CN113037393B - Control method of event-triggered communication system based on terahertz channel capacity - Google Patents

Control method of event-triggered communication system based on terahertz channel capacity Download PDF

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CN113037393B
CN113037393B CN202110274116.4A CN202110274116A CN113037393B CN 113037393 B CN113037393 B CN 113037393B CN 202110274116 A CN202110274116 A CN 202110274116A CN 113037393 B CN113037393 B CN 113037393B
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channel capacity
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常博
闫晓钰
唐威
陈智
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University of Electronic Science and Technology of China
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/90—Non-optical transmission systems, e.g. transmission systems employing non-photonic corpuscular radiation

Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to an event-triggered communication system control method based on terahertz channel capacity. Compared with the traditional periodic control scheme of the terahertz communication system, the event-triggered control scheme saves a large amount of control overhead and power consumption on the basis of ensuring the communication performance. The triggering method based on the terahertz real-time channel capacity can adapt to the change of the channel in real time and make corresponding control so as to save the expenditure of resources under the condition of ensuring the communication performance.

Description

Control method of event-triggered communication system based on terahertz channel capacity
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to an event-triggered communication system control method based on terahertz channel capacity.
Background
In recent thirty years, with the rapid development of the mobile communication industry, the 5G mobile network will further change the modern society and the 5G vertical industry through three application scenarios (enhanced mobile broadband eMBB, ultra-reliable low-delay communication URLLC, and mass machine type communication mtc). With the 5G mobile system becoming increasingly commercialized, research discussions on the next generation mobile system 6G have also begun. Mainstream operators have published a technology-driven initial draft of key performance indicators for 6G, including 1Tbps peak data rate, 0.1 millisecond broadcast delay, 10 times energy efficiency, 20 years battery life, and 100 equipment density per square meter. The terahertz communication technology has been recognized as a key technology with the potential of providing services for 6G.
In recent years, terahertz communication has rapidly become a research hotspot as the only currently known communication means satisfying the requirement of large data wireless transmission rate communication. However, terahertz communication still presents many challenges: terahertz bands suffer from severe path attenuation, transceiver antenna detuning, and transceiver hardware imperfections. Therefore, a great deal of research is invested in the modeling of the terahertz channel characteristics, the influence of the channel attenuation on the system performance is evaluated, and corresponding countermeasures are proposed. Meanwhile, due to high channel attenuation of the terahertz link, the antenna with extremely high gain and the directional sharp beam are forced to be used for transmission, so that the alignment disorder of the antenna can cause great damage to the link quality. Therefore, in the terahertz communication control system, the influence of detuning fading on the channel should be fully considered. On the other hand, compared with real-time control, since event-triggered control can reduce the system communication burden and the performance of event-triggered control is superior to real-time control at the same average transmission rate, event-triggered control has become the mainstream in recent years.
In a wireless control system based on terahertz service, by designing an event-triggered control method, the control resource loss of the system can be reduced and the control performance of the system can be improved on the premise of the quality of a terahertz communication link. Therefore, it is meaningful to study an event-triggered control method in the terahertz wireless communication control system.
Disclosure of Invention
The invention aims to ensure the communication quality of a system and reduce resource loss by designing an event-triggered control strategy in a terahertz communication control system, namely a control loop for communication by utilizing terahertz. Aiming at the problems, an event-triggered communication system control method based on terahertz channel capacity is provided.
The technical scheme of the invention is as follows:
an event trigger communication system control method based on terahertz channel capacity. Defining a state transition equation for a mobile device as xt+1＝Axt+But+wt. t denotes a control slot, a, B are state transition matrices, are 2 x 2 real matrices, denoted as a,
Figure GDA0003376840560000021
Figure GDA0003376840560000022
Figure GDA0003376840560000023
and
Figure GDA0003376840560000024
respectively representing the displacement of the mobile equipment in a horizontal x axis and a vertical y axis, and setting the displacement of the mobile equipment in the horizontal and vertical directions to obey 0 mean value independent Gaussian distribution with different variances.
Figure GDA0003376840560000025
Is system additive white Gaussian noise (AWGN noise), has a mean value of 0 and a variance of WtIs represented by wt～N(0,Wt). The scheduler observes and predicts the state of the mobile device. And (4) setting the observation of the scheduler side as a perfect observation, namely, the observation value is equal to the true value of the equipment. Defining a trigger flag deltat，δ t1 denotes triggering the scheduler to transmit the current device state xtFeeding the controller; otherwise the scheduler does not transmit. Defining predictive variables
Figure GDA0003376840560000026
Defining control input ut. Defining a predicted state of a scheduler port to a device
Figure GDA0003376840560000027
This equation illustrates that at time t +1, the scheduler's prediction of the plant state is based on the control inputs and predicted variables at the previous time t. Predicted variables
Figure GDA0003376840560000028
The definition is as follows:
Figure GDA0003376840560000029
i.e. when transmission is triggered (delta)t1), the prediction variable is the true value of the equipment state at the current moment; when transmission is not triggered (delta)t0), the predicted variable is the predicted state at time t. The device control inputs are represented as:
Figure GDA00033768405600000210
wherein K is- (R + B)TPB)-1BTPA, P is the only positive solution of the following algebraic ricatty equation: p is ATPA+Q-KT(R+BTPB) K, where R is a 2 × 2 positive definite matrix of real numbers and Q is a 2 × 2 positive semi-definite matrix of real numbers, expressed as:
Figure GDA00033768405600000211
considering a terahertz channel model under an ideal radio frequency front-end condition, the terahertz channel gain is as follows: h is hlhphfWherein h islFor channel gain, hpFor detuning fading, i.e. channel fading due to misalignment, hfIs a multipath fading. Let the beam radius of the receiving end RX be alpha and the beam radius of the transmitting end TX converged with RX be wdR is the radial error of the two beams and is offset-faded hpOnly with respect to the radial error r. The expression is as follows:
Figure GDA00033768405600000212
wherein weqFor equivalent beamwidth, AoCan be calculated as: a. theo＝erf(u)2，
Figure GDA00033768405600000213
Where erf () is an error function. Equivalent beam width weqAnd wdIn relation, the expression is:
Figure GDA0003376840560000031
where exp () represents an exponential function,. Defining the capacity of a terahertz transient channel as CidDefining the triggering threshold of channel capacity as Cth。
The method comprises the following steps:
and S1, initializing the system. Defining initial state of mobile device as x0Initial predicted state
Figure GDA0003376840560000032
Initial trigger flag delta0Initial control input u 10＝kx0；
S2, update t ═ t +1, update xt＝Axt-1+But-1+wt-1Updating scheduler prediction states
Figure GDA0003376840560000033
Then the prediction is wrongThe difference is as follows:
Figure GDA0003376840560000034
thereby radial error
Figure GDA0003376840560000035
Calculating the instantaneous channel capacity C of the link at the moment according to the radial erroridAnd Cth：
The instantaneous channel capacity is calculated by the following equation 1:
Figure GDA0003376840560000036
wherein P is0Representing the transmission power, N0Is the power spectral density of the noise. The dynamic trigger threshold C is calculated by the following equation 2thWherein
Figure GDA0003376840560000037
ptrTo know the trigger probability:
Figure GDA0003376840560000038
judgment Cid<CthIf yes, S3, otherwise, S4 is turned;
s3, update deltat＝1，
Figure GDA0003376840560000039
S4, update deltat＝0，
Figure GDA00033768405600000310
S5, update control input
Figure GDA00033768405600000311
Go to S2.
For dynamic trigger threshold C in S2thIn the calculation of (2)
Figure GDA0003376840560000041
Further description is made. Because the estimation error of the horizontal and vertical displacement of the device follows independent Gaussian distribution with different variances and a mean value of 0, the variances are respectively set as
Figure GDA0003376840560000042
And
Figure GDA0003376840560000043
the following table is shown:
Figure GDA0003376840560000044
order:
Figure GDA0003376840560000045
then there are: x to N (0, sigma)2),y～N(0,k2σ2). The radial error can be obtained
Figure GDA0003376840560000046
Obey the rayleigh distribution and the Probability Density Function (PDF) is as follows equation 3:
Figure GDA0003376840560000047
where E (|) is the second type of elliptic integral. At a given trigger probability ptrIn the case of (1), the dynamic trigger threshold C can be obtained according to the formula 2 and the formula 3th。
Compared with the traditional periodic control scheme of the terahertz communication system, the event-triggered control scheme has the beneficial effect that a large amount of control overhead and power consumption are saved on the basis of ensuring the communication performance. The triggering method based on the terahertz real-time channel capacity can adapt to the change of the channel in real time and make corresponding control so as to save the expenditure of resources under the condition of ensuring the communication performance.
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FIG. 1 is a schematic diagram of a system model of the present invention;
FIG. 2 is a diagram illustrating a comparison between the real-time channel capacity of the channel capacity trigger control and the two periodic control;
FIG. 3 is a diagram illustrating a comparison between a channel capacity trigger control and a Cumulative Distribution Function (CDF) of channel capacities for two periodic controls;
FIG. 4 is a diagram of the control states of channel capacity triggered control and periodic control with two norms | | xt||2Comparing the schematic diagrams;
FIG. 5 shows the trigger flag δ for channel capacity trigger controltA schematic graph of variation with sampling time;
FIG. 6 shows a dynamic trigger threshold C for channel capacity trigger controlthA schematic graph of variation with sampling time;
FIG. 7 shows the percentage of the total power saved by the channel capacity trigger control method versus the trigger probability p for the real-time control methodtrA schematic diagram of the relationship of (1);
FIG. 8 shows the average channel capacity and trigger probability p of the capacity trigger control methodtrA schematic diagram of the relationship of (1);
Detailed Description
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.
Considering a control system based on terahertz communication, a scheduler monitors the displacement state x of a mobile device in real timet+1＝Axt+But+wtThe scheduler has prediction capability, and the displacement state prediction value of the equipment is
Figure GDA0003376840560000051
Wherein:
Figure GDA0003376840560000052
defining a trigger flag deltat，δ t1 means that the scheduler transmission is triggered, otherwise no transmission is made. When the transmission is triggered
Figure GDA0003376840560000053
Otherwise
Figure GDA0003376840560000054
The error between the true value and the estimated value is:
Figure GDA0003376840560000055
Figure GDA0003376840560000056
where n denotes n time slots δ from t to t +1t0, i.e. the prediction length is n, let δ 01. And has the following components:
Figure GDA0003376840560000057
wherein
Figure GDA0003376840560000058
Representation matrix (A)n-iJ rows and m columns of elements. Due to estimation error et+1Expressed as a 0 mean Gaussian distribution wtIs linear combination of (a) and (b), so thatt+1Obeying a Gaussian distribution with mean 0 and variance ρ2The following were used:
Figure GDA0003376840560000059
therefore, the horizontal and vertical displacement errors of the apparatus
Figure GDA00033768405600000510
And
Figure GDA00033768405600000511
subject to independent Gaussian distributions with different variances and a mean of 0, they are expressed as x to N (0, σ) for simplicity2),y～N(0,k2σ2). Since the envelope of the sum of two orthogonal gaussian signals follows rayleigh distribution and the two independent zero-mean gaussian signals must be orthogonal, the radial error can be expressed as
Figure GDA00033768405600000512
And obey the Rayleigh distribution, its probability density function: (PDF) should have a standard form of rayleigh distribution:
Figure GDA00033768405600000513
and has a mean value of
Figure GDA00033768405600000514
Now analyze
Figure GDA00033768405600000515
By comparing the mean with a mean standard form
Figure GDA00033768405600000516
Can obtain sigmasThe relationship with k, σ. Since x, y are independent of each other, there are:
Figure GDA00033768405600000517
the mean radial error can be obtained as follows:
Figure GDA00033768405600000518
comparing the mean obtained by the above formula with the standard form mean, one can obtain:
Figure GDA0003376840560000061
where E (|) is the second type of elliptic integral. In summary, the radial error r follows rayleigh distribution, and its Probability Density Function (PDF) is formula 3.
The core idea of the technical scheme of the invention is to introduce the capacity of a terahertz instantaneous channel as a trigger transmission condition: when the channel capacity is lower than the threshold value, the alignment between the controller and the mobile equipment is deviated, and the real value of the equipment needs to be transmitted by the scheduler for the controller to control; when the channel capacity is higher than the threshold value, the mobile equipment is still in the alignment range, the transmission of the scheduler is not triggered any more, and the controller utilizes the predicted value to control, so that the expenditure of resources is saved.
The instantaneous channel capacity of the etherhertz channel is used as a trigger condition, and the trigger flag represents the following formula:
Figure GDA0003376840560000062
knowing the instantaneous channel capacity CidThe relation with the radial error is formula 1, and the radial error probability density function is formula 3, so that the probability density function of the terahertz channel instantaneous capacity can be obtained as the following formula 4:
Figure GDA0003376840560000063
design dynamic trigger threshold Cth: given trigger probability ptrI.e. ptr＝Pr{Ct≤CthObtaining the relationship between the trigger probability and the trigger threshold as follows:
Figure GDA0003376840560000064
thereby obtaining the relation between the trigger threshold and the trigger probability as formula 2. In summary, the trigger condition can be rewritten as:
Figure GDA0003376840560000065
the invention compares and analyzes the performances of the two period control methods and the channel capacity trigger control method of the invention to further verify the performances of the invention.
FIG. 1 is a schematic diagram of a system model of the present invention. The device is a mobile device with constantly and randomly changing displacement, and the scheduler observes the displacement state change x of the mobile devicetAnd predicting the state of the mobile equipment and calculating to obtain a radial error r, and determining whether to transmit or not by the scheduler according to the current relationship between the terahertz channel capacity and the channel capacity threshold. Setting a known prediction method for the controller, and if the scheduler transmits, using the real value to control the controller; otherwise, the controller uses the predicted valueAnd (5) controlling.
Fig. 2 is a diagram comparing the real-time channel capacity relationship between the channel capacity trigger control and the two periodic control. It can be seen from the figure that the control method has a control period of one time slot (T ═ 1), that is, the instantaneous channel capacity of real-time control is the largest, and the performance is the best; the control method of capacity triggering is slightly inferior to real-time control, and the performance is close to the real-time control; the control method with a control period of two slots (T-2) has the worst performance, and a channel interruption may occur.
FIG. 3 is a diagram illustrating a comparison between a channel capacity trigger control and a Cumulative Distribution Function (CDF) of channel capacities for two periodic controls; it can be seen from the figure that the control method with a control period of one time slot (T ═ 1), that is, the real-time control can ensure the best channel performance, the control strategy with a control period T of two time slots (T ═ 2) has the worst performance, and the highest interruption probability. The capacity triggered control method performance is between the two and is very close to the real-time control performance.
FIG. 4 is a diagram of the control states of channel capacity triggered control and periodic control with two norms | | xt||2Comparing the schematic diagram, wherein
Figure GDA0003376840560000071
It can be seen from the figure that the curves return to the preset point (0,0) under both control methodsTAnd finally remains at (0,0)TNearby. And the curve of the capacity control is very close to that of the real-time control, which shows the effectiveness of the capacity trigger control method.
FIG. 5 shows the trigger flag δ for channel capacity trigger controltA schematic graph of variation with sampling time; the dynamic change of the trigger mark is seen from the beginning of the figure, and the dynamic property of the capacity trigger control method is illustrated.
FIG. 6 shows a dynamic trigger threshold C for channel capacity trigger controlthA schematic graph of variation with sampling time; the dynamic change of the trigger threshold is seen from the beginning of the figure, and the dynamic property of the capacity trigger control method is illustrated. As can be seen from fig. 5 and 6, when the system decides not to trigger transmission, the corresponding trigger threshold is lowered. This is because when no transmission is taking placeWhich necessarily results in an accumulation of errors and thus a reduction in channel capacity, the purpose of lowering the trigger threshold is to increase the chance of triggering the next transmission, thereby keeping the channel capacity within an acceptable range. Fig. 5 together with fig. 6 illustrates the dynamics of the capacity trigger control method.
FIG. 7 shows the percentage of the total power saved by the channel capacity triggering method and the triggering probability p compared to the real-time control methodtrA schematic diagram of the relationship of (1); FIG. 8 shows the average channel capacity and trigger probability p of the capacity trigger control methodtrA schematic diagram of the relationship of (1); combining fig. 7 and 8, it can be seen that the probability p of triggeringtrThe number of times of trigger transmission is increased, and the capacity trigger control method is gradually reduced to a real-time control method, so that the channel capacity and the consumed power are simultaneously increased. By selecting the appropriate trigger probability ptr(about 0.3), a large amount of wireless transmission power (about 25 percent) can be saved on the premise of ensuring the channel capacity.
In summary, the present invention provides a new method for controlling an event-triggered communication system based on terahertz channel capacity. Compared with the traditional periodic trigger control method, the invention can meet the system stability and save a large amount of emission power resources under the condition of ensuring the communication quality. The invention has better system performance and also embodies the advantages of the invention.

Claims (1)

1. A control method of an event-triggered communication system based on terahertz channel capacity is disclosed, the system comprises a controller, a mobile device and a scheduler, the controller and the mobile device communicate through the terahertz channel, and the control input of the controller to the mobile device is represented as follows:
Figure FDA0003376840550000011
wherein K is- (R + B)TPB)-1BTPA, P is the only positive solution of the following algebraic ricatty equation: p is ATPA+Q-KT(R+BTPB) K, where R is a 2 × 2 positive definite matrix and Q is a 2 × 2 semi-positive definite matrix, and the scheduler observes and accounts for states of the mobile deviceThe prediction method of the scheduler end to the mobile equipment is represented by the formula
Figure FDA0003376840550000012
That is, at time t +1, the scheduler predicts the plant state based on the control inputs and predicted variables at the previous time t, A and B are state transition matrices, which are 2 x 2 real matrices, and the predicted variables are
Figure FDA0003376840550000013
Is defined as:
Figure FDA0003376840550000014
the scheduler controls delta by triggeringtSelecting whether to transmit the current device status to the controller when deltatTriggering transmission when the predicted variable is the actual value of the state of the equipment at the current moment, and when the predicted variable is deltatWhen the predicted variable is equal to 0, the transmission is not triggered, and the predicted variable is the predicted state at the moment t; the control method is characterized by comprising the following steps:
s1, system initialization: defining initial state of mobile device as x0Initial predicted state
Figure FDA0003376840550000015
Initial trigger flag delta0Initial device control input u ═ 10＝Kx0；
And S2, updating the state of the mobile equipment according to the state transition equation of the mobile equipment, wherein t is t + 1:
xt＝Axt-1+But-1+wt-1
wherein the content of the first and second substances,
Figure FDA0003376840550000016
Figure FDA0003376840550000017
and
Figure FDA0003376840550000018
respectively representing the displacement of the mobile equipment on an x axis and a y axis, and setting the displacement of the mobile equipment in the horizontal direction and the vertical direction to obey 0 mean value independent Gaussian distribution with different variances,
Figure FDA0003376840550000019
for AWGN noise, the mean is 0 and the variance is Wt；
The scheduler observes the current displacement state x of the mobile devicetAnd obtaining a predicted state based on a known prediction model
Figure FDA00033768405500000110
Figure FDA00033768405500000111
Obtaining a prediction error etComprises the following steps:
Figure FDA00033768405500000112
thereby radial error
Figure FDA00033768405500000113
Calculating the instantaneous channel capacity C of the link at the moment according to the radial erroridAnd a dynamic trigger threshold Cth：
Figure FDA0003376840550000021
Figure FDA0003376840550000022
Wherein, weqIn order to be the equivalent beam width,r is the radial error of the transmitted and received beams, Ao＝erf(u)2And erf () is an error function,
Figure FDA0003376840550000023
wdis the radius of the transmitted beam at distance d, N0Power spectral density, P, of noise0Which is indicative of the power of the transmission,
Figure FDA0003376840550000024
hffor multipath fading, ptrIn order to know the probability of a trigger,
Figure FDA0003376840550000025
e (|) is the second type of elliptic integral, so that the estimation error of the horizontal and vertical displacement of the equipment follows independent Gaussian distribution with different variances and 0 mean value, and the variances are respectively set as
Figure FDA0003376840550000026
And
Figure FDA0003376840550000027
Figure FDA0003376840550000028
judgment Cid<CthIf yes, go to step S3, otherwise go to step S4;
s3, update deltat＝1，
Figure FDA0003376840550000029
S4, update deltat＝0，
Figure FDA00033768405500000210
S5, update control input
Figure FDA00033768405500000211
Return to step S2.
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