RIS-assisted cellular-free large-scale MIMO system performance analysis method

Abstract

The invention provides an RIS-assisted cellular-free large-scale MIMO system performance analysis method. The RIS-assisted cellular-free large-scale MIMO system performance analysis method comprises the following steps: establishing an RIS-assisted cellular-free large-scale MIMO system model under a spatial correlation Rayleigh fading channel; performing uplink training based on the constructed cellular-free large-scale MIMO system model; performing uplink channel data transmission based on the trained uplink; designing a probability density function of an expected signal and an interference signal from other users according to the uplink channel data; according to the probability density function of the expected signal and the interference signal from other users, designing the probability density function of a single signal to interference plus noise ratio of different users; and based on a signal to interference plus noise ratio probability density function, accurately analyzing the outage probability, the coverage probability and the traversal capacity. According to the method, the accuracy of the performance index is verified through a numerical result, the potential advantage of integrating the RIS into the existing cellular-free large-scale MIMO system is shown, and theoretical support is provided for deployment of the RIS-assisted cellular-free large-scale MIMO system in a 6G scene.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a RIS-assisted non-cellular large-scale MIMO system performance analysis method. Background Art

[0002] To meet the growing demand for high-reliability, low-latency, and high-bandwidth wireless communications, various innovative network architectures have emerged. Among these advances, cell-free massive MIMO is considered a promising architecture for the sixth generation of mobile systems. Cell-free massive MIMO systems effectively mitigate inter-cell interference through simple signal processing techniques and ensure balanced quality of service for all users. Specifically, cell-free massive MIMO systems deploy a large number of access points in a specified coverage area to achieve seamless collaboration and provide services with a specific degree of collaboration to all users in the system. In order to significantly mitigate the shadow effect caused by obstacles in cell-free massive MIMO systems, a large number of distributed base stations must be established. However, this approach has become impractical due to the increased installation cost and energy consumption.

[0003] Although the shortcomings of cell-free massive MIMO systems cannot be ignored, a potential technology called RIS has emerged to overcome these limitations. RIS usually includes a large number of hardware-efficient passive scattering elements. These elements can independently introduce specific phase shifts, thereby being able to reflect the incident signal to any desired direction without the need for complex digital signal processing and active power amplifiers, which are usually required in amplify-and-forward relay systems. Therefore, RIS is considered to be an effective solution to promote large-scale connectivity, energy efficiency, high reliability, and wide-area coverage.

[0004] Given that both RIS and cell-free massive MIMO systems have the potential to improve the uniformity of wireless coverage, the introduction of RIS into cell-free massive MIMO systems can further achieve extensive high-capacity communication coverage in the upcoming 6G network. Therefore, the combination of cell-free massive MIMO systems and RIS has attracted extensive attention and research in academia and industry to achieve the expected functions of 6G networks. Specifically, the RIS-assisted cell-free massive MIMO system includes a central processing unit, multiple distributed BSs, and multiple distributed RISs. These BSs and RISs are connected to the CPU through a lossless backhaul network, so that they can use spatial multiplexing technology to perform cooperative transmission and reception on the same time-frequency resources to provide services to all users collectively. Therefore, the RIS-assisted cell-free massive MIMO system is regarded as a revolutionary approach, which is more than a simple integration of two technologies. In addition, the RIS-assisted cell-free massive MIMO system introduces many innovations in system architecture, channel estimation, signal processing and other related aspects.

[0005] Although several representative studies have investigated various aspects of RIS-assisted cell-free massive MIMO systems in recent years, the PDF of SINR, which is closely related to communication performance, has not been analyzed. In addition, many studies have only focused on the rate performance and energy efficiency of RIS-assisted cell-free massive MIMO systems, while other key communication indicators such as outage probability, coverage probability, and ergodic capacity, which reflect the effectiveness of communication systems, are still lacking. Summary of the invention

[0006] According to the technical problems raised above, a RIS-assisted non-cellular massive MIMO system performance analysis method is provided. The present invention considers the RIS-assisted non-cellular massive MIMO system under the conditions of spatially correlated Rayleigh fading channels and imperfect channel state information, which makes the system model closer to the real scenario.

[0007] The technical means adopted by the present invention are as follows:

[0008] A RIS-assisted non-cellular massive MIMO system performance analysis method, comprising:

[0009] S1. Establish a RIS-assisted non-cellular massive MIMO system model under spatially correlated Rayleigh fading channels;

[0010] S2. Perform uplink training based on the constructed non-cellular massive MIMO system model;

[0011] S3, based on the trained uplink, performing uplink channel data transmission;

[0012] S4. Designing probability density functions of desired signals and interference signals from other users based on the transmitted uplink channel data;

[0013] S5. Design a probability density function of a single signal to interference noise ratio of different users according to the probability density function of the desired signal and the interference signal from other users;

[0014] S6. Based on the signal-to-interference-noise ratio probability density function of different users, the outage probability, coverage probability and ergodic capacity are accurately analyzed.

[0015] Furthermore, step S1 specifically includes:

[0016] S11. Consider a RIS-assisted non-cellular massive MIMO system in the uplink, in which there are M base stations providing communication services for K single-antenna users with the help of N reconfigurable smart surfaces RIS, where each base station is equipped with L antennas and each RIS is equipped with I reflection units; there is a central processing unit CPU connecting multiple base stations and RIS through a backhaul network for signal processing and management;

[0017] S12, the base station, the user, the RIS and the reflection unit set of each RIS are represented as and

[0018] S13. Assume that multiple base stations and reconfigurable smart surfaces are placed at higher locations and close to each other, and multiple users are randomly distributed at lower geographical locations; assume that all channels between users and base stations and between users and RIS obey the Rayleigh fading model, and express the channel as and where β BU,mk represents the large-scale fading coefficient between user k and base station m, β RU,nk It is expressed as the large-scale fading coefficient between user k and RISn. Assuming that RIS is designed and installed at a location that provides a line-of-sight LoS channel with the base station, Represents the full-rank LoS channel matrix between RISn and base station m:

[0019]

[0020] Among them, β BR,mn is the large-scale fading coefficient between RISn and base station m, is the carrier wavelength, d BS is the antenna spacing of the base station, d RIS is the reflection unit spacing of RIS; and denote the elevation and azimuth line-of-sight angles AoD of base station m relative to the i-th reflector unit of RISn, respectively, and and denote the elevation and azimuth line-of-sight arrival angle AoA of RISn relative to the lth antenna of base station m, respectively;

[0021] S14: aggregate the channel between user k and base station m Defined as:

[0022]

[0023] in, is the phase shift matrix of RIS n, represents the phase shift coefficient of the i-th unit of RIS n; all and Large-scale fading coefficient β between user and base station BU,mk , the large-scale fading coefficient β between the user and the RIS RU,nk and the line-of-sight channel G between RIS and the base station BR,mn are assumed to be known.

[0024] Furthermore, step S2 specifically includes:

[0025] S21. Calculate the uplink pilot signal received by base station m as follows:

[0026]

[0027] τ represents the length of the coherence time, where τ p symbols are used for uplink training, and the remaining τ-τ p symbols are used for uplink data transmission; in the uplink pilot training phase, is defined as the pilot sequence sent by user k to all base stations, where p p is the power of the uplink pilot sequence; assuming τ p ≥K, so that when k=k′, φ k Designed to meet When k≠k′, represents the additive white Gaussian noise AWGN at base station m, each element of which follows a complex Gaussian distribution

[0028] S22. In order to enable base station m to estimate the state information of the aggregated channel from user k, the uplink pilot signal received by base station m is compared with Multiplying them, we get:

[0029]

[0030] S23. Based on the observed signal, use the minimum mean square error (LMMSE) channel estimation method to calculate the aggregate channel g mk The estimated values ​​are as follows:

[0031]

[0032] in,

[0033] Φ=diag{Φ 1 ,Φ 2 ,…,Φ N};

[0034] S24, according to the characteristics of the LMMSE channel estimation method, the channel estimation and channel estimation error Follow the distribution and in:

[0035]

[0036] Further, step S3 specifically includes:

[0037] S31. In the uplink data transmission phase, K users send data signals to M base stations at the same time. Therefore, the data signal received by base station m is:

[0038]

[0039] Among them, p u is the power of data transmission, x k is the modulation symbol of user k, and 0≤η k ≤1 is the power control coefficient; the additive white Gaussian noise vector at base station m is

[0040] S32. Based on step S31, the data received by the CPU from user k is:

[0041]

[0042] Base station m first receives the signal y m Multiply Then the result signals of all M base stations are sent to the central processing unit CPU through the backhaul network; represents the expected signal of user k; represents the channel estimation error, Indicates the interference signal caused by other users; represents noise interference, and its distribution is

[0043] Further, step S4 specifically includes:

[0044] S41. Assume that the modulation signals sent by all K users satisfy According to the formula of data received by the CPU from user k, the single SINR of user k is expressed as:

[0045]

[0046] in, represents the intensity of the noise, ρ k represents the expected signal strength of user k, represents the interference signal strength of user k,

[0047] S42. According to the expected signal strength formula of user k, the expected signal strength ρ of user k k The PDF expression of is:

[0048]

[0049] in,

[0050] S43, according to the interference signal strength formula of user k, the expected signal strength of user k The PDF expression of is:

[0051]

[0052] in,

[0053]

[0054] Furthermore, step S5 specifically includes:

[0055] S51, based on the expected signal strength ρ of user k k The PDF expression of and the expected signal strength of user k The PDF expression of SINR of user k is:

[0056]

[0057] In the above formula, Γ(x) represents the gamma function;

[0058] S52. Based on the PDF expression of SINR of user k and the Taylor series expansion of the upper incomplete gamma function, the PDF expression of SINR of user k is rewritten as:

[0059]

[0060] Further, step S6 specifically includes:

[0061] S61. Based on the single SINR expression of user k in step S41, define the outage probability and coverage probability of user k as follows:

[0062] OP k =Pr{γ k ≤γ th}

[0063] CP k =Pr{γ k >γ th}

[0064] Among them, γ th Indicates the required SINR threshold;

[0065] S62. Calculate the interruption probability of user k The calculation formula is as follows:

[0066]

[0067] In the above formula, 2 F 1 (α, β; γ; x) represents the Gaussian hypergeometric function, Beta(x, y) represents the beta function;

[0068] S63. Interruption probability based on user k Calculate the coverage probability of user k The calculation formula is as follows:

[0069]

[0070] S64. Using the single SINR expression of user k in step S41, the ergodic capacity expression of user k is expressed as:

[0071]

[0072] S65. Based on step S64, calculate the traversal capacity of the kth user The calculation formula is as follows:

[0073]

[0074] In the above formula, represents the Meijer-G function.

[0075] Compared with the prior art, the present invention has the following advantages:

[0076] 1. The present invention provides a performance analysis method for a RIS-assisted cell-free massive MIMO system. Compared with the RIS-assisted cell-free massive MIMO system under non-correlated Rayleigh fading channels and perfect channel state information conditions, the present invention considers the RIS-assisted cell-free massive MIMO system under spatially correlated Rayleigh fading channels and imperfect channel state information conditions, which makes the system model closer to the real scenario.

[0077] 2. The RIS-assisted non-cellular massive MIMO system performance analysis method provided by the present invention reduces the probability of interruption, which means that users can still maintain a stable connection in areas with poor signals, which improves the reliability of the system, especially in mobile scenarios.

[0078] 3. The RIS-assisted non-cellular massive MIMO system performance analysis method provided by the present invention also improves the coverage probability, which can ensure that more users can obtain services in different environments, especially in high-density user areas, which is crucial to improving user satisfaction and network availability.

[0079] 4. The RIS-assisted non-cellular massive MIMO system performance analysis method provided by the present invention improves the traversal capacity and allows each user to enjoy a higher data transmission rate, thereby improving the overall efficiency of the network, meeting the growing bandwidth demand, and supporting more applications and services.

[0080] Based on the above reasons, the present invention can be widely promoted in fields such as wireless communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0082] Figure 1 The figure is a flow chart of the method of the present invention.

[0083] Figure 2 The present invention provides a model structure of a RIS-assisted non-cellular massive MIMO system to which the solution of the present invention is applicable.

[0084] Figure 3 A multi-user simulation scene diagram applicable to the solution of the present invention.

[0085] Figure 4 A simulation diagram of the probability density function of the desired signal provided by an embodiment of the present invention.

[0086] Figure 5 A simulation diagram of the probability density function of the interference signal strength provided by an embodiment of the present invention.

[0087] Figure 6 A simulation diagram of the probability density function of SINR provided by an embodiment of the present invention.

[0088] Figure 7 A simulation diagram of the relationship between the average interruption probability and coverage probability of all users and the data transmission power provided by an embodiment of the present invention.

[0089] Figure 8 A simulation diagram of the relationship between the average traversal capacity and data transmission power of all users provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0090] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0091] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0092] like Figure 1 As shown, the present invention provides a RIS-assisted non-cellular massive MIMO system performance analysis method, comprising:

[0093] S1. Establish a RIS-assisted non-cellular massive MIMO system model under spatially correlated Rayleigh fading channels;

[0094] S2. Perform uplink training based on the constructed non-cellular massive MIMO system model;

[0095] S3, based on the trained uplink, performing uplink channel data transmission;

[0096] S4. Designing probability density functions of desired signals and interference signals from other users based on the transmitted uplink channel data;

[0097] S5. Design a probability density function of a single signal to interference noise ratio of different users according to the probability density function of the desired signal and the interference signal from other users;

[0098] S6. Based on the signal-to-interference-noise ratio probability density function of different users, the outage probability, coverage probability and ergodic capacity are accurately analyzed.

[0099] In specific implementation, as a preferred embodiment of the present invention, S11, consider a RIS-assisted non-cellular massive MIMO system in the uplink, such as Figure 2As shown, in the system, there are M base stations BS providing communication services for K single-antenna users with the help of N reconfigurable smart surfaces RIS, where each base station is equipped with L antennas and each RIS is equipped with I reflection units; there is a central processing unit CPU connecting multiple base stations and RIS through a backhaul network for signal processing and management;

[0100] S12, the base station, the user, the RIS and the reflection unit set of each RIS are represented as and

[0101] S13. Assume that multiple base stations and reconfigurable smart surfaces are placed at higher locations and close to each other, and multiple users are randomly distributed at lower geographical locations; assume that all channels between users and base stations and between users and RIS obey the Rayleigh fading model, and express the channel as and where β BU,mk represents the large-scale fading coefficient between user k and base station m, β RU,nk It is expressed as the large-scale fading coefficient between user k and RISn. Assuming that RIS is designed and installed at a location that provides a line-of-sight LoS channel with the base station, Represents the full-rank LoS channel matrix between RISn and base station m:

[0102]

[0103] Among them, β BR,mn is the large-scale fading coefficient between RISn and base station m, is the carrier wavelength, d BS is the antenna spacing of the base station, d RIS is the reflection unit spacing of RIS; and denote the elevation and azimuth line-of-sight angles AoD of base station m relative to the i-th reflector unit of RISn, respectively, and and denote the elevation and azimuth line-of-sight arrival angle AoA of RISn relative to the lth antenna of base station m, respectively;

[0104] S14: aggregate the channel between user k and base station m Defined as:

[0105]

[0106] in, is the phase shift matrix of RIS n, represents the phase shift coefficient of the i-th unit of RIS n; all and Large-scale fading coefficient β between user and base station BU,mk , the large-scale fading coefficient β between the user and the RIS RU,nk and the line-of-sight channel G between RIS and the base station BR,mn are assumed to be known.

[0107] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0108] S21. Calculate the uplink pilot signal received by base station m as follows:

[0109]

[0110] τ represents the length of the coherence time, where τ p symbols are used for uplink training, and the remaining τ-τ p symbols are used for uplink data transmission; in the uplink pilot training phase, is defined as the pilot sequence sent by user k to all base stations, where p p is the power of the uplink pilot sequence; assuming τ p ≥K, so that when k=k′, φ k Designed to meet When k≠k′, represents the additive white Gaussian noise AWGN at base station m, each element of which follows a complex Gaussian distribution

[0111] S22. In order to enable base station m to estimate the state information of the aggregated channel from user k, the uplink pilot signal received by base station m is compared with Multiplying them, we get:

[0112]

[0113] S23. Based on the observed signal, use the minimum mean square error (LMMSE) channel estimation method to calculate the aggregate channel g mk The estimated values ​​are as follows:

[0114]

[0115] in, Φ=diag{Φ 1 ,Φ 2 ,…,Φ N};

[0116] S24, according to the characteristics of the LMMSE channel estimation method, the channel estimation and channel estimation error Follow the distribution and in:

[0117]

[0118] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0119] S31. In the uplink data transmission phase, K users send data signals to M base stations at the same time. Therefore, the data signal received by base station m is:

[0120]

[0121] Among them, p u is the power of data transmission, x k is the modulation symbol of user k, and 0≤η k ≤1 is the power control coefficient; the additive white Gaussian noise vector at base station m is

[0122] S32. Based on step S31, the data received by the CPU from user k is:

[0123]

[0124] For uplink data detection, the maximum ratio combining (MRC) scheme is used. Specifically, the base station m first receives the signal y m Multiply Then the result signals of all M base stations are sent to the central processing unit CPU through the backhaul network; represents the expected signal of user k; represents the channel estimation error, Indicates the interference signal caused by other users; represents noise interference, and its distribution is

[0125] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0126] S41. Assume that the modulation signals sent by all K users satisfy According to the formula of data received by the CPU from user k, the single SINR of user k is expressed as:

[0127]

[0128] in, represents the intensity of the noise, ρ k represents the expected signal strength of user k, represents the interference signal strength of user k,

[0129] S42. According to the expected signal strength formula of user k, the expected signal strength ρ of user k k The PDF expression of is:

[0130]

[0131] in,

[0132] S43, according to the interference signal strength formula of user k, the expected signal strength of user k The PDF expression of is:

[0133]

[0134] in,

[0135] In specific implementation, as a preferred embodiment of the present invention, step S5 specifically includes:

[0136] S51, based on the expected signal strength ρ of user k k The PDF expression of and the expected signal strength of user k The PDF expression of SINR of user k is:

[0137]

[0138] In the above formula, Γ(x) represents the gamma function;

[0139] S52. Based on the PDF expression of SINR of user k and the Taylor series expansion of the upper incomplete gamma function, the PDF expression of SINR of user k is rewritten as:

[0140]

[0141] In this embodiment, in order to demonstrate the characteristics of the PDF of SINR from other perspectives, a rewritten formula is provided, which is helpful for theoretically deriving the outage probability and the coverage probability.

[0142] In specific implementation, as a preferred embodiment of the present invention, step S6 specifically includes:

[0143] S61. When the RIS-assisted non-cellular massive MIMO system experiences fading, the outage probability and coverage probability are key parameters for defining the quality of communication services. The outage probability indicates the possibility that the instantaneous SINR is lower than a specified threshold, while the coverage probability indicates the possibility that the instantaneous SINR exceeds a specified threshold. Based on the single SINR expression of user k in step S41, the outage probability and coverage probability of user k are defined as follows:

[0144] OP k =Pr{γ k ≤γ th}

[0145] CP k =Pr{γ k >γ th}

[0146] Among them, γ th Indicates the required SINR threshold;

[0147] S62. Calculate the interruption probability of user k The calculation formula is as follows:

[0148]

[0149] In the above formula, 2 F 1 (α, β; γ; x) represents the Gaussian hypergeometric function, Beta(x, y) represents the beta function;

[0150] S63. Interruption probability based on user k Calculate the coverage probability of user k The calculation formula is as follows:

[0151]

[0152] In this embodiment, since the sum of the outage probability and the coverage probability is equal to 1, they are complementary performance indicators, which effectively present the quality of service (QoS) of users in different geographical locations from two different theoretical perspectives.

[0153] S64. Using the single SINR expression of user k in step S41, the ergodic capacity expression of user k is expressed as:

[0154]

[0155] S65. Based on step S64, calculate the traversal capacity of the kth user The calculation formula is as follows:

[0156]

[0157] In the above formula, represents the Meijer-G function.

[0158] Example

[0159] In order to verify the effectiveness of the solution of the present invention, the following simulation experiments were carried out:

[0160] The specific simulation parameters of the RIS-assisted non-cellular massive MIMO system are:

[0161] In the simulation setting, a cell-free massive MIMO system consists of 2 BSs, each serving 8 single-antenna users, and each BS is equipped with 48 antennas. The system communication performance is severely limited due to obstacles such as high-rise buildings between the BSs and the users. To address this problem, 3 RISs, each with 64 reflection units, are deployed on three separate building surfaces, which are high enough to establish additional reflection links.

[0162] like Figure 3 As shown in the figure, the coordinates of the two base stations are assumed to be (0m, 25m, 25m) and (0m, -25m, 25m). The positions of the three RIS are (30m, 50m, 40m), (30m, 0m, 40m) and (30m, -50m, 40m). The position coordinates of the eight users are (x user m,y user m,1.5m), where 30m≤x user ≤130m and -50m≤y user ≤50m.

[0163] The large-scale path loss is calculated using the following formula:

[0164]

[0165] in, and are the distance between base station m and RISn, the distance between RISn and user k, and the distance between base station m and user k. The path loss index is and For the LoS channel between base station m and RISn, assume and In addition, other simulation parameters are set to τ p =8 and η k =1, for all

[0166] For p u =5dBm, Figure 4 , 5and 6 show the expected signal strength ρ at different pilot transmission powers k PDF, interference signal strength PDF and SINRγ k The PDF of p =∞dBm corresponds to perfect channel state information (CSI), which means that all BSs obtain perfect CSI from different users and use it for signal processing. p =0dBm and p p =5dBm corresponds to imperfect CSI. First, the Monte Carlo simulation results obtained from the expected signal strength formula of user k are consistent with the expected signal strength of user k ρ k The theoretical result of the PDF expression is completely consistent with that of The PDF expression of is aligned with that of , and the result obtained from the single SINR formula of user k is consistent with the PDF expression of SINR of user k and the rewritten PDF expression of SINR of user k. The simulation results verify the accuracy of the analytical expressions in S42, S43 and S5. In addition, as p p The increase of k and γ k The PDF curve of is shifted to the right, becomes wider and more uniform, while This shows that as p p With the increase of , the impact of channel estimation error is reduced, resulting in the improvement of the expected signal strength and SINR, while the interference signal strength is reduced, thereby enhancing the performance of the communication system.

[0167] exist Figure 7 In the figure, the outage probability, coverage probability and data transmission power p of all users are plotted. u The relationship curve, where the required SINR threshold γ th =3. Figure 7 A high degree of agreement between the numerical simulation results and the analytical expressions can be observed in the Monte Carlo simulation results. The SINRγ in the single SINR formula for user k is obtained by using k and the interruption probability and coverage probability formula of user k, and the analytical result is based on the formula in S62. u and p p As the power of data and pilot transmission increases, the average outage probability decreases and the average coverage probability increases, and finally converges to different fixed values. This shows that by increasing the data and pilot transmission power, better communication service quality (QoS) and wider service coverage can be achieved. However, even if p u and p pBoth are set to the maximum value, the average outage probability cannot be reduced to 0, and the average coverage probability cannot reach 1, indicating that continuously increasing the transmission power will not bring about an infinite improvement in network QoS and service range.

[0168] Figure 8 The average traversal capacity of all users and the data transmission power p are shown. u The Monte Carlo simulation results are obtained by using the SINRγ in the single SINR formula of user k. k The ergodic capacity expression for user k is calculated and compared with the analytical result based on the ergodic capacity expression for the kth user. There is a very good coincidence between the numerical simulation and the analytical expression. In addition, Figure 7 It shows that as the data transmission power p u and pilot transmission power p p As the power increases, the average channel capacity increases, but eventually tends to a constant value. This shows that increasing the data and pilot transmission power within a certain range can improve network capacity, but excessive increase in power will produce diminishing marginal returns and is not conducive to achieving green communication goals.

[0169] In summary, the above simulation results verify the accuracy of the expected signal PDF, interference signal PDF, SINR PDF, outage probability, coverage probability and ergodic capacity expressions derived by the solution of the present invention.

[0170] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A RIS-assisted non-cellular massive MIMO system performance analysis method, characterized in that: include: S1. Establish a RIS-assisted non-cellular massive MIMO system model under spatially correlated Rayleigh fading channels; S2. Perform uplink training based on the constructed non-cellular massive MIMO system model; S3, based on the trained uplink, performing uplink channel data transmission; S4. Designing probability density functions of desired signals and interference signals from other users based on the transmitted uplink channel data; S5. Design a probability density function of a single signal to interference noise ratio of different users according to the probability density function of the desired signal and the interference signal from other users; S6. Based on the signal-to-interference-noise ratio probability density function of different users, the outage probability, coverage probability and ergodic capacity are accurately analyzed.

2. The RIS-assisted non-cellular massive MIMO system performance analysis method according to claim 1, characterized in that: Step S1 specifically includes: S11. Consider a RIS-assisted non-cellular massive MIMO system in the uplink, in which there are M base stations BS providing communication services for K single-antenna users with the help of N reconfigurable smart surfaces RIS, where each base station is equipped with L antennas and each RIS is equipped with I reflection units; there is a central processing unit CPU connecting multiple base stations and RIS through a backhaul network for signal processing and management; S12, the base station, the user, the RIS and the reflection unit set of each RIS are represented as and S13. Assume that multiple base stations and reconfigurable smart surfaces are placed at higher locations and close to each other, and multiple users are randomly distributed at lower geographical locations; assume that all channels between users and base stations and between users and RIS obey the Rayleigh fading model, and express the channel as and where β BU,mk represents the large-scale fading coefficient between user k and base station m, β RU,nk It is expressed as the large-scale fading coefficient between user k and RISn. Assuming that RIS is designed and installed at a location that provides a line-of-sight LoS channel with the base station, Represents the full-rank LoS channel matrix between RISn and base station m: Among them, β BR,mn is the large-scale fading coefficient between RISn and base station m, is the carrier wavelength, d BS is the antenna spacing of the base station, d RIS is the reflection unit spacing of RIS; and denote the elevation and azimuth line-of-sight angles AoD of base station m relative to the i-th reflector unit of RISn, respectively, and and denote the elevation and azimuth line-of-sight arrival angle AoA of RISn relative to the lth antenna of base station m, respectively; S14: aggregate the channel between user k and base station m Defined as: in, is the phase shift matrix of RISn, represents the phase shift coefficient of the i-th unit of RISn; all and Large-scale fading coefficient β between user and base station BU,mk , the large-scale fading coefficient β between the user and the RIS RU,nk and the line-of-sight channel G between RIS and the base station BR,mn are assumed to be known.

3. The RIS-assisted non-cellular massive MIMO system performance analysis method according to claim 1, characterized in that: Step S2 specifically includes: S21. Calculate the uplink pilot signal received by base station m as follows: τ represents the length of the coherence time, where τ p symbols are used for uplink training, and the remaining τ-τ p symbols are used for uplink data transmission; in the uplink pilot training phase, is defined as the pilot sequence sent by user k to all base stations, where p p is the power of the uplink pilot sequence; assuming τ p ≥K, so that when k=k′, φ k Designed to meet When k≠k′, represents the additive white Gaussian noise AWGN at base station m, each element of which follows a complex Gaussian distribution S22. In order to enable base station m to estimate the state information of the aggregated channel from user k, the uplink pilot signal received by base station m is compared with Multiplying them, we get: S23. Based on the observed signal, use the minimum mean square error (LMMSE) channel estimation method to calculate the aggregate channel g mk The estimated values ​​are as follows: in, Φ=diag{Φ1,Φ2,…,Φ N }; S24, according to the characteristics of the LMMSE channel estimation method, the channel estimation and channel estimation error Follow the distribution and in:

4. The RIS-assisted non-cellular massive MIMO system performance analysis method according to claim 1, characterized in that: Step S3 specifically includes: S31. In the uplink data transmission phase, K users send data signals to M base stations at the same time. Therefore, the data signal received by base station m is: Among them, p u is the power of data transmission, x k is the modulation symbol of user k, and 0≤η k ≤1 is the power control coefficient; the additive white Gaussian noise vector at base station m is S32. Based on step S31, the data received by the CPU from user k is: Base station m first receives the signal y m Multiply Then the result signals of all M base stations are sent to the central processing unit CPU through the backhaul network; represents the expected signal of user k; represents the channel estimation error, Indicates the interference signal caused by other users; represents noise interference, and its distribution is 5. The RIS-assisted non-cellular massive MIMO system performance analysis method according to claim 1, characterized in that: Step S4 specifically includes: S41. Assume that the modulation signals sent by all K users satisfy According to the formula of data received by the CPU from user k, the single SINR of user k is expressed as: in, represents the intensity of the noise, ρ k represents the expected signal strength of user k, represents the interference signal strength of user k, S42. According to the expected signal strength formula of user k, the expected signal strength ρ of user k k The PDF expression of is: in, S43, according to the interference signal strength formula of user k, the expected signal strength of user k The PDF expression of is: in, 6. The RIS-assisted non-cellular massive MIMO system performance analysis method according to claim 1, characterized in that: Step S5 specifically includes: S51, based on the expected signal strength ρ of user k k The PDF expression of and the expected signal strength of user k The PDF expression of SINR of user k is: In the above formula, Γ(x) represents the gamma function; S52. Based on the PDF expression of SINR of user k and the Taylor series expansion of the upper incomplete gamma function, the PDF expression of SINR of user k is rewritten as:

7. The RIS-assisted non-cellular massive MIMO system performance analysis method according to claim 1, characterized in that: Step S6 specifically includes: S61. Based on the single SINR expression of user k in step S41, define the outage probability and coverage probability of user k as follows: OP k =Pr{γ k ≤γ th } CP k =Pr{γ k >γ th , Among them, γ th Indicates the required SINR threshold; S62. Calculate the interruption probability of user k The calculation formula is as follows: In the above formula, 2F1(α,β;γ;x) represents Gaussian hypergeometric function, Beta(x,y) represents beta function; S63. Interruption probability based on user k Calculate the coverage probability of user k The calculation formula is as follows: S64. Using the single SINR expression of user k in step S41, the ergodic capacity expression of user k is expressed as: S65. Based on step S64, calculate the traversal capacity of the kth user The calculation formula is as follows: In the above formula, represents the Meijer-G function.

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