CN110830080B - Generation method of aperiodic Hamming related short frequency hopping sequence set - Google Patents
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/69—Spread spectrum techniques
- H04B1/713—Spread spectrum techniques using frequency hopping
- H04B1/7136—Arrangements for generation of hop frequencies, e.g. using a bank of frequency sources, using continuous tuning or using a transform
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/69—Spread spectrum techniques
- H04B1/713—Spread spectrum techniques using frequency hopping
- H04B1/7136—Arrangements for generation of hop frequencies, e.g. using a bank of frequency sources, using continuous tuning or using a transform
- H04B2001/71362—Arrangements for generation of hop frequencies, e.g. using a bank of frequency sources, using continuous tuning or using a transform using a bank of frequency sources
Abstract
The invention discloses a method for generating an aperiodic Hamming related short frequency hopping sequence set, which solves the problems that the construction process of the frequency hopping sequence set in the prior art is too complicated, a large amount of software and hardware storage space is needed, and the complexity of operation is greatly increased. The invention comprises a method for generating an aperiodic Hamming related short frequency hopping sequence set. The invention can generate the frequency hopping sequence set only by calculating on the basis of the polynomial, realizes simple algorithm with low complexity, does not need excessive software and hardware storage space, and can greatly reduce software and hardware expenses and cost.
Description
Technical Field
The invention relates to the field of frequency hopping communication, in particular to a method for generating an aperiodic Hamming related short frequency hopping sequence set.
Background
With reference to the introduction of the frequency hopping sequence, the law of carrier frequency hopping can be represented by the frequency hopping sequence, and the purpose of frequency hopping is as follows: interference avoidance, interception prevention, multiple access networking and fading resistance; the aforementioned four frequency hopping communication objectives need to be realized by means of carrier frequency hopping, so a key problem in frequency hopping communication is: and designing a frequency hopping sequence with excellent performance. Frequency hopping to achieve spectrum spreading; when in frequency hopping networking, different frequency hopping sequences are adopted as address codes, and a transmitting end selects a communication object according to the address code of a receiving end. When many users operate in the same frequency band by frequency hopping, the frequency hopping sequence is a unique mark for distinguishing each user.
The prior art definition of maximum aperiodic hamming correlation and the existing method for constructing short sequence sets with excellent aperiodic hamming correlation using cyclic code subcode extraction are presented herein as follows:
definition of aperiodic hamming correlation function: is provided withF={f 1,f 2,...,f q Is a size ofqThe set of frequency slots of (a) is,Sis formed byFOn the upper partMHas a length ofNFor arbitrary frequency hopping sequencesf 1,f 2∈FLet us order
For any two hopping sequencesx=(x 0,x 1,...,x N−1),y=(y 0,y 1,...,y N−1)∈SAnd any integerτ,xAndyat the time ofDelay timeτOf the aperiodic hamming correlation functionH(x,y;τ) Is defined as
Where only positive delays are considered.
For frequency hopping sequenceSMaximum aperiodic Hamming autocorrelationH a (S) Maximum aperiodic Hamming cross-correlationH c (S) Correlation with maximum aperiodic HammingH m (S) Is defined as
For simplicity, let usH a =H a (S)，H c =H c (S)，H m =H m (S)。
The basic definitions related to the methods in the prior art are: GF (q) In order to be a finite field, the method comprises the following steps,qto the power of a prime number, ifqIs prime number 7, i.e. GF: (q) =0, 1,2,3,4,5, 6. Order toqIs the power of a prime number,kis an integer satisfying 1 ≦k≤q-1. Definition of
Definition ofn=q-1 andC RS
wherein the content of the first and second substances,αis GF (q) The generator of (1), thenC RS Is Reed-Solomon code, RS code for short.
Defining cyclic shift operatorsρWhen it is applied to a sequencex=(x 0,x 1,¼,x n−1) When going up, there are
ρx=(x 1,¼,x n−1,x 0)
For any purposex,y∈C RS If for any integerm，x=ρ m yThen, thenxAndyis called asρAnd equivalence.ρIs equivalent toC RS Into different subsets, eachρThe subset of all elements that are equivalent is called a round-robin equivalence class. The number of codewords in an equivalence class is referred to as the cycle length of the equivalence class. Thus, we select an element from each equivalence class and then reassemble all the selected elements into a set, which results inC RS A sub-code of
。
Does not exceed the number of corresponding bit overlaps after cyclic shifting of two different codewordsn−dWhereindIs composed ofC RS Hamming distance of.
The following subset we defineA RS The following were used:
defining:A RS contains all code words satisfying the following conditions
Thus, the device is provided withA RS Each codeword in (a) has a cycle length ofnThen, thenA RS Called full-round equivalence class.
We use (A)N,M,q,H m ) To indicate that one is in the size ofqOn the frequency slot setMHas a sequence lengthNIs selected from the group consisting of frequency hopping sequences of,H m is its maximum aperiodic hamming correlation.
Let Δ (n)=min{s:s|n,s>1} and Ω: (n)=min{t:t|n,t>Δ(n) Means other than 1, respectivelynAnd the second smallest factor.
The following is a description of the prior art based on the above basic definition:
the prior art is the series of frequency hopping sequences under adaptive Hamming correction [ J ] Advances in materials of Communications, Vol.8, No.3, pp.359-373, Aug.2014.
At present, the construction of a short sequence set with excellent aperiodic hamming correlation exists, but the methods are all methods for extracting cyclic code subcodes, the construction method is redundant and tedious, and the required software and hardware storage space is too large, so that the realization is difficult. A typical method for constructing a short sequence set with excellent aperiodic hamming correlation using a cyclic code (using an RS code, which is a relatively simple one of cyclic codes) is as follows:
for any integerk，1≤k<Ω(q-1), we can construct a frequency hopping sequenceS 1The following two cases:
case 1: 1 is less than or equal tok<Δ(q−1)
In this case, first, letn=q−1，A RS As defined above. For a given integerl，l|nAnd 1 is<l≤n−k+1, we have
Wherein all subscript operations are modulonThe following procedures were carried out.
Case 2: Δ (q−1)≤k<Ω(q−1)
In this case, it is preferable that the air conditioner,
as defined above. For a given integerl，l|[n/Δ(n)]And 1 is<l≤n−k+1, we have
And
wherein all subscript operations are modulonThe following procedures were carried out. Get the setQAnd collectionsRThen we can get the hopping sequenceS 1As follows
S 1=Q∪R
Theorem: collectionS 1Is al+k−1,
,q,k-1) a frequency hopping sequence.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the short frequency hopping sequence constructing process in the prior art is too tedious, a large amount of software and hardware storage space is needed, and the operation complexity is greatly increased. The invention provides a generation method of an excellent aperiodic hamming related short frequency hopping sequence set, which solves the problems.
In practical application, the aperiodic Hamming correlation of the short frequency hopping sequence can more accurately measure the performance of the frequency hopping communication system than the periodic Hamming correlation, and the constructed short frequency hopping sequence adopts the aperiodic Hamming correlation to measure the anti-interference performance of the short frequency hopping sequence; the generated short frequency hopping sequence contains a large number of sequences under aperiodic Hamming correlation, and is suitable for the communication system condition that a large number of users share a limited bandwidth.
In order to obtain the short frequency hopping sequence, in the prior art, the RS code is generated by using a polynomial, then the RS code is subjected to equivalent judgment and screening of code words, then the cycle length of the screened code words is judged, and then the code words are classified, on the basis, the classified code words are respectively truncated to construct the short frequency hopping sequence, so that the implementation process is complex in redundancy, a large software and hardware storage space is required, and the algorithm is also high in complexity.
The invention is realized by the following technical scheme:
a method for generating an aperiodic Hamming related short frequency hopping sequence set comprises the following steps:
a plurality of groups of users share one carrier frequency band, a known limited number of frequency slots exist in the carrier frequency band range, and the plurality of groups of users transmit information in the carrier frequency band;
when the number of frequency slots in the carrier frequency band range is a prime number, constructing a short frequency hopping sequence and distributing the short frequency hopping sequence for each group of users: the short frequency hopping sequence carries out frequency band encryption and anti-interference addition on information transmitted by each group of users, specifically, the short frequency hopping sequence carries out frequency shift on information sent by each group of users on a shared carrier frequency band, and the short frequency hopping sequence carries out reverse frequency shift on the information sent by a receiving end of each group of users on the shared carrier frequency band;
frequency slot forming set GF (p) The set GF: (p) A finite field of the number of ranges of carrier waves used for hopping frequency bins,pindicates the number of frequency slots andpis a prime number, set GF: (p) The descending order of elements according to frequency slots is GF: (p) = {0,1,...,p-1, the number of the frequency points of the short hopping sequence is 0, 1.,p－1；
the short frequency hopping sequence of each group of users is as follows:
in the formulamIs an integer and satisfies 1 ≦m≤p−1，f(x) For generating short hopping sequences for carrier hoppingxAs a function of (a) or (b),f(x) =ax m +bx m－1+c m－2 x m－2+ ... +c 1 x+c 0，a,bis two arbitrary values anda,b∈GF(p)，anot equal to 0, coefficientc 0, c 1,...,c m－2∈GF(p)，c 0, c 1,...,c m－2Optionally GF (p) After a value ofc 0, c 1,...,c m－2Generate a relationpIs/are as followsm-1 power combination of formula (I) whereinnIs less than or equal top−mA positive integer of + 1.
The short frequency hopping sequenceSIs provided with
In totaln+m-1 item, the short hopping sequenceSHas a sequence length ofn+m−1。
The short frequency hopping sequenceSThe number of sequences in (a) totals
Is composed ofpIs divided bynAnd take the integer downward.
The short frequency hopping sequenceSHas a frequency slot set size ofpAccording to GF (p) = {0,1,...,p-1, the frequency point of the short hopping sequence has a value range of 0, 1.,p-1 is a wholepAnd (4) frequency points.
The short frequency hopping sequenceSThe maximum aperiodic Hamming correlation of ism−1；
For short frequency hopping sequencesSMaximum aperiodic Hamming autocorrelationH a (S) Maximum aperiodic Hamming cross-correlation for characterizing frequency coincidence parameters between information of each group of users in information transmissionH c (S) Maximum aperiodic Hamming autocorrelation for characterizing frequency coincidence parameters of information between users in information transmission of multiple groups of usersH a (S) Maximum aperiodic hamming cross-correlationH c (S) Correlation with maximum aperiodic HammingH m (S) Is defined as
In the formula (I), the compound is shown in the specification,x=(x 0,x 1, ...,x N−1),y=(y 0,y 1, ...,y N−1) Is composed ofSIn the case of two different sequences of the sequence,τin order to be a time delay,
，
，
，
for arbitraryf 1 , f 2 ∈S，
，aIs composed ofxThe frequency points at the upper part of the frequency band,bis composed ofyThe frequency points at the upper part of the frequency band,
is taken as
，N=n+m-1, the short hopping sequenceSIs/are as follows
。
All operations being modulopIn the following, any operation is divided bypAnd take the remainder.
The invention has the following advantages and beneficial effects:
the method is simple to realizeGenerating the sequence using only functionsf(x) The calculation is complete.
The invention can generate the short frequency hopping sequence only by calculating on the basis of the polynomial, realizes simple algorithm with low complexity, does not need excessive software and hardware storage space, and can greatly reduce the software and hardware expenses and cost.
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 illustrates the generation of short hopping sequences according to the present inventionSA block diagram of (a).
Fig. 2 is a diagram comparing the generation of short hopping sequences according to the present invention with the prior art.
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.
As shown in figure 1 of the drawings, in which,
a method for generating an aperiodic Hamming correlation short frequency hopping sequence set.
In practical application, the aperiodic Hamming correlation of the short frequency hopping sequence can more accurately measure the performance of the frequency hopping communication system than the periodic Hamming correlation, and the constructed short frequency hopping sequence adopts the aperiodic Hamming correlation to measure the anti-interference performance of the short frequency hopping sequence; the generated short frequency hopping sequence contains a large number of sequences under aperiodic Hamming correlation, and is suitable for the communication system condition that a large number of users share a limited bandwidth.
In order to obtain the short frequency hopping sequence, in the prior art, the RS code is generated by using a polynomial, then the RS code is subjected to equivalent judgment and screening of code words, then the cycle length of the screened code words is judged, and then the code words are classified, on the basis, the classified code words are respectively truncated to construct the short frequency hopping sequence, so that the implementation process is complex in redundancy, a large software and hardware storage space is required, and the algorithm is also high in complexity.
The invention is realized by the following technical scheme:
a method for generating an aperiodic Hamming related short frequency hopping sequence set comprises the following steps:
a plurality of groups of users share one carrier frequency band, a known limited number of frequency slots exist in the carrier frequency band range, and the plurality of groups of users transmit information in the carrier frequency band;
when the number of frequency slots in the carrier frequency band range is a prime number, constructing a short frequency hopping sequence and distributing the short frequency hopping sequence for each group of users: the short frequency hopping sequence carries out frequency band encryption and anti-interference addition on information transmitted by each group of users, specifically, the short frequency hopping sequence carries out frequency shift on information sent by each group of users on a shared carrier frequency band, and the short frequency hopping sequence carries out reverse frequency shift on the information sent by a receiving end of each group of users on the shared carrier frequency band;
frequency slot forming set GF (p) The set GF: (p) A finite field of the number of ranges of carrier waves used for hopping frequency bins,pindicates the number of frequency slots andpis a prime number, set GF: (p) The descending order of elements according to frequency slots is GF: (p)={0,1,...,p-1, the number of the frequency points of the short hopping sequence is 0, 1.,p－1；
the short frequency hopping sequence of each group of users is as follows:
in the formulamIs an integer and satisfies 1 ≦m≤p−1，a,bIs two arbitrary values anda,b∈GF(p)，a≠ 0，f(x) For generating short hopping sequences for carrier hoppingxAs a function of (a) or (b),f(x) =ax m +bx m－1+c m－2 x m－2+...+c 1 x+c 0coefficient ofc 0, c 1,...,c m－2∈GF(p)，c 0, c 1,...,c m－2Optionally GF (p) After a value ofc 0, c 1,...,c m－2Generate a relationpIs/are as followsm-1 power combination of formula (I) whereinnIs less than or equal top−mA positive integer of + 1.
The short frequency hopping sequenceSIs provided with
In totaln+m-1 item, the short hopping sequenceSHas a sequence length ofn+m−1。
The short frequency hopping sequenceSThe number of sequences in (a) totals
Is composed ofpIs divided bynAnd take the integer downward.
The short frequency hopping sequenceSHas a frequency slot set size ofpAccording to GF (p) = {0,1,...,p-1, the frequency point of the short hopping sequence has a value range of 0, 1.,p-1 is a wholepAnd (4) frequency points.
The short frequency hopping sequenceSThe maximum aperiodic Hamming correlation of ism−1；
For short frequency hopping sequencesSMaximum aperiodic Hamming autocorrelationH a (S) Maximum aperiodic Hamming cross-correlation for characterizing frequency coincidence parameters between information of each group of users in information transmissionH c (S) Maximum aperiodic Hamming autocorrelation for characterizing frequency coincidence parameters of information between users in information transmission of multiple groups of usersH a (S) Maximum aperiodic hamming cross-correlationH c (S) Correlation with maximum aperiodic HammingH m (S) Is defined as
In the formula (I), the compound is shown in the specification,x=(x 0,x 1, ...,x N−1),y=(y 0,y 1, ...,y N−1) Is composed ofSIn the case of two different sequences of the sequence,τin order to be a time delay,
，
，
，
for arbitraryf 1 , f 2 ∈S，
，aIs composed ofxThe frequency points at the upper part of the frequency band,bis composed ofyThe frequency points at the upper part of the frequency band,
is taken as
，N=n+m-1, the short hopping sequenceSIs/are as follows
。
All operations are performed modulo p, and any operation is divided by p and the remainder is taken.
On the basis of the previous embodiment, the excellent functional effect of the invention is proved from the mathematical aspect, and the proving process is as follows:
obviously, the sequence length, the number of sequences and the size of the frequency slot set are respectivelyIs composed ofn+m−1,
,pWe only need to prove that the maximum aperiodic Hamming correlation ism-1. For time delayn≤τ≤n+mCase of-2, for any
Its aperiodic Hamming correlation is
We discuss 0 ≦ in the followingτ≤n-1 case. For aperiodic Hamming autocorrelation of a sequence, we consider the sequence at delay 0<τ≤n-a condition of 1, wherein,
the aperiodic Hamming autocorrelation of is
According tof(x) Definition of (1), to know
Due to the presence of GF (p) The upper frequency ismThe polynomial of-1 has at mostm1 root, so
Similarly, we can demonstrate that at delay 0 ≦ timeτ≤n-a condition of 1, wherein,
(i≠j) The aperiodic Hamming cross-correlation of
Therefore, it is not only easy to useSThe maximum aperiodic hamming correlation of (a) is m-1.
After the syndrome is confirmed.
In one embodiment, p =7, n =3, m =3, a =1, and b =0 are selected, and then the polynomial equation is passed
Generating short frequency hopping sequences
The following were used:
......
......
......
it can be verified by applying the present invention that the sequence set is a (5, 98, 7, 2) short hopping sequence. The method directly adopts a polynomial
The generation and implementation method is simple, and the required software and hardware storage space and the operation complexity are small.
On the basis of the previous embodiment, the short hopping sequence generation is compared with the method of the present invention, and the comparison result is as follows:
the prior art is as follows: using the prior art, as shown in fig. 2, q =7 is chosen,l=3, k =3, a (5,114, 7, 2) short hopping sequence can be obtained.
The invention comprises the following steps: with the present invention, as shown in fig. 2, selecting p =7, n =3, m =3, a =1, and b =0, a (5, 98, 7, 2) short frequency hopping sequence can be obtained.
It can be seen that although the prior art has 114-98 = 16 more sequences than the present invention, the implementation is very complex. In order to obtain the short frequency hopping sequence, in the prior art, the RS code is generated by using a polynomial, then the RS code is subjected to equivalent judgment and screening of code words, then the cycle length of the screened code words is judged, and then the code words are classified, on the basis, the classified code words are respectively truncated to construct the short frequency hopping sequence, so that the implementation process is complex in redundancy, a large software and hardware storage space is required, and the algorithm is also high in complexity.
The invention can generate the short frequency hopping sequence only by calculating on the basis of the polynomial, realizes simple algorithm with low complexity, does not need excessive software and hardware storage space, and can greatly reduce software and hardware expenses and cost.
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.
Claims (5)
1. A method for generating an aperiodic Hamming related short frequency hopping sequence set is characterized in that:
a plurality of groups of users share one carrier frequency band, a known limited number of frequency slots exist in the carrier frequency band range, and the plurality of groups of users transmit information in the carrier frequency band;
when the number of frequency slots in the carrier frequency band range is a prime number, constructing a short frequency hopping sequence and distributing the short frequency hopping sequence for each group of users: the short frequency hopping sequence carries out frequency band encryption and anti-interference addition on information transmitted by each group of users, specifically, the short frequency hopping sequence carries out frequency shift on information sent by each group of users on a shared carrier frequency band, and the short frequency hopping sequence carries out reverse frequency shift on the information sent by a receiving end of each group of users on the shared carrier frequency band;
frequency slot forming set GF (p) The set GF: (p) A finite field of the number of ranges of carrier waves used for hopping frequency bins,pindicates the number of frequency slots andpis a prime number, set GF: (p) Push buttonThe value range of the element of the irradiation gap is GF (p) = {0,1,...,p-1 }, which is the value range of the frequency points of the short hopping sequence, the value number of the frequency points isp；
The short hopping sequence for each group of users is:
in the formulamIs an integer and satisfies 1 ≦m≤p−1，f(x) For generating short hopping sequences for carrier hoppingxAs a function of (a) or (b),f(x) =ax m +bx m－1+c m－2 x m－2+...+c 1 x+c 0，a,bis two arbitrary values anda,b∈GF(p)，anot equal to 0, coefficientc 0, c 1,...,c m－2∈GF(p)，c 0, c 1,...,c m－2Optionally GF (p) The value of (1) is (b),c 0, c 1,...,c m－2generate a relationpIs/are as followsm-1 power combination of formula (I) whereinnIs less than or equal top−mA positive integer of + 1.
2. The method of claim 1, wherein the short hopping sequence set is generated according to aperiodic Hamming correlation short hopping sequence setSIs provided with
In totaln+m-1 item, the short hopping sequenceSHas a sequence length ofn+m−1。
3. The method of claim 1, wherein the short hopping sequence set is generated according to aperiodic Hamming correlation short hopping sequence setSThe number of sequences in (a) totals
Is composed ofpIs divided bynAnd take the integer downward.
4. The method of claim 1, wherein the short hopping sequence set is generated according to aperiodic Hamming correlation short hopping sequence setSHas a frequency slot set size ofpAccording to GF (p) = {0,1,...,p-1, the frequency point of the short hopping sequence has a value range of 0, 1.,p-1 is a wholepAnd (4) frequency points.
5. The method of claim 1, wherein the short hopping sequence set is generated according to aperiodic Hamming correlation short hopping sequence setSThe maximum aperiodic Hamming correlation of ism−1；
For short frequency hopping sequencesSMaximum aperiodic Hamming autocorrelationH a (S) Maximum aperiodic Hamming cross-correlation for characterizing frequency coincidence parameters between information of each group of users in information transmissionH c (S) Maximum aperiodic Hamming autocorrelation for characterizing frequency coincidence parameters of information between users in information transmission of multiple groups of usersH a (S) Maximum aperiodic hamming cross-correlationH c (S) Correlation with maximum aperiodic HammingH m (S) Is defined as
In the formula (I), the compound is shown in the specification,x=(x 0,x 1, ...,x N−1),y=(y 0,y 1, ...,y N−1) Is composed ofSIn the case of two different sequences of the sequence,τin order to be a time delay,
，
，
，
for arbitraryf 1 , f 2 ∈S，
，aIs composed ofxThe frequency points at the upper part of the frequency band,bis composed ofyThe frequency points at the upper part of the frequency band,
is taken as
，N=n+m-1, the short hopping sequenceSIs/are as follows
。
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