A rate analysis method for an intelligent metasurface system based on random geometric distribution

Abstract

The application discloses a rate analysis method of an intelligent metasurface system based on random geometry distribution, and comprises the following steps: constructing an initial optimization problem, in which a robustness problem of a distributed intelligent metasurface system under the influence of an initial mobile user is constructed; a receiver receives superimposed signals from multiple reflection links, and a determination formula of an initial reachable rate of the system is given; and the determination formula is further converted into an upper limit solution according to the Jesse inequality and a probability density function; the time intensity of vertical switching and beam selection caused by user movement is obtained; the total time overhead is further obtained; and an expression of a final area traversal reachable rate is obtained. The application is applied to an actual random distribution intelligent metasurface assisted communication system, an expression of an area spectrum rate limit is given, and the system performance can be effectively evaluated.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a communication rate analysis method based on a distributed intelligent metasurface assisted by random geometry. Background Technology

[0002] Smart metasurfaces are easily and flexibly deployed on indoor walls or outdoor public facilities, thus being considered a technological extension that can achieve large-scale multiple-input multiple-output advantages using passive devices. However, smart metasurfaces should not be confused with amplified relay-assisted systems or backscatter communication. On the one hand, traditional antenna arrays with fixed phase shifters typically operate in half-duplex mode, making it difficult to dynamically control signals from complex time-varying channels; conversely, smart metasurfaces operate in full-duplex mode, thus eliminating the need for analog-to-digital / digital-to-analog converters or power amplifiers. Because smart metasurface-assisted wireless network architectures introduce passive components, many techniques long used in traditional networks employing active components become ineffective, including but not limited to: channel modeling, hardware architecture, passive beamforming, channel estimation, and node deployment.

[0003] Random spatial processes are considered the most suitable analytical tool for multi-element deployments of wireless antennas, elucidating the ultimate performance limits of innovative technologies applied in wireless networks and guiding the design of optimal algorithms and protocols to achieve these limits. In particular, random spatial processes have been successfully applied multiple times in the analysis of cellular networks, multi-layer cellular networks, millimeter-wave cellular networks, multi-antenna cellular networks, wireless information and power transmission, and energy efficiency optimization. However, current research has not considered the beam management overhead and spillover probability caused by base station and smart metasurface handover due to mobile users. Therefore, this invention will use a random geometric framework to model the network distribution of smart metasurfaces, focusing on the coverage performance of smart metasurfaces within user-external infrastructure. Summary of the Invention

[0004] The technical problem this invention aims to solve is the performance analysis of cellular cooperative transmission communication systems assisted by intelligent metasurfaces based on random geometric distributions. It provides a rate analysis method for intelligent metasurface communication systems based on random geometry, which directly and effectively measures system performance. To achieve the above objective, this invention adopts the following technical solution:

[0005] A rate analysis method for intelligent metasurface systems based on random geometric distribution includes the following steps:

[0006] Step S1: Construct the robustness problem of the distributed intelligent metasurface system under the influence of the initial mobile user, establish the network and channel model, and make the phase shift of the intelligent metasurface the negative phase of the currently estimated channel.

[0007] Step S2: Give the determination of the initial reachable rate of the system, and further transform the determination into an upper bound based on the properties of the Jesse inequality and the probability density function, respectively.

[0008] Step S3: Calculate the time intensity of vertical switching and beam selection caused by user movement;

[0009] Step S4: Based on the results of S3, further obtain the total time cost;

[0010] Step S5: Based on the results of S2 and S4, obtain the expression for the final reachable rate of region traversal.

[0011] Furthermore, in step S1, considering the beam misalignment error caused by mobile users, a network and channel model is established:

[0012] (1) Establish the network topology and build a three-dimensional Cartesian coordinate system, where each smart metasurface is a two-dimensional uniform planar array composed of M rows and N columns. The horizontal position of all smart metasurfaces is modeled by a two-dimensional homogeneous Burson-Stokes process with a distribution density of λ (λ≥1). When the direct path between the base station and the user is blocked by an obstacle, the user can connect to the nearest smart metasurface within the cell to which the base station belongs, and the distance between the smart metasurface and the user should not exceed the service limit R. c At any given moment, each smart metasurface can serve at most one user simultaneously.

[0013] (2) The user is moving at a speed v parallel to the smart metasurface, which is triggered by a controller wirelessly connected to the base station. The reflection phase shift of its (m,n)th electromagnetic configuration is expressed as: The baseband equivalent channels from the base station to the (m,n)th electromagnetic configuration and from the (m,n)th electromagnetic configuration to the user are respectively represented by g. m,n and h m,n The cascaded base station-smart metasurface-user channel is modeled as a series of three parts: the base station-smart metasurface link, the smart metasurface with phase reflection, and the smart metasurface-user link. It is assumed that the cascaded channel phase ∠(g) through each smart metasurface element (m,n) can be obtained through channel estimation in each synchronization signal block period. m,n h m,n ), then you can set The phase shift of the smart metasurface is adjusted so that the signals from the MN reflected paths have the same phase at the receivers of the users they serve. However, since users move along the street, the referenced channel estimate is not necessarily updated in a timely manner, and the required phase shift cannot be precisely set. Therefore, the offset of the smart metasurface from the ideal phase shift is modeled as phase noise τ. m,n, distributed between [-π, π). At this time, the received signal can be written as:

[0014]

[0015] where, |·| represents the modulus value, and a m,n is the amplitude gain of the electromagnetic configuration path of the (m, n)-th intelligent metasurface, P is the transmission power of the transmitter, represents the average channel energy gain at a reference distance of 1 meter. X is the transmission symbol, and its mean is 0, W ∼ CN(0, 1) is the normalized received power. r1 and r2 represent the base station-intelligent metasurface link distance and the intelligent metasurface-user link distance respectively. τ m,n is modeled as a uniform distribution, denoted as τ m,n ∼ U(-bπ, bπ), 0 < b ≤ 1 represents the degree of phase offset; |g m,n | and |h m,n | follow the Rayleigh distribution.

[0016] Furthermore, define z m,n = |g m,n ||h m,n | and And according to the central limit theorem, for MN > 100, H is approximately Gaussian distributed, and its mean and variance can be calculated as: and We obtain the ergodic achievable efficiency of the intelligent metasurface-assisted large antenna system as R1 = log(1 + HH*): According to Jensen's inequality, it can be rewritten as

[0017]

[0018] where, ∈ i,j = τ m,n -τ i,j [[ID=4[7]]. [[ID=#48]]

[0019] Furthermore, in the step S2, according to tools such as probability theory, the upper bound of the ergodic achievable efficiency of the intelligent metasurface-assisted large antenna system is

[0020]

[0021] 6] In formula (3), indices i and j are not both equal to n and m simultaneously.

[0022] Furthermore, in the step S3, the vertical switching vc c and the time intensity μ b of beam selection caused by user movement are respectively:

[0023]

[0024]

[0025] Where r is the service radius of each smart metasurface, and L is the number of reflection directions of the base station / smart metasurface.

[0026] Furthermore, in step S4, the total time cost is further obtained;

[0027] T all =μ b T b +μ c T c #(6)

[0028] In formula (6), T b This refers to the re-alignment time of the beam when served by this base station / smart metasurface after mode switching, including the periodic synchronization block measurement and the receiver processing time of the synchronization block. c It is the beam scan time after vertical switching, including periodic synchronization block measurement, synchronization block reception and processing time, and handover interruption time due to mode switching and Radio Resource Control (RRC) reconfiguration.

[0029] Furthermore, in step S5, based on the results of S2 and S4, the final expression for the reachable rate of region traversal is obtained;

[0030] R T =λR1max(0,1-T) all ),#(7)

[0031] In formula (7), max(X,Y) means taking the maximum value of X and Y.

[0032] The beneficial effects of this invention are:

[0033] 1. This invention constructs an effective region traversal rate performance analysis model for intelligent metasurface auxiliary links based on random geometric distribution, and derives the convergence and overflow probability of the traversal rate of multiple links. It has low computational complexity and can effectively and clearly evaluate system performance.

[0034] 2. This invention constructs a beam management time intensity model for intelligent metasurface-assisted links based on random geometric distribution, calculates the total time overhead, and can effectively and clearly evaluate system performance. Attached Figure Description

[0035] Figure 1 This is a system block diagram of the performance analysis method for a distributed intelligent metasurface-assisted communication system based on random geometry proposed in this invention.

[0036] Figure 2 The figure shows the simulation results of the reachability rate analysis method for a distributed intelligent metasurface system provided in Example 1.

[0037] Figure 3 This refers to the number of mode switching events caused by changes in the service coverage radius of the intelligent metasurface. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and specific implementation examples.

[0039] This invention provides a rate analysis method for intelligent metasurface systems based on random geometric distribution, comprising the following steps:

[0040] Step S1: Construct the robustness problem of the distributed intelligent metasurface system under the influence of the initial mobile user, establish the network and channel model, and make the phase shift of the intelligent metasurface the negative phase of the currently estimated channel.

[0041] To verify the model proposed in this invention, the impact of smart metasurfaces on handover was studied using numerical methods to validate the analysis results and check the accuracy of the approximation of the precise expression. In the simulation, a two-level network was considered, consisting of a cell with a base station coverage radius R of 1000 meters and a smart metasurface service distance of r = 75 meters, establishing an observation area with a radius of 1000 meters. The smart metasurfaces were then uniformly distributed within the relevant area to ensure the total network coverage. Since the distribution of the smart metasurfaces follows the Hierarchical Public-Private Partnership (HPPP), the location of the observation area does not affect the analysis. Therefore, it was placed at the center of the considered area.

[0042] (1) Establish the network topology and build a three-dimensional Cartesian coordinate system, where each smart metasurface is a two-dimensional uniform planar array composed of M rows and N columns. The horizontal position of all smart metasurfaces is modeled by a two-dimensional homogeneous Burson-Stokes process with a distribution density of λ (λ≥1). When the direct path between the base station and the user is blocked by an obstacle, the user can connect to the nearest smart metasurface within the cell to which the base station belongs, and the distance between the smart metasurface and the user should not exceed the service limit R. c At any given moment, each smart metasurface can serve at most one user simultaneously.

[0043] (2) The user is moving at a speed v parallel to the smart metasurface, which is triggered by a controller wirelessly connected to the base station. The reflection phase shift of its (m,n)th electromagnetic configuration is expressed as: The baseband equivalent channels from the base station to the (m,n)th electromagnetic configuration and from the (m,n)th electromagnetic configuration to the user are respectively represented by g. m,n and h m,nrepresentation. The cascaded base station-intelligent metasurface-user channel is modeled as a series of three parts, namely the base station-intelligent metasurface link, the intelligent metasurface with phase reflection, and the intelligent metasurface-user link. It is assumed that through channel estimation, the cascaded channel phase ∠(g m,n h m,n ) passing through each intelligent metasurface element (m,n) can be obtained in each synchronization signal block period, then can be set to adjust the phase shift of the intelligent metasurface so that the signals of these MN reflection paths have the same phase at the user receiver they serve. However, since the user is moving along the street, the cited channel estimation is not necessarily updated in time, and the required phase shift cannot be accurately set. For this reason, the offset of the intelligent metasurface from the ideal phase shift is modeled as phase noise τ m,n , which is distributed between [-π,π). At this time, the received signal can be written as:

[0044]

[0045] where, |·| represents the modulus value, a m,n is the amplitude gain of the electromagnetic configuration path of the (m,n)th intelligent metasurface, P is the transmit power at the transmitter end, represents the average channel energy gain at a reference distance of 1 meter. X is the transmitted symbol, and its mean is 0, W~CN(0,1) is the normalized received power. r1 and r2 represent the base station-intelligent metasurface link distance and the intelligent metasurface-user link distance respectively. τ m,n is modeled as a uniform distribution, denoted as τ m,n ~U(-bπ,bπ), 0<b≤1 represents the degree of phase offset; |g m,n | and |h m,n | follow the Rayleigh distribution.

[0046] Step S2, give the determination formula of the initial achievable rate of the system, and further transform the determination formula into an upper bound according to Jensen's inequality and the properties of the probability density function respectively. Define z m,n =|g m,n ||h m,n | and and according to the central limit theorem, it is set that for MN>100, H is approximately Gaussian distributed, and its mean and variance can be calculated as: and The ergodic achievable efficiency of the intelligent metasurface-assisted large antenna system is obtained as R1 = log(1 + HH * ): According to Jensen's inequality, it can be rewritten as

[0047]

[0048] Where, ∈ i,j =τ m,n -τ i,j .

[0049] Based on probability theory and other tools, the upper bound of the ergodic achievable efficiency of intelligent metasurface-assisted large antenna systems is:

[0050]

[0051] In formula (3), indices i and j are not simultaneously equal to n and m.

[0052] Step S3: Calculate the vertical switching μ caused by user movement. c and the time intensity μ of beam selection b They are respectively:

[0053]

[0054]

[0055] Where r is the service radius of each smart metasurface, and L is the number of reflection directions of the base station / smart metasurface.

[0056] Step S4: Based on the results of S3, obtain the total time cost:

[0057] T all =μ b T b +μ c T c #(6)

[0058] In formula (6), T b This refers to the re-alignment time of the beam when served by this base station / smart metasurface after mode switching, including the periodic synchronization block measurement and the receiver processing time of the synchronization block. c It is the beam scan time after vertical switching, including periodic synchronization block measurement, synchronization block reception and processing time, and handover interruption time due to mode switching and Radio Resource Control (RRC) reconfiguration.

[0059] Step S5: Based on the results of S2 and S4, obtain the expression for the final reachable rate of region traversal:

[0060] R T =λR1max(0,1-T) all ),#(7)

[0061] In formula (7), max(X,Y) means taking the maximum value of X and Y.

[0062] In the simulation, a handover occurs when a user switches from a serving base station to a smart metasurface, or when a user disconnects from the smart metasurface due to an event outside the service range and attempts to seek service from the base station. To eliminate the impact of interference on the smart metasurface selection process, the base station and the smart metasurface are configured to operate at different frequencies.

[0063] To verify the effectiveness of the performance analysis provided in this embodiment, a simulation experiment was conducted. The parameters involved in the simulation experiment are shown in the table below:

[0064] Table 1 Simulation Experiment Parameters

[0065] parameter Value Number of base station transmit antennas 1 Number of user receiving antennas 1 Base station transmit power 43dBm <![CDATA[Receiver additive white Gaussian noise variance σ 2 > -80dBm Channel fading model Rayleigh fading channel <![CDATA[Beam selection overhead T b > 23ms <![CDATA[Mode switching overhead T c > 23ms User movement speed v 3km / h Bandwidth W 100MHz <![CDATA[Carrier frequency f c > 3.5GHz Base station coverage radius R 1km <![CDATA[Intelligent metasurface coverage radius R c > 75m

[0066] Based on the simulation results, Figure 2 The relationship between ergodicity and b is shown, revealing that the performance loss increases with increasing b. While more reflection elements can compensate for this loss, the cases of b < 0.7 and MN = 400 are superior to the ideal case of MN = 100. Figure 3 The diagram illustrates the number of mode switches resulting from changes in the service coverage radius of smart metasurfaces. As the coverage radius of a smart metasurface increases, the probability of a mobile user traversing its service area also increases. When the coverage radius exceeds a certain value, adjacent smart metasurfaces will form overlapping coverage areas, thus reducing the number of vertical switches. Similarly, increasing the deployment density of smart metasurfaces makes it easier for users to move into the service area of ​​a smart metasurface and switch horizontally between them, resulting in faster switching.

[0067] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0068] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for rate analysis of a random geometry distribution based intelligent surface system, characterized in that, Includes the following steps: Step S1: Construct the robustness problem of the distributed intelligent metasurface system under the influence of the initial mobile user, establish the network and channel model, and make the phase shift of the intelligent metasurface the negative phase of the currently estimated channel. Step S2: Give the formula for the initial traversal expression rate of the system and find its upper bound formula; Step S3: Calculate the time intensity of vertical switching and beam selection caused by user movement; Step S4: Based on the results of S3, further obtain the total time cost; Step S5: Based on the results of S2 and S4, obtain the expression for the final reachable rate of region traversal; In step S1, considering the beam misalignment error caused by mobile users, a network and channel model is established: (1) Establish the network topology and build a three-dimensional Cartesian coordinate system, in which each smart metasurface is a two-dimensional uniform plane array composed of M rows and N columns. The horizontal position of all smart metasurfaces is modeled by a two-dimensional homogeneous Burson-Warshall point process with a distribution density of λ, where λ ≥ 1. When the path between the base station and the user is blocked by an obstacle, the user can connect to the smart metasurface closest to the user in the cell to which the base station belongs, and the distance between the smart metasurface and the user should not be greater than the service limit r. At any given moment, each smart metasurface can serve at most one user at the same time. (2) The user is moving at a velocity v parallel to the smart metasurface, which is triggered by a controller wirelessly connected to the base station. The reflection phase shift of its (m, n)th electromagnetic configuration is expressed as: The baseband equivalent channels from the base station to the (m, n)th electromagnetic configuration and from the (m, n)th electromagnetic configuration to the user are respectively represented by... and The cascaded base station-smart metasurface-user channel is modeled as three concatenated parts: the base station-smart metasurface link, the smart metasurface with phase reflection, and the smart metasurface-user link. The offset of the smart metasurface from the ideal phase shift is modeled as phase noise. Distributed in Between; at this time, the received signal is represented as: （1）； in, Indicates the modulo value. It is the amplitude gain of the (m, n)th electromagnetic configuration path through the smart metasurface. It is the transmit power at the transmitting end. This represents the average channel energy gain at a reference distance of 1 meter; X is the transmitted symbol with a mean of 0. W ∼ CN (0, 1) is the normalized received power; and These represent the base station-smart metasurface link distance and the smart metasurface-user link distance, respectively. Model it as a uniform distribution, denoted as ~ U (-bπ, bπ), Indicates the degree of phase shift; and It follows a Rayleigh distribution.

2. The method of claim 1, wherein, Definitions and and according to the Central Limit Theorem, set for H is approximately Gaussian distributed with mean and variance that can be computed as: and ; The intelligent metasurface-assisted large antenna system exhaustive reachable efficiency is According to Jensen's inequality, it is rewritten as ； wherein = - , indices i and j are not simultaneously equal to n and m.

3. The method of claim 2, wherein, In step S2, according to probabilistic tools, the upper bound of the achievable efficiency of the intelligent metasurface-assisted large antenna system is: ； In formula (3), indices i and j are not simultaneously equal to n and m.

4. The method of claim 1, wherein, In said step S3, vertical handover due to user movement is obtained and time strength of beam selection are respectively: ; ； wherein, is the service radius of each smart hyper surface, L is the number of reflection directions of the base station / smart hyper surface, and R represents the maximum service distance of the base station.

5. The method of rate analysis for a random geometry distribution based intelligent surface system of claim 4, wherein In step S4, the total time cost is further calculated as follows; ； In formula (6), It is the re-alignment time of the beam when the base station / smart metasurface is served after the mode switch, including the periodic synchronization signal block measurement and the receiver processing time of the synchronization signal block; It is the beam scan time after vertical switching, including periodic synchronization block measurement, synchronization block reception and processing time, and handover interruption time due to mode switching and radio resource control reconfiguration.

6. The method of rate analysis for a random geometry distribution based intelligent surface system of claim 5, wherein In step S5, based on the results of S2 and S4, the final region traversal reachability expression is obtained and calculated as follows: ； In formula (7), max(X,Y) means taking the maximum value of X and Y.

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