CN114726402B - Anonymous frequency hopping sequence design method suitable for multi-antenna cognitive wireless network - Google Patents

Anonymous frequency hopping sequence design method suitable for multi-antenna cognitive wireless network Download PDF

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CN114726402B
CN114726402B CN202210354623.3A CN202210354623A CN114726402B CN 114726402 B CN114726402 B CN 114726402B CN 202210354623 A CN202210354623 A CN 202210354623A CN 114726402 B CN114726402 B CN 114726402B
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刘仁婷
谭雪松
甄云志
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University of Electronic Science and Technology of China
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Abstract

The invention belongs to the technical field of communication, and particularly relates to an asynchronous frequency hopping sequence design method suitable for a multi-antenna cognitive wireless network. The invention aims to design a distributed control cognitive radio network for clock asynchronization and antenna isomerismAn anonymous frequency hopping sequence generation method suitable for control information interaction ensures that two cognitive nodes with different local available channel sets and configured with different antenna numbers can realize frequency hopping convergence on all public available channels of the two cognitive nodes under any frequency hopping starting time difference, provides backward compatible frequency hopping convergence capacity with a single-antenna cognitive node for a multi-antenna cognitive node, and can realize the effect of being better than a theoretical upper limit O (N) under the condition that the number of the local available channels is far less than the total number N of the accessible channels of a cognitive wireless network 2 ) The MTTR value of the wireless sensor network, so that the anonymous control information interaction performance of any two antennas and the available channel heterogeneous cognitive node is effectively improved.

Description

Anonymous frequency hopping sequence design method suitable for multi-antenna cognitive wireless network
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a control information interaction mechanism design based on frequency hopping, which is suitable for a wireless communication network.
Background
Cognitive wireless networks are typically made up of a set of network communication nodes that do not have legally licensed spectrum resources. On the premise of ensuring that authorized users do not interfere with legal communication, the cognitive radio network nodes need to flexibly access to a proper authorized communication frequency band to complete the communication function among the nodes. In a cognitive wireless network based on distributed control, different physical locations of different cognitive nodes and different spectrum sensing capabilities of the different cognitive nodes cause different sets of available communication bands (or channels) sensed locally by the different cognitive nodes, thereby causing difficulty in selecting the communication bands among the different cognitive nodes. Therefore, each cognitive node needs to quickly find channels available for all the neighbor nodes in all locally available channels based on a proper frequency hopping mechanism, so that aggregation is realized, and an efficient and reliable frequency band basis is provided for interaction of various types of control information including frequency spectrum sensing results, clock information, node numbering, handshake negotiation and the like.
Specifically, in the arrangement of R A Cognitive node A and configured R of root antenna B In the process of realizing frequency hopping convergence among cognitive node Bs of a root antenna, at least one antenna of a node A and at least one antenna configured by the node B can establish communication and interaction control information only when the at least one antenna and the at least one antenna are switched to the same channel in the same time slot, wherein R A Not less than 1 and R B Not less than 1. Therefore, a frequency hopping sequence set composed of R frequency hopping sequences needs to be generated for each cognitive node with R antennas to respectively guide the frequency hopping process of the R antennas, so as to improve the control information interaction performance between adjacent nodes as much as possible. Generally, the performance parameters for measuring the goodness of a frequency hopping sequence set generation method include:
aggregation Degree (DoR), that is, the total number of channels that can be aggregated by any two cognitive nodes according to the frequency hopping sequence set generated by the method. Generally, the maximization of the convergence can effectively improve the anti-interference performance of the control information interaction of the cognitive radio network.
A Maximum aggregation time interval (MTTR for short), which is a Maximum time interval from when any two cognitive nodes start frequency hopping to when they realize aggregation for the first time when the frequency hopping sequence set generated by the method is adopted by any two cognitive nodes. When the MTTR value is smaller, the longest time delay for realizing aggregation of the two cognitive nodes is smaller, and the control information interaction performance between the two cognitive nodes is better.
Because different wireless communication devices are usually configured with different numbers of antennas at present, it is necessary to design a frequency hopping sequence generation algorithm capable of ensuring convergence for two cognitive nodes with different numbers of antennas. Particularly, when the frequency hopping sequence generation method adopted by the cognitive node has the backward compatibility (that is, the cognitive node supports a multi-antenna cognitive node and a single-antenna cognitive node to realize frequency hopping convergence on a common available channel), the flexibility and the application range of the cognitive node with any two antennas in a heterogeneous structure to realize frequency hopping convergence are effectively guaranteed.
In addition, the existing frequency hopping sequence aggregation method generally adopts two modes, namely anonymity and non-anonymity. The non-anonymous generation method needs unique addressing (such as 48-bit MAC address) of each cognitive node and proper expansion of each symbol in the addressing to generate the frequency hopping sequence set of the node, and the anonymous generation method does not need to use addressing information of the cognitive node to generate the frequency hopping sequence set of the node at all. Because the MTTR of the frequency hopping sequence set generated based on the non-anonymous mode is correspondingly increased along with the increase of the scale of network nodes and the increase of the addressing length required by the nodes, and the frequency hopping sequence set is easy to be subjected to security defects such as malicious node addressing analysis, monitoring and attack, the frequency hopping sequence set generated based on the non-anonymous mode is generally safer, and better frequency hopping convergence performance can be obtained under the condition that the scale of the cognitive wireless network is increased.
However, although the existing frequency hopping convergence algorithm can support any two cognitive nodes to realize anonymous convergence on any N different channels, the MTTR of the algorithm is O (N) when the number N of convergence channels increases 2 ) Increases, resulting in poor frequency hopping convergence performance. To compensate for this deficiency, each cognitive node a may pass N, which is only locally perceived a The frequency hopping mode on the available channels avoids the waste of time resources caused by accessing the local unavailable channels, thereby the number N of the local available channels can be used a The theoretical upper limit value of the realization is O (N) better than MTTR under the condition of being far less than the total number N of the accessible channels of the cognitive wireless network 2 ) Anonymous frequency hopping convergence performance.
Disclosure of Invention
The invention aims to design an anonymous frequency hopping sequence generation method suitable for control information interaction for a distributed control cognitive radio network with asynchronous clock and heterogeneous antennas, ensure that two cognitive nodes with different local available channel sets and different antenna numbers can realize frequency hopping convergence on all public available channels of the two cognitive nodes under any frequency hopping starting time difference, provide frequency hopping convergence capacity backward compatible with a single-antenna cognitive node for a multi-antenna cognitive node, and realize the effect of being superior to a theoretical upper limit O (N) under the condition that the number of the local available channels is far less than the total number N of accessible channels of a cognitive radio network 2 ) The MTTR value of the wireless sensor network, so that the anonymous control information interaction performance of any two antennas and the available channel heterogeneous cognitive node is effectively improved.
For the purpose of illustrating and understanding the technical solutions of the present invention, the basic concepts and principles involved in the present invention will be briefly described as follows:
definitions 1 if set Z n One k element subset a = {0,1, …, n-1} 0 ,a 1 ,…,a k-1 Satisfies the condition that for any non-zero integer d ∈ Z n Each having at least one ordered pair of elements (a) i ,a j ) Satisfies a i ∈A，a j E A and d = a i -a j modulo n, then set A is referred to as an (n, k) -relaxation cycle difference set or simply (n, k) -DS, where Z is n Representing the set of all integers modulo n.
Definition 2. For a set of k elements
Figure BDA0003582352930000031
The execution distance is r epsilon [0,n-1]Can result in a set of k elements, i.e.
Figure BDA0003582352930000032
Figure BDA0003582352930000033
For any n ≧ 2, (n, k) -DS always exists, and two corollaries hold as follows:
inference 1. If a set of k elements
Figure BDA0003582352930000034
Is (n, k) -DS, then its rotating set
Figure BDA0003582352930000035
Is also an (n, k) -DS.
Inference 2 for (n, k) -DS A
Figure BDA0003582352930000036
r j ∈[0,n-1]This is true.
Definition 3. If a Mk element set
Figure BDA0003582352930000037
Can be divided into M mutually disjoint(n, k) -DS, then the set U is referred to as an M-dimensional disjoint (n, k) -difference set combination or simply an (M, n, k) -UDDS.
Inference 3. If a set of Mk elements
Figure BDA0003582352930000038
Is an (M, n, k) -UDDS, then the set ROT (U, i)
Figure BDA0003582352930000039
Also constitute a (M, n, k) -UDDS.
Definitions 4 if one (3,15,5) -UDDSU (I) Can be divided into 3 mutually disjoint (15,5) -DSs
Figure BDA00035823529300000310
Figure BDA00035823529300000311
And
Figure BDA00035823529300000312
and satisfy
Figure BDA00035823529300000313
r∈[1,14]Then the UDDS is referred to as a first class (3,15,5) -UDDS.
Definitions 5. For a given (15,5) -DS that can be partitioned into 3 disjoint groups
Figure BDA00035823529300000314
And
Figure BDA00035823529300000315
of the first class (3,15,5) -UDDSU (I) If there is one (15,5) -DS which can be divided into 3 mutually disjoint
Figure BDA00035823529300000316
And
Figure BDA00035823529300000317
and satisfies the conditions
Figure BDA00035823529300000318
(3,15,5) -UDDS
Figure BDA00035823529300000319
Then the UDDS is called an AND U (I) The associated second class (3,15,5) -UDDSs. Further, for any two different ones of U and U (I) Associated second class (3,15,5) -UDDS
Figure BDA0003582352930000041
And
Figure BDA0003582352930000042
to say that they need to be satisfied
Figure BDA0003582352930000043
For example, because
Figure BDA0003582352930000044
So 3 mutually exclusive (15,5) -DSUs 0 ＝{0,8,9,10,11},U 1 = {1,2,4,7,12} and U 2 (3,15,5) -UDDSU constituted by = {3,5,6,13,14} is not a first class (3,15,5) -UDDS. On the other hand, the system consists of 3 mutually exclusive (15,5) -DSs
Figure BDA0003582352930000045
Figure BDA0003582352930000046
And
Figure BDA0003582352930000047
formed (3,15,5) -UDDS
Figure BDA0003582352930000048
Satisfy the requirement of
Figure BDA0003582352930000049
Figure BDA00035823529300000410
r∈[1,14]Thus, a first class (3,15,5) -UDDS is formed. In addition, the first (3,15,5) -UDDS
Figure BDA00035823529300000411
The associated 12 second classes (3,15,5) -UDDS can be represented as
Figure BDA00035823529300000412
Wherein
Figure BDA00035823529300000413
Can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000414
Figure BDA00035823529300000415
And
Figure BDA00035823529300000416
Figure BDA00035823529300000417
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000418
And
Figure BDA00035823529300000419
Figure BDA00035823529300000420
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000421
And
Figure BDA00035823529300000422
Figure BDA00035823529300000423
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000424
Figure BDA00035823529300000425
And
Figure BDA00035823529300000426
Figure BDA00035823529300000427
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000428
And
Figure BDA00035823529300000429
Figure BDA00035823529300000430
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000431
And
Figure BDA00035823529300000432
Figure BDA00035823529300000433
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000434
Figure BDA00035823529300000435
And
Figure BDA00035823529300000436
Figure BDA00035823529300000437
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000438
And
Figure BDA00035823529300000439
Figure BDA00035823529300000440
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000441
And
Figure BDA00035823529300000442
Figure BDA00035823529300000443
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000444
Figure BDA00035823529300000445
And
Figure BDA00035823529300000446
Figure BDA00035823529300000447
can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA00035823529300000448
And
Figure BDA00035823529300000449
Figure BDA0003582352930000051
can be divided into 3 mutually disjoint (15,5)-DS
Figure BDA0003582352930000052
Figure BDA0003582352930000053
and
Figure BDA0003582352930000054
the technical scheme of the invention is as follows:
for a cognitive wireless network with the total number of the accessible channels being N, each cognitive wireless network is provided with any N a An available channel
Figure BDA0003582352930000055
And R a Cognitive node CU of root antenna a Wherein
Figure BDA0003582352930000056
Figure BDA0003582352930000057
R a Not less than 1 and N a ≥3R a Can be based on the following steps for R thereof a The root antenna generates different periodic frequency hopping sequences respectively:
s1, cognitive node CU a R of (A) to (B) a The serial numbers of the root antennas are 0,1,2, … and R a -1。
S2, cognitive node CU a N of (A) a The available channels are divided into R satisfying the following conditions a One channel group:
each channel group i e [0,p-1]For a set V comprising G channels a,i ＝{v a,iG ,v a,iG+1 ,…,v a,(i+1)G-1 Where p = N a modulo R a And
Figure BDA0003582352930000058
and each channel group j ∈ [ p, R a -1]For a set V comprising H channels a,j ＝{v a,p(G-H)+jH ,v a,p(G-H)+jH+1 ,…,v a,p(G-H)+(j+1)H-1 Therein of
Figure BDA0003582352930000059
S3, initializing cognitive node CU a The antenna number of (d) is r =0.
S4, initializing the periodic frequency hopping sequence of the antenna r as
Figure BDA00035823529300000510
S5, initializing a frequency hopping sequence RS a,r Frame number of (d) is i =0.
S6, initializing set W r,i ＝V a,r \{V a,r [i]In which V is a,r [i]Representative set V a,r The i +1 th channel number in (1).
S7, initializing a frequency hopping sequence RS a,r The subframe number of frame i of (1) is j =0.
S8, if (| V) a,r 1) cannot be divisible by 2 and
Figure BDA00035823529300000511
then set V is initialized r,i,j ＝{V a,r [i],W r,i [0],W r,i [|V a,r |-2]}; otherwise, set V is initialized r,i,j ＝{V a,r [i],W r,i [|V a,r |-3-2j],W r,i [|V a,r |-2-2j]}. Here W r,i [j]Representative set W r,i The j +1 th channel number in (1).
S9, collecting the set V r,i,j Is rearranged in order from small to large so that V r,i,j [0]<V r,i,j [1]<V r,i,j [2]And is provided with u a,0 ＝V r,i,j [0]，u a,1 ＝V r,i,j [1]And u and a,2 ＝V r,i,j [2]。
s10, adopting the following 8 steps based on 3 available channels u a,0 ,u a,1 And u a,2 Generate a length of
Figure BDA0003582352930000061
Frequency hopping sequence T of one time slot a,r,i,j ：
S10.1, numbering each available channel u a,h Represented as a binary sequence u a,h [0]u a,h [1]…u a,h [l 1 -1]Wherein
Figure BDA0003582352930000062
h∈[0,2]And u and a,h [0]and u a,h [l 1 -1]Representing the highest and lowest weighted bits in the binary sequence, respectively.
S10.2, find u a,0 [L a ]＝u a,1 [L a ]≠u a,2 [L a ]Or u a,0 [L a ]≠u a,1 [L a ]＝u a,2 [L a ]Smallest integer of L a And mixing L a Expressed as an eleven-ary sequence L a [0]L a [1]…L a [l 2 -1]Wherein L is a ∈[0,l 1 -1]And
Figure BDA0003582352930000063
s10.3, if u a,0 [L a ]＝u a,1 [L a ]≠u a,2 [L a ]Then further find u a,0 [M a ]≠u a,1 [M a ]Smallest integer M of true a And M is a Expressed as an eleven-ary sequence M a [0]M a [1]…M a [l 2 -1]Then generate a 2l 2 +1 element sequence D a ＝{11,L a [0],L a [1],…,L a [l 2 -1],M a [0],M a [1],…,M a [l 2 -1]}; if u is a,0 [L a ]≠u a,1 [L a ]＝u a,2 [L a ]Then further find u a,1 [M a ]≠u a,2 [M a ]Minimum integer of true M a And M is a Expressed as an eleven-ary sequence M a [0]M a [1]…M a [l 2 -1]Then generate a 2l 2 +1 element sequence D a ＝{11,M a [0],M a [1],…,M a [l 2 -1],L a [0],L a [1],…,L a [l 2 -1]In which M is a ∈[0,l 1 -1]。
S10.4 UDDS based on the first class (3,15,5)
Figure BDA0003582352930000064
An available channel u is generated as follows a,0 ,u a,1 And u a,2 Up-hopped 15-slot periodic frequency hopping sequence S a,* ：
In each 15-slot period, the hopping sequence S a,* Need to be in each time slot
Figure BDA0003582352930000065
Internally switching to an available channel u a,h Where h e [0,2]。
S10.5, based on
Figure BDA0003582352930000066
Associated with each second class (3,15,5) -UDDS
Figure BDA0003582352930000067
Wherein g is from [0,11 ∈ [ ]]Generating a channel u in 3 available channels by using the following method a,0 ,u a,1 And u a,2 Up-hopped 15-slot periodic frequency hopping sequence S a,g ：
In each 15-slot period, the hopping sequence S a,g Need to be in each time slot
Figure BDA0003582352930000068
Internally handing over to channel u a,h Where g e [0,11]And h e [0,2]。
S10.6, initialization
Figure BDA0003582352930000069
And k =0.
S10.7, update
Figure BDA0003582352930000071
Wherein D a [k]Represents sequence D a The (k + 1) th element and the symbol | | | in (b) represent the concatenation of two hopping sequences.
S10.8, if k<2l 2 Then k = k +1 is updated and S10.7 is returned; otherwise, jump to S11.
S11, updating RS a,r ＝RS a,r ||T a,r,i,j 。
S12, if
Figure BDA0003582352930000072
Then j = j +1 is updated and S8 is returned; otherwise, jump to S13.
S13, if i<|V a,r I-1, then i = i +1 is updated and S6 is returned; otherwise, jump to S14.
S14, if r<R a -1, then update r = r +1 and return to S4; otherwise, ending the algorithm execution and outputting the hopping sequence
Figure BDA0003582352930000073
The invention has the beneficial effects that:
according to definition 4 and definition 5, when two are each provided with N a An available channel
Figure BDA0003582352930000074
And N b An available channel
Figure BDA0003582352930000075
Cognitive node CU a And CU b In case of starting frequency hopping at the same time, they are based on the first class (3,15,5) -UDDS
Figure BDA0003582352930000076
Respectively generated 30-slot periodic frequency hopping sequence S a,* ||S a,* And S b,* ||S b,* Can realize (u) a,0 ,u b,0 ),(u a,1 ,u b,1 ) And (u) a,2 ,u b,2 ) Convergence between equal 3 channel pairs, and CU a And CU b Based on the second class (3,15,5) -UDDS
Figure BDA0003582352930000077
And
Figure BDA0003582352930000078
wherein g is 1 ≠g 2 ,g 1 ∈[0,10]And g 2 ∈[0,10]Respectively generated 15-slot periodic frequency hopping sequences
Figure BDA0003582352930000079
And
Figure BDA00035823529300000710
can realize (u) a,0 ,u b,1 ),(u a,0 ,u b,2 ),(u a,1 ,u b,0 ),(u a,1 ,u b,2 ),(u a,2 ,u b,0 ) And (u) a,2 ,u b,1 ) And 6 channel pairs. On the other hand, when two cognitive nodes CU a And CU b In the case of starting the frequency hopping at any different time, they are based on the first class (3,15,5) -UDDS
Figure BDA00035823529300000711
Respectively generated 30-slot periodic frequency hopping sequence S a,* ||S a,* And S b,* ||S b,* All 9 channel pairs described above can be implemented (i.e., (u) a,i ,u b,j )
Figure BDA00035823529300000712
Figure BDA00035823529300000713
) To each other. Therefore, CU a And CU b Respectively generated 45-slot periodic frequency hopping sequences
Figure BDA00035823529300000714
And
Figure BDA00035823529300000715
the frequency hopping convergence among all the 9 channel pairs can be realized under any frequency hopping starting time difference, wherein g 1 ≠g 2 And g 1 ,g 2 ∈[0,11]. Based on this fact, when R a Antenna cognitive node CU a And R b Antenna cognitive node CU b Having at least one common available channel v a,x ＝v b,y In time, no matter how big the difference of the frequency hopping starting time of the two cognitive nodes is, the former accesses to the channel v a,x Of (a) an antenna r a,x With the latter accessing the channel v b,y Of (a) an antenna r b,y Can always be at
Figure BDA0003582352930000081
Frequency hopping convergence on the common available channel is achieved within a time slot.
Therefore, in a cognitive wireless network with the total number of accessible channels being N, if one has N a R of locally available channel a Antenna cognitive node CU a And one has N b R of locally available channel b Antenna cognitive node CU b There are at least 1 common available channel in between, then the invention can support them to implement frequency hopping convergence on all their C common available channels with arbitrary frequency hopping start time difference, where C e [1, min pocket n a ,N b }]And ensure that their maximum time interval from the start of frequency hopping to the first time hopping convergence is no greater than the MTTR
Figure BDA0003582352930000082
And a time slot. Since the theoretical upper limit of MTTR is
Figure BDA0003582352930000083
Therefore, the invention is particularly suitable for cognitive nodes CU a Number of locally available channels N a And cognitive node CU b Number of locally available channels N b All are far less than the total number N of accessible channels of the cognitive radio networkThe theoretical upper limit value of the realization of the MTTR under the condition is O (N) 2 ) The convergence performance of the existing anonymous frequency hopping algorithm.
On the other hand, there is an anonymous frequency hopping convergence algorithm of the same type, i.e. document [1 ]]MTP and document [2 ]]EE and document [3 ]]The theoretical upper limit values of MTTR for algorithms 3-5 are respectively
Figure BDA0003582352930000084
Figure BDA0003582352930000085
And
Figure BDA0003582352930000086
thus, at R a And R b Under given conditions, the method can always ensure that the total number N of the accessible channels of the cognitive wireless network is large enough or two cognitive nodes CU a And CU b Number of locally available channels N a And N b Less than that of the document [1 ] is obtained without much difference]MTP, reference of "Z.Gu, H.Pu, Q. -S.Hua, and F.C.M.Lau," Improved rendered less volatile alloys for heterologous radioactive networks, "in Proc.IEEE INFOCOM,2015, pp.154-162" [2 ]]EE and literature [3 ] of "Y. -C.Chang, C. -S.Chang, and J. -P.Sheu," An enhanced fast multi-radio rendering equivalent in heterologous radio networks, "IEEE trans.Cogn.Commun.Net.4, no.4, pp.847-859, december 2018]Deng Meijun, research on heterogeneous cognitive radio network frequency hopping blind convergence technology, university of electronic technology, university of Master graduate, 2021, 6 months, "MTTR theoretical upper limit of algorithm 3-5.
In addition, the present invention can also sufficiently support two cognitive nodes configured with any number of antennas to realize frequency hopping convergence, and has an existing Multiple-antenna anonymous frequency hopping algorithm (for example, documents [4] "l.yu, h.liu, y.leung, x.chu, and z.lin," Multiple radios for fast rendezvous in cognitive radio networks, "IEEE trans.mobile com, vol.14, no.9, pp.1917-1931, september 2015," and [5] "j.p.sheu and j." j.lin, "a Multiple-radio rendezvous in cognitive radio networks, complete on chip transceiver for the same antenna in cognitive radios) so as to provide an effective convergence capability for the two cognitive nodes, i.e., a single-antenna compatible with a common cognitive convergence capability, thereby providing a single-frequency hopping convergence capability for the two cognitive nodes (1990, 1990-1980) to realize the wireless network.
Finally, the frequency hopping sequence generated for each cognitive node is completely irrelevant to the addressing of the node, and the frequency hopping convergence capability based on an anonymous mode can be provided for any two cognitive nodes with at least 1 public available channel, so that the safety of control information interaction is effectively improved.
Drawings
Fig. 1 shows a cognitive node CU in a cognitive wireless network, where N =512 represents the total number of accessible channels a And CU b 3 and 1 antennas are configured respectively, the available channel number sets are {58,232,138,313,421,25,97,70,145,113,37,79,180,326,245} and {25,77,138,325,421,490} respectively, and the cognitive node CU is connected to the base station a Prior to cognitive node CU b Under the condition that the frequency hopping starts at exactly 5 time slots, the cognitive node CU a 3-antenna frequency hopping sequence set and cognitive node CU generated based on method b The convergence diagram of the single-antenna frequency hopping sequence generated based on the invention. Each double arrow in the figure represents a cognitive node CU a And CU b One frequency hopping aggregation on a common available channel.
FIG. 2 shows that when the cognitive radio network has N accessible channels 0,1, …, N-1, the cognitive node CU with single antenna a Has the locally available channel number of 1,2, …,0.5N, and a single-antenna cognitive node CU b Are numbered 0.1N,0.1N +1, …,0.6N, they are according to the present invention, document [1 ]]And document [2 ]]And document [3 ]]And (3) a simulation comparison graph of the maximum convergence time interval (namely MTTR) obtained by the four anonymous single-antenna frequency hopping convergence algorithms and the variation of the total number N of the accessible channels of the cognitive radio network.
FIG. 3 shows a cognitive node CU configured with 2 antennas when the cognitive wireless network has N accessible channels with numbers 0,1, …, N-1 a The number of the local available channel is 0.3N,0.3N +1, …,0.7N, and the cognitive node CU is configured with 5 antennas b Are numbered 0.4N,0.4N +1, …,0.6N, they are in accordance with the present invention and document [2 ]]And (3) a simulation comparison graph of the maximum convergence time interval (namely MTTR) obtained by the two anonymous antenna heterogeneous frequency hopping convergence algorithms along with the total number N of the accessible channels of the cognitive radio network.
Detailed Description
The technical scheme of the invention is described in detail in the following with reference to the accompanying drawings and embodiments:
examples
Given the total number of accessible channels in the cognitive radio network as N =512, cognitive nodes CU a The method is characterized in that 3 antennas are configured, an available channel number set {58,232,138,313,421,25,97,70,145,113,37,79,180,326,245} is provided, and the method is adopted to serve as a cognitive node CU a Generating a hopping sequence set comprising 3 hopping sequences:
s1, cognitive node CU a The 3 antennas of (2) are sequentially numbered 0,1,2.
S2, cognitive node CU a Is divided into 3 channel groups V a,0 ＝{58,232,138,313,421}，V a,1 = {25,97,70,145,113}, and V a,2 = {37,79,180,326,245}, such that antennas 0,1 and 2 are in channel group V, respectively a,0 ,V a,1 And V a,2 And (4) up frequency hopping.
S3, initializing cognitive node CU a The antenna number of (d) is r =0.
S4, initializing periodic hopping sequence of antenna r =0 as
Figure BDA0003582352930000101
S5, initializing a frequency hopping sequence RS a,0 Frame number of (d) is i =0.
S6, initializing set W r,i ＝W 0,0 ＝V a,0 \{V a,0 [0]} = {232,138,313,421}, where V a,0 [0]Representative set V a,0 The 1 st channel number in (1), i.e., 58.
S7, initializing a frequency hopping sequence RS a,0 The subframe number of frame 0 of (2) is j =0.
S8, if (| V) a,r 1) cannot be divisible by 2 and
Figure BDA0003582352930000102
then set V is initialized r,i,j ＝{V a,r [i],W r,i [0],W r,i [|V a,r |-2]}; otherwise, set V is initialized r,i,j ＝{V a,r [i],W r,i [|V a,r |-3-2j],W r,i [|V a,r |-2-2j]}。
At this time, | V a,0 I-1=4 is divisible by 2 and
Figure BDA0003582352930000103
thus initializing set V 0,0,0 ＝{V a,0 [0],W 0,0 [|V a,0 |-3],W 0,0 [|V a,0 |-2]}＝{58,313,421}。
S9, collecting the set V 0,0,0 Is rearranged in order from small to large so that V 0,0,0 [0]<V 0,0,0 [1]<V 0,0,0 [2]Thereby obtaining an updated V 0,0,0 Is {58,313,421}, and u is set a,0 ＝V 0,0,0 [0]＝58，u a,1 ＝V 0,0,0 [1]＝313,u a,2 ＝V 0,0,0 [2]＝421。
S10, adopting the following steps based on 3 available channels u a,0 ,u a,1 And u a,2 Generate a length of
Figure BDA0003582352930000111
Frequency hopping sequence T of one time slot a,0,0,0 ：
S10.1, numbering each available channel u a,h Expressed as a length of
Figure BDA0003582352930000112
Binary sequence u of a,h [0]u a,h [1]…u a,h [8]Wherein h is [0,2 ]]And u is a,h [0]And u a,h [8]Representing the bits with the highest and lowest weights in the binary sequence, respectively.
At this time, u is due to a,0 ＝58，u a,1 =313, and u a,2 =421, therefore there is u a,0 ＝000111010，u a,1 =100111001, and u a,2 ＝110100101。
S10.2, find u a,0 [L a ]＝u a,1 [L a ]≠u a,2 [L a ]Or u a,0 [L a ]≠u a,1 [L a ]＝u a,2 [L a ]Smallest integer of L a And mixing L a Expressed as an eleven-ary sequence L a [0]L a [1]…L a [l 2 -1]Wherein L is a ∈[0,l 1 -1]And
Figure BDA0003582352930000113
at this time, 0=u is due to a,0 [0]≠u a,1 [0]＝u a,2 [0]=1, therefore set L a =0, and mixing L a Is expressed as a length of
Figure BDA0003582352930000114
Eleven system sequence L a [0]＝0。
S10.3, if u a,0 [L a ]＝u a,1 [L a ]≠u a,2 [L a ]Then further find u a,0 [M a ]≠u a,1 [M a ]Minimum integer of true M a And M is a Expressed as an eleven-ary sequence M a [0]M a [1]…M a [l 2 -1]Then generate a 2l 2 +1 element sequence D a ＝{11,L a [0],L a [1],…,L a [l 2 -1],M a [0],M a [1],…,M a [l 2 -1]}; if u is a,0 [L a ]≠u a,1 [L a ]＝u a,2 [L a ]Then further find u a,1 [M a ]≠u a,2 [M a ]Minimum integer of true M a Will M a Expressed as an eleven-ary sequence M a [0]M a [1]…M a [l 2 -1]Then generate a 2l 2 +1 element sequence D a ＝{11,M a [0],M a [1],…,M a [l 2 -1],L a [0],L a [1],…,L a [l 2 -1]In which M is a ∈[0,l 1 -1]。
At this time, u is due to a,0 [L a ]≠u a,1 [L a ]＝u a,2 [L a ]And l 2 =1, therefore further finding u a,0 [M a ]≠u a,1 [M a ]Smallest integer M of true a =1, mixing M a =1 representing a length l 2 Eleven-system sequence M of =1 a [0]=1 and generates one 2l 2 +1=3 element sequence D a ＝{11,1,0}。
S10.4 UDDS based on first class (3,15,5)
Figure BDA0003582352930000115
An available channel u is generated as follows a,0 ,u a,1 And u a,2 Up-hopped 15-slot periodic frequency hopping sequence S a,* ：
In each 15-slot period, the hopping sequence S a,* Need to be in each time slot
Figure BDA0003582352930000121
Internally switching to an available channel u a,h Where h e [0,2]。
At this time, since the first class (3,15,5) -UDDS
Figure BDA0003582352930000122
Can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA0003582352930000123
And
Figure BDA0003582352930000124
thus having S a,* ＝{313,421,313,58,313,58,58,421,421,58,58,421,313,313,421}。
S10.5, based on
Figure BDA0003582352930000125
Associated with each second class (3,15,5) -UDDS
Figure BDA0003582352930000126
Wherein g is from [0,11 ∈ [ ]]Generating a channel u in 3 available channels by using the following method a,0 ,u a,1 And u a,2 Up-hopped 15-slot periodic frequency hopping sequence S a,g ：
In each 15-slot period, the hopping sequence S a,g Need to be in each time slot
Figure BDA0003582352930000127
Internal handover to channel u a,h Where g e [0,11]And h e [0,2]。
At this time, according to the first class (3,15,5) -UDDS
Figure BDA0003582352930000128
Associated 3 second classes (3,15,5) -UDDS
Figure BDA0003582352930000129
Figure BDA00035823529300001210
And
Figure BDA00035823529300001211
can be defined as S a,0 ＝{58,313,421,421,58,421,313,313,58,421,421,313,58,58,313},S a,1 = {58,313,421,421,58,58,313,58,421,313,421,313,313,58,421} and S a,11 ＝{58,313,58,421,421,313,421,58,58,421,421,313,58,313,313}。
S10.6, initialization
Figure BDA00035823529300001212
And k =0.
S10.7, updating T a,0,0,0 ＝T a,0,0,0 ||S a,* ||S a,* ||S a,Da[0] ＝S a,* ||S a,* ||S a,11 The symbol | | | represents the concatenation of two hopping sequences.
At this time, there is T a,0,0,0 ＝{313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,58,313,58,421,421,313,421,58,58,421,421,313,58,313,313}。
S10.8, if k<2l 2 Then update k = k +1 and return S10.7; otherwise, jump to S11.
At this time, k =0<2l 2 =2, so k = k +1=1 is updated and S10.7 is returned.
S10.7, updating T a,0,0,0 ＝T a,0,0,0 ||S a,* ||S a,* ||S a,Da[1] ＝S a,* ||S a,* ||S a,11 ||S a,* ||S a,* ||S a,1 。
At this time, there is T a,0,0,0 ＝{313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,58,313,58,421,421,313,421,58,58,421,421,313,58,313,313,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,58,313,421,421,58,58,313,58,421,313,421,313,313,58,421}。
S10.8, if k<2l 2 Then update k = k +1 and return S10.7; otherwise, jump to S11.
At this time, since k =1<2l 2 =2, so k = k +1=2 is updated and S10.7 is returned.
S10.7, update
Figure BDA0003582352930000131
Figure BDA0003582352930000132
At this time, there is T a,0,0,0 ＝{313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,58,313,58,421,421,313,421,58,58,421,421,313,58,313,313,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,58,313,421,421,58,58,313,58,421,313,421,313,313,58,421,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,313,421,313,58,313,58,58,421,421,58,58,421,313,313,421,58,313,421,421,58,421,313,313,58,421,421,313,58,58,313}。
S10.8, if k<2l 2 Then k = k +1 is updated and S10.7 is returned; otherwise, jump to S11.
At this time, k =2=2l 2 =2, thus jumping to S11.
S11, updating RS a,0 ＝RS a,0 ||T a,0,0,0 ＝T a,0,0,0 。
S12, if
Figure BDA0003582352930000133
Then j = j +1 is updated and S8 is returned; otherwise, jump to S13.
At this time, since
Figure BDA0003582352930000134
So j = j +1=1 is updated and returns to S8.
S8, if (| V) a,r 1) cannot be divisible by 2 and
Figure BDA0003582352930000135
then set V is initialized r,i,j ＝{V a,r [i],W r,i [0],W r,i [|V a,r |-2]}; otherwise, set V is initialized r,i,j ＝{V a,r [i],W r,i [|V a,r |-3-2j],W r,i [|V a,r |-2-2j]}。
At this time, | V a,0 I-1=4 is divisible by 2, thus initializing set V 0,0,1 ＝{V a,0 [0],W 0,0 [|V a,0 |-3-2],W 0,0 [|V a,0 |-2-2]}＝{58,232,138}。
S9, collecting the set V 0,0,1 Is rearranged in order from small to large so that V 0,0,1 [0]<V 0,0,1 [1]<V 0,0,1 [2]Thereby obtaining an updated V 0,0,1 Is {58,138,232}, and u is set a,0 ＝V 0,0,1 [0]＝58，u a,1 ＝V 0,0,1 [1]＝138,u a,2 ＝V 0,0,1 [2]＝232。
S10, adopting the following steps based on 3 available channels u a,0 ,u a,1 And u a,2 Generate a length of
Figure BDA0003582352930000141
Frequency hopping sequence T of one time slot 0,0,1 ：
S10.1, numbering each available channel u a,h Expressed as a length of
Figure BDA0003582352930000142
Binary sequence u of a,h [0]u a,h [1]…u a,h [8]Where h is [0,2 ]]And u is a,h [0]And u a,h [8]Representing the highest and lowest weighted bits in the binary sequence, respectively.
At this time, u is due to a,0 ＝58，u a,1 =138, and u a,2 =232, and therefore has u a,0 ＝000111010，u a,1 =010001010, and u a,2 ＝011101000。
S10.2, find u a,0 [L a ]＝u a,1 [L a ]≠u a,2 [L a ]Or u a,0 [L a ]≠u a,1 [L a ]＝u a,2 [L a ]Smallest integer of L a And mixing L a Expressed as an eleven-ary sequence L a [0]L a [1]…L a [l 2 -1]Wherein L is a ∈[0,l 1 -1]And
Figure BDA0003582352930000143
at this time, the process of the present invention,since 0=u a,0 [1]≠u a,1 [1]＝u a,2 [1]=1, therefore set L a =1, and will L a Expressed as a length of
Figure BDA0003582352930000144
Eleven system sequence L a [0]＝1。
S10.3, if u a,0 [L a ]＝u a,1 [L a ]≠u a,2 [L a ]Then further find u a,0 [M a ]≠u a,1 [M a ]Smallest integer M of true a And M is a Expressed as an eleven-ary sequence M a [0]M a [1]…M a [l 2 -1]Then generate a 2l 2 +1 element sequence D a ＝{11,L a [0],L a [1],…,L a [l 2 -1],M a [0],M a [1],…,M a [l 2 -1]}; if u is a,0 [L a ]≠u a,1 [L a ]＝u a,2 [L a ]Then further find u a,1 [M a ]≠u a,2 [M a ]Smallest integer M of true a Will M a Expressed as an eleven-ary sequence M a [0]M a [1]…M a [l 2 -1]Then generate a 2l 2 +1 element sequence D a ＝{11,M a [0],M a [1],…,M a [l 2 -1],L a [0],L a [1],…,L a [l 2 -1]In which M is a ∈[0,l 1 -1]。
At this time, u is due to a,0 [L a ]≠u a,1 [L a ]＝u a,2 [L a ]And l 2 =1, therefore further finding u a,0 [M a ]≠u a,1 [M a ]Minimum integer of true M a =2, will M a =2 expressed as a length of l 2 Eleven-ary sequence M of =1 a [0]=2 and generates one 2l 2 +1=3 element sequence D a ＝{11,2,1}。
S10.4 UDDS based on first class (3,15,5)
Figure BDA0003582352930000151
An available channel u is generated as follows a,0 ,u a,1 And u a,2 Up-hopped 15-slot periodic hopping sequence S a,* ：
In each 15-slot period, the hopping sequence S a,* Need to be in each time slot
Figure BDA0003582352930000152
Internally switching to an available channel u a,h Where h e [0,2]。
At this time, since the first class (3,15,5) -UDDS
Figure BDA0003582352930000153
Can be divided into 3 mutually exclusive (15,5) -DSs
Figure BDA0003582352930000154
And
Figure BDA0003582352930000155
thus having S a,* ＝{138,232,138,58,138,58,58,232,232,58,58,232,138,138,232}。
S10.5, based on
Figure BDA0003582352930000156
Associated with each second class (3,15,5) -UDDS
Figure BDA0003582352930000157
Wherein g is epsilon [0,11]The method for generating a channel u in 3 available channels is as follows a,0 ,u a,1 And u a,2 Up-hopped 15-slot periodic frequency hopping sequence S a,g ：
In each 15-slot period, the hopping sequence S a,g Need to be in each time slot
Figure BDA0003582352930000158
Internally handing over to channel u a,h In the above-mentioned manner,wherein g is from [0,11 ∈ [ ]]And h e [0,2]。
At this time, according to the first class (3,15,5) -UDDS
Figure BDA0003582352930000159
Associated 3 second classes (3,15,5) -UDDS
Figure BDA00035823529300001510
Figure BDA00035823529300001511
And
Figure BDA00035823529300001512
can be defined as S a,1 ＝{58,138,232,232,58,58,138,58,232,138,232,138,138,58,232}，S a,2 = {58,138,138,58,138,232,138,232,58,232,232,138,58,232,58} and S a,11 ＝{58,138,58,232,232,138,232,58,58,232,232,138,58,138,138}。
S10.6, initialization
Figure BDA00035823529300001513
And k =0.
S10.7, update
Figure BDA00035823529300001514
At this time, there is T a,0,0,1 ＝{138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,58,138,58,232,232,138,232,58,58,232,232,138,58,138,138}。
S10.8, if k<2l 2 Then k = k +1 is updated and S10.7 is returned; otherwise, jump to S11.
At this time, k =0<2l 2 =2, so k = k +1=1 is updated and S10.7 is returned.
S10.7, update
Figure BDA0003582352930000161
At this time, there is T a,0,0,1 ＝{138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,58,138,58,232,232,138,232,58,58,232,232,138,58,138,138,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,58,138,138,58,138,232,138,232,58,232,232,138,58,232,58}。
S10.8, if k<2l 2 Then k = k +1 is updated and S10.7 is returned; otherwise, jump to S11.
At this time, k =1<2l 2 =2, so update k = k +1=2 and return S10.7.
S10.7, update
Figure BDA0003582352930000162
Figure BDA0003582352930000163
At this time, there is T a,0,0,1 ＝{138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,58,138,58,232,232,138,232,58,58,232,232,138,58,138,138,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,58,138,138,58,138,232,138,232,58,232,232,138,58,232,58,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,138,232,138,58,138,58,58,232,232,58,58,232,138,138,232,58,138,232,232,58,58,138,58,232,138,232,138,138,58,232}。
S10.8, if k<2l 2 Then k = k +1 is updated and S10.7 is returned; otherwise, jump to S11.
At this time, k =2=2l 2 =2, so jump to S11.
S11, updating RS a,0 ＝RS a,0 ||T a,0,0,1 ＝T a,0,0,0 ||T a,0,0,1 。
S12, if
Figure BDA0003582352930000164
Then update j = j +1 and returnReturning to S8; otherwise, jump to S13.
At this time, since
Figure BDA0003582352930000165
Thus jumping to S13.
S13, if i<|V a,r I-1, then i = i +1 is updated and S6 is returned; otherwise, go to S14.
At this time, i =0<|V a,r I-1=4, so i = i +1=1 is updated and S6 is returned.
……
By analogy, the cognitive node CU can be finally generated a Of the hopping sequence RS a,0 ,RS a,1 And RS a,2 . FIG. 1 shows that the cognitive node CU a Frequency hopping sequence RS for antenna 0 a,0 First 270 time slots of (1), the frequency hopping sequence RS of antenna a,1 First 270 time slots of (c), and a frequency hopping sequence RS of antenna 2 a,2 The first 270 slots. The cycle lengths of the hopping sequences are all
Figure BDA0003582352930000171
And a time slot.
Similarly, when the total number of accessible channels N =512 in the cognitive wireless network, the cognitive user CU b When 1 antenna is configured and the available channel number set {25,77,138,325,421,490} is provided, fig. 1 also shows a single-antenna cognitive node CU b Frequency hopping sequence RS generated by adopting the invention b,0 The first 265 slots of =421,490,421,25,421, …. The frequency hopping sequence has a period length of
Figure BDA0003582352930000172
Figure BDA0003582352930000173
And a time slot.
When cognitive node CU as shown in FIG. 1 a Prior to cognitive node CU b When the frequency hopping starts at exactly 5 time slots, the cognitive node CU a Using 3 hopping sequences RS a,0 ,RS a,1 And RS a,2 And cognitive node CU b Using a single hopping sequence RS b,0 At cognitive node CU a The frequency hopping convergence can be achieved on all the commonly available channels, i.e., channels 25,138 and 421, in time slots 0-152, and they are 3 time slots from the beginning of the frequency hopping to the first time that the frequency hopping convergence is achieved on channel 421. This time interval is much less than
Figure BDA0003582352930000174
Figure BDA0003582352930000175
The MTTR for a slot is a theoretical upper bound.
The following combined simulation shows that the invention achieves the effects:
as shown in fig. 2, when the cognitive wireless network has N accessible channels 0,1, …, N-1, the cognitive node CU with single antenna a Has the locally available channel number of 1,2, …,0.5N, and a single-antenna cognitive node CU b Is 0.1N,0.1N +1, …,0.6N, they are according to the present invention, document [1 ]]And document [2 ]]And document [3 ]]And (3) a simulation comparison graph of the maximum convergence time interval (namely MTTR) obtained by the four anonymous single-antenna frequency hopping convergence algorithms and the change of the total number N of the accessible channels of the cognitive radio network. It can be seen that the present invention always achieves a lower maximum convergence time interval than the other three anonymous single-antenna frequency hopping convergence algorithms.
As shown in fig. 3, when the number of N accessible channels of the cognitive wireless network is 0,1, …, N-1, a cognitive node CU with 2 antennas is configured a The number of the local available channel is 0.3N,0.3N +1, …,0.7N, and the cognitive node CU is configured with 5 antennas b Are numbered 0.4N,0.4N +1, …,0.6N, they are in accordance with the present invention and document [2 ]]And (3) a simulation comparison graph of the maximum convergence time interval (namely MTTR) obtained by the two anonymous antenna heterogeneous frequency hopping convergence algorithms along with the total number N of the accessible channels of the cognitive radio network. It can be seen that the invention can always obtain the comparison document [2 ] when the total number N of accessible channels of the cognitive wireless network is more than 600]The anonymous antenna heterogeneous frequency hopping convergence algorithm has a lower maximum convergence time interval.

Claims (1)

1. An anonymous frequency hopping sequence design method suitable for a multi-antenna cognitive wireless network is characterized in that the total number of accessible channels of the multi-antenna cognitive wireless network is defined to be N, and each cognitive node CU a Is provided with N a An available channel
Figure FDA0003988155080000011
And R a Root antenna, where 0 ≦ v a，0 ＜v a，1 ＜v a，2 ≤N-1，R a ≥1，N a ≥3R a Characterized by being R a The method for generating different periodic frequency hopping sequences by the root antenna respectively comprises the following steps:
s1, cognitive node CU a R of (A) a The root antennas are numbered 0,1,2 a -1；
S2, cognitive node CU a N of (A) a The available channels are divided into R satisfying the following conditions a One channel group: each channel group i e [0,p-1]For a set V comprising G channels a，i ＝{v a，iG ，v a，iG+1 ，...，v a，(i+1)G-1 Where p = N a moduloR a And
Figure FDA0003988155080000012
and each channel group j ∈ [ p, R a -1]For a set V comprising H channels a，j ＝{v a，p(G-H)+jH ，v a，p(G-H)+jH+1 ，...，v a，p(G-H)+(j+1)H-1 Therein of
Figure FDA0003988155080000013
S3, initializing cognitive node CU a The antenna number of (1) is r =0;
s4, initializing the periodic frequency hopping sequence of the antenna r as
Figure FDA0003988155080000014
S5, initializing a frequency hopping sequence RS a，r Frame number of (1) is i =0;
s6, initializing set W r，i ＝V a，r \{V a，r [i]In which V is a，r [i]Representative set V a，r The i +1 th channel number in (a);
s7, initializing a frequency hopping sequence RS a，r The subframe number of frame i of (a) is j =0;
s8, if (| V) a，r 1) cannot be divisible by 2 and
Figure FDA0003988155080000015
then set V is initialized r，i，j ＝{V a，r [i]，W r ，i[0]，W r，i [|V a，r |-2]}; otherwise, set V is initialized r，i，j ＝{V a，r [i]，W r，i [|V a，r |-3-2j]，W r，i [|V a，r |-2-2j]}，W r，i [j]Representative set W r，i The j +1 th channel number in (a);
s9, collecting the set V r，i，j Is rearranged in order from small to large so that V r，i，j [0]＜V r，i，j [1]<V r，i，j [2]And is provided with u a，0 ＝V r，i，j [0]，u a，1 ＝V r，i，j [1]And u and a，2 ＝V r，i，j [2]；
s10, adopting the following steps based on 3 available channels u a，0 ，u a，1 And u a，2 Generate a length of
Figure FDA0003988155080000016
Frequency hopping sequence T of one time slot a，r，i，j ：
S101, numbering each available channel u a，h Represented as a binary sequence u a，h [0]u a，h [1]...u a，h [l 1 -1]Wherein
Figure FDA0003988155080000021
And u a，h [0]And u a，h [l 1 -1]Respectively representing the bits with the highest weight and the lowest weight in the binary sequence;
s102, finding u a，0 [La]＝u a，1 [L a ]≠u a，2 [L a ]Or u a，0 [L a ]≠u a，1 [L a ]＝u a，2 [L a ]Smallest integer of L a And mixing L a Expressed as an eleven-ary sequence L a [0]L a [1]...L a [l 2 -1]Wherein L is a ∈[0，l 1 -1]And
Figure FDA0003988155080000022
s103, if u a，0 [L a ]＝u a，1 [L a ]≠u a，2 [L a ]Then further find u a，0 [M a ]≠u a，1 [M a ]Minimum integer of true M a And M is a Expressed as an eleven-ary sequence M a [0]M a [1]...M a [l 2 -1]Then generate a 2l 2 +1 element sequence D a ＝{11，L a [0]，L a [1]，...，L a [l 2 -1]，M a [0]，M a [1]，...，M a [l 2 -1]}; if u is a，0 [L a ]≠u a，1 [L a ]＝u a，2 [L a ]Then further find u a，1 [M a ]≠u a，2 [M a ]Minimum integer of true M a And M is a Expressed as an eleven-ary sequence M a [0]M a [1]...M a [l 2 -1]Then generate a 2l 2 +1 element sequence D a ＝{11，M a [0]，M a [1]，...，M a [l 2 -1]，L a [0]，L a [1]，...，L a [l 2 -1]In which M is a ∈[0，l 1 -1]；
S104, UDDS based on first class (3, 15,5)
Figure FDA0003988155080000023
An available channel u is generated as follows a，0 ，u a，1 And u a，2 Up-hopped 15-slot periodic frequency hopping sequence S a，* The first class of (3, 15,5) -UDDS
Figure FDA0003988155080000024
Is defined as if a (3, 15,5) -UDDS U (I) Can be divided into 3 mutually disjoint (15,5) -DSs which are respectively defined as
Figure FDA0003988155080000025
And
Figure FDA0003988155080000026
and satisfy
Figure FDA0003988155080000027
Then the UDDS is referred to as a first class (3, 15,5) -UDDS: in each 15-slot period, the hopping sequence S a，* Need to be in each time slot
Figure FDA0003988155080000028
Internally switching to an available channel u a，h Where h e [0,2]；
Wherein, (3, 15,5) -UDDS is defined such that if a 15-element set U can be divided into 3 mutually disjoint (15,5) -DS, the set U is referred to as a 3-dimensional disjoint (15,5) -difference set combination and simply referred to as a (3, 15,5) -UDDS; for any j e [0,2]，(15，5)-DS
Figure FDA0003988155080000029
Is defined as if set Z is 15 A subset of 5 elements of = {0,1
Figure FDA00039881550800000210
Satisfies the condition that for any non-zero integer d ∈ Z 15 Each having at least one ordered pair of elements (a) x ，a y ) Satisfy the requirements of
Figure FDA00039881550800000211
And d = a x -a y modulo 15, then set
Figure FDA00039881550800000212
Is referred to as a (15,5) -relaxation cycle difference set and is abbreviated as (15,5) -DS, i.e.
Figure FDA00039881550800000213
And
Figure FDA0003988155080000031
three (15,5) -DSs, respectively; function(s)
Figure FDA0003988155080000032
Is defined as, for a 5-element set
Figure FDA0003988155080000033
Figure FDA0003988155080000034
The execution distance is r epsilon [0, 14 ∈ ]]Can result in a 5-element set, i.e.
Figure FDA0003988155080000035
Figure FDA0003988155080000036
S105, based on
Figure FDA0003988155080000037
Each associated second class (3, 15,5) -UDDS
Figure FDA0003988155080000038
Wherein g ∈ [0,11 ]]Generating a channel u in 3 available channels by using the following method a，0 ，u a，1 And u a，2 Up-hopped 15-slot periodic frequency hopping sequence S a，g The second class (3, 15,5) -UDDS
Figure FDA0003988155080000039
Is defined as if there is one (15,5) -DS which can be divided into 3 mutually disjoint (15,5) -DSs
Figure FDA00039881550800000310
And
Figure FDA00039881550800000311
and satisfies the conditions
Figure FDA00039881550800000312
(3, 15,5) -UDDS
Figure FDA00039881550800000313
Then the UDDS is called an AND U (I) The associated second class (3, 15,5) -UDDS:
in each 15-slot period, the hopping sequence S a，g Need to be in each time slot
Figure FDA00039881550800000314
Internally handing over to channel u a，h Where g ∈ [0,11 ]]And h e [0,2]。
S106, initialization
Figure FDA00039881550800000315
And k =0;
s107, updating
Figure FDA00039881550800000316
Wherein D a [k]Represents sequence D a The (k + 1) th element and the symbol | | | in the sequence represent the series connection of two frequency hopping sequences;
s108, if k is less than 2l 2 Then k = k +1 is updated and returns to S107; otherwise, jumping to S11;
s11, updating RS a，r ＝RS a，r ||T a，r，i，j ；
S12, if
Figure FDA00039881550800000317
Then j = j +1 is updated and S8 is returned; otherwise, jumping to S13;
s13, if i < | V a，r I-1, then i = i +1 is updated and S6 is returned; otherwise, jumping to S14;
s14, if R is less than R a -1, then update r = r +1 and return to S4; otherwise, ending the algorithm execution and outputting the hopping sequence
Figure FDA00039881550800000318
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