CN103905178B - Distributed system and closed-loop type phase synchronization method based on directional negative feedback - Google Patents
Distributed system and closed-loop type phase synchronization method based on directional negative feedback Download PDFInfo
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Abstract
The invention provides a distributed system and a closed-loop type phase synchronization method based on directional negative feedback, and belongs to the technical field of wireless communication. In several initial time slots, when the intensity of a received signal is smaller than the threshold of a next stage, a large-step-length disturbance is adopted, and the intensity of the received signal of a receiver can be increased quickly. In the late time slots, when the intensity of the received signal is smaller than the threshold of the next stage, a small-step-length disturbance is adopted, the stability of the prior art can be achieved, and the signal intensity of the receiver can be iteratively converged to the ideal condition. Furthermore, the direction of the step length of the disturbance of transmitters is firstly determined in the adjusting process, after the direction is determined, it is indicated that the adjustment direction of each transmitter is correct, only is the magnitude of the step length of the disturbance adjusted in the subsequent time slots, and the convergence of the intensity of a subsequent received signal can be further accelerated.
Description
Technical field
The invention belongs to wireless communication technology field, more particularly, to a kind of distributed system and its degenerative based on orientation
Closed loop phase synchronization method.
Background technology
Single bit feedback algorithm is to realize the common technology that transmitter signal reaches carrier phase synchronization in receiving terminal.This calculation
Method achievement up-to-date at present is a kind of single bit feedback algorithm of the mixing based on distributed beams forming technique, specifically using connecing
- 1 bit information that receipts machine feeds back, carries out a step-length disturbance δ to each transmitter of transmitting terminaliThe phase compensation of (n)
And in receiver continuous feedback cnWhen individual " -1 " bit information, with a scale factor εi(n) decay δi(n), Neng Gouji
When adjustment transmitter phase compensation.The advantage of this technology is can to make received signal strength rapid growth by phase compensation,
Promote received signal strength can restrain in certain time slot by phase-noise.
But found according to research, transmitter has different convergence rates under different step-lengths, and different anti-
Under feedback Regulation mechanism, convergence of algorithm gain can be different, and therefore existing convergence of algorithm speed and convergence capabilities have lifting
Space.
Content of the invention
First technical problem to be solved by this invention is to provide a kind of distributed system degenerative based on orientation
Closed loop phase synchronization method is it is intended to accelerate received signal strength convergence rate and the convergence capabilities of receiver.
The present invention is achieved in that a kind of distributed system is based on and orients degenerative closed loop phase synchronization method,
Following step including executing in each time slot:
Step a, receiver judges whether the intensity of current time slots receipt signal is more than or equal to next stage threshold value, and according to
Judged result feeds back corresponding single bit of information to transmitter;
Step b, transmitter is parsed after receiving described single bit of information, if disturbance step-length optimal direction is not true
Fixed, analysis result is more than or equal to next stage threshold value, then execution step c for the intensity of receiver receipt signal simultaneously, otherwise holds
Row step d;If disturbance step-length optimal direction determine, simultaneously analysis result be receiver receipt signal intensity be more than or equal under
One phase threshold, then execution step c, otherwise execution step e;Described disturbance step-length optimal direction is receipt signal strong
After degree is less than the situation of next stage threshold value, when received signal strength occurring first more than or equal to next stage threshold value, with
The disturbance step-length direction of a upper time slot is the disturbance step-length optimal direction of all time slots afterwards;
Step c, transmitter still takes it in the optimum phase of current time slots in the optimum phase of next time slot, and in lower a period of time
Gap does not produce disturbance step-length, and next time slot directly below the optimum phase of a time slot add initial phase as transmitter, phase
Carry out transmission signal, number of stages adds one simultaneously;Described initial phase receives according to transmitter in first time slot for transmitter
Signal estimation obtain;
Step d, the disturbance step-length of next time slot is equal to the product in its disturbance step-length direction and current phase threshold step-length,
Transmitter is that the optimum phase of current time slots adds that the disturbance step-length of next time slot deducting is worked as in the optimum phase of next time slot
The disturbance step-length of front time slot, the optimum phase of transmitter time slot below next time slot adds initial phase as transmitter, phase
Carry out transmission signal;Wherein, described disturbance step-length direction is generated at random by transmitter;
Step e, the disturbance step-length of next time slot is equal to its disturbance step-length optimal direction and current phase threshold step-length
Product, transmitter adds the disturbance step-length of next time slot and subtracts for the optimum phase of current time slots in the optimum phase of next time slot
Go the disturbance step-length of current time slots.The optimum phase of transmitter time slot below next time slot adds initial phase as transmitting
Phase place carrys out transmission signal.Second technical problem to be solved by this invention is to provide a kind of distributed system, including some
Whether the intensity that receiver described in individual transmitter and receiver is used for judging current time slots receipt signal in each time slot is more than etc.
In next stage threshold value, and corresponding single bit of information is fed back to transmitter according to judged result;Described transmitter is used for connecing
Parsed after receiving described single bit of information;
If disturbance step-length optimal direction does not determine, analysis result is more than or equal to for the intensity of receiver receipt signal simultaneously
Next stage threshold value, then transmitter still take it in the optimum phase of current time slots in the optimum phase of next time slot, and at next
Time slot does not produce disturbance step-length, and next time slot directly below the optimum phase of a time slot add initial phase as transmitting phase
Transmission signal is carried out in position, and number of stages adds one simultaneously;Described initial phase is that transmitter receives according to transmitter in first time slot
The signal estimation arriving obtains;Otherwise, transmitter is equal to its disturbance step-length direction and current rank in the disturbance step-length of next time slot
The product of section threshold steps, transmitter is the optimum phase of current time slots plus next time slot in the optimum phase of next time slot
Disturbance step-length simultaneously deducts the disturbance step-length of current time slots, and the optimum phase of transmitter time slot below next time slot adds initial
Phase place carrys out transmission signal as transmitter, phase;Wherein, described disturbance step-length direction is generated at random by transmitter;Described disturbance step
Long optimal direction is after the situation that received signal strength is less than next stage threshold value, received signal strength first big
In or when being equal to next stage threshold value, the disturbance step-length direction of an above time slot be after all time slots disturbance step-length optimum
Direction;
If disturbance step-length optimal direction determine, simultaneously analysis result be receiver receipt signal intensity be more than or equal under
One phase threshold, then transmitter still take it in the optimum phase of current time slots in the optimum phase of next time slot, and in lower a period of time
Gap does not produce disturbance step-length, and next time slot directly below the optimum phase of a time slot add initial phase as transmitter, phase
Carry out transmission signal, number of stages adds one simultaneously;Described initial phase receives according to transmitter in first time slot for transmitter
Signal estimation obtain;Otherwise, transmitter next time slot disturbance step-length be equal to its disturbance step-length optimal direction with current
The product of phase threshold step-length, transmitter is the optimum phase of current time slots plus next time slot in the optimum phase of next time slot
Disturbance step-length and deduct the disturbance step-length of current time slots, the optimum phase of transmitter time slot below next time slot adds just
Beginning phase place carrys out transmission signal as transmitter, phase.Further, described phase threshold step-length subtracts with being incremented by of number of stages
Little.
Further, described number of stages, phase threshold step-length, the corresponding relation of phase threshold are as follows:
The present invention compared with prior art, has the beneficial effects that:
1) it is directed to the given little step-length disturbance of original technology, the present invention proposes a step-length disturbance selection mechanism: stage
Threshold steps selection mechanism.In initial several time slots, using big step-length disturbance, receiver received signal strength can be made quick
Increase.In later stage time slot, using little step-length disturbance, it is obtained in that preferable stability, even if receiver signal strength convergence
To preferable situation.
2) direction of the disturbance step-length to transmitter for original technology is random, both adjustment direction and being sized, this
Invention first determines the direction of transmitter disturbance step-length, after direction determines, illustrates that the adjustment direction of each transmitter is correct
, only adjust disturbance step sizes in subsequent timeslot, the convergence of subsequent received signals intensity can be further speeded up.
Brief description
Fig. 1 is the Organization Chart of the distributed system that the present invention provides;
Fig. 2 is the chart of the step-length threshold value selection mechanism that the present invention provides;
Fig. 3 is the feedback adjustment flow chart of the phase synchronization method that the present invention provides;
Fig. 4 is the flow chart that in the phase synchronization method that the present invention provides, rss is more than present threshold value;
Fig. 5 is that in the phase synchronization method that the present invention provides, rss is less than the flow chart being more than present threshold value.
Specific embodiment
In order that the objects, technical solutions and advantages of the present invention become more apparent, below in conjunction with drawings and Examples, right
The present invention is further elaborated.It should be appreciated that specific embodiment described herein is only in order to explain the present invention, and
It is not used in the restriction present invention.
For the given little step-length of original technology, the present invention proposes a step-length selection mechanism, in the different stages, adopts
With different step-lengths, to accelerate the convergence rate under different received signal strengths.And, original technology is to transmitter
The direction of phase compensation is random, both adjustment direction and being sized, and the present invention proposes a determination transmitter compensation phase
The method in the direction of position, the determination in direction, can speed up the convergence subsequently accepting signal intensity.
Fig. 1 shows the framework of the distributed system that the present invention is suitable for, and multiple transmitters launch letter to receiver simultaneously
Number, and according to receiver feedback single bit of information adjust next time slot transmission signal phase place, eventually through phase place mend
The mode repaid makes the Phase synchronization of each receipt signal of arrival receiver.
Specifically, in the feedback closed loop system of this single-bit of Fig. 1, in n-th time slot, transmitter receives and feeds back
Single bit of information, it is determined whether adjustment transmission signal phase place.The transmitter, phase formula of each transmitter, as follows:
φi=γi+θi(n)+ψiγi,ψi∈[0,2π) (1)
Wherein, γiRepresent the unknown phase skew of i-th transmitter, ψiRepresent the phase place between i-th transmitter and receiver
Response is it is assumed that γiAnd ψiAlways static during algorithmic statement, meet and be uniformly distributed [0,2 π) with entering variable and right
It is all unknown for transmitter and receiver, both are referred to as initial phase c.We are by by the digital ratio from receiver
Special feedback information adjusts the variable θ of n-th time slot of transmitter iiN () is referred to as optimum phase.Initial value is set to θi(0)=0.Due to
The target of algorithm be exactly reach Phase synchronization it is assumed that each transmitter has unit power in receiver end, each transmitter with connect
The channel gain of receipts machine is 1.Therefore, receiver is as follows in the receiving signal strength expression of time slot n:
Wherein, j represents -1 root of opening, and records optimum phase θ in internal memoryiN (), simultaneously in each time slot, according to receiver
The single bit of information of feedback, compensates disturbance step-length δi(n), i.e. optimum phase θiN () is δiThe function of (n), so that algorithm
The Phase synchronization of receiver end can be realized in certain time slot.
Present invention introduces new disturbance step-length production method realizes the phase compensation of each transmitter, i.e. disturbance step-length δi
N () is stage by stage, and from big to small.And in phase threshold step-length selection mechanism, disturbance step-length δiN () is by the rank in Fig. 2
Section threshold steps g (k) produces size, and direction is then random.In the training process of whole algorithm, if current generation k
Received signal strength rss is more than phase threshold th (k+1) (table 1) setting, then training process then enters next stage k+1.
Illustrate that current adjustment is useful, so that the phase place between transmitter is drawn close toward certain common direction.
First it should distinguish the concept of phase threshold step-length and phase threshold.Phase threshold step-length is in different phase, sends out
Penetrate machine interpolation random disturbance size, phase threshold is through formula (4), by transmitter between maximum phase difference x (k) determine
, this value is compared with received signal strength r (n) in receiver end, is used to determine whether enter next stage.Both
Mainly produced by following two formula:
x(k)=π/2kk=0:1:s-1 (3)
Wherein, s is the stage sum in given training process, and n is transmitter number, and x (k) is in kth between transmitter
The maximum phase in stage is poor, corresponding, and th (k) is then the minimum received signal strength rss in the kth stage, that is, the stage
The concept of threshold value.According to maximum phase difference x (k), then can produce phase threshold step-length g (k) in each stage, generation rule
It is:
g(k)=x(k)/2 (5)
That is, phase threshold step-length is the half of maximum phase difference.As can be seen that being [0,2 in transmitter phase excursion
In the case of π), transmitter phase difference then be [0, π) it is clear that phase threshold step-length be maximum phase difference half purpose have two
Individual: one is the phase contrast that can regularly reduce between transmitter, two is that the step-length adjusting will from big to small, and early stage accelerates
Algorithmic statement, the later stage ensures algorithmic statement to ideal situation.
Fig. 3,4,5 describe the feedback adjustment mechanism between the transmitter and receiver of the present invention.In the lump with reference to Fig. 3 extremely
Fig. 5.The distributed system that the present invention provides is based on the degenerative closed loop phase synchronization method of orientation and comprises the steps:
Step a, receiver judges whether the intensity of current time slots receipt signal is more than or equal to next stage threshold value, and according to
Judged result feeds back corresponding single bit of information to transmitter;
Step b, transmitter is parsed after receiving described single bit of information, if disturbance step-length optimal direction is not true
Fixed, analysis result is more than or equal to next stage threshold value, then execution step c for the intensity of receiver receipt signal simultaneously, otherwise holds
Row step d;If disturbance step-length optimal direction determine, simultaneously analysis result be receiver receipt signal intensity be more than or equal under
One phase threshold, then execution step c, otherwise execution step e;Described disturbance step-length optimal direction is receipt signal strong
After degree is less than the situation of next stage threshold value, when received signal strength occurring first more than or equal to next stage threshold value, with
The disturbance step-length direction of a upper time slot is the disturbance step-length optimal direction of all time slots afterwards;
Step c, transmitter still takes it in the optimum phase of current time slots in the optimum phase of next time slot, and in lower a period of time
Gap does not produce disturbance step-length, and next time slot directly below the optimum phase of a time slot add initial phase as transmitter, phase
Carry out transmission signal, number of stages adds one simultaneously;Described initial phase receives according to transmitter in first time slot for transmitter
Signal estimation obtain;
Step d, the disturbance step-length of next time slot is equal to the product in its disturbance step-length direction and current phase threshold step-length,
Transmitter is that the optimum phase of current time slots adds that the disturbance step-length of next time slot deducting is worked as in the optimum phase of next time slot
The disturbance step-length of front time slot, the optimum phase of transmitter time slot below next time slot adds initial phase as transmitter, phase
Carry out transmission signal;Wherein, described disturbance step-length direction is generated at random by transmitter;
Step e, the disturbance step-length of next time slot is equal to its disturbance step-length optimal direction and current phase threshold step-length
Product, transmitter adds the disturbance step-length of next time slot and subtracts for the optimum phase of current time slots in the optimum phase of next time slot
Go the disturbance step-length of current time slots.The optimum phase of transmitter time slot below next time slot adds initial phase as transmitting
Phase place carrys out transmission signal.Wherein step c, d, e correspond to+1 block process of Fig. 4 and -1 block process of Fig. 5 respectively.The present invention is first
First adjust disturbance step-length δiN the direction of (), after determining its direction, the direction that each transmitter phase compensates will no longer change
Become, simply in different phase, according to the feedback information of each time slot receiver, adjust the size of disturbance step-length, accelerate transmitter
Phase place is in effective merging of receiver.
Compensate closed-loop synchronization algorithm in orientation negative feedback, we introduce two state variables state_a and state_b,
And a direction variable direct.Direct shows disturbance step-length δiThe phase compensation direction of (n) transmitter in time slot n.
We initialize optimum phase θi(0)=0, state variable state_a=0 and state_b=0 in time slot n=0.
Work as state_a=0, show that transmitter, from time slot 0 to each time slot of time slot n, can smoothly jump into the next one
Stage, i.e. r (n) >=th (k+1).Physically illustrate, receiver is all feedback "+1 " bit information from 0 time slot to n time slot, the phase
Between do not occur feed back " -1 " bit information situation.As state_b=0, show that transmitter occurs not jumping into the next one first
The situation in stage, that is, receiver feed back " -1 " bit information first, if following slots continuous feedback " -1 " bit information,
State_b=0 keeps constant, and meanwhile, the direction direct of step-length disturbance is also undetermined.The training process of this algorithm is deposited
In two crucial change points.One is that transmitter receives " -1 " bit information first, and another is from time slot n to time slot n+
1, the transformation from " -1 " to "+1 " there is first, i.e. n reception " -1 " feedback information, n+1 reception "+1 " feedback information,
And, in whole process, it is to occur first.
When transmitter receives " -1 " feedback information first, state_a will be set to 1, i.e. state_a=1, and not
Change again.In follow-up iterative process, state_a will be used for controlling when occurring from the situation of " -1 " to "+1 " first
State_b is so as to put 1.State_b=1 shows that the direction of disturbance step-length is determined in certain time slot n, meanwhile, from the n+1 moment
Rise, state_b will no longer change, show that follow-up training process will no longer be required to adjust the direction of the phase compensation of transmitter,
Each transmitter can adjust disturbance step sizes along fixed direction.
From the above, it can be seen that state_a controls the adjustment of state_b, state_b control direction variable direct.
, only when receiver feedback negative bit information, the state of state_b is adjusting for direct.When transmitter receives " -1 " feedback
When, direct adjustment is as follows:
As state_b=0, we generate the direction of disturbance step-length at random, and work as and occur first to moment n+1 from moment n
When " -1 " arrives the transformation of "+1 ", direct will keep constant, and no longer change in follow-up training process, i.e. transmitter phase
The direction that position compensates has determined.
It is obvious that except the adjustment of three above variable, in whole training process, we also need to adjust two other
Variable: disturbance step-length δ of adjustment according to receiver feedback information, direction variable direct and phase threshold step-length g (k)i
(n), optimum phase θiThe adjustment of (n).Both adjustment formula are as follows:
δi(n+1)=direct×g(k)r(n)<th(k+1) (7)
When transmitter receives " -1 " feedback, in the step-length disturbance δ in n+1 momenti(n+1) entered according to formula (5) and (6)
Row updates, i.e. δi(n+1)=direct×g(k).If feedback "+1 " bit information, do not produce disturbance step-length.When receiver is anti-
During feedback "+1 " information, according to formula (8), keep optimum phase constant, i.e. θi(n+1)=θi(n).If feedback " -1 " information,
θi(n+1)=θi(n)+δi(n+1)-δi(n).
The present invention can be with wireless environments, and multiple wireless transmit nodes launch identical signal to receiver, lead to
The feedback adjustment mechanism crossing the present invention forms a closed loop, and under complicated channel, makes the signal intensity of receiver quick
Convergence.
The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all essences in the present invention
Any modification, equivalent and improvement made within god and principle etc., should be included within the scope of the present invention.
Claims (6)
1. a kind of distributed system is based on and orients degenerative closed loop phase synchronization method it is characterised in that including at each
The following step of time slot execution:
Step a, receiver judges whether the intensity of current time slots receipt signal is more than or equal to next stage threshold value, and according to judgement
Result feeds back corresponding single bit of information to transmitter;
Step b, transmitter is parsed after receiving described single bit of information, if disturbance step-length optimal direction does not determine, with
When analysis result be receiver receipt signal intensity be more than or equal to next stage threshold value, then execution step c, otherwise execution step
d;If disturbance step-length optimal direction determines, analysis result is the intensity of receiver receipt signal more than or equal to next stage simultaneously
Threshold value, then execution step c, otherwise execution step e;Described disturbance step-length optimal direction is to be less than received signal strength
After the situation of next stage threshold value, when received signal strength occurring first more than or equal to next stage threshold value, above a period of time
The disturbance step-length direction of gap is the disturbance step-length optimal direction of all time slots afterwards;
Step c, transmitter still takes it in the optimum phase of current time slots in the optimum phase of next time slot, and in next time slot not
Produce disturbance step-length, and next time slot directly below the optimum phase of a time slot to send out as transmitter, phase plus initial phase
Penetrate signal, number of stages adds one simultaneously;The letter that described initial phase receives according to transmitter in first time slot for transmitter
Number estimation obtain;
Step d, the disturbance step-length of next time slot is equal to the product in its disturbance step-length direction and current phase threshold step-length, transmitting
Machine is when the optimum phase of next time slot is that the optimum phase of current time slots adds the disturbance step-length of next time slot and deducts current
The disturbance step-length of gap, the optimum phase of transmitter time slot below next time slot to be sent out as transmitter, phase plus initial phase
Penetrate signal;Wherein, described disturbance step-length direction is generated at random by transmitter;
Step e, the disturbance step-length of next time slot is equal to the product of its disturbance step-length optimal direction and current phase threshold step-length,
Transmitter is that the optimum phase of current time slots adds that the disturbance step-length of next time slot deducting is worked as in the optimum phase of next time slot
The disturbance step-length of front time slot, the optimum phase of transmitter time slot below next time slot adds initial phase as transmitter, phase
Carry out transmission signal.
2. closed loop phase synchronization method as claimed in claim 1 is it is characterised in that described phase threshold step-length is with the stage
Count is incremented by and reduces.
3. closed loop phase synchronization method as claimed in claim 2 it is characterised in that described number of stages, phase threshold step-length,
The corresponding relation of phase threshold such as following table, wherein s is the stage sum in given training process:
4. a kind of distributed system, including several transmitter and receivers it is characterised in that described receiver is used at each
Time slot judges whether the intensity of current time slots receipt signal is more than or equal to next stage threshold value, and corresponding according to judged result feedback
Single bit of information to transmitter;Described transmitter is used for being parsed after receiving described single bit of information;
If disturbance step-length optimal direction does not determine, analysis result is the intensity of receiver receipt signal more than or equal to next simultaneously
Phase threshold, then transmitter still take it in the optimum phase of current time slots in the optimum phase of next time slot, and in next time slot
Do not produce disturbance step-length, and next time slot directly below the optimum phase of a time slot add that initial phase comes as transmitter, phase
Transmission signal, simultaneously number of stages add one;Described initial phase receives according to transmitter in first time slot for transmitter
Signal estimation obtains;Otherwise, transmitter is equal to its disturbance step-length direction and current stage threshold in the disturbance step-length of next time slot
Value step-length product, transmitter next time slot optimum phase be current time slots optimum phase add next time slot disturbance
Step-length simultaneously deducts the disturbance step-length of current time slots, and the optimum phase of transmitter time slot below next time slot adds initial phase
Carry out transmission signal as transmitter, phase;Wherein, described disturbance step-length direction is generated at random by transmitter;Described disturbance step-length is
Excellent direction be occur received signal strength be less than next stage threshold value situation after, occur first received signal strength be more than or
When person is equal to next stage threshold value, the disturbance step-length direction of an above time slot is the disturbance step-length optimum side of all time slots afterwards
To;
If disturbance step-length optimal direction determines, analysis result is the intensity of receiver receipt signal more than or equal to lower single order simultaneously
Section threshold value, then transmitter still do not take it in the optimum phase of current time slots in the optimum phase of next time slot, and in next time slot not
Produce disturbance step-length, and next time slot directly below the optimum phase of a time slot to send out as transmitter, phase plus initial phase
Penetrate signal, number of stages adds one simultaneously;The letter that described initial phase receives according to transmitter in first time slot for transmitter
Number estimation obtain;Otherwise, transmitter is equal to its disturbance step-length optimal direction and current stage in the disturbance step-length of next time slot
The product of threshold steps, transmitter adds disturbing of next time slot in the optimum phase of next time slot for the optimum phase of current time slots
Dynamic step-length simultaneously deducts the disturbance step-length of current time slots, and the optimum phase of transmitter time slot below next time slot adds initial phase
Transmission signal is carried out as transmitter, phase in position.
5. distributed system as claimed in claim 4 is it is characterised in that described phase threshold step-length is incremental with number of stages
And reduce.
6. distributed system as claimed in claim 5 is it is characterised in that described number of stages, phase threshold step-length, phase threshold
Corresponding relation such as following table, wherein s be in given training process stage sum:
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CN103944710B (en) * | 2014-04-10 | 2017-01-25 | 深圳大学 | Distributed system and close-loop phase synchronization method based on continuous negative feedback |
CN103905178B (en) * | 2014-04-10 | 2017-01-25 | 深圳大学 | Distributed system and closed-loop type phase synchronization method based on directional negative feedback |
CN105306190B (en) * | 2015-12-08 | 2018-04-03 | 深圳大学 | Closed loop phase synchronization method and distributed communication system based on accumulation positive feedback |
WO2019006715A1 (en) * | 2017-07-05 | 2019-01-10 | 深圳大学 | Distributed secure beamforming method and apparatus based on feedback control |
CN110350964B (en) * | 2019-07-04 | 2022-04-26 | 佛山科学技术学院 | Distributed beam forming method and device based on probability constraint |
CN112887010B (en) * | 2021-01-22 | 2022-07-19 | 中国人民解放军国防科技大学 | Inter-satellite link signal level cooperative communication method and device and computer equipment |
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US8634405B2 (en) * | 2008-09-08 | 2014-01-21 | The Trustees Of Princeton University | System and method for synchronizing phases and frequencies of devices in multi-user, wireless communications systems |
CN103944710B (en) * | 2014-04-10 | 2017-01-25 | 深圳大学 | Distributed system and close-loop phase synchronization method based on continuous negative feedback |
CN103905178B (en) * | 2014-04-10 | 2017-01-25 | 深圳大学 | Distributed system and closed-loop type phase synchronization method based on directional negative feedback |
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