CN115913291A

CN115913291A - Non-line-of-sight channel modeling method for underground coal mine intelligent super-surface wireless communication

Info

Publication number: CN115913291A
Application number: CN202211333148.8A
Authority: CN
Inventors: 李世银; 杨瑞鑫; 马帅; 沈胜强; 张鹏; 张梦迪
Original assignee: China University of Mining and Technology CUMT
Current assignee: China University of Mining and Technology CUMT
Priority date: 2022-10-28
Filing date: 2022-10-28
Publication date: 2023-04-04

Abstract

The invention provides a non-line-of-sight channel modeling method for intelligent super-surface wireless communication in an underground coal mine, which can be used for identifying and extracting characteristics of complex multipath fading and intelligent super-surface passive relay in a limited space in the underground coal mine, and acquiring parameters such as path loss, scattering cluster distribution, multipath time delay and the like. Based on actual channel measurement data and a propagation scene space reconstruction method, a corresponding scatterer digital map is established according to the position, texture and reflection characteristics of an environment structure in an original propagation scene, an intelligent super surface is equivalent to a virtual scatterer, the analysis modeling difficulty can be effectively reduced, then the actual scatterer is matched with a multi-path clustering result to form a cluster core, the non-line-of-sight channel modeling process is converted into the analysis and modeling of a plurality of direct paths, the modeling requirements of a wireless communication system in a coal mine can be effectively met, and the complexity and difficulty of the modeling process are effectively reduced.

Description

Non-line-of-sight channel modeling method for underground coal mine intelligent super-surface wireless communication

Technical Field

The invention relates to the field of underground wireless communication of coal mines, in particular to a non-line-of-sight channel modeling method for underground intelligent super-surface wireless communication of a coal mine.

Background

Non-line-of-sight propagation scenes such as roadway turning, turnouts, chambers and equipment shielding which commonly exist in the underground coal mine cause difficulty in edge coverage of a communication cell and blind areas and blind spots covered by wireless signals. Moreover, the more important and critical production places are the excavation working face, the more obvious the interference such as space dynamic change, equipment moving shielding, dust water mist and the like is, the more difficult the effective and reliable coverage of wireless signals is, and the more serious the influence of blind spots and blind areas is. The traditional solution means is mainly to add a relay base station or introduce a leaky cable mode, but can bring new problems of high construction and use cost, difficult maintenance and use, signal coverage overlapping interference, frequent switching of a mobile terminal base station and the like, and the latter also causes the problems of complex system structure and the like. The intelligent super-surface appeared in recent years provides possibility for artificially reshaping wireless channels, shows great potential in improving wireless transmission and coverage capability of non-line-of-sight propagation scenes, is widely concerned and is listed as one of key alternative technologies of next-generation mobile communication networks. In addition, the intelligent super surface is used as a passive device, so that the power consumption and the cost are low, the deployment is easier, and the intelligent super surface is particularly suitable for underground coal mine scenes which are difficult to supply power and have strict explosion-proof requirements on active equipment. The method provides a new way and a new idea for solving the problem of wireless coverage of the underground non-line-of-sight propagation scene of the coal mine.

The existing intelligent super-surface research mainly focuses on classical problems of channel estimation, modeling, beam forming, deployment strategies and the like. The introduction of a large-scale electromagnetic unit array into the intelligent super surface can make the near field characteristic more obvious, and simultaneously can cause the changes of the number, the path and the like of propagation links, so as to form an intelligent super surface coupling channel with a brand new mode. However, currently, research on wireless propagation characteristics of the intelligent super-surface coupling channel is not sufficient, and the rayleigh channel model or the standardized wireless channel model defined by 3GPP and ITU is generally directly followed, and the intelligent super-surface phase response is simplified into a diagonal matrix. The methods can effectively simplify the model, but the changes of the propagation link caused by introducing the intelligent super surface and the interaction between the new link and the original link are not fully considered. Particularly in a limited space under a coal mine with serious multipath characteristics, the difference between the simplified model and the actual propagation characteristic is more obvious, and the intelligent super-surface application effect is influenced. At present, research results aiming at an intelligent super-surface coupling channel in an actual scene are few, and the prior work generally adopts a ray tracing method, a multipath clustering theory and other classical methods to build a theoretical model around large-scale fading or simple multipath channels in a free space, and generally only relates to the far-field propagation characteristic of a single-carrier narrow-band signal. In the existing research and practice, an intelligent super surface is equivalent to an ideal reflector or a virtual scatterer cluster, and a free space path loss model is established without considering multipath effect and shadow effect. Or a free space channel model with multipath effect is established by adopting classical methods such as a ray tracing method, a multipath clustering theory and the like, but the multipath quantity and the scattering body characteristics are greatly simplified, and the multipath effect between the intelligent super surface and the receiving end is ignored. Roadway turning and bifurcation, chambers, large equipment and facility shielding widely exist in a limited space under a coal mine, shadow effect and multipath effect are more obvious and complex, signals of different paths are greatly different after being reflected by an intelligent super surface due to difference of arrival angles, the existing research result based on free space is difficult to accurately reflect the state of a complex real channel under the coal mine, and the measurement and modeling of the intelligent super surface coupling channel under the coal mine belong to the blank field.

Disclosure of Invention

The invention aims to: the invention aims to provide a channel modeling method for an underground coal mine intelligent super-surface wireless communication system, which is used for identifying and extracting the characteristics of complex multipath fading and intelligent super-surface passive relay in a limited space under a coal mine, acquiring parameters such as path loss, scattering cluster distribution and multipath time delay and the like, and eliminating or improving one or more defects in the prior art.

The invention provides a non-line-of-sight channel modeling method for intelligent super-surface wireless communication in an underground coal mine, which comprises the following steps:

step 1: selecting parameters of a channel measurement platform for a multi-input multi-output intelligent super-surface wireless communication system according to a wireless communication system which is required in the existing or future in a coal mine underground environment to be measured, and building a transmitting end, an intelligent super-surface and a receiving end of the channel measurement platform in a ground conventional environment;

step 2: determining and calibrating the self characteristics of the channel measuring platform;

and step 3: in a wireless communication scene of a coal mine to be measured, deploying a channel measurement platform which is measured and calibrated in a ground conventional environment, carrying out channel measurement on the spot, controlling the working states of a transmitting antenna array, an intelligent super-surface array and a receiving antenna array through an antenna high-speed switching module, sequentially measuring non-line-of-sight channel impact responses among each transmitting antenna unit, each intelligent super-surface array unit and each receiving antenna unit based on a time division multiple access principle, and storing the non-line-of-sight channel impact responses in a data storage unit so as to facilitate later-stage data processing and analysis;

and 4, step 4: deploying a laser radar in a wireless communication scene under a coal mine to be measured, scanning and reconstructing a three-dimensional image of a channel measurement site by utilizing a synchronous positioning and Mapping (SLAM) technology, and acquiring and calibrating the position, texture characteristics and reflection characteristics of objects such as large equipment, a metal protective net, a rock mass, a wall and the like;

and 5: after the underground coal mine wireless communication scene is measured on the spot, image semantic segmentation is carried out on SLAM measurement data and results through a computer vision method on the ground, the SLAM measurement data and the results are matched with each object on the spot to form a scatterer digital map, and the intelligent super surface is equivalent to a virtual scatterer according to the previously determined intelligent super surface array characteristics and is inserted into the scatterer digital map;

step 6: after the coal mine underground wireless communication scene is measured on the spot, a complete multi-input multi-output intelligent super-surface wireless communication system channel impact response matrix is obtained on the ground by using a sliding correlation method, a measurement result data set is formed, channel parameters such as signal amplitude attenuation, multipath time delay, a horizontal departure angle, a vertical departure angle, a horizontal arrival angle, a vertical arrival angle, a complex polarization matrix, doppler frequency shift and the like are obtained from the measurement result data set through an SAGE algorithm, then multipath clustering is carried out through a K-adjacent clustering algorithm, and the parameters such as the number of scattering clusters, intra-cluster time delay, intra-cluster angle expansion and the like are determined;

and 7: matching scattering clusters and scatterers by combining a multipath clustering result and a scatterer map through reinforcement learning to obtain a limited number of multipath scatterer clusters and an intelligent super-surface equivalent cluster core;

and 8: taking a cluster core as a node, decomposing and splitting a non-line-of-sight propagation link through which a wireless signal passes into a plurality of logical sub-channels, connecting the logical sub-channels with each other to form a propagation path, obtaining an effective propagation path of which a connection node sequentially comprises a transmitting antenna unit, the cluster core and a receiving antenna unit, and if the end point of the propagation path is not the receiving antenna unit, determining the effective propagation path as an invalid propagation path which can be eliminated;

and step 9: and combining all effective propagation paths to obtain channel impact response from a sending end to a receiving end, and obtaining a non-line-of-sight channel model facing the underground intelligent super-surface wireless communication of the coal mine in the current scene.

In step 1, the transmitting end, the intelligent super surface and the receiving end of the channel measurement platform comprise a transmitting antenna array, a receiving antenna array, an intelligent super surface, a synchronous clock, a signal generator, a signal receiver, a data storage unit and a control terminal, wherein parameters of the channel measurement platform comprise transmitting signal parameters, transmitting antenna array parameters, intelligent super surface parameters and receiving antenna array parameters, the transmitting signal parameters comprise a frequency range to be measured, transmitting signal power and transmitting signal type, and the transmitting antenna array parameters, the intelligent super surface parameters and the receiving antenna array parameters comprise the number, spacing distance, position and orientation of antenna units or array units;

in step 2, the characteristics of the channel measurement platform include measurement and calibration of antenna feed transmission power error, high-frequency coaxial cable transmission loss, adapter insertion loss, transmitting antenna array, intelligent super-surface array, receiving antenna array and other instrument and equipment system response error, wherein the measurement and calibration method uses a direct-reflection-transmission line calibration mode, a short-circuit-open-load-direct calibration mode, a direct-reflection-matching calibration mode or a direct-open-short-matching calibration mode.

In step 3, the time division multiple access among the transmitting antenna array, the uniform rectangular RIS array and the receiving antenna array is realized by the antenna high-speed switching module, wherein the transmitting antenna array has M in total _T A transmitting antenna unit, a receiving antenna array having M _R The RIS array comprises MN RIS array units, M and N are the number of the RIS array units on the long side and the narrow side of the rectangle respectively; only one combination of a transmitting antenna unit, an RIS array unit and a receiving antenna unit is measured in each time slot, non-line-of-sight channel impact response between each transmitting antenna unit, each intelligent super-surface array unit and each receiving antenna unit is obtained through measurement in sequence, and a channel sampling snapshot is obtained after all combinations are traversed, and the method specifically comprises the following steps:

define the following activation time function

Said activation time function

Has an activation time ranging from 0 to time->

The purpose is to control whether the transmit antenna unit, the intelligent super-surface unit or the receive antenna unit is activated at time t, 1 for activation and 0 for deactivation;

for the ith channel sampling snapshot, the activation time function of the pth transmitting antenna unit is defined according to the activation time function

Activation time function ^ based on the qth receiving antenna unit>

And an activation time function of the r-th RIS array unit>

Respectively as follows:

wherein, T _T For the activation time of a single transmit antenna element, T _R For the activation time of a single receiving antenna unit, T _RIS For the activation time of a single RIS array element, the period of traversing all combinations of transmit antenna elements, RIS array elements and receive antenna elements is T _cycle ，M _S Sampling the number of snapshots for the channel;

the transmission signal u (t) is represented as:

/>

wherein s (t) is PN sequence signal, vector

And &>

Respectively as a function of the activation time of the 1 st transmit antenna element, as a function of the activation time of the 2 nd transmit antenna element, and as a function of the Mth transmit antenna element _T An activation time function for each transmit antenna element;

signal after RIS reflection

Comprises the following steps:

wherein phi is the RIS array response matrix,

for the channel transfer matrix of the transmit antenna array to the RIS array,

for propagation delay, the superscript T is the matrix transpose operator, vector @>

And &>

Respectively is the activation time function of the 1 st RIS array unit, the activation time function of the 2 nd RIS array unit and the activation time function of the MN th RIS array unit;

the signal vector y (t) received by the receiving antenna array is:

wherein the content of the first and second substances,

a channel transfer matrix for the RIS array to the receiving antenna array, in which->

For propagation delay, H _NLoS (t,τ _NLoS ) NLOS channel transfer matrix for transmit antenna array to receive antenna array, where τ _NLoS For transmission delay, n (t) is a complex Gaussian white noise vector;

finally, the received signal Y (t) obtained at each measurement is:

wherein the vector

And &>

Respectively as a function of the activation time of the 1 st receive antenna element, as a function of the activation time of the 2 nd receive antenna element, and as a function of the Mth receive antenna element _R The activation time of each receiving antenna element.

The step 6 comprises the following steps:

the radio signal arrives at the receiving antenna array in clusters, in the nth cluster component, the channel h from the p-th transmitting antenna element to the q-th receiving antenna element _p,q,n (t) is expressed as:

wherein, M _c Indicates the number of sub-paths in the nth cluster component, α _n,m 、Ψ _n,m 、v _n,m And τ _n,m Respectively representing the amplitude attenuation, the complex polarization matrix, the Doppler shift and the propagation delay corresponding to the mth sub-path in the nth cluster component, omega _Tx,n,m ＝{θ _Tx,n,m ,φ _Tx,n,m And Ω _Rx,n,m ＝{θ _Rx,n,m ,φ _Rx,n,m Denotes angle information of the transmitting antenna array and angle information of the receiving antenna array, respectively, θ _Tx,n,m And phi _Tx,n,m Respectively representing the pitch angle and the horizontal angle theta of the transmitting antenna array corresponding to the mth sub-path in the nth cluster component _Rx,n,m And phi _Rx,n,m Respectively representing the pitch angle and the horizontal angle of the receiving antenna array corresponding to the mth sub-diameter in the nth cluster component _Tx,p (Ω _Tx,n,m ) And Γ _Rx,q (Ω _Rx,n,m ) Respectively transmitting antenna array response and receiving antenna array response, exp is a natural exponential function, and j is an imaginary number unit;

will receive the first

Root of Lei ZiNumber set->

Is defined as:

/>

wherein the content of the first and second substances,

and &>

Respectively denote a fifth->

The corresponding amplitude attenuation, repolarization matrix, doppler shift, and propagation delay of the bar path, <' >>

And &>

Represents the angle information of the transmit antenna array and the receive antenna array, respectively, in->

And &>

Respectively denote a fifth->

A strip diameter corresponding to the pitch angle and horizontal angle of the transmit antenna array, based on the elevation angle and horizontal angle of the transmit antenna array>

And &>

Respectively denote a fifth->

The strip diameter corresponds to the pitch angle and the horizontal angle of the receiving antenna array, and the sign->

Represents->

The numerical value of (b) is any value within the value range thereof;

for a known PN sequence s (t) and a measured received signal Y (t), the likelihood function determined by the set of parameters is

SAGE Algorithm solves parameter set->

Finding a set of multipath clustering parameters that maximizes the likelihood function L, at each iteration, only for the set { } in each iteration>

And estimating the medium single parameter, keeping the rest parameters unchanged, updating the single parameter after the solution is finished, substituting the single parameter into the next iteration for solving other parameters, and for the kth iteration, wherein one iteration updating sequence is as follows:

where the function argmax is the value of the variable that maximizes the function immediately to the right, the sign below the function argmax being the variable that is adjusted,

and->

Denotes the time of the kth and the k-1 th iteration, respectively>

And

the value of (d);

obtaining a parameter set of each sub-path through SAGE algorithm estimation, and then forming a feature vector

And clustering the characteristic vectors of all the sub-paths in a vector space by a K-adjacent clustering algorithm to realize clustering and determine the number of clusters and sub-paths in the clusters.

The channel parameter indicators obtained from the measurement data set by the SAGE algorithm in step 6 include:

signal amplitude attenuation, multipath delay, horizontal departure angle, vertical departure angle, horizontal arrival angle, vertical arrival angle, complex polarization matrix, doppler shift, number of clusters, and intra-cluster sub-paths.

In step 7, the environment of the reinforcement learning is a wireless channel containing direct incidence, primary reflection and secondary reflection, the action is to randomly match a multipath scattering cluster and a scattering body, and the reward is the reciprocal of the Frobenius norm of the difference value between a channel impact response matrix generated in the environment based on a ray tracing method and the actual channel impact response matrix obtained in step 6.

In step 7, combining the multi-path clustering result and the scatterer map, matching the scatterer cluster and the scatterer by reinforcement learning to obtain M _C A cluster core of multipath scatterer and 1 RIS equivalent cluster core, and defining the cluster core set of multipath scatterer as

Wherein C is ₁ 、C ₂ And &>

Respectively being the 1 st multipath scatterer cluster kernel, the 2 nd multipath scatterer cluster kernel and the Mth multipath scatterer cluster kernel _c A cluster kernel of multipath scatterers;

the environment of reinforcement learning is set as a wireless channel containing direct incidence, primary reflection and secondary reflection, and under the condition that the positions and the characteristics of a transmitting end, a receiving end and a scattering body are known, a channel impact response matrix H from the transmitting end to the receiving end is obtained by calculation through a ray tracing method _RT (ii) a The action of reinforcement learning is that multipath scattering clusters and scatterers are matched randomly, so that a cluster core is formed, the position of the cluster core corresponds to the position of the scatterers in a digital map of the scatterers, and the characteristics of the cluster core correspond to the parameters of the multipath scattering clusters; combining the characteristics of the transmitting end and the receiving end obtained in the step 1 and the step 2, substituting the positions and the characteristics of the cluster cores into an environment for reinforcement learning, and obtaining a channel impact response matrix H of a wireless channel by using a ray tracing method _RT (ii) a The reward of reinforcement learning is set as a channel shock response matrix generated in the environment based on ray tracing and an actual channel shock response matrix H obtained in the step 6 _true Reciprocal of Frobenius norm of difference, according to the commonFormula H _RT -H _true || ^-1 Calculations were performed where the notation | | | | represents the Frobenius norm with the superscript-1 representing the reciprocal.

The step 8 comprises the following steps:

NLOS channel from the p-th transmitting antenna unit to the q-th receiving antenna unit for non-line-of-sight links that do not undergo RIS reflection

The method comprises the following steps of sequentially splitting a cluster core into the following visual distance logic sub-channels:

wherein Tx ^(p) Denotes the p-th transmitting antenna element, rx ^(q) Denotes the q-th receiving antenna element, → denotes a signal propagation path,

clustering for the multipath scatterers obtained in step 7>

And &>

Is the ^ th ^ in the set>

Is and/or>

A cluster kernel of multipath scatterers;

the RIS-reflected channels are divided into RIS-only virtual line-of-sight channels

NLOS channel @, where a scatterer is present before the RIS reflection>

NLOS channel @, where a scatterer is present after a RIS reflection>

And NLOS channel with scatterers present before and after the RIS reflection>

Sequentially splitting the cluster cores into the following visual range logic sub-channels according to the cluster cores:

Tx ^(p) →RIS→Rx ^(q) ,

substituting the parameters obtained in the step 6 and the step 7, including signal amplitude attenuation, multipath time delay, horizontal departure angle, vertical departure angle, horizontal arrival angle, vertical arrival angle, complex polarization matrix, doppler frequency shift, scattering cluster number, in-cluster time delay, in-cluster angle expansion, multipath scatterer cluster core and RIS equivalent cluster core, into the split logical sub-channels, and calculating the channel impulse response of each logical channel in sequence to obtain five channels

Respective channel impulse response ≥>

And &>

The step 9 comprises the following steps:

at the transmitting time t, after the propagation delay tau, the complex channel impulse response h from the p-th transmitting antenna unit to the q-th receiving antenna unit _p,q (t, τ) is expressed as:

the corresponding MIMO intelligent super-surface RIS wireless communication system channel model is expressed as M _R ×M _T Complex matrix H (t, τ):

compared with the prior art, the invention has the following beneficial effects:

according to the method, a corresponding scatterer digital map is established according to the position, texture and reflection characteristics of an environment structure in an original propagation scene, the intelligent super surface is equivalent to a virtual scatterer, the analysis modeling difficulty can be effectively reduced, then the actual scatterer is matched with a multi-path clustering result to form a cluster core, the non-line-of-sight channel modeling process is converted into the analysis and modeling of a plurality of direct paths, the modeling requirement of a wireless communication system under a coal mine can be effectively met, and the complexity and difficulty of the modeling process are effectively reduced.

Drawings

The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.

Fig. 1 is a flow chart of channel modeling based on cluster kernel formation in the present invention.

Fig. 2 is a schematic diagram of a channel measurement platform and process in the present invention.

FIG. 3 is a schematic view of a non-line-of-sight propagation scene of an underground coal mine intelligent super-surface wireless communication system.

FIG. 4 is a logic diagram of the timing of the signals of the channel measurement platform according to the present invention.

Detailed Description

The definitions of abbreviations and key terms used in the present invention are as follows:

TABLE 1

As shown in FIG. 1, the invention provides a non-line-of-sight channel modeling method for intelligent super-surface wireless communication in an underground coal mine, which mainly comprises three stages of platform building and ground test, underground coal mine actual measurement, post data processing and channel modeling.

In a ground conventional environment, a channel measurement platform of a coal mine underground multiple-input multiple-output (MIMO) intelligent super-surface (RIS) wireless communication system shown in figure 2 is built, and platform determination, calibration and test are carried out, wherein the channel measurement platform mainly comprises the following steps:

step 1: according to the existing or future required wireless communication system in the underground environment of the coal mine to be measured, parameters of a channel measurement platform for the MIMO RIS wireless communication system are selected, a transmitting end, an intelligent super surface and a receiving end of the channel measurement platform shown in figure 2 are set up, and the Sounder system for measuring the channel of the underground MIMO RIS wireless communication system of the coal mine is formed.

The channel measurement platform shown in fig. 2 mainly comprises a transmitting end (Tx), an intelligent super surface and a receiving end (Rx), wherein the transmitting end includes but is not limited to a transmitting end control terminal, a transmitting end synchronous clock, a transmitting end signal generator and a transmitting antenna array, the intelligent super surface includes but is not limited to an intelligent super surface control terminal, an intelligent super surface synchronous clock, an intelligent super surface antenna high-speed switching module and an intelligent super surface array, and the receiving end includes but is not limited to a receiving end control terminal, a receiving end synchronous clock, a receiving end signal receiver, a receiving end antenna high-speed switching module, a receiving antenna array and a data storage unit. All equipment and components of the channel measurement platform need to meet the safety regulation of electrical equipment in a coal mine. The control terminals of the transmitting terminal, the intelligent super surface and the receiving terminal can adopt an intrinsically safe portable computer which is subjected to safety certification and used for observing and controlling the operation of each device and composition, and can be used as a data storage unit at the same time. Compared with the open environment on the ground, the closed environment under the well causes serious refraction and reflection, so that a large amount of multipath information is generated, incident waves in all directions exist, the transmitting antenna array can adopt a uniform planar antenna array, the intelligent super-surface array can adopt a uniform rectangular planar array, and the receiving antenna array can adopt an omnidirectional antenna array consisting of eight planes. Because colliery is working environment in the pit not convenient to synchronous cable lay and peg graft to when carrying out channel measurement, transmitting terminal, intelligent super surface and receiving terminal need guarantee time synchronization, can use the rubidium atomic clock to come as the synchronous clock of transmitting terminal, intelligent super surface and receiving terminal. Because channel measurement requires the use of a dedicated signal sequence and waveform, and the frequency range to be measured is large, the transmitting-end signal generator and the receiving-end signal receiver can be implemented separately using two Universal Software Radio Peripherals (USRP). The frequency range and the power of a transmitting signal of the transmitting end are set according to the working frequency of a wireless communication system which is in the underground of a coal mine or required in the future, the transmitting signal adopts a pseudo-random (PN) sequence and is generated by a signal generator of the transmitting end.

The parameters of the channel measurement platform include transmit signal parameters, transmit antenna array parameters, intelligent super-surface parameters, and receive antenna array parameters. The parameters of the transmitted signal comprise a frequency range to be measured, the power of the transmitted signal and the type of the transmitted signal. The transmit antenna array, smart super surface, and receive antenna array parameters include the number of antenna elements or array elements, separation distance, location, and orientation.

The step is mainly realized by the prior art, and is not described herein again.

Step 2: and (4) determining and calibrating the self characteristics of the channel measurement platform. And in the ground measurement, the whole frequency response of the system, the frequency response of a transmitting antenna array, the frequency response of an intelligent super-surface array and the frequency response of a receiving antenna array are measured in a microwave darkroom environment. The system is calibrated and error and interference characteristics are recorded in order to eliminate the error and interference effects of the measurement platform from the measurement results. The measuring and calibrating method uses a direct-reflection-transmission line calibrating mode, a short-circuit-open-load-direct calibrating mode, a direct-reflection-matching calibrating mode or a direct-open-circuit-short-matching calibrating mode, and the detailed steps of measuring and calibrating are mainly realized by the prior art and are not described again.

In the coal mine underground NLOS wireless communication scene shown in FIG. 3, a channel measurement platform and SLAM equipment which are measured and calibrated are deployed, and channel measurement and scene information acquisition are carried out on the spot. Wherein the transmitting antenna array has M _T The number of the transmitting antenna units is M multiplied by N, the number of the receiving antenna arrays is M _R And a plurality of receiving antenna units, thereby constituting a MIMO RIS wireless communication system. Due to the obstruction of bend, large-scale equipment and the like, no LOS path exists between the transmitting antenna array and the receiving antenna array, and the wireless signals pass through a large number of scatterer clusters C ₁ 、C ₂ ……C _i The NLOS path is formed by the reflection and scattering of the signal, and the VLOS path is formed by the signal reflected by the RIS array due to the presence of the RIS array in the scene. The channel measurement and scene information acquisition steps comprise:

and step 3: in order to accurately and independently acquire the characteristics of each sub-channel of the MIMO RIS wireless communication system, the time division multiple access among the transmitting antenna array, the RIS array and the receiving antenna array is realized by using an antenna high-speed switching module, only one combination of the transmitting antenna unit, the RIS array unit and the receiving antenna unit is measured in each time slot, and the measuring process is carried out according to the channel measuring platform information shown in the figure 4The number sequential logic proceeds. Wherein, T _T For the activation time of a single transmit antenna element, T _R For the activation time of a single receiving antenna unit, T _RIS For the activation time of a single RIS array element, the period of traversing all combinations of transmit antenna elements, RIS array elements and receive antenna elements is T _cycle . After the signal timing logic of the channel measurement platform shown in fig. 4 is executed, the channel measurement platform will traverse all the transmitting antenna units, the RIS array units and the receiving antenna units to form a channel sampling snapshot, and the actual measurement process needs to repeatedly execute the above process to obtain multiple channel sampling snapshots.

In the measuring process, a transmitting end signal generator generates a pseudo-random sequence, the pseudo-random sequence is processed by a modulation module, an AD conversion module, an up-conversion module and the like, and finally, a corresponding transmitting antenna unit is selected by an antenna high-speed switching module to transmit. The wireless signals are transmitted in the space, reflected by the RIS array unit selected by the antenna high-speed switching module, and reach the receiving antenna unit selected by the antenna high-speed switching module, then processed, down-converted, demodulated and DA-converted in a receiving end signal receiver, and then sequentially measured to obtain the non-line-of-sight channel impact response between each transmitting antenna unit, each intelligent super-surface array unit and each receiving antenna unit, and stored in a data storage unit, so as to facilitate the later data processing and analysis.

Defining an activation time function:

the activation time of this activation time function ranges from 0 to the time of the moment

The purpose is to control whether the transmit antenna element, the smart super-surface element or the receive antenna element is activated at time t, 1 for activation and 0 for deactivation.

For the ith channel sampling snapshot, according to the definition of the activation time function, the activation time functions of the pth transmitting antenna unit, the qth receiving antenna unit and the r RIS array unit are respectively:

wherein M is _S The number of snapshots is sampled for the channel.

Thus, the transmitted signal can be expressed as:

wherein s (t) is PN sequence signal, vector

And &>

Respectively being the 1 st transmitting antenna unit, the 2 nd transmitting antenna unit and the Mth transmitting antenna unit _T The activation time of each transmit antenna element.

The signal after reflection over the RIS is:

wherein phi is the RIS array response matrix,

a channel transfer matrix for the transmit antenna array to the RIS array, wherein->

For propagation delay, the vector->

And

respectively being the activation time functions of the 1 st RIS array unit, the 2 nd RIS array unit and the MN th RIS array unit;

the signal vector received by the receiving antenna array is:

wherein the content of the first and second substances,

For propagation delay, H _NLoS (t,τ _NLoS ) NLOS channel transfer matrix for transmit antenna array to receive antenna array, where τ _NLoS For the transmission delay, n (t) is a complex white gaussian noise vector.

Finally, the received signal obtained at each measurement is:

wherein the vector

Respectively being the 1 st receiving antenna unit, the 2 nd receiving antenna unit and the Mth receiving antenna unit _R The activation time function of each receiving antenna element.

And 4, step 4: the method comprises the steps of utilizing a laser radar and a synchronous positioning and mapping technology (SLAM) to carry out three-dimensional image scanning and reconstruction on a channel measurement site, and collecting and calibrating the position, texture characteristics and reflection characteristics of objects such as large equipment, a metal protective net, a rock mass, walls and the like.

After the underground measurement of the coal mine is finished, post data processing and channel modeling are carried out on the ground, and the method mainly comprises the following steps:

and 5: the method comprises the steps of utilizing SLAM measurement data and technology to carry out three-dimensional image scanning and reconstruction on a channel measurement site, then carrying out image semantic segmentation on the SLAM measurement data and results through a computer vision method, matching with each object on the site to form a scatterer digital map, and enabling an intelligent super surface to be equivalent to a virtual scatterer to be inserted into the scatterer digital map according to the measured intelligent super surface array characteristics.

Step 6: for the wireless channel data measured by the platform shown in FIG. 2, the complete channel impulse response matrix H of the MIMO RIS wireless communication system is obtained by using the sliding correlation method _true And forming a measurement data set. Then, the RIS is regarded as a special scatterer cluster, channel parameters such as signal amplitude attenuation, multipath time delay, a horizontal departure angle, a vertical departure angle, a horizontal arrival angle, a vertical arrival angle, a complex polarization matrix, doppler frequency shift and the like are obtained from the measurement result data set through the SAGE algorithm, then multipath clustering is carried out through the K-neighbor clustering algorithm, and the parameters such as the number of scattering clusters, time delay in clusters, angle expansion in clusters and the like are determined.

The radio signal arrives at the receiving antenna array in clusters, and in the nth cluster component, the channel from the pth transmitting antenna element to the qth receiving antenna element can be expressed as:

wherein, M _c Indicates the number of sub-paths in the nth cluster component, alpha _n,m 、Ψ _n,m 、v _n,m And τ _n,m Respectively representing the amplitude attenuation, the complex polarization matrix, the Doppler frequency shift and the propagation delay corresponding to the mth sub-path in the nth cluster component, and omega _Tx,n,m ＝{θ _Tx,n,m ,φ _Tx,n,m And Ω _Rx,n,m ＝{θ _Rx,n,m ,φ _Rx,n,m Denotes angle information of the transmitting antenna array and the receiving antenna array, respectively, theta _Tx,n,m And phi _Tx,n,m Respectively representing the pitch angle and the horizontal angle theta of the transmitting antenna array corresponding to the mth sub-path in the nth cluster component _Rx,n,m And phi _Rx,n,m Respectively representing the pitch angle and the horizontal angle of the receiving antenna array corresponding to the mth minor diameter in the nth cluster component _Tx,p (Ω _Tx,n,m ) And Γ _Rx,q (Ω _Rx,n,m ) Respectively, a transmitting antenna array response and a receiving antenna array response, exp is a natural exponential function, and j is an imaginary number unit.

Thus, the first to be received

The parameter set of the bar path is defined as:

/>

wherein, the first and the second end of the pipe are connected with each other,

and &>

Respectively denote a fifth->

Corresponding amplitude attenuation, repolarization matrix, doppler shift and propagation delay for the bar paths, <' > in >>

And &>

And &>

Respectively denote a fifth->

The strip diameter corresponds to the elevation angle and the horizontal angle of the transmitting antenna array>

And &>

Respectively denote a fifth->

Represents->

The numerical value of (b) is any value within the range of the numerical value.

SAGE Algorithm solves a parameter set by a number of iterations>

Finding a set of multipath clustering parameters that maximizes the likelihood function L, and at each iteration, only the set->

Estimating the medium single parameter, keeping the rest parameters unchanged, updating the parameter after the solution is completed, substituting the parameter into the next iteration for solving other parameters, and for the kth iteration, wherein one iteration updating sequence is as follows:

and->

Denotes the time of the kth and the k-1 th iteration, respectively>

And

the value of (d);

And 7: matching the scattering clusters and the scatterers by combining a multipath clustering result and a scatterer map through reinforcement learning to obtain M _C A cluster core of multipath scatterer and 1 RIS equivalent cluster core, and defining a cluster core set of multipath scatterers as

Wherein C ₁ 、C ₂ And &>

Respectively being the 1 st multipath scatterer cluster kernel, the 2 nd multipath scatterer cluster kernel and the Mth multipath scatterer cluster kernel _c A cluster kernel of multipath scatterers.

The environment of reinforcement learning is set as a wireless channel containing direct incidence, primary reflection and secondary reflection, and under the condition that the positions and the characteristics of a transmitting end, a receiving end and a scattering body are known, a channel impact response matrix H from the transmitting end to the receiving end can be obtained by utilizing a ray tracing method _RT . For reinforcement of learningThe action serves as a random matching of the multipath scattering clusters and the scatterers, thereby forming cluster nuclei, the positions of which correspond to the positions of the scatterers in the digital map of the scatterers, and the characteristics of which correspond to the parameters of the multipath scattering clusters. Therefore, the characteristics of the transmitting end and the receiving end are obtained in the step 1 and the step 2, the positions and the characteristics of the cluster cores are substituted into the environment of the reinforcement learning, and the channel impact response matrix H of the wireless channel is obtained by utilizing a ray tracing method _RT . The reward of reinforcement learning is set as a channel shock response matrix generated in the environment based on ray tracing and an actual channel shock response matrix H obtained in the step 6 _true The reciprocal of the Frobenius norm of the difference, i.e. according to the formula | | H _RT -H _true || ^-1 Calculations were performed where the notation | | | | represents the Frobenius norm with the superscript-1 representing the reciprocal. The specific implementation method of reinforcement learning and ray tracing method is mainly implemented by the prior art, and is not described herein again.

And 8: the cluster core is used as a node, a non-line-of-sight propagation link through which a wireless signal passes is decomposed and split into a plurality of logical sub-channels, the logical sub-channels are mutually connected to form a propagation path, an effective propagation path with the connection node sequentially comprising a transmitting antenna unit, the cluster core and a receiving antenna unit is obtained, and if the end point of the propagation path is not the receiving antenna unit, the effective propagation path is an invalid propagation path which can be eliminated.

For the scenario shown in FIG. 3, for a non-line-of-sight (NLOS) link that does not undergo RIS reflection, the NLOS channel from the p-th transmit antenna element to the q-th receive antenna element

The method can be sequentially split into the following visual range logical sub-channels according to the cluster core:

wherein, tx ^(p) Denotes the p-th transmitting antenna element, rx ^(q) Denotes the q-th receiving antenna element, → denotes a signal propagation path,

for the multipath scatterer cluster kernel set obtained in step 7, a value is selected>

And &>

Is the ^ th ^ in the set>

Is and/or>

A cluster kernel of multipath scatterers.

The channel reflected by the RIS can be divided into virtual line-of-sight channels that pass through the RIS only

NLOS channel @, where a scatterer is present before the RIS reflection>

NLOS channel @, where a scatterer is present after a RIS reflection>

And NLOS channel with scatterers present before and after the RIS reflection->

The method comprises the following steps of sequentially splitting a cluster core into the following visual range logical sub-channels:

Tx ^(p) →RIS→Rx ^(q) ,

substituting the parameters obtained in the step 6 and the step 7, namely signal amplitude attenuation, multipath time delay, horizontal departure angle, vertical departure angle, horizontal arrival angle, vertical arrival angle, complex polarization matrix, doppler frequency shift, scattering cluster number, in-cluster time delay, in-cluster angle expansion, multipath scatterer cluster core and RIS equivalent cluster core into the split logic sub-channels, and calculating the channel impulse response of each logic channel in sequence, thereby obtaining the respective channel impulse response of the five channels in the step

And &>

And step 9: and combining all effective propagation paths to obtain channel impact response from a sending end to a receiving end, and obtaining a non-line-of-sight channel model facing the coal mine underground intelligent super-surface wireless communication system in the current scene.

At the transmitting time t, after a propagation delay tau, the complex Channel Impulse Response (CIR) h from the p-th transmitting antenna element to the q-th receiving antenna element _p,q (t, τ) can be expressed as:

the corresponding MIMO RIS wireless communication system channel response matrix is M _R ×M _T Complex matrix:

in a concrete implementation, the application provides a computer storage medium and a corresponding data processing unit, wherein the computer storage medium can store a computer program, and the computer program can run the inventive content of the non-line-of-sight channel modeling method for the coal mine underground intelligent super-surface wireless communication and part or all steps in each embodiment provided by the invention when being executed by the data processing unit. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), a Random Access Memory (RAM), or the like.

It is clear to those skilled in the art that the technical solutions in the embodiments of the present invention can be implemented by means of a computer program and its corresponding general-purpose hardware platform. Based on such understanding, the technical solutions in the embodiments of the present invention may be essentially or partially implemented in the form of a computer program or a software product, where the computer program or the software product may be stored in a storage medium and include instructions for enabling a device (which may be a personal computer, a server, a single chip microcomputer, an MUU, or a network device) including a data processing unit to execute the method according to the embodiments or some parts of the embodiments of the present invention.

The invention provides a non-line-of-sight channel modeling method for intelligent super-surface wireless communication in an underground coal mine, and a plurality of methods and ways for realizing the technical scheme are provided. All the components not specified in the present embodiment can be realized by the prior art.

Claims

1. A non-line-of-sight channel modeling method for intelligent super-surface wireless communication in a coal mine is characterized by comprising the following steps:

step 1: selecting parameters of a channel measurement platform for a multi-input multi-output intelligent super-surface wireless communication system according to a wireless communication system which is required in the existing or future environment of the underground coal mine to be measured, and building a transmitting end, an intelligent super-surface and a receiving end of the channel measurement platform;

and step 3: in a wireless communication scene under a coal mine to be measured, deploying a channel measurement platform which is measured and calibrated, carrying out channel measurement on the spot, controlling the working states of a transmitting antenna array, an intelligent super-surface and a receiving antenna array through an antenna high-speed switching module, sequentially measuring non-line-of-sight channel impact responses among each transmitting antenna unit, each intelligent super-surface array unit and each receiving antenna unit based on a time division multiple access principle, and storing the non-line-of-sight channel impact responses in a data storage unit;

and 4, step 4: deploying a laser radar in a wireless communication scene under a coal mine to be measured, scanning and reconstructing a three-dimensional image of a channel measurement field by utilizing a synchronous positioning and mapping technology, and acquiring and calibrating the position, texture characteristics and reflection characteristics of an object;

and 5: after the on-site measurement of the wireless communication scene under the coal mine is finished, image semantic segmentation is carried out on the measurement data and results of the synchronous positioning and mapping technology on the ground through a computer vision method, the measurement data and results are matched with various objects on site to form a scatterer digital map, and the intelligent super surface is equivalent to a virtual scatterer and inserted into the scatterer digital map according to the previously determined intelligent super surface array characteristic;

and 6: after the coal mine underground wireless communication scene is measured on site, a complete multi-input multi-output intelligent super-surface wireless communication system channel impact response matrix is obtained on the ground by using a sliding correlation method, a measurement result data set is formed, channel parameters are obtained from the measurement result data set through an SAGE algorithm, then multipath clustering is carried out through a K-neighbor clustering algorithm, and the number of scattering clusters, the time delay in the clusters and the intra-cluster angle expansion parameters are determined;

and 7: matching scattering clusters with scatterers by combining a multipath clustering result and a scatterer map through reinforcement learning to obtain a limited number of multipath scatterer clusters and an intelligent super-surface equivalent cluster core;

and 8: taking a cluster core as a node, decomposing and splitting a non-line-of-sight propagation link through which a wireless signal passes into more than two logic sub-channels, connecting the logic sub-channels with each other to form a propagation path, obtaining an effective propagation path of which a connection node sequentially comprises a transmitting antenna unit, the cluster core and a receiving antenna unit, and if the end point of the propagation path is not the receiving antenna unit, determining the propagation path as an invalid propagation path which can be eliminated;

and step 9: and combining all effective propagation paths to obtain channel impact response from a transmitting end Tx to a receiving end Rx, and obtaining a non-line-of-sight channel model facing the coal mine underground intelligent super-surface wireless communication in the current scene.

2. The method according to claim 1, wherein in step 1, the transmitting end, the intelligent super-surface and the receiving end of the channel measurement platform are composed of a transmitting antenna array, a receiving antenna array, an intelligent super-surface, a synchronous clock, a signal generator, a signal receiver, a data storage unit and a control terminal, wherein the parameters of the channel measurement platform include transmitting signal parameters, transmitting antenna array parameters, intelligent super-surface parameters and receiving antenna array parameters, the transmitting signal parameters include a frequency range to be measured, transmitting signal power size and transmitting signal type, and the transmitting antenna array, intelligent super-surface and receiving antenna array parameters include the number, spacing distance, position and orientation of antenna units or array units.

3. The method of claim 2, wherein in step 2, the channel measurement platform characteristics include measurement and calibration of antenna feed transmit power error, high frequency coaxial cable transmission loss, adapter insertion loss, transmit antenna array, smart super-surface array, receive antenna array, and other instrumentation system response errors.

4. According to claim 3The method is characterized in that in step 3, the time division multiple access among the transmitting antenna array, the uniform rectangular RIS array and the receiving antenna array is realized by the antenna high-speed switching module, wherein the transmitting antenna array has M in total _T A transmitting antenna unit, a receiving antenna array having M _R The RIS array comprises MN RIS array units, M and N are the number of the RIS array units on the long side and the narrow side of the rectangle respectively; only one combination of a transmitting antenna unit, an RIS array unit and a receiving antenna unit is measured in each time slot, the non-line-of-sight channel impact response between each transmitting antenna unit, each intelligent super-surface array unit and each receiving antenna unit is obtained through measurement in sequence, and a channel sampling snapshot is obtained after all combinations are traversed, and the method specifically comprises the following steps:

define the following activation time function

The activation time function

Has an activation time ranging from 0 to time->

The purpose is to control whether the transmitting antenna unit, the intelligent super-surface unit or the receiving antenna unit is activated at time t, 1 means activated and 0 means not activated;

Activation time function +for the qth receiving antenna unit>

And an activation time function of the r-th RIS array unit>

Respectively as follows:

wherein, T _T For activation of a single transmitting antenna element, T _R For the activation time of a single receiving antenna unit, T _RIS For the activation time of a single RIS array element, the period of traversing all combinations of transmit antenna elements, RIS array elements and receive antenna elements is T _cycle ，M _S Sampling the number of snapshots for the channel;

the transmission signal u (t) is represented as:

wherein s (t) is PN sequence signal, vector

And

respectively as a function of the activation time of the 1 st transmit antenna element, as a function of the activation time of the 2 nd transmit antenna element, and as a function of the Mth transmit antenna element _T An activation time function of each transmit antenna element;

signal after reflection by RIS

Comprises the following steps:

wherein phi is the RIS array response matrix,

for the channel transfer matrix of the transmit antenna array to the RIS array, the base station is selected>

For propagation delay, superscript T is the matrix transpose operator, vector @>

/>

And &>

the signal vector y (t) received by the receiving antenna array is:

finally, the received signal Y (t) obtained at each measurement is:

wherein the vector

And &>

Respectively as a function of the activation time of the 1 st receive antenna element, as a function of the activation time of the 2 nd receive antenna element, and as a function of the Mth receive antenna element _R The activation time function of each receiving antenna element.

5. The method of claim 4, wherein step 6 comprises:

wherein M is _c Indicates the number of sub-paths in the nth cluster component, alpha _n,m 、Ψ _n,m 、v _n,m And τ _n,m Respectively representing the amplitude attenuation, the complex polarization matrix, the Doppler frequency shift and the propagation delay corresponding to the mth sub-path in the nth cluster component, and omega _Tx,n,m ＝{θ _Tx,n,m ,φ _Tx,n,m And Ω _Rx,n,m ＝{θ _Rx,n,m ,φ _Rx,n,m Denotes angle information of the transmitting antenna array and angle information of the receiving antenna array, respectively, θ _Tx,n,m And phi _Tx,n,m Respectively representing the pitch angle and the horizontal angle theta of the transmitting antenna array corresponding to the mth sub-path in the nth cluster component _Rx,n,m And phi _Rx,n,m Respectively representing the pitch angle and the horizontal angle of the receiving antenna array corresponding to the mth sub-diameter in the nth cluster component _Tx,p (Ω _Tx,n,m ) And Γ _Rx,q (Ω _Rx,n,m ) Respectively transmitting antenna array response and receiving antenna array response, exp is a natural exponential function, and j is an imaginary number unit;

will receive the first

Parameter set of bar diameter->

Is defined as follows:

wherein the content of the first and second substances,

and &>

Respectively denote a fifth->

And &>

And &>

Respectively denote a first>

And &>

Respectively denote a fifth->

The strip path corresponds to the pitch angle, the horizontal angle and the symbol of the receiving antenna array

Represents->

The numerical value of (b) is any value within the value range thereof;

SAGE Algorithm solves parameter sets->

And (3) estimating the medium single parameter, keeping the rest parameters unchanged, updating the single parameter after solving, substituting the single parameter into the next iteration for solving other parameters, and for the kth iteration, wherein one iteration updating sequence is as follows:

and->

Denotes the time of the kth and the k-1 th iteration, respectively>

And

the value of (d);

And clustering the characteristic vectors of all the sub-paths in a vector space by a K-neighborhood clustering algorithm to realize clustering and determine the number of clusters and the sub-paths in the clusters.

6. The method of claim 5, wherein the channel parameter index obtained from the measurement dataset by the SAGE algorithm in step 6 comprises:

7. The method of claim 6, wherein in step 7, the environment of the reinforcement learning is a wireless channel comprising direct, primary and secondary reflections, the action is to randomly match multipath scattering clusters and scatterers, and the reward is the reciprocal of the Frobenius norm of the difference between the channel impulse response matrix generated in the environment based on ray tracing and the actual channel impulse response matrix obtained in step 6.

8. The method of claim 7, wherein M is obtained by combining the multipath clustering results with a scatterer map and matching the scattering clusters and scatterers to each other by reinforcement learning in step 7 _C A cluster core of multipath scatterer and 1 RIS equivalent cluster core, and defining the cluster core set of multipath scatterer as

Wherein C is ₁ 、C ₂ And &>

Respectively being the 1 st multipath scatterer cluster kernel, the 2 nd multipath scatterer cluster kernel and the Mth multipath scatterer cluster kernel _c A multipath scatterer cluster kernel;

the environment of reinforcement learning is set as a wireless channel containing direct incidence, primary reflection and secondary reflection, and under the condition that the positions and the characteristics of a transmitting end, a receiving end and a scattering body are known, a channel impact response matrix H from the transmitting end to the receiving end is obtained by calculation through a ray tracing method _RT (ii) a The action of reinforcement learning is that multipath scattering clusters and scatterers are matched randomly, so that a cluster core is formed, the position of the cluster core corresponds to the position of the scatterers in a digital map of the scatterers, and the characteristics of the cluster core correspond to the parameters of the multipath scattering clusters; combining the characteristics of the transmitting end and the receiving end obtained in the step 1 and the step 2, substituting the position and the characteristics of the cluster core into the environment of reinforcement learning, and obtaining a channel impact response matrix H of a wireless channel by using a ray tracing method _RT (ii) a The reward of reinforcement learning is set as the channel impact response matrix generated in the environment based on ray tracing method and step 6Obtaining actual channel impulse response matrix H _true Reciprocal of Frobenius norm of the difference, according to the formula | | H _RT -H _true || ^-1 Calculations were performed where the notation | | | | represents the Frobenius norm with the superscript-1 representing the reciprocal.

9. The method of claim 8, wherein step 8 comprises:

clustering for the multipath scatterers obtained in step 7>

And &>

Is the ^ th ^ in the set>

Is and/or>

A cluster kernel of multipath scatterers;

channels that undergo RIS reflection are divided into R-only channelsVirtual line-of-sight channel for IS

NLOS channel @, where a scatterer is present before the RIS reflection>

NLOS channel in the presence of a scatterer after a RIS reflection>

And NLOS channel with scatterers present before and after the RIS reflection>

Tx ^(p) →RIS→Rx ^(q) ,

substituting the parameters obtained in the step 6 and the step 7, including signal amplitude attenuation, multipath time delay, horizontal departure angle, vertical departure angle, horizontal arrival angle, vertical arrival angle, complex polarization matrix, doppler frequency shift, scattering cluster number, in-cluster time delay, in-cluster angle expansion, multipath scatterer cluster core and RIS equivalent cluster core, into the split logic sub-channel, and calculating each logic sub-channel in sequenceThe channel impulse response of the channel obtains five channels

Respective channel impulse response ≥>

And &>

10. The method of claim 9, wherein step 9 comprises:

/>