CN112637103B - Signal detection method of cooperative backscattering communication system - Google Patents

Signal detection method of cooperative backscattering communication system Download PDF

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CN112637103B
CN112637103B CN202011503992.1A CN202011503992A CN112637103B CN 112637103 B CN112637103 B CN 112637103B CN 202011503992 A CN202011503992 A CN 202011503992A CN 112637103 B CN112637103 B CN 112637103B
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梁应敞
李东益
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/36—Modulator circuits; Transmitter circuits
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/38—Demodulator circuits; Receiver circuits

Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to a signal detection method of a cooperative backscattering communication system. In the present invention, the receiver uses a sphere decoding signal detection algorithm to simultaneously detect the direct link signal and the reflected link signal. In the signal detection process, a weight value called the spherical radius is set first. With the progress of the algorithm, the spherical radius is dynamically reduced, the signal detection process is constrained by taking the spherical radius as a constraint condition, and finally, the direct link signal and the reflected link signal are simultaneously estimated by the receiver. The invention has the beneficial effects that: on the premise of reducing the calculation complexity, the error rate performance which is the same as that of the maximum likelihood signal detection algorithm is obtained.

Description

Signal detection method of cooperative backscattering communication system
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a signal detection method of a cooperative backscattering communication system.
Background
With the development and the commercial use of the 5G technology, the Internet of things technology is applied to more and more scenes, and the quality of social production and life is greatly improved by applying the Internet of things technology. Since more and more intelligent devices are connected to the internet of things, the power consumption and the cost of the intelligent devices are issues that must be considered, and therefore, the development of a low-power-consumption and low-cost communication system of the internet of things is urgently needed to meet the actual demand of the internet of everything interconnection nowadays.
In the face of the requirements of low power consumption and low cost, the cooperative environment backscatter communication technology shows a good application prospect. There are three types of devices in cooperative environment backscatter communication: a transmitter, a receiver, and a reflection device.
The wireless signal sent by the transmitter is called a direct link signal, and the reflection device adjusts the antenna coefficient of the reflection device according to the information of the reflection device and modulates the direct link signal to obtain a reflection link signal. The receiver receives the direct link signal and the reflected link signal at the same time, demodulates the two received signals and recovers the symbols sent by the transmitter and the reflecting device at the same time. The cooperative environment backscatter communication system has the following advantages: first, the reflection device completes communication by reflecting the direct link signal, so that no additional signal emission source and no additional energy source are needed, and no additional spectrum resource is occupied. The advantages enable the cooperative environment backscatter communication technology to have a wide application prospect of the Internet of things, and ensure the realization of large-scale coverage of low-power consumption equipment on a geographic space.
In a cooperative environment backscatter communication system, when designing a signal detection algorithm, considering that a direct link signal is stronger than a reflected link signal, a concept of cooperative signal detection is generally adopted, that is, the direct link signal is not regarded as interference any more, but the direct link signal and the reflected link signal are both received at the same time. At present, a maximum likelihood detection algorithm is available in a cooperative environment backscatter communication system, but the maximum likelihood detection algorithm has higher complexity.
Disclosure of Invention
Aiming at the problems, the invention provides a spherical decoding signal detection method based on the principle of reducing the search times as much as possible for reducing the algorithm complexity, and the adopted spherical decoding method obtains the same error rate performance as the maximum likelihood signal detection algorithm on the premise of reducing the calculation complexity.
In the present invention, the receiver uses a sphere decoding signal detection algorithm to simultaneously detect the direct link signal and the reflected link signal. In the signal detection process, a weight value called the spherical radius is set first. With the progress of the algorithm, the spherical radius is dynamically reduced, the signal detection process is constrained by taking the spherical radius as a constraint condition, and finally, the direct link signal and the reflected link signal are simultaneously estimated by the receiver.
The technical scheme of the invention is as follows:
a signal detection method of a cooperative backscatter communication system, the cooperative backscatter communication system comprising a transmitter, M single-antenna reflecting devices, and a receiver with N antennas, comprising the steps of:
s1, establishing a received signal model as follows:
yk(n)＝Hxk(n)+uk(n)
wherein H ═ H0,h1,...,hM]，xk(n)＝[sk(n),sk(n)c1(n),...,sk(n)cM(n)]TFor combining signal fields, sk(n) is a direct link signal, cm(n) is a reflected signal of the mth reflecting device,
Figure BDA0002844338400000021
Ptf ═ f for the average transmit power of the transmitter1,...,fN]TFor the channel between the transmitter and the receiver,/mFor the channel between the transmitter and the m-th reflecting device, gmFor the channel between the mth reflecting device and the receiver, α is the reflection coefficient of the reflecting device, uk(n)＝[uk,1(n),uk,2(n),...,uk,N(n)]TEach component in u (n) is a circularly symmetric complex Gaussian variable with a mean value of 0 and a variance of σ2；
S2, the signal detection problem is equivalent to the following problem under the maximum likelihood theory:
Figure BDA0002844338400000022
wherein A issAnd AcA set of constellation points representing the direct link signal and the reflected link signal, respectively;
subjecting H to QL decomposition, QTQ is I, Q is an orthogonal matrix, L is a lower triangular matrix, and y is | |k(n)-Hxk(n)||2The decomposition is as follows:
||yk(n)-Hxk(n)||2＝||QTyk(n)-Lxk(n)||2+||(I-QQT)yk(n)||2
then
Figure BDA0002844338400000023
Is equivalent to
Figure BDA0002844338400000024
Will be provided with
Figure BDA0002844338400000031
Further decomposition:
Figure BDA0002844338400000032
wherein
Figure BDA0002844338400000033
Figure BDA0002844338400000034
Defining:
Figure BDA0002844338400000035
Figure BDA0002844338400000036
then the final problem of signal detection is established as follows:
Figure BDA0002844338400000037
s3, converting the signal detection final problem established in the step S2 into a node searching problem of a tree graph with nodes considering the M +2 layer, wherein all the nodes of the second layer of the tree graph respectively represent S0(n),...,sK-1(n)]TAll possible constellation points of (2) are not repeated, and the constellation point combination represented by each point is brought into F0(s0(n),...,sK-1(n)), the calculation result is the point weight value, and all nodes at the m +1 th level in the tree diagram respectively represent [ s ]0(n),...,sK-1(n),c1(n),...,cm(n)]TAnd do not repeat [ s ] of all possible occurrences of the combined constellation point0(n),...,sK-1(n),c1(n),...,cm-1(n)]TInherit to its father node, and brings the constellation point combination represented by each point into Fm(s0(n),...,sK-1(n),c1(n),...,cm(n)), the weight value of the parent node is added, namely the weight value of each point of the mth layer is expressed as:
F0(s0(n),...,sK-1(n))+...+Fm(s0(n),...,sK-1(n),c1(n),...,cm(n))
each node of the last layer in the tree represents a combination of constellation points for a corresponding set of direct and reflected links in the combined signal domain;
s4, firstly searching to a leaf node at the leftmost end in the tree graph by adopting a depth-first traversal search mode, calculating a weight value of the leaf node, setting the weight value as an initial spherical radius R, and taking a combined constellation point represented by the leaf node as an estimated signal;
continuing the depth-first traversal search, calculating the weight value of each node along with the progress of the traversal search, and comparing the weight value with R; for a leaf node, if the weight value of the leaf node is smaller than R, replacing the R with the weight value of the point, and replacing the estimated signal with the combined constellation point corresponding to the leaf node; if the weight value is larger than R, continuing depth-first traversal search; for a non-leaf node, if the weight value of the node is smaller than R, continuing the traversal process until the leaf node is traversed, if the weight value of the node is larger than R, skipping a subtree taking the node as a root, and continuing the depth-first traversal search until the leaf node is searched; and obtaining a final estimation result after the depth-first traversal search is finished. .
The invention has the beneficial effects that: on the premise of reducing the calculation complexity, the error rate performance which is the same as that of the maximum likelihood signal detection algorithm is obtained.
Drawings
FIG. 1 is a schematic diagram of the system of the present invention;
FIG. 2 is a process of spherical encoding in the present invention;
FIG. 3 is an algorithm flow diagram of a sphere decoding signal detection algorithm;
FIG. 4 shows the error rate performance of the transmitter signal at different SNR conditions for the receiver designed by the present invention;
FIG. 5 is a graph showing the bit error rate performance of the first reflecting device signal for receivers designed according to the present invention under different SNR conditions;
fig. 6 shows the error rate performance of the second reflecting device signal under different snr conditions for the receiver designed by the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
The invention considers the condition that the transmitter and the reflecting equipment adopt a single antenna, the receiver adopts a plurality of antennas, the number of the antennas is N, the system is provided with a plurality of reflecting equipment, the channel is a flat weak channel, and the direct link signal and the reflecting link signal are synchronous. The direct link signal adopts QPSK modulation mode, and the symbol period of the direct link is Ts. The signal generated by the reflection equipment adopts a BPSK modulation mode, the symbol periods of all the reflection equipment are the same, and the symbol period of the reflection link is Tc. Let T bec＝KTsAnd K is a positive integer. The direct link signal is then denoted as s (n) ═ s0(n),s1(n),...,sK-1(n)]TReflection of the m-th reflecting deviceThe signal is denoted by cm(n) of (a). The system model is shown in fig. 1. Assuming that there are M reflecting devices, the channel between the transmitter and the receiver is called a direct link channel with f ═ f1,...,fN]TExpress, define
Figure BDA0002844338400000051
The channel between the transmitter and the m-th reflecting device is lmDefinition of
Figure BDA0002844338400000052
The channel between the mth reflecting device and the receiver is gm＝[gm,1,...,gm,N]Definition of
Figure BDA0002844338400000053
The reflection coefficient of the reflecting device is alpha. gmAnd lmTogether forming a reflected link channel. The whole system is shown in fig. 1.
While the channel model is described above, and the signal model is discussed next, for convenience of discussion, it is assumed that the average transmission power of the transmitter is Pt。
The signal received by the receiver is expressed as:
Figure BDA0002844338400000054
wherein u isk(n)＝[uk,1(n),uk,2(n),...,uk,N(n)]TAnd each component in u (n) is a circularly symmetric complex Gaussian variable with a mean value of 0 and a variance of σ2。
The direct link signal-to-noise ratio is defined as:
Figure BDA0002844338400000055
accordingly, the signal-to-noise ratio of each reflection link is defined as:
Figure BDA0002844338400000056
the relative signal-to-noise ratios of the respective reflected and direct links are then defined as:
Figure BDA0002844338400000057
definition of
Figure BDA0002844338400000058
Therefore, equation (1) is further rewritten as:
yk(n)＝h0sk(n)+h1sk(n)c1(n)+,...,+hMsk(n)cM(n)+uk(n) (5)
yk(n)＝Hxk(n)+uk(n) (6)
wherein H ═ H0,h1,...,hM]，xk(n)＝[sk(n),sk(n)c1(n),...,sk(n)cM(n)]T。xk(n) is the combination of the direct link signal and the reflected link signal, all xk(n) together constitute a combined signal domain in the signal detection process.
The sphere decoding algorithm is described in detail below.
The signal detection problem in the present system may be equivalent to considering the problem expressed by the following formula under the maximum likelihood theory:
Figure BDA0002844338400000061
wherein A issAnd AcRespectively representing the set of constellation points for the direct link signal and the reflected link signal.
First, H is subjected to QL decomposition, QTQ is I, Q is an orthogonal matrix, and L is a lower triangular matrix. Then | purplek(n)-Hxk(n)||2The decomposition is in the form:
||yk(n)-Hxk(n)||2＝||QQT(yk(n)-Hxk(n))||2+||(I-QQT)(yk(n)-Hxk(n))||2 (8)
||yk(n)-Hxk(n)||2＝||QTyk(n)-Lxk(n)||2+||(I-QQT)yk(n)||2 (9)
in formula (9) | (I-QQ)T)yk(n)||2Does not contain xk(n), can be ignored, and then the conclusion can be drawn:
Figure BDA0002844338400000062
can be equivalent to
Figure BDA0002844338400000063
Will be provided with
Figure BDA0002844338400000064
Further decomposed, appearing in the form:
Figure BDA0002844338400000065
wherein
Figure BDA0002844338400000066
Figure BDA0002844338400000067
For convenience of the subsequent description, the following is defined:
Figure BDA0002844338400000071
Figure BDA0002844338400000072
after the above processing procedure, equation (10) is converted into:
Figure BDA0002844338400000073
the above problem may continue to translate into a node search problem that considers a tree graph with nodes at level M + 2. All nodes of the second level of the tree represent s0(n),...,sK-1(n)]TAnd do not occur repeatedly. Bringing the constellation point combinations represented by each point into F0(s0(n),...,sK-1(n)), the result of the calculation is the point weight value. All nodes at the m +1 th level in the tree diagram respectively represent s0(n),...,sK-1(n),c1(n),...,cm(n)]TAnd do not repeat [ s ] of all possible occurrences of the combined constellation point0(n),...,sK-1(n),c1(n),...,cm-1(n)]TInherit from its parent node. Bringing the constellation point combinations represented by each point into Fm(s0(n),...,sK-1(n),c1(n),...,cm(n)), the weight value of its parent node is added at the same time. That is, the weighting values of the points of the mth layer can be expressed as:
F0(s0(n),...,sK-1(n))+...+Fm(s0(n),...,sK-1(n),c1(n),...,cm(n)) (14)
each node of the last layer of the tree represents a combination of constellation points for a corresponding set of direct and reflected links in the combined signal domain.
The process of the sphere decoding algorithm is as follows:
1) firstly searching to the leaf node at the leftmost end in the tree graph by adopting a depth-first traversal search mode, calculating a weight value of the leaf node, setting the weight value as an initial spherical radius R, and taking a combined constellation point represented by the leaf node as an estimation signal.
2) And continuing the depth-first traversal search, calculating the weight value of each node as the traversal search progresses, and comparing the weight value with R. And for the leaf node, if the weight value of the leaf node is smaller than R, replacing the R with the weight value of the point, and replacing the estimated signal with the combined constellation point corresponding to the leaf node. And if the weight value is greater than R, continuing the depth-first traversal search. And for the non-leaf node, if the weight value of the node is less than R, continuing the traversal process until the leaf node is traversed. And if the weight value of the node is greater than R, skipping the subtree taking the node as the root, and continuing the depth-first traversal search until the leaf node is searched.
The algorithm flow chart of sphere decoding is shown in fig. 3.
In terms of computational complexity, in the maximum likelihood detection algorithm, the search number is | As|K|Ac|MIf a sphere decoding detection algorithm is adopted, the search number is between 1 and As|K|Ac|MIn the meantime. It can be seen that in the sphere decoding detection algorithm, only in the most extreme case, the computational complexity is equal to the maximum likelihood detection algorithm. Which is typically less complex than the maximum likelihood detection algorithm.
Examples
In this example, K is 1, an ambient backscatter communications system with two reflecting devices. The transmitter transmits a signal, and the system has 2 reflecting devices. The signal detection process translates into the node search process shown in fig. 2. The weight value of each point is calculated according to the formulas (9) - (12)
In this example, the weight value of the leftmost leaf node is first calculated and is taken as R. The leaf node represents s ═ 1+ j, c1＝1,c2The weight value of the combined constellation point of 1 is calculated to be 9, R is set to be 9, and the estimated signal is s 1+ j, c1＝1,c 21. Continuing the depth-first traversal search to s ═ 1+ j, c1＝-1,c2Node corresponding to-1, with weight value of 7, R>7, then change R to 7, the estimated signal to s 1+ j, c1＝-1,c2Is-1. Continuing the depth-first traversal search to s ═ 1+ j, c1＝-1,c 21, with a weight of 6, R>6, then change R to 6, the estimated signal to s 1+ j, c1＝-1,c 21. Continuing the depth-first traversal search to s ═ 1+ j, c1＝-1,c2Node corresponding to-1, with weight value of 7, R<7, R is not changed. And continuing to traverse to the node corresponding to the s-1-j, wherein the weight value is 6, and the R is 6, so that the traversal is stopped, turning to the node corresponding to the s-1 + j, and continuing the depth-first traversal search, wherein the weight value of the s-1 + j is 4, and the R is>And 4, continuing to perform traversal search until s is equal to-1 + j, c 11 corresponds to a node. Its weight value is 6, R is 6, so the downward traversal stops. Traversing search goes to s-1 + j, c1Calculating s-1 + j, c1A weight value of 7R 1<7, so the traversal stops. And turning to the node corresponding to the s-1-j to continue traversing, and calculating the weight value of 8, R<8, so the depth-first traversal search stops continuing, at which point the depth-first traversal search ends. The sphere decoding algorithm ends. The final estimation result is s ═ 1+ j, c1＝-1,c2＝1。
Fig. 4 shows the error rate performance of the direct link signal for receivers designed by the present invention under different direct link snr conditions. Fig. 5 shows the error rate performance of the first reflection device symbol under different direct link snrs of the receiver designed by the present invention, and fig. 6 shows the error rate performance of the second reflection device symbol under different direct link snrs of the receiver designed by the present invention. In practice, a plurality of reflecting devices can exist, and the simulation shows that the number of the reflecting devices is 2 and the error rate curves of the two reflecting devices are respectively shown.
In the simulation, there are two reflecting devices, and the reflected link signals are c respectively1And c2。fn，g1,n，g2,nAnd lmThe three are in accordance with the complex Gaussian distribution with the mean value of 0 and the variance of beta respectivelyf，
Figure BDA0002844338400000091
And betal. Let betaf＝10-7. In the simulation, it is assumed that the two reflecting devices are at the same distance from the transmitter and at different distances from the receiver, and that the second reflecting device is at a greater distance from the receiver, so
Figure BDA0002844338400000092
βl＝10-5Let the reflection coefficient α be 0.2+0.3j, the number of receiving antennas N be 4, P t1. Altered σ in simulation2Value to change gammad. The direct link signal adopts QPSK modulation mode, and the reflected link signal adopts BPSK modulation mode. Channel realization times of 106。
Fig. 4 shows the trend of the bit error rate of the direct link signal along with the change of the signal-to-noise ratio of the direct link when the spherical decoding detection and the maximum likelihood detection are respectively adopted when K is different. The spherical decoding detection has the same error rate performance as the maximum likelihood detection, and simultaneously, the error rate performance of two detection algorithms is improved along with the increase of K. It can be seen that this boost is gradually reduced for larger K. It can be seen that in practice a smaller K is preferred.
Fig. 5 and fig. 6 show respectively the trend of the bit error rate of the reflected signals of the two reflection devices in the simulation along with the change of the signal-to-noise ratio of the direct link when the K is different and the sphere decoding detection and the maximum likelihood detection are respectively adopted. Through observation, when the signal detection is carried out on the reflected link signal, the spherical decoding detection algorithm has the same error rate performance as the maximum likelihood detection algorithm. Meanwhile, under the same signal-to-noise ratio of the direct link, the bit error rate of the reflected link signal is obviously improved along with the increase of K. In particular, we have observed that the error rate performance of two reflective devices achieves a signal-to-noise ratio gain of about 3dB when K is increased by a factor of two. Comparing fig. 5 and fig. 6 in this simulation, it can be seen that c is the same as the snr of the direct link2Bit error rate performance is weaker than c1This is because c is in simulation2Farther away from the receiver.

Claims (1)

1. A signal detection method of a cooperative backscatter communication system, the cooperative backscatter communication system comprising a transmitter, M single-antenna reflecting devices, and a receiver having N antennas, the method comprising the steps of:
s1, establishing a received signal model as follows:
yk(n)＝Hxk(n)+uk(n)
wherein H ═ H0,h1,...,hM]，xk(n)＝[sk(n),sk(n)c1(n),...,sk(n)cM(n)]TFor combining signal fields, sk(n) is a direct link signal, cm(n) is a reflected signal of the mth reflecting device,
Figure FDA0003233427160000011
1≤m≤M，Ptf ═ f for the average transmit power of the transmitter1,...,fN]TFor the channel between the transmitter and the receiver,/mFor the channel between the transmitter and the m-th reflecting device, gmFor the channel between the mth reflecting device and the receiver, α is the reflection coefficient of the reflecting device, uk(n)＝[uk,1(n),uk,2(n),...,uk,N(n)]T，ukEach component in (n) is a circularly symmetric complex Gaussian variable with a mean value of 0 and a variance of sigma2；
S2, the signal detection problem is equivalent to the following problem under the maximum likelihood theory:
Figure FDA0003233427160000012
wherein A issAnd AcA set of constellation points representing the direct link signal and the reflected link signal, respectively;
subjecting H to QL decomposition, QTQ is I, Q is an orthogonal matrix, L is a lower triangular matrix, and y is | |k(n)-Hxk(n)||2The decomposition is as follows:
||yk(n)-Hxk(n)||2＝||QTyk(n)-Lxk(n)||2+||(I-QQT)yk(n)||2
then
Figure FDA0003233427160000013
Is equivalent to
Figure FDA0003233427160000014
Will be provided with
Figure FDA0003233427160000015
Further decomposition:
Figure FDA0003233427160000016
wherein
Figure FDA0003233427160000021
Figure FDA0003233427160000022
Defining:
Figure FDA0003233427160000023
Figure FDA0003233427160000024
then the final problem of signal detection is established as follows:
Figure FDA0003233427160000025
s3, converting the signal detection final problem established in the step S2 into a node search problem considering a tree graph with nodes of an M +2 layer and a second node of the tree graphAll nodes of a layer represent s respectively0(n),...,sK-1(n)]TAll possible constellation points of (2) are not repeated, and the constellation point combination represented by each point is brought into F0(s0(n),...,sK-1(n)), the calculation result is the point weight value, and all nodes at the m +1 th level in the tree diagram respectively represent [ s ]0(n),...,sK-1(n),c1(n),...,cm(n)]TAnd do not repeat [ s ] of all possible occurrences of the combined constellation point0(n),...,sK-1(n),c1(n),...,cm-1(n)]TInherit to its father node, and brings the constellation point combination represented by each point into Fm(s0(n),...,sK-1(n),c1(n),...,cm(n)), the weight value of the parent node is added, namely the weight value of each point of the mth layer is expressed as:
F0(s0(n),...,sK-1(n))+...+Fm(s0(n),...,sK-1(n),c1(n),...,cm(n))
each node of the last layer in the tree represents a combination of constellation points for a corresponding set of direct and reflected links in the combined signal domain;
s4, firstly searching to a leaf node at the leftmost end in the tree graph by adopting a depth-first traversal search mode, calculating a weight value of the leaf node, setting the weight value as an initial spherical radius R, and taking a combined constellation point represented by the leaf node as an estimated signal;
continuing the depth-first traversal search, calculating the weight value of each node along with the progress of the traversal search, and comparing the weight value with R; for a leaf node, if the weight value of the leaf node is smaller than R, replacing the R with the weight value of the point, and replacing the estimated signal with the combined constellation point corresponding to the leaf node; if the weight value is larger than R, continuing depth-first traversal search; for a non-leaf node, if the weight value of the node is smaller than R, continuing the traversal process until the leaf node is traversed, if the weight value of the node is larger than R, skipping a subtree taking the node as a root, and continuing the depth-first traversal search until the leaf node is searched; and obtaining a final estimation result after the depth-first traversal search is finished.
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