Channel capacity lower bound analysis method and system based on super-large scale array system

Abstract

The invention discloses a channel capacity lower bound analysis method and system based on a super-large-scale array system, and the method comprises the steps: considering the spatial non-stationarity of a bilateral correlation super-large-scale array system, obtaining the complex channel gain of a channel, and obtaining the correlation of the proposed super-large-scale array system; the complex channel gain is subjected to Rayleigh fading, and the spatial correlation assumption occurs under the background of both the transmitting end and the receiving end, so that the channel capacity of the super-large-scale array system is obtained; the expression of the channel capacity is expanded by using the primary and secondary determinant expansion theorem, the determinant is solved by using the Baenechy theorem, the obtained lower bound of the channel capacity of the super-large-scale array system is related to all characteristic values of a correlation matrix, and the obtained lower bound of the channel capacity is verified. The method provided by the invention can provide powerful support for exploration of key technologies of a super-large-scale antenna communication system, and provides a basis for future system performance analysis and precoding algorithm design.

Description

Technical Field

[0001] The present invention relates to wireless communication technology, and in particular to a method and system for analyzing a lower bound of channel capacity based on an ultra-large-scale array system. Background Art

[0002] The advent of the 5G era has ushered in a series of technological revolutions, and 5G-related research and applications are constantly emerging. Increasing antenna size from hundreds to thousands, channel hardening, asymptotic inter-user channel orthogonality, and large array gain promise massive Multiple Input Multiple Output (MIMO) are key. From a theoretical perspective, ultra-large-scale MIMO (XL-MIMO), which deploys ultra-large antenna arrays (ELAA) at the base station (BS), can simultaneously serve multiple users, achieving significant spatial multiplexing gains and spectral efficiency, and is considered a potential solution for fifth-generation (5G) communications.

[0003] J. Zhang's paper, "On the downlink average energy efficiency of nonstationary XL-MIMO," IEEE Trans. Commun., vol. 72, no. 11, pp. 7294-7307, November 2024, discloses existing research. This study shows that when antenna dimensions reach large sizes, the spherical wave assumption can accurately describe the radiation characteristics of electromagnetic waves. Consequently, the transmitted signal power varies across the antenna array, leading to spatial non-stationarity. H.Shin, and J.H. Lee, "Capacity of multiple-antenna fading channels: Spatial fading correlation, double scattering, and keyhole," IEEE Trans. Inf. Theory., vol. 49, no. 10, pp. 2636-2647, Oct. 2003. When multiple antennas are deployed at the transmitter (Tx) and receiver (Rx), the spatial correlation between the Tx and Rx antennas affects the system performance gain. X. Li, S. Zhou, E. Bjornson, and J. Wang, "Capacity Analysis for Spatially Non-Widesense Stationary Uplink Massive MIMO Systems," IEEE Trans. Wireless Commun., vol. 14, no. 12, pp. 7044–7056, December 2015, presents a closed-form upper bound on the channel capacity derived using combinatorial methods from probability theory, resulting in a higher complexity for ultra-large-scale antenna systems. However, there is currently a lack of research exploring the impact of transmit and receive correlation on the performance of ultra-large-scale antenna systems while also considering the traversal capacity bound. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method and system for analyzing the lower bound of channel capacity based on a very large-scale array system, which can provide strong support for the exploration of key technologies of very large-scale antenna communication systems.

[0005] Technical solution: The method for analyzing the lower bound of channel capacity based on a very large-scale array system according to the present invention comprises the following steps:

[0006] Considering the spatial non-stationarity of the bilaterally correlated VLSI system in the visible region, the complex channel gain of the channel is obtained, and the correlation between the transmitter and the receiver is obtained based on the spatial non-stationarity.

[0007] The complex channel gain undergoes Rayleigh fading, and spatial correlation is assumed to occur at both the transmitter and receiver ends, resulting in the channel capacity of the very large-scale array system.

[0008] By using the major and minor determinant expansion theorem to expand the expression of channel capacity and using Binet-Cauchy's theorem to find the determinant, the lower bound of the channel capacity of the ultra-large-scale array system is obtained, which is related to all eigenvalues of the correlation matrix, and the obtained lower bound of the channel capacity is verified.

[0009] Furthermore, the complex channel gain H is expressed as:

[0010]

[0011] Where α = (4π / λ) -2 represents the path loss from the base station to the receiving end, λ represents the carrier wavelength, Φ and Ψ represent the correlation between the receiving end and the transmitting end respectively, and H ω is a zero-mean independent and identically distributed Gaussian matrix.

[0012] Furthermore, the channel capacity C is expressed as;

[0013] C=Ε[log2det(I Q +ρHH H )]

[0014] Where ρ = P t / Pσ 2 , P t represents the total transmit power, σ 2 represents channel noise, det() represents the determinant operation of the matrix, I Q represents the unit matrix of size Q*Q, Q represents the number of receiving antennas, E represents the averaging operation, H is the complex channel gain, H H is the conjugate transposed matrix of H.

[0015] Furthermore, the lower bound of the channel capacity C2 is expressed as:

[0016]

[0017] Among them, Q represents the number of receiving antennas, k is the variable of traversal summation operation, p and q are the variables of traversal multiplication operation, is the dimension permutation of Φ and Ψ, that is The rows and columns are i k 、i k, The rows and columns are u k 、u k , Φ and Ψ represent the correlation between the receiving end and the transmitting end respectively, is the kqth matrix The eigenvalues of is the kp-th matrix is the eigenvalue of , and γ is Euler's constant.

[0018] Furthermore, the derivation process of the lower bound of the channel capacity is:

[0019] Let μ = αρ,

[0020] Among them, Φ and Ψ represent the correlation between the receiving end and the transmitting end respectively, H ω is a zero-mean independent and identically distributed Gaussian matrix, is the conjugate transposed matrix of ;

[0021] The expression of channel capacity C is rewritten as: C = E[log2det(I Q +μA)]

[0022] According to Binet-Cauchy's theorem, we get:

[0023]

[0024] Among them, I Q represents the unit matrix of size Q*Q, Q represents the number of receiving antennas, k is the variable for traversal and summation operation, are Φ, Ψ, and H ω Dimension permutation, that is The rows and columns are i k 、j k , The rows and columns are u k 、v k , The rows and columns are j k 、u k , The rows and columns are v k 、i k ;

[0025] If any matrix X satisfies I P is a unit matrix of size P*P, where P represents the total number of transmitting antennas. When i1=j1,...,i k =j k u1=v1,...,u k =v k ;

[0026]

[0027] in, is the dimension permutation of X, that is The rows and columns are i k 、u k ;X H is the transposed conjugate matrix of , For X H Dimension permutation, that is The rows and columns are v k 、j k ;

[0028] Through this inequality and the domain of the lnx function, we can conclude that:

[0029] C>C2

[0030]

[0031] in, are Φ, Ψ, and H ω H ω H Dimension permutation, that is The rows and columns are i k 、i k , The rows and columns are u k 、u k , The rows and columns are i k 、i k ;

[0032] if C2 is expressed as:

[0033]

[0034] in, is the kqth matrix The eigenvalues of is the kp-th matrix is the eigenvalue of , and γ is Euler's constant.

[0035] The channel capacity lower bound analysis system based on a very large-scale array system of the present invention comprises:

[0036] The complex channel gain and correlation calculation unit is used to consider the spatial non-stationarity of the bilateral correlation ultra-large-scale array system based on the visible area, obtain the complex channel gain of the channel, and obtain the correlation between the transmitter and the receiver based on the spatial non-stationarity;

[0037] A channel capacity calculation unit is used to obtain the channel capacity of a very large-scale array system under the background that the complex channel gain undergoes Rayleigh fading and spatial correlation is assumed to occur at both the transmitter and the receiver;

[0038] The channel capacity lower bound calculation unit is used to expand the expression of channel capacity by using the major and minor determinant expansion theorem, and use the Binet-Cauchy theorem to find the determinant. The obtained channel capacity lower bound of the ultra-large-scale array system is related to all eigenvalues of the correlation matrix, and the obtained channel capacity lower bound is verified.

[0039] Optionally, the lower bound of the channel capacity C2 is expressed as:

[0040]

[0041] Among them, Q is the total number of receiving antennas, k, p, q are the variables of traversal and cumulative multiplication operations, is the dimension permutation of Φ and Ψ, that is The rows and columns are i k 、i k , The rows and columns are u k 、u k , is the kqth matrix The eigenvalues of is the kp-th matrix is the eigenvalue of , and γ is Euler's constant.

[0042] The electronic device of the present invention comprises:

[0043] a memory storing executable program code;

[0044] a processor coupled to the memory;

[0045] The processor calls the executable program code stored in the memory to execute the steps of the channel capacity lower bound analysis method based on the ultra-large-scale array system.

[0046] The computer-readable storage medium of the present invention stores computer instructions, which, when called, are used to execute the steps of the method for analyzing the lower bound of channel capacity based on a very large-scale array system.

[0047] The computer program product of the present invention includes a computer program / instruction, which, when executed by a processor, implements the steps of the method for analyzing the lower bound of channel capacity based on a very large-scale array system.

[0048] Beneficial effects: Compared with the existing technology, the significant technical effects of the present invention are: in order to accurately describe the performance of the bilateral correlation very large-scale array system model based on the visible area, a bilateral correlation very large-scale array system based on the visible area is constructed, and its complex channel gain function is obtained; the lower bound of the channel capacity of the system model of the very large-scale antenna array is obtained; the performance level of the bilateral correlation very large-scale array system based on the visible area can be better explored; and a basis can be provided for future system performance analysis and precoding algorithm design. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flow chart of the method of the present invention;

[0050] Figure 2 Schematic diagram of the bilateral correlation ultra-large-scale array system model based on the visible region;

[0051] Figure 3 To compare the two lower bounds C1 and C2 with the Monte Carlo results;

[0052] Figure 4 Schematic diagram of the Monte Carlo results and lower bounds with respect to the number of C2 transmitting antennas;

[0053] Figure 5 Schematic diagram of the Monte Carlo results and the lower bound C2 as the visible area N changes. DETAILED DESCRIPTION

[0054] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The following examples will help those skilled in the art further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that those skilled in the art may make several changes and modifications without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0055] The present invention describes a method for analyzing the lower bound of capacity for ultra-large-scale array systems. This method includes proposing a bilaterally correlated ultra-large-scale array system model based on the visible region and studying the corresponding lower bound of the channel capacity. When the visible region size is constant, the lower bound of the channel capacity decreases with the number of transmitting antennas. Because the closed-form expression for the lower bound of the channel capacity is related to a Laguerre polynomial, numerical integration is required. The lower bound of the channel capacity is obtained using the major and minor determinant theorem, an expansion, and the Binet-Cauchy theorem. Compared to Monte Carlo simulation results, this lower bound is compact and therefore accurately describes performance.

[0056] like Figure 1 As shown, the method of the present invention comprises the following steps:

[0057] S1. Considering the spatial non-stationarity of the bilaterally correlated VLSI system in the visible region, the complex channel gain of the channel is obtained, and the correlation between the transmitter and the receiver is obtained based on the spatial non-stationarity.

[0058] The complex channel gain H of the bilateral correlation VLSA system model based on the visible region in step S1 is:

[0059]

[0060] Where α = (4π / λ) -2 represents the path loss from the base station to the receiving end, λ represents the carrier wavelength, Φ and Ψ represent the correlation between the receiving end and the transmitting end respectively, and H ω is a zero-mean independent and identically distributed Gaussian matrix.

[0061] S2. The channel capacity of the VLSI system is obtained under the background that the complex channel gain is considered to undergo Rayleigh fading and spatial correlation is assumed to occur at both the transmitter and receiver ends.

[0062] The expression of channel capacity C is:

[0063] C=Ε[log2det(I Q +ρHH H )]

[0064] Where ρ = P t / Pσ 2 , P t represents the total transmit power, σ 2 represents channel noise, det() represents the determinant operation of the matrix, I Q represents the unit matrix of size Q*Q, Q represents the number of receiving antennas, E represents the operation of finding the mean, and H H is the conjugate transposed matrix of H.

[0065] S3. To analyze the performance characteristics, a mathematical formula is used to derive the lower bound of the channel capacity of the ultra-large-scale array system. This lower bound is compact and can be proven to be accurate in describing the performance.

[0066] Corollary of the lower bound of channel capacity: This paper obtains a very tight lower bound by using the primary and secondary determinant expansion theorem to expand the expression of channel capacity and using Binet-Cauchy's theorem to find the determinant:

[0067] Will Substitute C = E[log2det(I Q +ρHH H )]. We get the following formula:

[0068] C=Ε[log2det(I Q+μA)]

[0069] Where μ = αρ,

[0070] By using Binet-Cauchy's theorem, we can get:

[0071]

[0072] in It is the previous Φ, Ψ, H ω Dimension permutation, that is The rows and columns are i k 、j k . The rows and columns are u k 、v k , The rows and columns are j k 、u k , The rows and columns are v k 、i k .

[0073] If any matrix X satisfies I P is the unit matrix of size , P represents the total number of transmitting antennas, when i1=j1,...,i k =j k ,u1=v1,...,u k =v k ,have:

[0074]

[0075] in, is the dimension permutation of X, that is The rows and columns are i k 、u k .

[0076] From this inequality and the requirement of the lnx function that x>0, we can conclude that:

[0077] C>C2

[0078]

[0079] in are Φ, Ψ, and H ω H ω H Dimension permutation, that is The rows and columns are i k 、i k , The rows and columns are u k、u k , The rows and columns are i k 、i k .

[0080] if C2 can be expressed as:

[0081]

[0082] in, is the kqth matrix The eigenvalues of is the kp-th matrix The eigenvalue of .

[0083] Next, we provide a conventional method for deriving the lower bound of the channel capacity, and compare it with the lower bound derivation of the method of the present invention:

[0084]

[0085] Substituting H and performing dimension conversion yields:

[0086]

[0087] in It's HH H Dimension permutation, that is The rows and columns are i k 、i k .

[0088] because is a square matrix, so we can get:

[0089]

[0090] because λ k (Ψ) is the kth eigenvalue of the matrix Ψ.

[0091] so

[0092] Through these operations, the lower bound of the channel capacity can be expressed as:

[0093]

[0094] if C1 can be expressed as:

[0095] C≥C1

[0096]

[0097] Among them, p and q are variables of ergodic multiplication operation, and γ is Euler's constant.

[0098] However, it is a loose upper bound because it ignores the impact of other eigenvalues on the channel capacity.

[0099] Next, we use mathematical derivation to prove that C2 is a tighter lower bound than C1:

[0100] By using the Binet-Cauchy theorem, C2 can be written as:

[0101]

[0102] According to the theorem:

[0103]

[0104] It can be concluded that C2 is a tighter lower bound than C1. A tighter lower bound allows for more accurate channel performance assessment, aids in optimizing coding and transmission schemes, and promotes the integration of theoretical research and practical applications.

[0105] The embodiments of the present invention demonstrate, through both mathematical proof and simulation comparison, that the lower bound obtained by the method of the present invention is a tighter lower bound than the lower bound obtained by the prior art.

[0106] The channel capacity lower bound analysis system based on a very large-scale array system of the present invention comprises:

[0107] The complex channel gain and correlation calculation unit is used to consider the spatial non-stationarity of the bilateral correlation ultra-large-scale array system based on the visible area, obtain the complex channel gain of the channel, and obtain the correlation between the transmitter and the receiver based on the spatial non-stationarity;

[0108] A channel capacity calculation unit is used to obtain the channel capacity of a very large-scale array system under the background that the complex channel gain undergoes Rayleigh fading and spatial correlation is assumed to occur at both the transmitter and the receiver;

[0109] The channel capacity lower bound calculation unit is used to expand the expression of channel capacity by using the major and minor determinant expansion theorem, and use the Binet-Cauchy theorem to find the determinant. The obtained channel capacity lower bound of the ultra-large-scale array system is related to all eigenvalues of the correlation matrix, and the obtained channel capacity lower bound is verified.

[0110] Optionally, the lower bound of the channel capacity C2 is expressed as:

[0111]

[0112] Among them, Q is the total number of receiving antennas, k, p, q are the variables of traversal and cumulative multiplication operations, is the dimension permutation of Φ and Ψ, that is The rows and columns are i k 、i k , The rows and columns are u k 、u k , is the kqth matrix The eigenvalues of is the kp-th matrix is the eigenvalue of , and γ is Euler's constant.

[0113] The electronic device of the present invention comprises:

[0114] a memory storing executable program code;

[0115] a processor coupled to the memory;

[0116] The processor calls the executable program code stored in the memory to execute the steps of the channel capacity lower bound analysis method based on the ultra-large-scale array system.

[0117] The computer-readable storage medium of the present invention stores computer instructions, which, when called, are used to execute the steps of the method for analyzing the lower bound of channel capacity based on a very large-scale array system.

[0118] The computer program product of the present invention includes a computer program / instruction, which, when executed by a processor, implements the steps of the method for analyzing the lower bound of channel capacity based on a very large-scale array system.

[0119] Figure 2 The figure shows a model of a very large-scale antenna array. The base station and the receiver are equipped with a very large uniform linear array. The scatterer distribution near the receiver is represented by the radius r, the distance from the base station to the receiver is ε, the elevation angle θ and the azimuth angle φ are represented by and respectively, and the size of the visible area VR is represented by N.

[0120] Figure 3 The figure compares the lower bounds C1 and C2 with the Monte Carlo results. The simulation results show that the upper bound C2 proposed by this invention is a more compact closed-form expression. As Q increases, the difference between the Monte Carlo simulation results and C2 increases only slightly, demonstrating the accuracy of the lower bound proposed by this invention. C2 can accurately describe the performance of very large-scale antenna arrays.

[0121] Figure 4The figure shows the Monte Carlo results and the lower bound C2. As the number of transmit antennas P increases, the channel capacity decreases. This is because the visible area does not increase as P increases, while the transmit power decreases with the number of transmit antennas. The figure shows that C2 remains a very tight lower bound in this case.

[0122] Figure 5 The figure plots the Monte Carlo results and the lower bound C2 as the visible area N changes. As the transmit power increases, the channel capacity gradually increases, but as N increases, the channel capacity gradually decreases. This is because the visible area does not increase with the number of transmit antennas P.

[0123] The method of the present invention studies the corresponding channel capacity. When the visible area size is constant, the channel capacity decreases as the number of transmitting antennas increases. Since the closed-form expression of the channel capacity is related to the Laguerre polynomial, which requires numerical integration, the lower bound of the channel capacity is studied. In a very large-scale multi-input multi-output system, the number of transmitting antennas is significantly greater than the number of channels in the very large-scale multi-input multi-output system. The lower bound of the closed-form expression of the channel capacity is obtained by using the expansion formula and the Binet-Cauchy theorem using the major and minor determinant theorem. Compared with the Monte Carlo simulation results, the lower bound proposed by the present invention is very suitable for very large-scale multi-input multi-output communication systems, providing effective support for the next generation of wireless communication technologies.

Claims

1. A method for analyzing the lower bound of channel capacity based on a very large-scale array system, characterized in that: The following steps are involved: Considering the spatial non-stationarity of the bilaterally correlated VLSI system in the visible region, the complex channel gain of the channel is obtained, and the correlation between the transmitter and the receiver is obtained based on the spatial non-stationarity. The complex channel gain undergoes Rayleigh fading, and spatial correlation is assumed to occur at both the transmitter and receiver ends, resulting in the channel capacity of the very large-scale array system. By using the major and minor determinant expansion theorem to expand the expression of channel capacity and using Binet-Cauchy's theorem to find the determinant, the lower bound of the channel capacity of the ultra-large-scale array system is obtained, which is related to all eigenvalues of the correlation matrix, and the obtained lower bound of the channel capacity is verified.

2. The method for analyzing the lower bound of channel capacity based on a very large-scale array system according to claim 1, characterized in that: The complex channel gain H is expressed as: Where α = (4π / λ) -2 represents the path loss from the base station to the receiving end, λ represents the carrier wavelength, Φ and Ψ represent the correlation between the receiving end and the transmitting end respectively, and H ω is a zero-mean independent and identically distributed Gaussian matrix.

3. The method for analyzing the lower bound of channel capacity based on a very large-scale array system according to claim 1, wherein: The channel capacity C is expressed as; C=Ε[log2det(I Q +ρHH H )] Where ρ = P t / Pσ 2 , P t represents the total transmit power, σ 2 represents channel noise, det() represents the determinant operation of the matrix, I Q represents the unit matrix of size Q*Q, Q represents the number of receiving antennas, E represents the averaging operation, H is the complex channel gain, H H is the conjugate transposed matrix of H.

4. The method for analyzing the lower bound of channel capacity based on a very large-scale array system according to claim 1, wherein: The lower bound of channel capacity C2 is expressed as: Among them, Q represents the number of receiving antennas, k is the variable of traversal summation operation, p and q are the variables of traversal multiplication operation, is the dimension permutation of Φ and Ψ, that is The rows and columns are i k 、i k , The rows and columns are u k 、u k , Φ and Ψ represent the correlation between the receiving end and the transmitting end respectively, is the kqth matrix The eigenvalues of is the kp-th matrix is the eigenvalue of , and γ is Euler's constant.

5. The method for analyzing the lower bound of channel capacity based on a very large-scale array system according to claim 1, wherein: The derivation process of the lower bound of channel capacity is: Let μ = αρ, Among them, Φ and Ψ represent the correlation between the receiving end and the transmitting end respectively, H ω is a zero-mean independent and identically distributed Gaussian matrix, is the conjugate transposed matrix of ; The expression of channel capacity C is rewritten as: C = E[log2det(I Q +μA)] According to Binet-Cauchy's theorem, we get: Among them, I Q represents the unit matrix of size Q*Q, Q represents the number of receiving antennas, k is the variable for traversal and summation operation, are Φ, Ψ, and H ω Dimension permutation, that is The rows and columns are i k 、j k , The rows and columns are u k 、v k , The rows and columns are j k 、u k , The rows and columns are v k 、i k ; If any matrix X satisfies I P is a unit matrix of size P*P, where P represents the total number of transmitting antennas. When i1=j1,...,i k =j k u1=v1,...,u k =v k ; in, is the dimension permutation of X, that is The rows and columns are i k 、u k ;X H is the transposed conjugate matrix of , For X H Dimension permutation, that is The rows and columns are v k 、j k ; Through this inequality and the domain of the lnx function, we can conclude that: C>C2 in, are Φ, Ψ, and H ω H ω H Dimension permutation, that is The rows and columns are i k 、i k , The rows and columns are u k 、u k , The rows and columns are i k 、i k ; if C2 is expressed as: in, is the kqth matrix The eigenvalues of is the kp-th matrix is the eigenvalue of , and γ is Euler's constant.

6. A channel capacity lower bound analysis system based on a very large-scale array system, characterized in that: include: The complex channel gain and correlation calculation unit is used to consider the spatial non-stationarity of the bilateral correlation ultra-large-scale array system based on the visible area, obtain the complex channel gain of the channel, and obtain the correlation between the transmitter and the receiver based on the spatial non-stationarity; The channel capacity calculation unit is used to obtain the channel capacity of the very large-scale array system under the background that the complex channel gain undergoes Rayleigh fading and spatial correlation is assumed to occur at both the transmitter and the receiver; The channel capacity lower bound calculation unit is used to expand the expression of channel capacity by using the major and minor determinant expansion theorem, and use the Binet-Cauchy theorem to find the determinant. The obtained channel capacity lower bound of the ultra-large-scale array system is related to all eigenvalues of the correlation matrix, and the obtained channel capacity lower bound is verified.

7. The capacity lower bound analysis system based on a very large-scale array system according to claim 6, characterized in that: The lower bound of channel capacity C2 is expressed as: Among them, Q is the total number of receiving antennas, k, p, q are the variables of traversal and cumulative multiplication operations, is the dimension permutation of Φ and Ψ, that is The rows and columns are i k 、i k , The rows and columns are u k 、u k , is the kqth matrix The eigenvalues of is the kp-th matrix is the eigenvalue of , and γ is Euler's constant.

8. An electronic device, characterized in that: The device comprises: a memory storing executable program code; a processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the steps of the channel capacity lower bound analysis method based on a very large-scale array system according to any one of claims 1 to 5.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions, and when the computer instructions are called, they are used to execute the steps of the method for analyzing the lower bound of channel capacity based on a very large-scale array system according to any one of claims 1 to 5.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method for analyzing the lower bound of channel capacity based on a very large-scale array system according to any one of claims 1 to 5 are implemented.

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