CN101959289B - 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 periodic polyphase complementary sequence sets

Technical field

The present invention relates to a kind of communication sequence, particularly can realize communication system without multiple access disturb transmission, channel estimating, communication system synchronously, the reduction of peak-to-average power ratio (PAPR) and the generation method that designs the periodic complementary sequence sets with impulse Cyclic autocorrelation characteristic of other signal.

Background technology

In many practical communication Design of Engineering Systems, must consider multi-access interference suppression, channel estimating, synchronously, the factor such as peak-to-average power ratio (PAPR).In addition, also need to design the 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 thus the multiple access interference, has seriously reduced the performance of communication system, capacity and the transmission rate of system.In the 4th generation (4G) mobile communication, realize that the target of multimedia communication need to have than the transmission rate of 2G and the high decades of times of 3G, higher power system capacity and the availability of frequency spectrum especially, multiple access disturbs and must limit in 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 WirelessCommunications, 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 realize with complementary series 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, because the signal transmission of OFDM has adopted the linear combination of a plurality of subcarrier transmission symbols, therefore, than carrier wave communication system higher peak-to-average power ratio (PAPR) is arranged.If to high PAPR establishment in addition not, can cause so transmitter amplifier to produce serious non-linear breaking-up.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 well the high problem of ofdm communication system PAPR.

(4) synchronous

In communication system, has synchronously considerable status.The communication system can, work reliably, depend on to a great extent and 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 to 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 ^NdInt.Conf.on Wireless Broadband and Ultra Wideband Commun., 2007).

(5) other signal

In actual applications, also need to produce the signal with various special characteristics, for example, the sequence with impulse autocorrelation performance is desirable communication system synchronizing signal, and AS-CDMA, the LAS-CDMA communication system disturbed without multiple access 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 $\left|s_k^{\left(i\right)}\right|=1(0\≤k\≤M-1).$ 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 cConsisted of by N subsequence, namely

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.

Such as infructescence cIn all subsequence periodic auto-correlation functions and satisfy

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

So, claim sequence cBe periodic polyphase complementary sequence sets.

Complementary sequence set is comprised 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 to reach this requirement.Complementary sequence set be divided into again the periodic complementary sequence sets 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 use perfect sequence (perfect sequences) design polyphase complementary sequence sets 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 polyphase complementary sequence sets, subsequence quantity and sub-sequence length all are L.The design of another kind of periodic polyphase complementary sequence sets is based on perfect array (perfect array) (P.H.Fan, et al.Sequence design forcommunications applications.New York:John Wiley﹠amp; Sons Inc., 1996, pp.331-334), a L ₁Row, L ₂Every delegation 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 ₂Periodic polyphase complementary sequence sets.The common shortcoming of these two kinds of methods is that subsequence quantity and the sub-sequence length of the polyphase complementary sequence sets that obtains cannot arrange arbitrarily.

Summary of the invention

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

According to first aspect, the generation method of periodic polyphase complementary sequence sets of the present invention comprises:

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

Then obtain periodic polyphase complementary sequence sets by making up described one group of subsequence.

According to first aspect, the generation method of periodic polyphase complementary sequence sets of the present invention may further comprise the steps:

A) according to the communication system demand, determine subsequence quantity N and the sub-sequence length M of the needed periodic complementary sequence sets 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) 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 obtain periodic polyphase complementary sequence sets.

Wherein, step C) comprising:

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

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

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

C-4) then with the N continuous-1 perfect sequence code element after described the first start element respectively as the second start element to the N start element, repeat respectively above-mentioned steps C-1) 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 is the long-pending perfect sequence as length take any positive integer N and any positive integer M.

According to three aspects:, the method based on perfect sequence generating period polyphase complementary sequence sets of the present invention may further comprise the steps:

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

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

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

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

Resulting N bar subsequence is carried out combined treatment in any order, thereby obtain periodic polyphase complementary sequence sets.

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 is the long-pending perfect sequence as length take any positive integer N and any positive integer M.

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 continuously N-1 sampling schematic diagram uniformly-spaced of the present invention;

Fig. 2 is the schematic diagram of device according to the heterogeneous complementary series of perfect sequence generating period of the present invention;

Fig. 3 is the circuit diagram that shows the concrete structure of device shown in Figure 2;

Fig. 4 is the schematic diagram according to the heterogeneous complementary series of communication system demand generating period of the present invention;

Fig. 5 be the periodic polyphase complementary sequence sets 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 periodic polyphase complementary sequence sets 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 periodic polyphase complementary sequence sets 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 periodic polyphase complementary sequence sets 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 periodic polyphase complementary sequence sets of the present invention is by the continuous systematic sampling of perfect sequence is obtained one group of subsequence, then to obtain periodic polyphase complementary sequence sets by making up described one group of subsequence.

Fig. 1 has shown that the present invention obtains the principle of periodic polyphase complementary sequence sets 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 NM code element, and complementary series has N subsequence, and its each sub-sequence length is M code element.Be convenient expression, suppose the code element a of selected perfect sequence _λ(0≤λ≤L-1) is start element, and subsequence number is designated as (λ+i) _N(0≤i≤N-1), here symbol (x) _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 periodic polyphase complementary sequence sets of perfect sequence.This device comprises that a continuous uniformly-spaced N-1 of the code element to perfect sequence samples 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 extract whole N bar subsequences; And the assembled unit 2 that N bar subsequence is made up to form periodic polyphase complementary sequence sets.

Fig. 3 shown one can be in communication equipment performance period polyphase complementary sequence sets 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 respectively temporary storage location to every the subsequence that extracts In the respective shift register in 12 in N shift register, form thus N bar subsequence, and then by assembled unit 2 it is made up, form thus periodic polyphase complementary sequence sets.

Utilize said apparatus, the present invention just can be by following steps Cheng Sheng based on the periodic polyphase complementary sequence sets of perfect sequence:

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

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

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

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

Resulting N bar subsequence is carried out combined treatment in any order, thereby obtain periodic polyphase complementary sequence sets.

Wherein in the 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, the below will be elaborated.

Fig. 4 shown one can be according to the communication system demand, namely according to disturb without multiple access 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. the method for numerous application generating period polyphase complementary sequence sets.This device comprises a 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 periodic polyphase complementary sequence sets that is adapted to communication system by following steps:

A) according to the communication system demand, determine subsequence quantity N and the sub-sequence length M of the needed periodic complementary sequence sets 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) 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 periodic polyphase complementary sequence sets.

Step C wherein) comprising:

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

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

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

C-4) then with the N continuous-1 perfect sequence code element after described the first start element respectively as the second start element to the N start element, repeat respectively above-mentioned steps C-1) 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 is the Chu perfect sequence take any positive integer N as length preferably.

As everyone knows, Chu perfect sequence (the D.Chu.Polyphase codeswith good periodic correlation properties of existence take any positive integer N as length, IEEE Trans.On Inf.Theory, vol.18, No.4,1972, pp.531-532), there is square (N with any positive integer N ²) be Frank perfect sequence (the R.Frank.Phase shift pulse codes with good periodic correlation properties 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 periodic polyphase complementary sequence sets.Therefore, can draw to draw a conclusion.

(1) perfect sequence required for the present invention has abundant source, to any 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 greater than 1 positive count length to fixing subsequence quantity; Can produce subsequence greater than any positive integer quantity of 1 to fixing sub-sequence length; Can produce the periodic polyphase complementary sequence sets of any given sub-sequence length (greater than 1) and norator sequence quantity (greater than 1).

(3) quantity of the periodic polyphase complementary sequence sets of the inventive method generation is identical with the quantity of the perfect sequence of selecting.

(4) the 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.

The below proves that all subsequences that the present invention obtains consist of periodic polyphase complementary sequence sets.

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

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

${\underset{\‾}{b}}^{{\left(\mathrm{\λ}\right)}_N}=(b_0^{{(\mathrm{\λ}+1)}_N},b_1^{{(\mathrm{\λ}+1)}_N},b_2^{{(\mathrm{\λ}+1)}_N},...,b_{M-1}^{{(\mathrm{\λ}+1)}_N})---\left(7\right)$

${\underset{\‾}{b}}^{{(\mathrm{\λ}+N-1)}_N}=(b_0^{{(\mathrm{\λ}+N-1)}_N},b_1^{{(\mathrm{\λ}+N-1)}_N},b_2^{{(\mathrm{\λ}+N-1)}_N},...,b_{M-1}^{{(\mathrm{\λ}+N-1)}_N})$

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 $\underset{\‾}{c}=({\underset{\‾}{b}}^{{\left(\mathrm{\λ}\right)}_N},{\underset{\‾}{b}}^{{(\mathrm{\λ}+1)}_N},{\underset{\‾}{b}}^{{(\mathrm{\λ}+2)}_N},...,{\underset{\‾}{b}}^{{(\mathrm{\λ}+N-1)}_N})$ 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 periodic polyphase complementary sequence sets, formula (8) shows sequence cIt is periodic polyphase complementary sequence sets.

Formula (8) shows periodic polyphase complementary sequence sets cAll subsequences periodic auto-correlation function and have an impulse characteristic.

Sub-sequence length is 8, subsequence quantity is 6 if example 1 needs, 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 (namely b ⁽³⁾First sample value), through continuously uniformly-spaced 5 sampling, the periodic polyphase complementary sequence sets 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 this routine periodic polyphase complementary sequence sets and absolute value figure.

If the sub-sequence length that example 2 needs 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 continuously uniformly-spaced 3 sampling, the periodic polyphase complementary sequence sets 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 this routine periodic polyphase complementary sequence sets all subsequence periodic auto-correlation functions and absolute value figure.

If the sub-sequence length that example 3 needs changes into 15, 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 continuously uniformly-spaced 5 sampling, the periodic polyphase complementary sequence sets 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 this routine periodic polyphase complementary sequence sets all subsequence periodic auto-correlation functions and absolute value figure.

If sub-sequence length and subsequence quantity that example 4 needs all change, be 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 continuously uniformly-spaced 4 sampling, the periodic polyphase complementary sequence sets 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 this routine periodic polyphase complementary sequence sets 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 (9)

1. the generation method of a periodic polyphase complementary sequence sets may further comprise the steps:

A) according to the communication system demand, determine subsequence quantity N and the sub-sequence length M of the needed periodic complementary sequence sets 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) 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 obtain periodic polyphase complementary sequence sets.

2. method according to claim 1, wherein step C) comprising:

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

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

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

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

3. method according to claim 2, the every strip sequence period in the wherein said N bar subsequence all is M.

4. according to claim 2 or 3 described methods, the periodic auto-correlation function of wherein said N bar subsequence and have an impulse characteristic.

5. method according to claim 1 and 2, wherein said perfect sequence are take any positive integer N and any long-pending perfect sequence as length of positive integer M.

6. method based on perfect sequence generating period polyphase complementary sequence sets may further comprise the steps:

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

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

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

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

Resulting N bar subsequence is carried out combined treatment in any order, thereby obtain periodic polyphase complementary sequence sets.

7. method according to claim 6, the every strip sequence period in the wherein said N bar subsequence all is M.

8. according to claim 6 or 7 described methods, the periodic auto-correlation function of wherein said N bar subsequence and have an impulse characteristic.

9. according to claim 6 or 7 described methods, wherein said perfect sequence is take any positive integer N and any long-pending perfect sequence as length of positive integer M.

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