{\overset{M-1}{\mathrm{\Σ}}}{a}_{\mathrm{\λ}+\mathrm{dN}+i}{\left[a_{\mathrm{\λ}+(d+\mathrm{\τ})N+i}\right]}^{*}---\left(8\right)$

$=\underset{k=0}{\overset{L-1}{\mathrm{\Σ}}}{a}_{k+\mathrm{\λ}}{\left(a_{k+\mathrm{\λ}+\mathrm{\τN}}\right)}^{*}$

$=R_{a,a}\left(\mathrm{\τN}\right)$

$=\left\{\begin{array}{cc}L& \mathrm{\τ}=0\\ 0& \mathrm{\τ}\≠0\end{array}\right.---\left(6\right)$

According to the definition of heterogeneous complementary sequence set of cycle, formula (8) shows sequence cIt is heterogeneous complementary sequence set of cycle.

Formula (8) shows heterogeneous complementary sequence set of cycle cAll subsequences periodic auto-correlation function and have an impulse characteristic.

Sub-sequence length is 8 to example 1 if desired, subsequence quantity is 6, that is, N=6, M=8 realizes that so once can select length is the Chu sequence of L=48.

a＝(0，1，4，9，16，25，36，49，64，81，4，25，48，73，4，33，64，1，36，73，16，57，4，49，0，49，4，57，16，73，36，1，64，33，4，73，48，25，4，81，64，49，36，25，16，9，4，1)

Wherein, code element

Represent with " x ".

Getting the sampling starting point is a ₃=9 (promptly b ⁽³⁾First sample value), through uniformly-spaced 5 sampling continuously, the heterogeneous complementary sequence set of cycle that the present invention produces is

c＝( b ⁽³⁾， b ⁽⁴⁾， b ⁽⁵⁾， b ⁽⁰⁾， b ⁽¹⁾， b ⁽²⁾)

Wherein,

b ⁽⁰⁾＝(36，48，36，0，36，48，36，0)

b ⁽¹⁾＝(49，73，73，49，1，25，25，1)

b ⁽²⁾＝(64，4，16，4，64，4，16，4)

b ⁽³⁾＝(9，81，33，57，57，33，81，9)

b ⁽⁴⁾＝(16，4，64，4，16，4，64，4)

b ⁽⁵⁾＝(25，25，1，49，73，73，49，1)

Fig. 5 provided all subsequence periodic auto-correlation functions of heterogeneous complementary sequence set of this example cycle and absolute value figure.

Example 2 sub-sequence length if desired is constant, still be 8, but subsequence quantity becomes 4, that is, N=4, M=8 realizes that so once can select length is the Chu sequence of L=32

a＝(0，1，4，9，16，25，36，49，0，17，36，57，16，41，4，33，0，33，4，41，16，57，36，17，0，49，36，25，16，9，4，1)

Getting the sampling starting point is a ₁₅=33, through uniformly-spaced 3 sampling continuously, the heterogeneous complementary sequence set of cycle that the present invention produces is

c＝( b ⁽³⁾， b ⁽⁰⁾， b ⁽¹⁾， b ⁽²⁾)

Wherein,

b ⁽⁰⁾＝(0，16，0，16，0，16，0，16)

b ⁽¹⁾＝(33，57，49，9，1，25，17，41)

b ⁽²⁾＝(4，36，36，4，4，36，36，4)

b ⁽³⁾＝(33，41，17，25，1，9，49，57)

Fig. 6 provided heterogeneous complementary sequence set of this example cycle all subsequence periodic auto-correlation functions and absolute value figure.

Example 3 sub-sequence length if desired changes into 15, and subsequence quantity is constant, still is 6, that is, N=6, M=15 realizes that so once can select length is the Chu sequence of L=90

a＝(0，1，4，9，16，25，36，49，64，81，100，121，144，169，16，45，76，109，144，1，40，81，124，169，36，85，136，9，64，121，0，61，124，9，76，145，36，109，4，81，160，61，144，49，136，45，136，49，144，61，16，0，81，4，109，36，145，76，9，124，61，0，121，64，9，136，85，36，169，124，81，40，1，144，109，76，45，16，169，144，121，100，81，64，49，36，25，16，9，4，1)

Getting the sampling starting point is a ₈₃=49, through uniformly-spaced 5 sampling continuously, the heterogeneous complementary sequence set of cycle that the present invention produces is

c＝( b ⁽⁵⁾， b ⁽⁰⁾， b ⁽¹⁾， b ⁽²⁾， b ⁽³⁾， b ⁽⁴⁾)

Wherein,

b ⁽⁰⁾＝(36，0，36，144，144，36，0，36，144，144，36，0，36，144，144)

b ⁽¹⁾＝(25，1，49，169，1，85，61，109，49，61，145，121，169，109，121)

b ⁽²⁾＝(16，4，64，16，40，136，124，4，136，160，76，64，124，76，100)

b ⁽³⁾＝(9，9，81，45，81，9，9，81，45，81，9，9，81，45，81)

b ⁽⁴⁾＝(4，16，100，76，124，64，76，160，136，4，124，136，40，16，64)

b ⁽⁵⁾＝(49，1，25，121，109，169，121，145，61，49，109，61，85，1，169)

Fig. 7 provided heterogeneous complementary sequence set of this example cycle all subsequence periodic auto-correlation functions and absolute value figure.

Example 4 sub-sequence length and subsequence quantity if desired all changes, and is respectively 21 and 5, that is, N=5 and M=21 realize that so once can select length is the Chu sequence of L=105

a＝(0，2，6，12，20，30，42，56，72，90，110，132，156，182，0，30，62，96，132，170，0，42，86，132，180，20，72，126，182，30，90，152，6，72，140，0，72，146，12，90，170，42，126，2，90，180，62，156，42，140，30，132，26，132，30，140，42，156，62，180，90，2，126，42，170，90，12，146，72，0，140，72，6，152，90，30，182，126，72，20，180，132，86，42，0，170，132，96，62，30，0，182，156，132，110，90，72，56，42，30，20，12，6，2，0)

Getting the sampling starting point is a ₅₅=140, through uniformly-spaced 4 sampling continuously, the heterogeneous complementary sequence set of cycle that the present invention produces is

c＝( b ⁽⁰⁾， b ⁽¹⁾， b ⁽²⁾， b ⁽³⁾， b ⁽⁴⁾)

Wherein,

b ⁽⁰⁾＝(140，90，90，140，30，180，170，0，90，20，0，30，110，30，0，20，90，0，170，180，30)

b ⁽¹⁾＝(42，2，12，72，182，132，132，182，72，12，2，42，132，62，42，72，152，72，42，62，132)

b ⁽²⁾＝(156，126，146，6，126，86，96，156，56，6，6，56，156，96，86，126，6，146，126，156，26)

b ⁽³⁾＝(62，42，72，152，72，42，62，132，42，2，12，72，182，132，132，182，72，12，2，42，132)

b ⁽⁴⁾＝(180，170，0，90，20，0，30，110，30，0，20，90，0，170，180，30，140，90，90，140，30)

Fig. 8 provided heterogeneous complementary sequence set of this example cycle all subsequence periodic auto-correlation functions and absolute value figure.

Although above the present invention is had been described in detail, the invention is not restricted to this, those skilled in the art of the present technique can carry out various modifications according to principle of the present invention.Therefore, all modifications of doing according to the principle of the invention all should be understood to fall into protection scope of the present invention.

Claims (10)

1. the generation method of a heterogeneous complementary sequence set of cycle wherein by the continuous systematic sampling of perfect sequence is obtained one group of subsequence, obtains heterogeneous complementary sequence set of cycle by making up described one group of subsequence then.

2. the generation method of a heterogeneous complementary sequence set of cycle may further comprise the steps:

A) according to the communication system demand, determine the subsequence quantity N and the sub-sequence length M of the needed cycle complementary sequence set of communication system, wherein N and M are respectively the positive integer more than or equal to 2;

B) selecting length from database is the perfect sequence of L=MN;

C) the perfect sequence of having selected is carried out continuously uniformly-spaced N-1 sample process, obtaining N bar length is the subsequence of M;

D) acquired N bar subsequence is carried out combined treatment in any order, thus heterogeneous complementary sequence set of the cycle that obtains.

3. method according to claim 2, wherein step C) comprising:

C-1) in perfect sequence one-period, select code element of perfect sequence as first start element arbitrarily;

C-2) to described first start element sampling, every N-1 perfect sequence code element described perfect sequence code element is sampled then, thereby obtain M code element that obtains by sampling;

C-3) more described M code element that obtains by sampling formed article one subsequence in proper order by sampling;

C-4) then with the perfect sequence code element of the N continuous after described first start element respectively as second start element to the N start element, repeat above-mentioned steps C-1 respectively) to C-3), obtain second to N bar subsequence.

4. method according to claim 3, the every strip sequence period in the wherein said N bar subsequence all is M.

5. according to claim 3 or 4 described methods, the periodic auto-correlation function of wherein said all subsequences and have an impulse characteristic.

6. according to claim 2 or 3 described methods, wherein said perfect sequence be with any positive integer N and arbitrarily the long-pending of positive integer M be the perfect sequence of length.

7. one kind generates the method for heterogeneous complementary sequence set of cycle based on perfect sequence, may further comprise the steps:

1) in the perfect sequence one-period of length L=MN, select code element of perfect sequence as first start element arbitrarily, wherein N and M are respectively the positive integer more than or equal to 2;

2) to described first start element sampling, every N-1 perfect sequence code element described perfect sequence code element is sampled then, thereby obtain M code element that obtains by sampling;

3) more described M code element that obtains by sampling formed article one subsequence in proper order by sampling;

4) then with the perfect sequence code element of the N continuous after described first start element respectively as second start element to the N start element, repeat above-mentioned steps 1 respectively) to 3), obtain second to N bar subsequence; And

Resulting N bar subsequence is carried out combined treatment in any order, thus heterogeneous complementary sequence set of the cycle that obtains.

8. method according to claim 7, the every strip sequence period in the wherein said N bar subsequence all is M.

9. according to claim 7 or 8 described methods, the periodic auto-correlation function of wherein said all subsequences and have an impulse characteristic.

10. according to claim 7 or 8 described methods, wherein said perfect sequence be with any positive integer N and arbitrarily the long-pending of positive integer M be the perfect sequence of length.

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