阅读说明：本技术 一种具有宽间隔特性的低碰撞区跳频序列集的构造方法 (Construction method of low collision region frequency hopping sequence set with wide interval characteristic ) 是由 刘星 洪绍方 曾琦 周李梦男 于 2020-01-19 设计创作，主要内容包括：本发明公开了一种具有宽间隔特性的低碰撞区跳频序列集的构造方法,解决了在准同步跳频通信系统中,低碰撞区跳频序列集是适用于该系统的序列集,而目前尚未有具有宽间隔特性的低碰撞区跳频序列集的构造方法的问题。本发明包括构建具有特定排列方式的素数序列集<I>S</I>、构建级联序列<I>S’</I>和生成跳频序列集<I>T</I>。本发明方法构建的跳频序列集<I>T</I>有利于对抗宽带阻塞干扰和窄带干扰,有利于对抗跟踪干扰,有利于对抗多径衰落。(The invention discloses a construction method of a low collision area frequency hopping sequence set with a wide interval characteristic, which solves the problem that in a quasi-synchronous frequency hopping communication system, the low collision area frequency hopping sequence set is a sequence set suitable for the system, but the construction method of the low collision area frequency hopping sequence set with the wide interval characteristic does not exist at present. The invention includes constructing prime number sequence set with specific arrangement mode S Construction of the Cascade sequence S’ And generating a set of hopping sequences T . Frequency hopping sequence set constructed by the method of the invention T The method is favorable for resisting broadband blocking interference and narrowband interference, is favorable for resisting tracking interference and is favorable for resisting multipath fading.)

1. A construction method of a low collision zone frequency hopping sequence set with a wide interval characteristic is characterized by comprising the following steps:

step 1: construction of prime number sequence setS；

Step 2: given a positive integerdPrime number ofpSelecting a plurality of subscripts from the prime number sequence set of greater than or equal tod+1 and not more thanp−dThe sequence of-1 is cascaded end to end in sequence to construct a cascade sequence, and the cascade sequence construction rule is as follows: repeatable selection of same subscript greater than or equal tod+1 and not more thanp−d-1 but the sequences of adjacent cascades are different, and the cascade sequences are constructed in any combination of the construction rules of the cascade sequencesS’；

And step 3: defining cyclic left shift operators, for cascaded sequencesS’Generating a frequency hopping sequence set after performing cyclic left shift by adopting a cyclic left shift operatorT。

2. The method for constructing a low collision zone frequency hopping sequence set with wide interval characteristic as claimed in claim 1, wherein in the step 1, the prime number sequence setSComprises the following steps:

wherein the operation is performed modulo p.

3. The method for constructing a low collision zone frequency hopping sequence set with wide spacing characteristics according to claim 1, wherein in the step 2,

4. The method for constructing a low collision zone frequency hopping sequence set with wide spacing characteristics as claimed in claim 1, wherein in said step 3, setting is performedTo cycle the left shift operator, the number of left shifts isjA bit whereinjIs any non-negative integer, for positive integersZ，Z+1|p+1，Z+1 integer divisionp+1, frequency hopping sequence setT：

Technical Field

The invention relates to the field of frequency hopping communication, in particular to a construction method of a low collision region frequency hopping sequence set with a wide interval characteristic.

Background

The basic idea of the frequency hopping system is to adopt the frequency hopping sequence to control the carrier to randomly hop so as to avoid the channel where the interference exists, and therefore, the design of the frequency hopping sequence becomes one of the key technologies of frequency hopping communication. The frequency hopping sequence with excellent performance is designed, and the sequence is required to have good Hamming correlation characteristics and randomness and certain wide interval so as to enhance the anti-interference performance of the system. For the evasive anti-interference frequency hopping communication technology, the frequency band stays on a certain frequency slot for too long time and is easily interfered, so that the frequency hopping sequence is required to meet the requirement of wide interval, namely, the frequency points of two adjacent time slots have a certain interval, and the interference resistance is facilitated. Therefore, in practical application of the frequency hopping communication technology, a requirement is first placed on a wide interval of the frequency hopping sequence.

Definition of the wide spacing: is provided with

Is one size ofqThe size of the number represents the height of the frequency point,Sis formed byFOn the upper partMHas a length ofNFor any arbitrary set of hopping sequences

If it is satisfied with

Then called the frequency hopping sequence setSHaving a wide spacing, wherein the spacing isd. Where the subscripts are in the modulusNThe following operations are performed.

And the low collision region frequency hopping sequence set is applied to the quasi-synchronous frequency hopping communication system (the relative time delay of the users of the quasi-synchronous frequency hopping communication system is controlled within a small range), even if the relative time delay exists among the users, the relative time delay is controlled within a small range (namely corresponding to the low collision region of the frequency hopping sequence set), as long as the relative time delay does not exceed the low collision region, the Hamming correlation of the frequency hopping sequence set can be kept at a low value, and the size of the Hamming correlation value corresponds to the size of the interference degree, so that the interference can be effectively reduced.

Definition of low collision zone hopping sequence set: frequency hopping sequence set for low collision zoneSLow collision zone size ofZ，

，NMaximum period Hamming autocorrelation for sequence lengthH _a (S) Maximum period Hamming cross-correlationH _c (S) Correlation with maximum period hammingH _m (S) Is defined as:

wherein the content of the first and second substances,

is composed ofxAndyat a time delayτIs determined. For simplicity, let us

。

If low collision zone hopping sequence setSWith wide spacing at the same time, then callSA set of low collision zone hopping sequences with a wide spacing characteristic.

Currently, although there are some constructions of hopping sequence sets with wide spacing characteristics, these constructions are for conventional hopping sequence sets, not low collision zone hopping sequence sets. In the quasi-synchronous frequency hopping communication system, the low collision zone frequency hopping sequence set is a sequence set suitable for the system, and a construction method of the low collision zone frequency hopping sequence set with a wide interval characteristic does not exist at present.

Disclosure of Invention

The invention provides a construction method of a low collision zone frequency hopping sequence set with wide interval characteristic, which solves the problems. The method overcomes the defect that the conventional low collision area frequency hopping sequence set does not have a wide interval characteristic, and meanwhile, the frequency hopping sequence set has excellent cycle Hamming correlation in the low collision area.

The invention is realized by the following technical scheme:

a construction method of a low collision zone frequency hopping sequence set with a wide interval characteristic comprises the following steps:

step 1: constructing sequence setsSSaid sequence setSA prime number sequence set with a specific arrangement mode is obtained;

step 2: given a positive integerdPrime number ofpSelecting a plurality of subscripts from the prime number sequence set of greater than or equal tod+1 and not more thanp−dThe sequence of-1 is cascaded end to end in sequence to construct a cascade sequence, and the cascade sequence construction rule is as follows: repeatable selection of same subscript greater than or equal tod+1 and not more thanp−d-1 but the sequences of adjacent cascades are different, and the cascade sequences are constructed in any combination of the construction rules of the cascade sequencesS’；

And step 3: defining cyclic left shift operators, for cascaded sequencesS’Generating a frequency hopping sequence set after performing cyclic left shift by adopting a cyclic left shift operatorT。

In the step 1, the step of processing the raw material,pis a prime number, the prime number sequence setSComprises the following steps:

wherein the operation is performed modulo p.

In the step 2, in the step of processing,

said cascade sequenceS’：In the formula (I), wherein,nis a positive integer and is a non-zero integer,

and for anyIs provided withWhereiniSubscript of (1) is in the form ofnThe following operations are performed.

In the step 3, setting

To cycle the left shift operator, the number of left shifts isjA bit whereinjIs any non-negative integer, for positive integersZ，Z+1|p+1, Z +1 integer divisionp+1, becausepA prime number, e.g. Z =3, p =7, so 4|8, i.e. 4 divided by 8, hopping sequence setT：

In the formula (I), wherein,

，

。

the following is a frequency hopping sequence set constructed by the method of the present inventionTThe correlation mathematics of (2) prove that:

theorem: frequency hopping sequence setTIs a low collision region frequency hopping sequence set with wide interval characteristicTIs at an interval ofdFrequency hopping sequence setTThe sequence length, the sequence number and the frequency slot set size are respectively

In the low collision zone ofZThe maximum period Hamming correlation atn。

And (3) proving that: obviously, the sequence length, the number of sequences and the size of the frequency slot set are respectively

. For each sequence

It is easy to verify that each sequence is at intervals ofdIs still spaced by a distance ofdThe wide spacing sequence of (2). In the following, we only need to demonstrate that it is of a low collision zone sizeZThe maximum period Hamming correlation atn。

First, we consider its periodic hamming autocorrelation. For time delayDue to the fact that

Therefore, it isWhen is coming into contact with

Thus, it is

The periodic hamming autocorrelation of (a) can be expressed as

Obviously for the sequence

At 0<τ<pThe periodic hamming autocorrelation of time is 0. Due to the fact thatTherefore, sequence of

And sequence

In thatThe periodic hamming cross-correlation of time is 1. Then there is

(ii) a When inWhen we have

。

Below we consider its periodic hamming cross-correlation. For time delay

And

the periodic Hamming cross-correlation can be expressed as

Due to the fact thatAnd is

Therefore, it is

And is

. Similar to the discussion of periodic hamming autocorrelation, there are

In summary, the size of the low collision zone isZLower partTHas a maximum period Hamming correlation ofn。

After the syndrome is confirmed.

Further, the frequency hopping constructed by the method of the invention is due to the broadband blocking interference and the narrowband interference in the frequency band transmissionSequence setTThe interval of the sequence is large enough to jump out of the frequency band of broadband blocking interference, and when the narrowband interference exists, only the information in one time slot interfered by the single-frequency signal is lost, and the information in a plurality of time slots is not lost continuously.

Furthermore, the frequency hopping sequence set constructed by the method of the inventionTThe frequency hopping sequence frequency band with wide interval and large span increases the search time of enemy jammers, thereby prolonging the tuning time and reducing the threat to frequency hopping radio stations.

Further, when the frequency interval is larger than the coherent bandwidth of the channel, the frequency hopping sequence set constructed by the method of the inventionTFrequency diversity can be realized to resist the effect of multipath fading.

The invention has the following advantages and beneficial effects:

frequency hopping sequence set constructed by the method of the inventionTThe method is favorable for resisting broadband blocking interference and narrowband interference.

Frequency hopping sequence set constructed by the method of the inventionTIt is advantageous to combat tracking interference.

Frequency hopping sequence set constructed by the method of the inventionTIs beneficial to resisting multipath fading.

Drawings

The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:

FIG. 1 is a schematic flow chart of the steps of the present invention.

Fig. 2 is a graph of the maximum period hamming correlation distribution for the set of hopping sequences of the present invention.

Detailed Description

Before any embodiments of the invention are explained in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangements of components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any inventive changes, are within the scope of the present invention.

A method for constructing a low collision zone frequency hopping sequence set with wide interval characteristics, as shown in fig. 1, includes the following steps:

step 1: constructing prime number sequence set with specific arrangement modeS；

Step 2: given a positive integerdPrime number ofpSelecting a plurality of subscripts from the prime number sequence set of greater than or equal tod+1 and not more thanp−dThe sequence of-1 is cascaded end to end in sequence to construct a cascade sequence, and the cascade sequence construction rule is as follows: repeatable selection of same subscript greater than or equal tod+1 and not more thanp−d-1 but the sequences of adjacent cascades are different, and the cascade sequences are constructed in any combination of the construction rules of the cascade sequencesS’；

And step 3: defining cyclic left shift operators, for cascaded sequencesS’Generating a frequency hopping sequence set after performing cyclic left shift by adopting a cyclic left shift operatorT。

In the step 1, the prime number sequence setSComprises the following steps:

wherein the operation is performed modulo p.

In the step 2, in the step of processing,said cascade sequenceS’：

In the formula (I), wherein,nis a positive integer and is a non-zero integer,

and for any

Is provided with

WhereiniSubscript of (1) is in the form ofnThe following operations are performed.

In the step 3, settingTo cycle the left shift operator, the number of left shifts isjA bit whereinjIs any non-negative integer, for positive integersZ，Z+1|p+1, frequency hopping sequence setT：

In the formula (I), wherein,，

。

the following is a frequency hopping sequence set constructed by the method of the present inventionTThe correlation mathematics of (2) prove that:

theorem: frequency hopping sequence setTIs a low collision region frequency hopping sequence set with wide interval characteristicTIs at an interval ofdFrequency hopping sequence setTThe sequence length, the sequence number and the frequency slot set size are respectively

In the low collision zone ofZThe maximum period Hamming correlation atn。

And (3) proving that: obviously, the sequence length, the number of sequences and the size of the frequency slot set are respectively

. For each sequenceIt is easy to verify that each sequence is at intervals ofdIs still spaced by a distance ofdThe wide spacing sequence of (2). Below we need only prove that it is at low collisionThe cell size isZThe maximum period Hamming correlation atn。

First, we consider its periodic hamming autocorrelation. For time delay

Due to the fact that

Therefore, it is

When is coming into contact with

Thus, it is

The periodic hamming autocorrelation of (a) can be expressed as

,

Obviously for the sequence

At 0<τ<pThe periodic hamming autocorrelation of time is 0. Due to the fact that

Therefore, sequence ofAnd sequenceIn that

The periodic hamming cross-correlation of time is 1. Then there is

(ii) a When in

When we have

。

Below we consider its periodic hamming cross-correlation. For time delay And

the periodic Hamming cross-correlation can be expressed as

Due to the fact thatAnd is

Therefore, it is

And is

. Similar to the discussion of periodic hamming autocorrelation, there are

,

In summary, the size of the low collision zone isZLower partTHas a maximum period Hamming correlation ofn。

After the syndrome is confirmed.

Based on the above embodiments, selectingp= 7,d= 1,Z=3, the following sequence set can be obtained:

T=

{(0,3,6,2,5,1,4,0,5,3,1,6,4,2,0,2,4,6,1,3,5,0,4,1,5,2,6,3,0,2,4,6,1,3,5,0,3,6,2,5,1,4,0,4,1,5,2,6,3,0,5,3,1,6,4,2,0,4,1,5,2,6,3),

(5,1,4,0,5,3,1,6,4,2,0,2,4,6,1,3,5,0,4,1,5,2,6,3,0,2,4,6,1,3,5,0,3,6,2,5,1,4,0,4,1,5,2,6,3,0,5,3,1,6,4,2,0,4,1,5,2,6,3,0,3,6,2)}。

can verify, sequence setTIs a low collision region frequency hopping sequence set with wide interval characteristic, wherein the interval isd= 1, sequence length, number of sequences and frequency slot set size are 63, 2, 7 respectively, and size is 63 in low collision zoneZMaximum period hamming correlation of =3 is 9.TMaximum period hamming correlation ofH _m At relative time delayτThe lower profile is shown in figure 2.

Furthermore, due to the broadband blocking interference and the narrowband interference in the frequency band transmission, the frequency hopping sequence set constructed by the method of the inventionTThe interval of the sequence is large enough to jump out of the frequency band of broadband blocking interference, and when the narrowband interference exists, only the information in one time slot interfered by the single-frequency signal is lost, and the information in a plurality of time slots is not lost continuously.

Furthermore, the frequency hopping sequence set constructed by the method of the inventionTThe frequency hopping sequence frequency band with wide interval and large span increases the search time of enemy jammers, thereby prolonging the tuning time and reducing the threat to frequency hopping radio stations.

Further, when the frequency interval is larger than the coherent bandwidth of the channel, the frequency hopping sequence set constructed by the method of the inventionTFrequency diversity can be realized to resist the effect of multipath fading.

The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.