This application claims the priority benefit of China application no. 202010569496.X, filed on Jun. 20, 2020. The entirety of the above-mentioned patent application is hereby incorporated by reference herein and made a part of this specification.
The disclosure belongs to the technical field of wireless communication networks in communication transmission systems, and more specifically, relates to a construction method for TFDMA random self-organizing ad hoc networks. The method involves the framework structure design of time-frequency division multiple access (TFDMA) random access ad hoc networks, as well as the multi-dimensional dual-domain modulation signal modeling and multi-dimensional high-order dual-domain modulation signal permutation array constellation diagram architecture suitable for accessing TFDMA ad hoc networks, and their structural design methods.
In order to satisfy the application requirements that multiple robots can operate simultaneously in the future, such as the operation of multiple flying robots (UAVs) making turns simultaneously and carrying heavy objects jointly when flying in the air, it is required to measure the synchronous behavior of multiple robots and control signals to perform reliable (uninterrupted) transmission. To meet the above requirement, the inventor of the disclosure provides a time-frequency division multiple access self-organizing wireless access ad hoc network model, which is referred to as TFDMA ad hoc network, abbreviated as TFDMA network. The purpose of TFDMA network is to support the transmission requirement for measurement of simultaneous operation of multiple robots and signal control. In order for this TFDMA ad hoc network to operate normally, it is necessary to design a coded modulation access signal model for the physical layer of the transceiver that allows multiple users to access the TFDMA network, and construct a modulation signal constellation diagram that can access the TFDMA ad hoc network, thereby establishing a system structure of which the transceiver system can be designed based on the constellation diagram in the future. Another application is that the TFDMA network enables large-scale sensors or large-scale machines to access the network without mutual interference, so that the user access density can be increased significantly by 10 times or even 100 times that of the user density of existing technology Zigbee.
For a TFDMA transceiver running in a TFDMA network, its physical layer coding, modulation, and access signal models are established based on the permutation matrix, and a permutation matrix is isomorphic with a permutation codeword (permutation vector). At present, the permutation code set with application prospects is coset partition based (n,n(n−1), n−1) permutation group code. In other words, the constellation diagram having the coding, modulation, and access signal with TFDMA characteristics will consist of a subset of the coset partition based permutation group codes. In the early stage of the inventor's project, a coset partition based construction method for (n,n(n−1),n−1) permutation group code and code set generator thereof have been provided, and for which an disclosure patent was applied with the CNIPA (China National Intellectual Property Administration); the application or patent number of the disclosure is 201610051144.9. In the meantime, a oversea disclosure patent was filed for the above disclosure with the United States Patent and Trademark Office (USTPO, Application Number: 15060111) (Title of Disclosure: COSET PARTITION BASED CONSTRUCTION METHOD FOR (n,n(n−1),n−1) PERMUTATION GROUP CODE AND CODE SET GENERATOR THEREOF). Currently, the patent right of disclosure has been obtained.
Based on the algebraic structure of the coset partition based (n,n(n−1), n−1) permutation group code, the inventor of the disclosure provides an n-dimensional dual-domain modulation signal model and n-dimensional high-order dual-domain modulation signal permutation array constellation diagram. Therefore, the disclosure seek to protect three core contents: the first one is the TFDMA random access ad hoc network framework, which is suitable for interference-free access of robots in high intensity, and can support simultaneous access and operation of multiple robots; the second one is permutation matrix based n-dimensional dual-domain modulation signal model; and the third one is a structure of permutation array constellation diagram of the n-dimensional high-order dual-domain modulation signal. In the disclosure, the time diversity and modulation domain diversity are simultaneously introduced into the permutation matrix based signal model. An encoding gain and a spread spectrum gain are introduced into the permutation modes based permutation array constellation diagram. All of the above advantages allow the signal model and its signal constellation diagram to have higher reliability, thus capable of resisting multipath interference, continuous narrow-band signal interference (such as the narrow pulse of the factory's FM equipment), wide-band pulse interference (such as noise from electronic ignition devices) and multi-user interference. In the disclosure, the permutation array constellation diagram framework can provide encoding, decoding and detection algorithm with ultra-low complexity due to its high algebraic structure characteristics. It can be predicted that a TFDMA transceiver equipped with an n-dimensional high-order dual-domain modulation signal permutation array constellation diagram can effectively access the TFDMA ad hoc network.
The disclosure provides a construction method for a TFDMA random self-organizing ad hoc network, which divides the spectrum resources of the full frequency domain as well as the full time domain resources in 24 hours a day occupied by the network system. First, the divided frequency domain and time domain units are constructed into a period-frequency slot epoch-ring net, and then N period-frequency slot epoch-ring nets are stacked into a cylindrical web according to the time slot alignment principle, and finally U cylindrical webs are formed into the time-frequency division multiple access random self-organizing ad hoc network that covers the full frequency domain and the full time domain. The specific steps of network construction are as follows.
The full frequency domain resource is the total frequency spectrum allocated to the TFDMA ad hoc network. W is set to represent the bandwidth of the total frequency spectrum, and the total frequency spectrum of the network system with bandwidth W is divided into N sub-channels. Δf is set to represent the bandwidth of each sub-channel, which is equivalent to the interval between two adjacent center frequencies, Δf=fi−fi-1. Then, this TFDMA ad hoc network includes N frequency hopping points or N sub-channels center frequency. N=W/Δf, wherein Δf is called frequency slot or frequency chip.
The full-time domain resource in 24 hours a day is divided as follows. 24 hours are divided into U epochs, each epoch determines a cylindrical web, thereby determining the minimum loop time of a TFDMA ad hoc network. Each epoch is divided into V time frames, each time frame is the basic time unit of the time division multiple access mode. A time frame is divided into S time slots, and each time slot is the basic time unit of the TFDMA ad hoc network which the user terminal can assess. A time slot is divided into E time chips, each time chip is the time occupied by a pulse symbol packet with a definite or adjustable duty cycle, which is also a duration of a symbol in a codeword in the permutation group code, and is also the duration of a single carrier waveform.
The epoch-frequency slot ring net, referred to as an epoch-ring net or a net, is determined by one of U epochs combined with a frequency slot Δf. Specifically, the last one of V·S time slots in an epoch is connected to the first time slot to form an epoch-frequency slot ring net formed by the V·S time slots and a frequency slot Δf, which is also called a time-slot-frequency-slot ring net, or epoch-ring net for short. The network system includes a total of N epoch-ring nets that can operate independently, each epoch-ring net is allocated a frequency hopping point or the center frequency of the sub-channel.
The cylindrical web is formed by stacking the N independently operable epoch-ring nets into a cylindrical web in a manner that time slots are aligned. When each corresponding time slot of the N epoch-ring nets is aligned, the web contains V·S time slices, and each time slice is composed of a time slot and N frequency slots.
The TFDMA ad hoc network is composed of U cylindrical webs, that is, one web is repeatedly used for U times, thereby forming a time-frequency division multiple access self-organizing network covering the full frequency domain and the full time domain.
The access signal model of the TFDMA ad hoc network is a dual-domain modulation signal composed of an n-dimensional time domain modeled by a permutation matrix and a modulation multi-domain. The permutation matrix set for constructing a multi-dimensional dual-domain modulation signal is isomorphic with the permutation group code. A subset of the permutation group code is used to construct the permutation array constellation diagram of the multi-dimensional dual-domain modulation signal running on the TFDMA network.
In order to make the objectives, technical solutions, and advantages of the present disclosure clearer, the following further describes the present disclosure in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific implementation cases described here are only used to explain the present disclosure, but not to limit the present disclosure. In addition, the technical features involved in the various embodiments of the present disclosure described below can be combined with each other as long as they do not conflict with each other.
Basic Principle
The section basic principle describes the theoretical basis and mathematical model based on which the structure of the signal model and permutation array constellation diagram of the disclosure are designed, and mainly involves: the method of generating permutation group code.
The set formed by all n! permutations of n elements defined in a finite domain Zn={1, 2, . . . , n} of positive integers is called a symmetric group, which is expressed as Sn={π1, . . . πk, . . . , πn!}, wherein each element can be represented by a permutation vector πk=[a1 . . . ai . . . an], wherein k=1, 2, . . . , n! represents the index of the permutation vector contained in the symmetric group Sn. All elements of each permutation vector are different, wherein a1, . . . , ai, . . . , an∈Zn. The degree (dimension, size) of each permutation is |πk|=n, and the potential (order) of the symmetric group is expressed as |Sn|=n!. Set π0=e=[a1a2 . . . an]=[12 . . . n], which represents the identity element of the symmetric group Sn. The general permutation group code is defined as a sub-group of the symmetric group Sn, and the four axioms of the permutation group code abstract algebraic group are: closure, associativity, identity, and inverse. A permutation group code can be expressed as (n, μ, d)-PGC, wherein n represents the length of the codeword, μ represents the maximum potential (maximum size) of this code set, and d represents the minimum Hamming distance between any two permutation codewords in this code set. For example, (n,n(n−1),n−1) permutation group code PGC is a group code with code length n, potential n(n−1), and minimum Hamming distance n−1.
(n,n(n−1), n−1) Coset partition structure of permutation group code:
The inventor's research results that have been published show that when any n>1 is a prime number, the code set Pn of (n,μ,d) permutation group codes can be equivalently calculated by the following two algebraic calculation methods for each codeword to obtain:
In the expression, the expression (1) represents the first method of generating the code set Pn, indicating that Pn is obtained by calculating two smaller sub-groups, namely the standard loop sub-group Cn and the maximum single-fixed-point sub-group Ln about the fixed-point n∈Zn through the composition operator “∘”. The expression (2) represents the second method of generating the code set Pn, which shows that each permutation codeword of Pn can be calculated by the affine transformation fa,b(l1)−al1+b.
It can be seen from the two methods of generating Pn that they all adopt the maximum single fixed point sub-group Ln. Therefore, the key problem is to first generate Ln, which is generated by the proportional transformation fa(x)=ax, wherein a∈Zn-1, x∈Sn. For the maximum single fixed point sub-group, the first requirement is that n>1 is a prime number to ensure that a and n are mutually exclusive, so that the set {ax|a∈Zn-1} reaches the maximum; the second requirement is that x∈Sn must be the identity element to ensure that the set {ax|a∈Zn-1} is a permutation group, that is, the algebraic group must contain the identity element. Therefore, the specific calculation formula of Ln is
Ln={al1|a∈Zn-1;l1=[12 . . . n]}={1·l1,2·l1, . . . ,a·l1, . . . ,(n−1)·l1}{l1,l2, . . . ,la, . . . ,ln-1}
It can be seen that all permutation vectors in Ln contain a fixed-point n∈Zn, and other symbols are transferable. Ln contains n−1 permutation vectors l1, l2, . . . , la, . . . , ln-1, which is called coset leader permutation codeword or orbit leader permutation codeword, Ln is also called coset leader set or orbit leader set.
The coset characteristics of the code set Pn can be summarized as follows:
1) The code set Pn is composed of n−1 Cn right cosets Cnl1, Cnl2, . . . , Cnln-1 under the condition of multiplication, and each coset contains n codewords. Another type of coset generating method is the translation group, that is, the maximum fixed-point subgroup Ln is translated. Specifically, an equal element vector
of n length is adopted to translate Ln, that is, Pn={Ln+b|b∈Zn}={Ln+[b]n}={l1+[b]n, l2+[b]n, . . . , ln-1+[b]n}. It can be seen that Pn consists of n−1 Ln right cosets l1+[b]n, l2+[b]n, . . . , ln-1+[b]n under the add group condition, and each coset contains n codewords.
2) The code set Pn can also be regarded as composed of n−1 orbits, and each orbit contains n codewords. There are two ways to form orbits, and they are equivalent. The first method is: the standard loop sub-group Cn acts on the n−1 orbit leader permutation vectors l1, l2, . . . , la, . . . , ln-1 in Ln to obtain n−1 orbits Cnl1, Cnl2, . . . , Cnln-1. The second method is: n-dimensional equal element vector [b]n is adopted to perform translation operations on n−1 orbit leader permutation vectors l1, l2, . . . , la, . . . , ln-1 in Ln to obtain n−1 orbits l1+[b]n, l2+[b]n, . . . , ln-1+[b]n.
Permutation matrix and permutation matrix set isomorphic to (n,n(n−1), n−1) permutation group code:
The permutation matrix is defined as an n×n square matrix with only one element “1” in each row and each column, and the remaining elements are “0”.
Any permutation matrix can be represented by a permutation vector, vice versa, any permutation vector can also be represented by a permutation matrix. The corresponding relationship between the two is that the index coordinates of each element in the permutation vector give the column index of the permutation matrix, and the value of each element in the permutation vector gives the line number of each element “1” in the permutation matrix.
All n! permutation vectors in the symmetric group Sn have a one-to-one corresponding permutation matrix. Therefore, Sn can also be expressed as a set of n! permutation matrices. Similarly, the n(n−1) permutation vectors in the permutation group code Pn can also be represented isomorphically as n(n−1) n×n permutation matrices.
In the first example, the permutation vector is generated by n=7, and the corresponding permutation matrix can be written. For example, take the unit permutation vector [1234567], it can be written that it corresponds to a 7×7 permutation matrix, which is an identity matrix.
In another example, take any permutation vector with n=7 [3164275], and its corresponding permutation matrix is
In the disclosure, the n×n permutation matrix is a mathematical model for establishing an n-dimensional dual-domain modulation signal, and the permutation group code Pn is a mathematical tool for establishing an n-dimensional high-order dual-domain modulation signal permutation array constellation diagram.
The technical solution is divided into three parts. The first part is the frame structure design of the TFDMA ad hoc network; the second part is the permutation matrix based n-dimensional dual-domain modulation signal structure design; and the third part is the structure design of permutation group code based n-dimensional high-order dual-domain modulation signal permutation array constellation diagram.
Part 1: TFDMA Random Access (Ad Hoc) Network Frame Structure Design
The frequency resource allocated to the TFDMA ad hoc network is divided. W is set to represent the bandwidth of the frequency spectrum allocated to the TFDMA ad hoc network in the disclosure. Δf is set to represent the minimum interval between any two adjacent sub-channels or adjacent hopping frequencies. Then the TFDMA network contains N=W/Δf hopping frequency points or N sub-channels with center frequency fc+i·Δf, wherein i=0, 1 . . . , N−1, and the frequency unit is hertz (Hz). If the bandwidth of a sub-channel is equal to the interval between two adjacent center frequencies, then Δf is also called the frequency slot (frequency chip) of the TFDMA network, or the bandwidth of the sub-channel.
The time resource in 24 hours a day is divided as follows. 24 hours may be divided into U epochs, each epoch determines the minimum loop time of a TFDMA ad hoc network. Each epoch is divided into V time frames, each time frame is the basic time unit of the time division multiple access of multiple users. Each time frame is divided into S time slots, and one time slot is the basic time unit of the TFDMA ad hoc network which the user terminal can assess. Each time slot is divided into E time chips. One time chip is a pulse symbol duration unit with a suitable duty cycle, and it is also the duration of one symbol in the permutation codeword.
T is set to denote the duration of a time slot. A time-frequency slot is defined as a square formed by the abscissa of a time slot and the ordinate of a frequency slot, expressed as T·Δf. The TFDMA network allows many user terminals to access the network in the manner of combination of time division multiple access and frequency division multiple access, thus a new concept of time-frequency division multiple access is introduced.
Definition 1: A multi-user network access scheme is called time-frequency division multiple access (TFDMA) access, if it satisfies the following operating conditions: 1) N user terminals access N sub-nets in the manner of frequency division multiple access and time division multiplexing without frequency interference, that is, N users respectively occupy N different frequencies and reuse the same time slot. 2) S user terminals access one sub-net in the manner of time division multiple access and frequency division multiplexing without symbol interference, that is, the S user terminals respectively occupy S different time slots and reuse the same frequency. 3) Each user terminal accessing a sub-net must occupy at least one time slot frequency slot T·Δf, in a sub-net, a user terminal can occupy at most V time slots from V different time frames. 4) In a time frame, the maximum number of users of N sub-nets is N·S, a sub-net (one time band) contains N time division multiple access frequency multiplexing time frames, and the maximum number of users is S·V.
Each epoch occupies a sub-channel, that is, occupies a frequency slot with a center frequency of fi and a bandwidth of Δf, or occupies a hopping frequency fi, i=1, . . . , N. An epoch related to a frequency slot is composed of V·S time slots. If the last time slot is connected to the first time slot, the V·S time slot forms a time-frequency loop, which is called an epoch-ring net, as shown in
N epoch-ring nets corresponding to N center frequencies f1, f2, . . . , fN are stacked in a slot-aligned form to form a cylindrical web, as shown in
It can be seen from
N users respectively access to N independent epoch-ring nets, operating in frequency division multiple access and time division multiplexing modes, that is, N users use different N frequencies to multiplex the same time slot, enabling N robot terminals to operate simultaneously by accessing the network simultaneously in a time slot. S users access an epoch-ring net in a time frame, and operate in a time division multiple access mode and multiplexing one frequency. S·N users access N independent epoch-ring nets or access a web within a time frame. In each of the N epoch-ring nets, there are S users accessing the network in the time division multiple access mode and multiplexing the same frequency. Within the duration of one time frame of the web, in each of the S time slices, there are N users accessing the network in the frequency division multiple access mode and multiplexing the same time slot. A user accessing a epoch-ring net will occupy a time-frequency slot, namely T·Δf, wherein T represents the duration of a time slot. A user in the epoch-ring net can use V time slots from V different time frames, and can also use V time slots from V different time frames in the next epoch, and the same is continued in the next epoch. Therefore, a user can use up to V·U time slots in 24 hours. In the same time frame of N epoch-ring nets, the maximum number of users is N·S. A epoch-ring net contains V TDMA-time frames, and the maximum number of users accommodated is S·V. The maximum number of users accommodated in a web is N·S·V. In a time-frequency slot, a terminal can access the web, and a web is composed of N×V·S time-frequency slots. Therefore, the maximum number of users of a web is N·V·S, wherein each user terminal occupies a time slot.
From the above, it seems very easy to construct a TFDMA network. The key lies its feasibility, which requires solving two basic problems. The first is: what kind of signal model has access to the TFDMA network, so that such signal model can be used to construct a transceiver system running with the TFDMA network; the second is: how to design the structure of the time slot to consider the key technical factors. The time slot structure determines how to choose timing (time reference), synchronization strategy, anti-jitter mechanism and protection scheme. This disclosure does not take into consideration the design of the structure of time slot for the time being because it involves a specific application environment, and different applications require different time slot structures. Only the structural design of the signal model is taken into consideration below.
Part 2: The n-Dimensional Dual-Domain Modulation Signal Model that can Access the TFDMA Network
This part uses permutation matrix as a mathematical tool to invent an n-dimensional dual-domain modulation signal model. The so-called “dual-domain” refers to: one domain is the time domain, and the other domain is the modulation single domain, or a joint domain of multiple domains, wherein the modulation single domain refers to the amplitude modulation domain, the phase modulation domain and the frequency modulation domain, and the modulation multi-domain refers to the two-by-two combination of three modulation domains or even the combination of three modulation domains.
The n-dimensional dual-domain modulation signal is modeled by a permutation matrix. The row index 1, 2, . . . , n of the permutation matrix is used to determine the specific value of the discrete modulation domain from bottom to top. di is set to represent the i-th value among the n values of multi-domain modulation, its subscript gives the index of n discrete values, i=0, 1, 2, . . . , n, d0=0 represents the starting value 0 of the modulation domain. Multi-domain modulation refers to amplitude modulation domain, phase modulation domain, frequency modulation domain, pulse position modulation domain, polarization modulation domain, spatial domain (antenna) modulation, and effective combinations of these modulation domains, such as joint multi-domain modulation of amplitude domain and phase domain. Δdb=di−di-1 is set to represent the domain chip or domain slot of the modulation domain, which means a difference between two adjacent values among n values d1, d2, . . . , dn arranged from small to large, or the smallest difference between any two of the n modulation domain values, b=1, 2, . . . , n, giving the index of, Δdb, the domain chip or domain slot of the modulation domain.
The column index 1, 2, . . . , n of the permutation matrix is processed from left to right into n discrete moments that appear at once in the time domain, expressed as ti, which refers to the i-th moment of the n moments in the time domain, and gives the index of these moments, i=0, 1, 2, . . . , n, t0=0 represents the starting moment 0 of the time domain. One domain of the dual-domain modulation signal is a modulation multi-domain determined by the row index of the permutation matrix, and the other domain is a time domain determined by the column index of the permutation matrix. The difference between two adjacent moments of n moments in the time domain is defined as a time chip, wherein n moments correspond to n time chips, and the duration of each time chip is Tc=Δtb−ti−ti-1, b=1, 2, . . . , n gives the time chip index; Tc=Δtb is also the duration of one symbol in a permutation codeword. Then Tw=nTc is the duration of a codeword and the duration of an n-dimensional dual-domain modulation signal.
The n domain chips Δdb of the modulation multi-domain and n time chips Δtb of the time domain define the n-dimensional dual-domain modulation signal model composed of the modulation multi-domain and the time domain, wherein b=1, 2, . . . , n. In the time interval of n time chips Δtb corresponding to n elements “1” in the permutation matrix, the carrier modulated by the b-th value of a permutation vector in the modulation domain is transmitted. In the permutation matrix, no signal is emitted at the position where each element “0” is located.
When the modulation domain is determined, a dual-domain signal composed of the determined time domain and modulation multi-domain can be obtained. This disclosure only invents six n-dimensional dual-domain modulation signal models for three parameters of the carrier, including amplitude, phase, and frequency, and including the mathematical expressions and signal patterns of the signal models. The mathematical symbols and equivalent expression used for modeling time domain and modulating multi-domain n-dimensional dual-domain modulation signals are described as follows.
Following the above description of symbols and simplified equivalent expression, the disclosure establishes the following six n-dimensional dual-domain modulation signal models.
Model 1: It is set that the modulation multi-domain is the carrier amplitude, that is, di=Ai, then the domain chip of the modulation multi-domain is the amplitude chip or the amplitude slot, that is, Δdb=di−di-1=ΔAb−Ai−Ai-1, b=1, 2, . . . , n. This is, an n×n permutation matrix is adopted to construct a dual-domain modulation signal composed of an n-dimensional time domain and an n-dimensional amplitude domain, abbreviated as n-dimensional time-amplitude dual-domain modulation signal model (n-TAM). The element “1” in the permutation matrix is replaced by the amplitude value Ai corresponding to the time chip Δtb in the corresponding permutation vector. Ai is a symbol value in the permutation codeword Am(a; l1; (tl1)q
Model 2: It is set that the modulation multi-domain is the carrier phase, i.e., di=pi, then the value chip of the modulation domain is the phase chip or the phase slot, i.e., Δdb=di−di-1=Δpb−pi−pi-1, b, i=1, 2, . . . , n. That is, an n×n permutation matrix can be used to construct an n-dimensional dual-domain modulation signal composed of the n-dimensional time domain and the n-dimensional phase domain, which is referred to as n-dimensional time-phase dual-domain modulation signal model (n-TPM) for short. The element “1” in the permutation matrix is replaced by the phase value pi corresponding to the time chip Δtb in the permutation vector, and pi is determined by a symbol value v in the permutation codeword v=Pm(a; l1; (tl1)q
can be obtained. If a k-bit binary message sequence selects a codeword [v1v2 . . . vn] in the permutation array code Γn2={(tl1)Q
(a phase unit) sequence Δp1, Δp2, . . . , Δpb, . . . , Δpn, each square is the product
of Δpb and Δtb, b=1, 2, . . . , n. Each element 1 in the permutation matrix is replaced with the phase value
vi corresponding to the time chip Δtb in the corresponding permutation vector, which is equivalent to using a phase value
generated by a symbol value vi of each corresponding time chip Δtb of a permutation codeword v=Pm(a; l1; (tl1)q
Model 3: It is set that the modulation multi-domain is the carrier frequency, i.e., di=fi. Then the domain chip of the modulation multi-domain is frequency chip or frequency slot, i.e., Δdb=di−di-1=Δfb−fi−fi-1, b, i=1, 2, . . . , n. That is, an n×n permutation matrix can be used to construct an n-dimensional dual-domain modulation signal of the n-dimensional time-domain and n-dimensional frequency domain, which is referred to as n-dimensional time-frequency dual-domain modulation signal model (n-TFM).
Since spectrum is a scarce natural resource, the spectrum bandwidth allocated to the TFDMA network is W. In the method of dividing the total system frequency W in this disclosure, two issues need to be considered: one is the design scheme of the sub-channel bandwidth Δf; the other is the allocation scheme of allocating n frequencies of the number of total system frequency N to each user. Specifically, the first method is Δf=fi−fi-1, which is the coherent bandwidth, and is defined as the minimum bandwidth that does not cause frequency interference. This frequency allocation method makes it possible that the number of sub-channels N=W/Δf without frequency interference reaches the maximum, and which is the design scheme for sub-channel bandwidth Δf under the condition where the number of users reaches the maximum. The second method is Δf=fi−fi-1, which is much larger than the coherent bandwidth. The number of frequency points of the system is still calculated through N=W/Δf, but the total number of frequency points of the system is much smaller than the first method. Each user still uses n frequency points to access the TFDMA network, but the way of taking n frequency points is random hopping, and the n frequency points taken each time are different, forming a fast frequency hopping system, which is the design scheme with the strongest anti-interference ability but the reasonable minimum sub-channel bandwidth Δf for the number of users. It is further required that the design scheme of the sub-channel bandwidth Δf can be changed in the above-mentioned maximum and minimum scheme.
The way each user obtains n frequencies from the N frequencies of the system is specifically as follows. The first method is a continuous n discrete frequency allocation scheme, and the sub-channel bandwidth Δf is the coherent bandwidth. f0 is set as the minimum center frequency of the system, and other center frequencies can be calculated through f0 and Δf, that is, flc=f0+(l−1)·Δf, l=1, 2, . . . , N, l=1, 2, . . . , N. If each user is assigned n different frequencies, the n frequencies of the first user can be calculated by using the expression f1c,i-1=f0+(i−1)·Δf, i=1, 2, . . . , n. The n frequencies of the first user can be calculated by using the expression f2c,i-1=f1c,n-1+(i−1)·Δf, i=1, 2, . . . , n; . . . ; the n frequencies of the Nth user can be calculated by using the expression fNc,i-1=f(N-1)c,n-1+(i−1) Δf, i=1, 2, . . . , n. The maximum number of users of frequency division multiple access that the system can operate in a time slot is N/n. The second method is n hopping frequency allocation scheme, the sub-channel bandwidth Δf=fi−fi-1 is much larger than the coherent bandwidth, and the number of frequency points of the system is still calculated through N=W/Δf. Each user still uses n frequency points to access the TFDMA network, but the way to take n frequency points is random hopping. After each user gets n frequency points, they can use permutation codeword [w1w2 . . . wn] to number n frequency points, that is, the n hopping frequency points of each user can be expressed as fw
(a frequency unit) sequence Δf1, Δf2, . . . , Δfb, . . . , Δfn. Each square is the product Δfb·Δtb of Δfb and Δtb, m=1, 2, . . . , M. Each element 1 of the permutation matrix is replaced with the frequency value fi=fw
Model 4: It is set that the modulation multi-domain is the joint modulation domain of the amplitude domain and phase domain of the carrier, set di=Ai and di=pi, then the domain chip of the modulation multi-domain is the combination of the amplitude chip and the phase chip, that is, Δdb=di−di-1=ΔAb−Ai−Ai-1 and Δdb=di−di-1=Δpb=pi−pi-1, b,i=1, 2, . . . , n. That is, two different n×n permutation matrices can be used to construct an n-dimensional dual-domain modulation signal composed of a joint modulation multi-domain composed of the n-dimensional time domain and n-dimensional amplitude as well as n-dimensional phase, which is referred to as n dimensional time-amplitude-phase dual-domain modulation signal model (n-TAPM). The element “1” in the two permutation matrices are respectively replaced by the amplitude value Ai and the phase value pi corresponding to the time chip Δtb. Ai is a symbol value of the permutation codeword Am(a; l1; (tl1)q
can be obtained. If a k-bit binary message sequence selects a codeword [u1u2 . . . un] of [u1u2 . . . un], Q1≤n−1, 1≤q1≤Q1, and another k-bit binary message sequence selects a codeword [v1v2 . . . vn] of Γn2={(tl1)Q
Model 5: It is set that the modulation domain is the joint modulation of the amplitude and frequency of the carrier, set di=Ai and di=fi, then the domain chip of the modulation domain are the amplitude slot and frequency slot, namely Δdb=di−di-1=ΔAb−Ai−Ai-1 and Δdb=di−di-1=Δfb−fi−fi-1, b, i=1, 2, . . . , n. That is, two different n×n permutation matrices can be used to construct an n-dimensional dual-domain modulation signal composed of the joint modulation multi-domain of the n-dimensional time domain and the n-dimensional amplitude domain as well as the n-dimensional frequency, which is referred to as n-dimensional time-amplitude frequency dual-domain modulation signal model (n-TAFM). The elements “1” in the two permutation matrices are respectively replaced by the amplitude value Ai and the frequency value fi corresponding to the time chip Δtb. Ai is the i-th symbol value of the permutation codeword Am(a; l1; (tl1)q
Model 6: It is set that the modulation multi-domain is the joint modulation domain of the amplitude, phase and frequency of the carrier, set di=Ai, di=pi and di=fi, then the domain chip of the modulation multi-domain are the amplitude chip Δdb=di−di-1=ΔAb=Ai−Ai-1, phase chip Δdb=di−di-1=Δpb=pi−pi-1 and frequency chip Δdb=di−di-1=Δfb=fi−fi-1, b, i=1, 2, . . . , n. That is, three different n×n permutation matrices can be used to construct a dual-domain modulation signal model (n-TAPFM) composed of the n-dimensional time domain and the amplitude-phase-frequency joint modulation multi-domain. The elements “1” in the three permutation matrices are respectively replaced by the amplitude value Ai, the phase value pi and the frequency value fi corresponding to the time chip Δtb in the permutation vector. Ai is the i-th symbol value of the permutation codeword Am(a; l1; (tl1)q
and fi=fw
Part 3: Multi-Dimensional High-Order Dual-Domain Modulation Signal Permutation Array Constellation Diagram
The main purpose of this section is to invent a constructing method for an n-dimensional high-order dual-domain modulation signal permutation array constellation method based on the permutation group code Pn. That is, the n-dimensional dual-domain modulation signal model in Part 2 is used as the signal point, and the 2k codewords in a subset of the permutation group code Pn are used to control the transmission of this signal point, thereby forming the permutation array constellation diagram of an n-dimensional 2k order dual-domain modulation signal.
This section will describe three points. One is related to the method of selecting 2k codewords from p codewords of (n,μ,d) permutation group code Pn to form a permutation array code Γn when n>1 is any positive integer, which involves the method of using the cycle-shifted technology to generate the permutation array code Γn. The second is related to an disclosure of a method for constructing coset leader set Ln in the case of any n. The third is related to a structure and design method of the permutation array constellation architecture of n-dimensional high-order dual-domain modulation signal by using the six n-dimensional dual-domain modulation signal models in Part 2 based on the structural design of the permutation array code Γn.
First, when n>1 is any positive integer, the design method of the coset leader set Ln is invented. From the method of generating expressions (1) and (2), it can be found that the key to enumerating the permutation group code Pn is to first calculate the coset leader set Ln. This disclosure uses a scale transformation fa(x)=ax(wherein a∈Zn-1 and x∈Sn) to calculate Ln={al1|a∈Zn-1; l1=[12 . . . n]∈Sn}∪Sn. φ(n) is set to denote the number of numbers in a=1, 2, . . . , n−1 that do not have a common factor with n, {φ} denotes the set of numbers in a that do not have a common factor with n. The value range of a is a∈{φ}, which determines the size of the coset leader set, that is, |L_n|=|{φ}|=φ(n). The maximum number of fixed-points of any permutation vector except the unit permutation vector in Ln is expressed as δ, which gives the minimum Hamming distance of Ln, that is, dL
1. When n is a prime number, all the values of a=1, 2, . . . , n−1 and n are mutually prime numbers, that is, GCD(a,n)=1, there is no common factor of all values of a with n. Therefore, φ(n)=n−1, a∈{φ}={1, 2, . . . , n−1}=Zn-1, then Ln is referred to as the maximum single fixed point subgroup. A simple calculation expression L={al1|a∈Zn-1; l1=[12 . . . n]∈Sn} can be used to enumerate all permutation codewords in Ln. When the size of Ln is |L_n|=|{φ}|=φ(n)=n−1, it reaches the maximum. Since each permutation of the maximum single fixed point subgroup Ln contains only single-fixed-point, that is, δ=1, the minimum Hamming distance is dL
2. When n is not a prime number but a power of 2, that is, when n=2q is a power of 2, and q≥2 is a positive integer, the size of Ln is |Ln|=2q-1, the maximum fixed-point is δ=2q-1, the minimum Hamming distance of Ln is dL
3. When n>1 is the product of two prime numbers and contains 3, let h be another prime number, and the size of Ln is |Ln|=φ(n)=|{From 1 to n−1, the set of numbers that do not contain multiples of 3 and multiples of h}|. The maximum fixed-point of Ln is δ=the number of co-values of all 3 from 1 to n−1. The minimum Hamming distance of Ln is dL
In summary, for any positive integer n>1, the design method for Ln is: i) calculating the set {φ} formed by a=1, 2, . . . , n−1 and the value a which has no common factor with n, determining the number of the set |{φ}|=φ(n)=|Ln|; ii) calculating L={al1|a∈{φ}; GCD(a, n)=1; l1=[12 . . . n]}, obtaining the coset leader set Ln or listing Ln through observation; iii) using the method of observation or analysis to find the maximum fixed-point codeword from the set Ln, obtaining δ, and obtaining the minimum Hamming distance dL
Secondly, when n>1 is any positive integer, the design method of (n, μ, d) permutation group code Pn is provided first, and then the permutation array code Γn is generated from Pn. Specifically, the cycle-shifted technique is used to generate the permutation group code Pn. In the basic principle, it describes the algebraic generating method of permutation group code (n,n(n−1),n−1) when n is a prime number, and the permutation synchronous operation method (such as (1) calculation operation expression) and the calculation method of affine transformation (such as (2) calculation operation expression) are adopted. In the calculation operation expression (1), it is difficult to enumerate the code set Pn in the form of hardware and software, and the complexity in time calculation is quite high. In the calculation operation expression (2), it is required to use modulo-n addition and modulo-n multiplication operations, which has certain time complexity. Cycle-shifted technology is an effective method to reduce time complexity. For this purpose, the following cycle-shifted operator is defined, and a composition function based on the cycle-shifted operator is constructed.
The cycle-right-shifted operator trn is defined, when it acts on any permutation vector x=[x1x2 . . . xn], the rightmost element of this vector is moved to the leftmost, and the remaining n−1 elements are moved to the right in turn, namely trnx=trn[x1x2 . . . xn]=[xnx1x2 . . . xn-1]. The cycle-left-shifted operator tl1 is defined, when it acts on any permutation vector x=[x1x2 . . . xn], the leftmost element of this vector is moved to the rightmost, and the remaining n−1 elements are moved to the left in turn, namely tl1x=tl1[x1x2 . . . xn]=[x2x3 . . . xn-1xnx1].
A composition function of the cycle-right-shifted operator and the left-shifted operator are constructed. The composition function (trn)n-1 of the right-shifted operator trn is constructed, when it acts on any permutation codeword x=[x1x2 . . . xn], n permutation codeword including this permutation codeword x are obtained, thereby constituting a loop Latin square, and constituting an orbit set of permutation codewords with x as the leader of the orbit, or constituting a coset with x as the leader of the coset, thereby obtaining a set {(trn)n-1x}={x, (trn)1x, (trn)2x, . . . , (trn)n-1x}={(trn)n-1[x1x2 . . . xn])}={[x1x2 . . . xn], (trn)1[x1x2 . . . xn], (trn)2[x1x2 . . . xn], [x1x2 . . . xn]}={[x1x2 . . . xn], [xnx1x2 . . . xn-1], [xn-1xnx1x2 . . . xn-2], . . . , [x2x3 . . . xnx1]} constituted by n permutation codewords containing the permutation codeword x. The composition function (t1l)n-1 of the left-shifted operator tl1 is constructed, when it acts as any permutation codeword x=[x1x2 . . . xn], n permutation codewords including this permutation codeword x is obtained, thereby constituting a loop Latin square, and constituting an orbit set of permutation codewords with x as the leader of the orbit, or constituting a coset with x as the leader of the coset, thereby obtaining a set {(tl1)n-1x}={x, (tl1)1x, (tl1)2x, . . . , (tl1)n-1x}={(tl1)n-1 [x1x2 . . . xn]}={[x1 . . . xn], (tl1)1[x1 . . . xn], (tl1)2[x1 . . . xn], . . . , (tl1)n-1[x1 . . . xn]}={[x1 . . . xn], [xnx1 . . . xn-1], [xn-1xnx1 . . . xn-2], . . . , [x2 . . . xnx1]} constituted by n permutation codewords containing the permutation codeword x. These two composition functions act on the same permutation codeword x, and get the same code set {(trn)n-1x}={(tl1)n-1x}, but the order of the codewords in these two sets is different.
If the cycle-right-shifted composition function (trn)n-1 and the cycle-left-shifted composition function (tl1)n-1 both act on the maximum single-fixed-point subgroup Ln, the permutation group code Pn={(trn)n-1Ln}={(tl1)n-1Ln} can be obtained. More specifically, the cycle-left-shifted composition function (tl1)n-1 and the cycle-right-shifted composition function (trn)n-1 are used to act on the orbit leader permutation vector l1, l2, . . . , la, . . . , l|L
The method of generating permutation group code Pn in different situations is given below.
1) When n is a prime number, Ln={al1|a∈Zn-1; l1=[12 . . . n]∈Sn} is the maximum single fixed point subgroup of Sn, and Pn is calculated as follows.
Pn is a (n,n(n−1),n−1) permutation group code. This generating method has been protected in the patent “communication channel encoding method and permutation code set generator (Patent No.: ZL 2016 1 0051144.9, patent right obtained on Jan. 26, 2019)”. Here, the above disclosure is described again in different ways, and the description is easier to understand and clearer for operation.
2) When n is not a prime number, L={al1|a∈Zn-1; GCD(a,n)=1; l1=[12 . . . n]∈Sn} is a fixed-point subgroup of Sn, and Pn is calculated as follows.
Pn is a (n,n·φ(n),n−δ) permutation group code, wherein δ is the maximum fixed-points in all permutation vectors of Ln, and δ can be used to determine the minimum Hamming distance dL
Set n=8 as a power of 2, not a prime number. The value of a in a∈Zn-1=Z7={1,2,3,4,5,6,7} which has no common factor with n=8 can be taken from {φ}={1,3,5,7}′ φ(n)=φ(8)=4′ |{φ}|=φ(8)=|L8|=4. First of all, L8 is calculated.
L8 {al1|a∈Zn-1; GCD(a,n); l1=[12 . . . n]}={al1|a∈{1,3,5,7}; l1=
={l1, l3, l5, l7}={[12345678], [36147258], [52741638], [76543218]}
It can be verified that the three vectors in the set {al1|a∈{2,4,6}; l1=[12345678]}={l2, l4, l6}={[24682468, [48484848], [64286428]} are all constituted by positive numbers, but none of them is permutation vector. The cycle-left-shifted composition function (tl1)n-1 can be used to act on L8 to generate P8.
In digital communication systems, since binary sequences are used to control the emission of signal points in the constellation diagram, which requires the size of the constellation diagram to be a power of 2, and the size of the permutation group code Pn is not necessarily a power of 2, so the permutation array code Γn needs to be incorporated.
The limiting condition for constructing permutation array code Γn is: i) Γn must be a subset of Pn, so |Γn|≤|Pn| is incorporated; ii) Γn must have a coset structure similar to Pn, and be able to use the reduced order functions (tl1)Q and (trn)Q of the cycle-shifted bit composition function (tl1)n-1 and (trn)n-1 to act on Ln, wherein Q≤n−1, and the value of Q must be a power of 2 minus 1; iii) since the size of the permutation array constellation diagram is a power of 2, this requires that the size of the permutation array code Γn must be a power of 2, wherein the number of cosets in Γn is also a power of 2, and the number of codewords in each coset is also a power of 2; iv) under the condition that |Γn| is a power of 2, Γn should be as large as possible to obtain a larger data rate.
According to the above limiting conditions of the permutation array code Γn set in the disclosure, a design criterion for Γn can be determined as follows: For Γn={(tl1)QLn}⊂Pn or Γn={(trn)QLn}⊂Pn, the size |Ln| of Ln is preferably a power of 2, as set in the above condition iii).
In the limiting condition i) of permutation array code Γn, |Γn|≤|Pn|, which implies that codewords need to be discarded when obtaining Γn from Pn, and the above design criterion ensures that, when Γn is obtained from Pn, none of coset in Pn should be discarded. Therefore, this design criterion ensures that the number of cosets of Γn is equal to the number of cosets of Pn, and both need to be a power of 2, which also ensures that |Γn| is as large as possible, so as to obtain the most codewords from Pn to reach the maximum data rate, therefore, Γn is the optimal permutation array code.
Pn={(trn)n-1Ln}={(tl1)n-1Ln} is the permutation group, but Γn={(trn)QLn}={(trn)Ql1, (trn)Ql2, . . . , (trn)Qln-1} or Γn={(tl1)QLn}={(tl1)Ql1, (tl1)Ql2, . . . , (tl1)Qln-1} is no longer the permutation group because there is Q=2p−1≤n−1 from Pn to Γn. In other words, at least n−2Q codewords must be deleted from each coset of Pn to form Γn. The deletion of these codewords from Pn destroys the group structure of Γn, making it not satisfy the four axioms of the group, that is, some codewords in Γn do not have inverses, and not all codewords satisfy the associative law. Therefore, Γn is called permutation array code. Additionally, each subset {(tl1)Qla} in Γn={(tl1)QLn}={(tl1)Ql1, (tl1)Ql2, . . . , (tl1)Qln- 1} is still a coset, but is no longer the orbit of the permutation codeword of the coset leader, because every orbit in original Pn can migrate from the last orbit back to the orbit leader permutation, and every coset in Γn no longer has orbit characteristics. It is set that the binary sequence to be transmitted is decomposed into segments of length k, then the size of the permutation array code is |Γn|=2k.
Table 1 shows the generating expression and related parameters of the permutation array codes. The disclosure seeks to protect 9 permutation array codes.
In the expression, n is the code length, and the code length of the permutation array code sought to be protected is n=4, 5, 8, 15, 16, 17, 32, 51, 64, refer to the first column of Table 1.
The length of the binary message sequence carried by the 9 permutation array codes is k=3, 4, 5, 6, 7, 8, 9, 10, 11 bits, as shown in the second column of Table 1.
The number of cosets contained in these 9 permutation array codes are |Ln|=2k
The size of the 9 permutation array codes is |Γn|=2k=8, 16, 32, 64, 128, 256, 512, 1024, 2048, see the fifth column of Table 1.
Among all the codewords of the 9 permutation array codes, the corresponding maximum fixed-points are δ=2, 1, 4, 5, 8, 1, 16, 17, 32, as shown in the second last column of Table 1.
The minimum Hamming distances of the 9 permutation array codes are dΓ
The expression for generating 9 permutation array codes is
Γ4={(tl1)3L4}={(tl1)3{al1}|a∈{1,3};l1=[x1x2x3x4]}
Γ5={(tl1)3L5}={(tl1)3{al1}|a∈{1,2,3,4};l1=[x1x2x3x4x5]}
Γ8={(tl1)7L8}={(tl1)7{al1}|a∈{1,3,5,7};l1=[x1x2. . . x7x8]}
Γ15={(tl1)7L15}={(tl1)7{al1}|a∈{1,2,4,7,8,11,13,14};l1=[x1x2 . . . x14x15]}
Γ16={(tl1)15L16}={(tl1)15{al1}|a∈{1,3,5,7,9,11,13,15};l1=[x1x2 . . . x15x16]}
Γ17={(tl1)15L17}={(tl1)15{al1}|a∈{1,2, . . . ,15};l1=[x1x2 . . . x16x17]}
Γ32={(tl1)31L32}={(tl1)31{al1}|a∈{1,3,5,7, . . . ,29,31};l1=[x1x2. . . x31x32]}
Γ51={(tl1)31L51}={(tl1)31{al1}|a∈{Remove multiples of 3 and multiples of 17 from natural numbers from i to 51};l1=[x1x2. . . x50x51]}
Γ64={(tl1)63L64}={(tl1)63{al1}|a∈{All odd numbers from 1 to 64}; l1 [x1x2 . . . x63x64]}}
Specifically, in order to make each codeword well represented when the codeword length n>9, the unit vector l1=[123 . . . n] of each permutation array code is expressed as l1=[x1x2x3 . . . xn], that is, the subscript value of each element in the vector is used to represent the permutation codeword of the long code.
From Pn to Γn, the number of discarded codewords for 9 permutation array codes is described as follows: codeword is not discarded from Γ4, Γ8, Γ16, Γ32, Γ64, four codewords are discarded from P5 to Γ5, 56 codewords are discarded from P15 to Γ15, 16 codewords are discarded from P17 to Γ17, 608 codewords are discarded from P51 to Γ51, see the last third column in Table 1.
From the n-dimensional dual-domain modulation signal model in Part 2, it can be seen that the n-dimensional vector modulating the amplitude, phase, and frequency of n carriers is derived from the permutation codewords in the permutation array code set Γn. Then, the six signal models sm(t) are controlled by the subscript m=1, 2, . . . , |Γn| to form signal points generated by |Γn|=2k permutation codewords. This |Γn| signal points form a high-order permutation array constellation diagram of an n-dimensional dual-domain modulation signal, and represented as a set {sm(t)|m=1, 2, . . . , |Γn|; sm(t)=n-TAM, n-TPM, n-TFM, n-TAPM, n-TAFM, n-TAPFM}. For these 6 permutation array constellations, the specific structure design is as follows:
1) The permutation array constellation diagram of the n-dimensional 2k order time-amplitude dual-domain modulation signal is a set {sm(t)|m=1, 2, . . . , 2k; sm(t)=[u1u2 . . . un]g(t) cos ωct; [u1u2 . . . un]∈Γn} of 2k signal points sm(t), which is a constellation diagram constituted by 2k “amplitude signals sequentially controlled by n time chips”.
2) The n-dimensional 2k order time-phase dual-domain modulation signal permutation array constellation diagram is a set
constituted by 2k signal points sm(t), which is a constellation diagram constituted by 2k “phase signals sequentially controlled by n time chips”.
3) The n-dimensional 2k-order time-frequency dual-domain modulation signal permutation array constellation diagram is a set {sm(t)|m=1, 2, . . . , 2k; sm(t)=g(t)[(cos 2πfw
4) The permutation array constellation diagram of the dual-domain modulation signal composed of n-dimensional 2k-order time-amplitude-phase joint modulation multi-domain is a set
constituted by 2k signal points sm(t), which is a constellation diagram constituted by 2k “joint modulation domain signals of amplitude and phase sequentially controlled by n time chips”, wherein Γn1={(tl1)Q
5) The permutation array constellation diagram of the dual-domain modulation signal composed of n-dimensional 2k-order time-amplitude-frequency joint modulation multi-domain is a set {sm(t)|m=1, 2, . . . , 2k; sm(t)=g(t)[(u1 cos(2πfw
6) The permutation array constellation diagram of the dual-domain modulation signal composed of n-dimensional 2k-order time-amplitude-phase-frequency joint modulation multi-domain is a set
composed of 2k signal points sm(t), which is a constellation diagram composed of 2k “variable power phase modulation-frequency modulation joint modulation domain signal sequentially controlled by n time chips”, wherein Γn1={(tl1)Q
Permutation array code Γn={(tl1)Q{al1}} and its subset Γn1={(tl1)Q
It is worth noting that the permutation array constellation diagrams of the 6 kinds of n-dimensional 2k-order dual-domain modulation signals constructed above is described and exhibited in a different form as compared with conventional or currently adopted constellation diagrams of the 2-dimensional 2k-order modulation signals. For example, the commonly adopted QAM constellation diagram is defined as a two-dimensional plane quadrature amplitude phase modulation constellation diagram. Because QAM constellation diagram is two-dimensional, the points on the two-dimensional plane can be adopted to represent the signal points. The discrete dots on the plane represent the signal constellation diagram. The permutation array code is a hyperball code of equal power, which means that the n-dimensional 2k-order dual-domain modulation signal of the hyperball code based on the permutation array code cannot visually display the geometric shape of the signal point in the 2-dimensional plane and the 3-dimensional space. Therefore, the permutation array constellation diagram of the n-dimensional 2k-order dual-domain modulation signal can only be described by the above-mentioned calculation expression at present. It should be emphasized that the permutation array constellation diagrams of the above-mentioned 6 kinds of n-dimensional 2k-order dual-domain modulation signals are represented by mathematical symbols and operation expressions formed by them, but it neither belongs to any mathematical category, nor is it universal or natural mathematical tools and laws of nature. All signal expressions and constellation diagram expressions are constructed by the inventor by borrowing mathematical symbols.
Number | Date | Country | Kind |
---|---|---|---|
202010569496.X | Jun 2020 | CN | national |
Number | Name | Date | Kind |
---|---|---|---|
20170214414 | Peng et al. | Jul 2017 | A1 |
Number | Date | Country |
---|---|---|
105680992 | Jun 2016 | CN |
Number | Date | Country | |
---|---|---|---|
20210368346 A1 | Nov 2021 | US |