Intelligent metasurface enabled cellular-free network symbol error rate analysis method

Abstract

The invention provides an intelligent metasurface enabled cellular-free network symbol error rate analysis method. The method comprises the following steps: establishing an intelligent metasurface enabled cellular-free network model under a spatial correlation Rayleigh fading channel; performing uplink training based on the constructed model; transmitting uplink channel data based on the trained uplink; according to the transmitted uplink channel data, designing a probability density function of the expected signal and the equivalent noise; and according to the probability density function of the designed desired signal, designing analytical expressions of SER of M-PAM, M-QAM and M-PSK. According to the invention, the error rate is reduced, so that a communication network can stably transmit under a higher signal-to-noise ratio, the reliability of data transmission is improved, the low error rate means that the situation of disconnection or data errors encountered by a user in the use process is reduced, and the overall user experience is improved. A simulation result verifies the reliability of the analyzed symbol error rate, shows the advantage of enabling the intelligent metasurface to a cellular-free network, and provides a theoretical basis for 6G development and deployment.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular to a method for analyzing symbol error rate in a non-cellular network enabled by an intelligent metasurface. Background Art

[0002] In recent years, the cellular network has become an indispensable architecture for exploring 6G. It can not only send and receive signals simultaneously through multiple antennas, significantly improve the capacity of the system and meet the needs of a large number of users, but also realize spatial multiplexing and increase the efficiency of spectrum utilization. In addition, the network can be dynamically adjusted according to different environments and needs to adapt to user distribution and traffic changes. However, high complexity, difficult channel estimation, and limited coverage are also problems it has.

[0003] Despite the above shortcomings of non-cellular networks, an emerging technology called reconfigurable smart surfaces is gradually being seen as a potential solution to overcome these limitations. Compared with traditional base stations, smart metasurfaces have lower deployment and maintenance costs, especially in environments where wiring is difficult. Secondly, it can also optimize signal propagation to reduce multipath interference and improve the overall performance of the system.

[0004] Since both smart metasurfaces and cellular-free networks can enhance signal quality and improve spectrum efficiency, smart metasurfaces are applied to cellular-free networks. First, the combination of the two can further improve the signal quality and coverage of cellular-free networks and reduce fading and interference; second, through reasonable power allocation and signal processing, combined with the low power consumption characteristics of smart metasurfaces, the overall energy consumption can be significantly reduced and the energy efficiency of the system can be improved; finally, the capacity of the network can be significantly increased to meet the growing needs of users.

[0005] Although some representative studies have investigated various aspects of cellular-free networks enabled by smart metasurfaces in recent years, most of them only delved into their energy efficiency and frequency efficiency, but lacked relevant research on symbol error rate, which reflects the reliability of communication networks. Summary of the invention

[0006] According to the technical problems raised above, a method for analyzing symbol error rate of non-cellular networks enabled by intelligent metasurface is provided. The present invention first analyzes the PDF expressions of the desired signal and the interference signal from other users under different modulation schemes, where the equivalent noise is considered to be the sum of the interference from other users and the received noise. Then, based on the PDF of the desired signal and the equivalent noise, the analytical expressions of SER of M-PAM, M-QAM and M-PSK are designed. Finally, the numerical results show the effectiveness and reliability of the designed expressions compared with Monte Carlo simulation.

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

[0008] A method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface, comprising:

[0009] S1. Establish a cellular-free network model enabled by smart metasurfaces under spatially correlated Rayleigh fading channels;

[0010] S2, performing uplink training based on the constructed non-cellular network model;

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

[0012] S4. Designing probability density functions of the expected signal and equivalent noise according to the transmitted uplink channel data;

[0013] S5. According to the designed probability density function of the expected signal, design the analytical expression of SER of M-PAM, M-QAM and M-PSK.

[0014] Furthermore, step S1 specifically includes:

[0015] S11. Build a cellular-free network enabled by smart metasurfaces in the uplink, in which M base stations BS provide communication services for K single-antenna users with the help of N reconfigurable smart metasurfaces, where each base station is equipped with L antennas and each smart metasurface is equipped with I reflection units; a central processing unit CPU connects multiple base stations and smart metasurfaces through a backhaul network to manage signal processing;

[0016] S12, the base station, the user, the smart metasurface and the set of reflection units of each smart metasurface are represented as and

[0017] S13. Assume that multiple BSs and smart metasurfaces are placed at higher locations and close to each other, while multiple users are randomly distributed at lower geographical locations; therefore, assume that all channels between users and base stations and users and smart metasurfaces obey the Rayleigh fading model, and these channels are expressed 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 smart metasurface n;

[0018] S14. Assuming that the smart metasurface is designed and installed at a location that provides a line-of-sight LoS channel with the base station, calculate the full-rank LoS channel matrix between the smart metasurface n and the base station m.

[0019]

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

[0021] S15: aggregate the channel between user k and base station m Defined as:

[0022]

[0023] in, represents the phase shift matrix of smart metasurface n, represents the phase shift coefficient of the i-th unit of smart metasurface 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 smart metasurface RU,nk and the line-of-sight channel G between the smart metasurface and the base station BR,mn are assumed to be known.

[0024] Further, step S2 specifically includes:

[0025] S21, in the uplink pilot training phase, is defined as the pilot sequence sent by user k to all base stations, where p p represents the power of the uplink pilot sequence, assuming that τ p ≥K, when k=k′, it satisfies When k≠k′, Therefore, the uplink pilot signal received by base station m is expressed as:

[0026]

[0027] in, 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 gives the observed signal:

[0029]

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

[0031]

[0032] in, Φ=diag{Φ1,Φ2,…,Φ N};

[0033] S24, according to the characteristics of the LMMSE channel estimation method, the channel estimation and channel estimation error Follow the distribution and in:

[0034]

[0035] Further, step S3 specifically includes:

[0036] 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:

[0037]

[0038] Among them, p u represents the power of data transmission, x k represents 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

[0039] S32: For the data signal received by base station m, a maximum ratio combining scheme is used, and base station m combines the received signal y m Multiply The result signals of all M base stations are then sent to the central processing unit CPU through the backhaul network, and the CPU receives the data from user k as follows:

[0040]

[0041] in, 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 follows

[0042] Further, step S4 specifically includes:

[0043] S41. Based on the formula for receiving data from user k by the CPU, the signal received by user k is expressed at the CPU as:

[0044] r k =ρ k x k +ε k

[0045] Among them, ρ k represents the expected signal of user k, ε k represents the equivalent noise of user k, in

[0046] S42. According to the expected signal of user k, the expected signal strength ρ of user k k The PDF expression of is:

[0047]

[0048] in,

[0049]

[0050] S43. Based on the equivalent noise of user k, the expected signal strength of user k The PDF expression of is:

[0051]

[0052] in,

[0053] Furthermore, step S5 specifically includes:

[0054] S51. According to the designed probability density function of the desired signal, an analytical expression of the SER of the M-PAM is designed, including:

[0055] S511. In a cellular-free network enabled by a smart metasurface, when M-ary pulse amplitude modulation (PAM) is used for signal modulation, all users are from the set {-M PAM +1,-M PAM +3,…,M PAM -1} select its transmission signal, where M PAM Indicates the modulation order of M-PAM;

[0056] S512: Establish expected signal strength ρ of user k k The expected signal strength in the PDF expression of The PDF of follows the gamma distribution Ga(θ mk ,ω mk ), where x~Ga(θ,ω) represents the PDF of the variable x that follows the gamma distribution, that is,

[0057] S513, Analysis and The probability density function of , and based on the results sought, assume that they approximately obey two complex Gaussian distributions, as follows:

[0058]

[0059] S514, based on two complex Gaussian distributions, and considering that the transmission signal is from the set {-M PAM +1,-M PAM +3,…,M PAM -1}, design The PDFs of the real and imaginary parts of are:

[0060]

[0061] S515, based on design The PDF of the real and imaginary parts of and the equivalent noise of user k give ε k The PDFs of the real and imaginary parts of are as follows:

[0062]

[0063] in, express The jth row of

[0064] The definition of z=Cross_add(x,y) is the new vector generated Is and The result elements of cross addition operation on all elements of ;

[0065] S516: based on the expected signal strength ρ of user k k PDF expressions and formulas The SER expression of M-PAM for designed user k is:

[0066]

[0067] in, 2F1(α,β;γ;x) represents Gaussian hypergeometric function;

[0068] S517. When 2PAM is used for signal modulation, the SER of user k can be simplified to:

[0069]

[0070] S52. According to the designed probability density function of the desired signal, an analytical expression of the SER of M-QAM is designed, including:

[0071] S521, in a cellular-free network enabled by a smart metasurface, M-ary quadrature amplitude modulation (QAM) is used, and each user selects from the set {Cross_add(Amplitude QAM ,i×Amplitude QAM )} select its transmission signal, where M QAM represents the modulation order of M-QAM, and

[0072] S522, analytical formula f ρk (ρ k ) in which the expected signal strength ρ k ~Ga(θ mk ,ω mk ) and calculate the PDF expression of the formula For all k, The error terms of the real and imaginary parts of The PDF is as follows:

[0073]

[0074] S523, based on the equivalent noise ε of user k k and formula For all The error term ε k The PDF expressions for the real and imaginary parts of are:

[0075]

[0076] in, express The jth row of

[0077] S524, based on formula and formula The SER expression of M-QAM for user k is designed as:

[0078]

[0079] Among them, c1=1.09500814703333, c2=0.75651138383854, D p (x) represents the parabolic cylindrical function,

[0080] S525. Simplify the SER of 4QAM of user k to:

[0081]

[0082] in,

[0083] S53. According to the designed probability density function of the desired signal, an analytical expression of the SER of M-PSK is designed, including:

[0084] S531. In a cellular-free network enabled by a smart metasurface, when M-ary phase modulation PSK is used, all users are from the set Select its transmission signal, where M PSK represents the modulation order of PSK, and the error term ε of M-PSK is obtained k , The PDFs of the real and imaginary parts of in

[0085] S532, using formula and the error term ε k The PDF expressions of the real and imaginary parts of , the SER expression of M-PSK of user k is:

[0086]

[0087] Compared with the prior art, the present invention has the following advantages:

[0088] 1. The present invention provides a method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface, which reduces the bit error rate and enables the communication network to transmit stably at a higher signal-to-noise ratio, thereby improving the reliability of data transmission. And the low bit error rate means that users encounter fewer disconnections or data errors during use, thereby improving the overall user experience.

[0089] 2. The present invention provides a method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface. Compared with the traditional MIMO system, the present invention uses an intelligent metasurface to empower the non-cellular network. It can actively adjust the signal propagation path, reduce multipath interference and shadow fading, enhance the system's resistance to interference, and make network deployment easier. It can be dynamically adjusted according to specific needs to adapt to different user needs and environmental changes.

[0090] Based on the above reasons, the present invention can be widely promoted in fields such as wireless communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] 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.

[0092] Figure 1 The figure is a flow chart of the method of the present invention.

[0093] Figure 2 A model structure of a cellular-free network enabled by an intelligent metasurface applicable to the solution of the present invention.

[0094] Figure 3 A multi-user simulation scene diagram applicable to the solution of the present invention.

[0095] Figure 4 This is a simulation diagram of the relationship between the average SER of all users and the data transmission power provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0096] 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.

[0097] 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.

[0098] like Figure 1 As shown, the present invention provides a method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface, comprising:

[0099] S1. Establish a cellular-free network model enabled by smart metasurfaces under spatially correlated Rayleigh fading channels;

[0100] S2, performing uplink training based on the constructed non-cellular network model;

[0101] S3, based on the trained uplink, transmitting uplink channel data;

[0102] S4. Designing probability density functions of the expected signal and equivalent noise according to the transmitted uplink channel data;

[0103] S5. According to the designed probability density function of the expected signal, design the analytical expression of SER of M-PAM, M-QAM and M-PSK.

[0104] During specific implementation, as a preferred embodiment of the present invention, a Figure 2 The cellular-free network enabled by smart metasurfaces in the uplink shown in the figure, in which M base stations BS provide communication services for K single-antenna users with the help of N reconfigurable smart metasurfaces, where each base station is equipped with L antennas and each smart metasurface is equipped with I reflection units; a central processing unit CPU connects multiple base stations and smart metasurfaces through a backhaul network to manage signal processing;

[0105] S12, the base station, the user, the smart metasurface and the set of reflection units of each smart metasurface are represented as and

[0106] S13. Assume that multiple BSs and smart metasurfaces are placed at higher locations and close to each other, while multiple users are randomly distributed at lower geographical locations; therefore, assume that all channels between users and base stations and users and smart metasurfaces obey the Rayleigh fading model, and these channels are expressed 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 smart metasurface n;

[0107] S14. Assuming that the smart metasurface is designed and installed at a location that provides a line-of-sight LoS channel with the base station, calculate the full-rank LoS channel matrix between the smart metasurface n and the base station m.

[0108]

[0109] Among them, β BR,mn represents the large-scale fading coefficient between the smart metasurface n and the base station m, represents the carrier wavelength, d BS Denotes the antenna spacing of the base station, d RIS represents the spacing between reflection units of the smart metasurface; and denote the elevation and azimuth line-of-sight angles AoD of base station m relative to the i-th reflector unit of smart metasurface n, respectively. and denote the line-of-sight arrival angle AoA of the smart metasurface n relative to the lth antenna of the base station m in elevation and azimuth respectively;

[0110] S15: aggregate the channel between user k and base station m Defined as:

[0111]

[0112] in, represents the phase shift matrix of smart metasurface n, represents the phase shift coefficient of the i-th unit of smart metasurface 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 smart metasurface RU,nk and the line-of-sight channel G between the smart metasurface and the base station BR,mn are assumed to be known.

[0113] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0114] S21, in the uplink pilot training phase, is defined as the pilot sequence sent by user k to all base stations, where p p represents the power of the uplink pilot sequence, assuming that τ p ≥K, when k=k′, it satisfies When k≠k′, Therefore, the uplink pilot signal received by base station m is expressed as:

[0115]

[0116] in, represents the additive white Gaussian noise AWGN at base station m, each element of which follows a complex Gaussian distribution

[0117] 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 gives the observed signal:

[0118]

[0119] S23, based on the observed signal, use the minimum mean square error channel estimation method to calculate the aggregate channel g mk The estimated values ​​are as follows:

[0120]

[0121] in, Φ=diag{Φ1,Φ2,…,Φ N};

[0122] S24, according to the characteristics of the LMMSE channel estimation method, the channel estimation and channel estimation error Follow the distribution and in:

[0123]

[0124] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0125] 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:

[0126]

[0127] Among them, p u represents the power of data transmission, x k represents 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

[0128] S32: For the data signal received by base station m, a maximum ratio combining (MRC) scheme is used, and base station m combines the received signal y m Multiply The result signals of all M base stations are then sent to the central processing unit CPU through the backhaul network, and the CPU receives the data from user k as follows:

[0129]

[0130] in, 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 follows

[0131] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0132] S41. Symbol Error Rate (SER) refers to the ratio of the total number of symbols with errors to the total number of symbols transmitted in a specific time period. This indicator is particularly important for evaluating system reliability, especially in multi-modulation signal systems. In this section, we will analyze the SER performance of the smart metasurface-enabled cellular-free network when users transmit modulated signals through various schemes (including M-PAM, M-QAM, and M-PSK). Based on the formula for the CPU receiving data from user k, the signal received by user k at the CPU is expressed as:

[0133] r k =ρ k x k +ε k

[0134] Among them, ρ k represents the expected signal of user k, ε k represents the equivalent noise of user k, in

[0135] S42. According to the expected signal of user k, the expected signal strength ρ of user k k The PDF expression of is:

[0136]

[0137] in,

[0138] In this embodiment, it can be seen that the expected signal strength ρ k The PDF expression is closely related, and It is also related to the parameter setting of uplink pilot training and the statistical channel state information (CSI) between the base station, smart metasurface and users.

[0139] S43. Based on the equivalent noise of user k, the expected signal strength of user k The PDF expression of is:

[0140]

[0141] in,

[0142] In this embodiment, the interference signal strength The PDF expression of is mainly affected by the CSI and the channel estimation errors of different channels.

[0143] In specific implementation, as a preferred embodiment of the present invention, step S5 specifically includes:

[0144] S51. According to the designed probability density function of the desired signal, an analytical expression of the SER of the M-PAM is designed, including:

[0145] S511. In a cellular-free network enabled by a smart metasurface, when M-ary pulse amplitude modulation (PAM) is used for signal modulation, all users are from the set {-M PAM +1,-M PAM +3,…,M PAM -1} select its transmission signal, where M PAM Indicates the modulation order of M-PAM;

[0146] S512: Establish expected signal strength ρ of user k k The expected signal strength in the PDF expression of The PDF of follows the gamma distribution Ga(θ mk ,ω mk ), where x~Ga(θ,ω) represents the PDF of the variable x that follows the gamma distribution, that is,

[0147] S513, Analysis The probability density function of , and based on the results sought, assume that they approximately obey two complex Gaussian distributions, as follows:

[0148]

[0149] S514, based on two complex Gaussian distributions, and considering that the transmission signal is from the set {-M PAM +1,-M PAM +3,…,M PAM -1}, design The PDFs of the real and imaginary parts of are:

[0150]

[0151] S515, based on design The PDF of the real and imaginary parts of and the equivalent noise of user k give ε k The PDFs of the real and imaginary parts of are as follows:

[0152]

[0153] in, express The jth row of

[0154] The definition of z=Cross_add(x,y) is the new vector generated Is and The result elements of cross addition operation on all elements of ;

[0155] S516: based on the expected signal strength ρ of user k k PDF expressions and formulas The SER expression of M-PAM for designed user k is:

[0156]

[0157] in, 2F1(α,β;γ;x) represents Gaussian hypergeometric function;

[0158] S517. When 2PAM is used for signal modulation, the SER of user k can be simplified to:

[0159]

[0160] S52. According to the designed probability density function of the desired signal, an analytical expression of the SER of M-QAM is designed, including:

[0161] S521, in a cellular-free network enabled by a smart metasurface, M-ary quadrature amplitude modulation (QAM) is used, and each user selects from the set {Cross_add(Amplitude QAM ,i×Amplitude QAM )} select its transmission signal, where M QAM represents the modulation order of M-QAM, and

[0162] S522, analytical formula The expected signal strength ρ k ~Ga(θ mk ,ω mk ) and calculate the PDF expression of the formula For all k, The error terms of the real and imaginary parts of The PDF is as follows:

[0163]

[0164] S523, based on the equivalent noise ε of user k k and formula For all The error term ε k The PDF expressions for the real and imaginary parts of are:

[0165]

[0166] in, express The jth row of

[0167] S524, based on formula and formula The SER expression of M-QAM for user k is designed as:

[0168]

[0169] Among them, c1=1.09500814703333, c2=0.75651138383854, D p (x) represents the parabolic cylindrical function,

[0170] S525. Simplify the SER of 4QAM of user k to:

[0171]

[0172] in,

[0173] S53. According to the designed probability density function of the desired signal, an analytical expression of the SER of M-PSK is designed, including:

[0174] S531. In a cellular-free network enabled by a smart metasurface, when M-ary phase modulation PSK is used, all users are from the set Select its transmission signal, where M PSK represents the modulation order of PSK, and the error term ε of M-PSK is obtained k , The PDFs of the real and imaginary parts of in

[0175] S532, using formula and the error term ε k The PDF expressions of the real and imaginary parts of , the SER expression of M-PSK of user k is:

[0176]

[0177] Example

[0178] In order to verify the effectiveness of the solution of the present invention, the following simulation experiments were carried out:

[0179] The specific simulation parameters of the cellular-free network enabled by the smart metasurface are:

[0180] In the simulation setting, a cellular-free network consists of 2 BSs, each serving 8 single-antenna users, and each BS is equipped with 48 antennas. The network communication performance is severely limited due to obstacles such as high-rise buildings between the BSs and the users. To address this problem, we deploy 3 smart metasurfaces on three separate building surfaces, each with 64 reflective units, which are high enough to establish additional reflective links.

[0181] 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 smart metasurfaces 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. Large-scale path loss is calculated using the following formula: and in, and They are the distance between base station m and smart metasurface n, the distance between smart metasurface n 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 smart metasurface n, assume and In addition, other simulation parameters are set to τ p =8 and η k =1, for all

[0182] exist Figure 4 In the figure, the perfect channel state information (p p =∞dBm) and imperfect CSI(p p =5dBm), the SER of all users and the data transmission power p u First, for 4PAM, 4QAM, 2PSK, 4PSK, and 8PSK, the formula formula and formula The given SER analytical expressions closely match the Monte Carlo simulation results, verifying the reliability of the SER analytical expressions under these modulation modes. Then, it is observed that the SER of 2PSK is better than that of 4PSK, 4PAM and 4QAM, and the SER of the latter three is better than that of 8PSK. This shows that although higher modulation orders can achieve better rate performance, the reliability of network communication is also sacrificed. In addition, when the data transmission power is low, the SER performance of 4PAM is better than that of 4QAM and 4PSK. Secondly, at higher data transmission power, the SER performance of 4QAM and 4PSK becomes very similar, and both exceed 4PAM. This shows that for the same modulation order, the SER performance of different modulation modes is significantly affected by the signal-to-noise ratio and constellation layout. Finally, with the increase of data transmission power, the SER of various modulation modes decreases consistently and tends to different constant values, which shows that further increasing the data transmission power cannot infinitely improve the SER performance.

[0183] In summary, the above simulation results verify the accuracy of the SER expression derived by the solution of the present invention.

[0184] 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 them; although the present invention has been described in detail with reference to the aforementioned embodiments, those of ordinary skill in the art should understand that it is still possible to modify the technical solutions recorded in the aforementioned embodiments, or to replace some or all of the technical features therein by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention. 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 them; although the present invention has been described in detail with reference to the aforementioned embodiments, those of ordinary skill in the art should understand that it is still possible to modify the technical solutions recorded in the aforementioned embodiments, or to replace some or all of the technical features therein by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface, characterized in that: include: S1. Establish a cellular-free network model enabled by smart metasurfaces under spatially correlated Rayleigh fading channels; S2, performing uplink training based on the constructed non-cellular network model; S3, based on the trained uplink, transmitting uplink channel data; S4. Designing probability density functions of the expected signal and equivalent noise according to the transmitted uplink channel data; S5. According to the designed probability density function of the expected signal, design the analytical expression of SER of M-PAM, M-QAM and M-PSK.

2. According to claim 1, the method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface is characterized in that: Step S1 specifically includes: S11. Build a cellular-free network enabled by smart metasurfaces in the uplink, in which M base stations BS provide communication services for K single-antenna users with the help of N reconfigurable smart metasurfaces, where each base station is equipped with L antennas and each smart metasurface is equipped with I reflection units; a central processing unit CPU connects multiple base stations and smart metasurfaces through a backhaul network to manage signal processing; S12, the base station, the user, the smart metasurface and the set of reflection units of each smart metasurface are represented as and S13. Assume that multiple BSs and smart metasurfaces are placed at higher locations and close to each other, while multiple users are randomly distributed at lower geographical locations; therefore, assume that all channels between users and base stations and users and smart metasurfaces obey the Rayleigh fading model, and these channels are expressed as Hehe 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 smart metasurface n; S14. Assuming that the smart metasurface is designed and installed at a location that provides a line-of-sight LoS channel with the base station, calculate the full-rank LoS channel matrix between the smart metasurface n and the base station m. Among them, β BR,mn represents the large-scale fading coefficient between the smart metasurface n and the base station m, represents the carrier wavelength, d BS Denotes the antenna spacing of the base station, d RIS represents the spacing between reflection units of the smart metasurface; and denote the elevation and azimuth line-of-sight angles AoD of base station m relative to the i-th reflector unit of smart metasurface n, respectively. and denote the line-of-sight arrival angle AoA of the smart metasurface n relative to the lth antenna of the base station m in elevation and azimuth respectively; S15: aggregate the channel between user k and base station m Defined as: in, represents the phase shift matrix of smart metasurface n, represents the phase shift coefficient of the i-th unit of smart metasurface 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 smart metasurface RU,nk and the line-of-sight channel G between the smart metasurface and the base station BR,mn are assumed to be known.

3. According to claim 1, the method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface is characterized in that: Step S2 specifically includes: S21, in the uplink pilot training phase, is defined as the pilot sequence sent by user k to all base stations, where p p represents the power of the uplink pilot sequence, assuming that τ p ≥K, when k=k′, it satisfies When k≠k′, Therefore, the uplink pilot signal received by base station m is expressed as: in, 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 gives the observed signal: S23, based on the observed signal, use the minimum mean square error channel estimation method to calculate the aggregate channel g mk The estimated values ​​are as follows: Among them, 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. According to claim 1, the method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface is 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 represents the power of data transmission, x k represents 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: For the data signal received by base station m, a maximum ratio combining scheme is used, and base station m combines the received signal y m Multiply The result signals of all M base stations are then sent to the central processing unit CPU through the backhaul network, and the CPU receives the data from user k as follows: in, 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 follows 5. According to claim 1, the method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface is characterized in that: Step S4 specifically includes: S41. Based on the formula for receiving data from user k by the CPU, the signal received by user k is expressed at the CPU as: r k =ρ k x k +e k Among them, ρ k represents the expected signal of user k, ε k represents the equivalent noise of user k, in S42. According to the expected signal of user k, the expected signal strength ρ of user k k The PDF expression of is: in, S43. Based on the equivalent noise of user k, the expected signal strength of user k The PDF expression of is: in, 6. According to claim 1, the method for analyzing symbol error rate of a non-cellular network enabled by an intelligent metasurface is characterized in that: Step S5 specifically includes: S51. According to the designed probability density function of the desired signal, an analytical expression of the SER of the M-PAM is designed, including: S511. In a cellular-free network enabled by a smart metasurface, when M-ary pulse amplitude modulation (PAM) is used for signal modulation, all users are from the set {-M PAM +1,-M PAM +3,…,M PAM -1} select its transmission signal, where M PAM Indicates the modulation order of M-PAM; S512: Establish expected signal strength ρ of user k k The expected signal strength in the PDF expression of The PDF of follows the gamma distribution Ga(θ mk ,ω mk ), where x~Ga(θ,ω) represents the PDF of the variable x that follows the gamma distribution, that is, S513, Analysis and The probability density function of , and based on the results sought, assume that they approximately obey two complex Gaussian distributions, as follows: S514, based on two complex Gaussian distributions, and considering that the transmission signal is from the set {-M PAM +1,-M PAM +3,…,M PAM -1}, design The PDFs of the real and imaginary parts of are: S515, based on design The PDF of the real and imaginary parts of and the equivalent noise of user k give ε k The PDFs of the real and imaginary parts of are as follows: in, express The jth row of The definition of z=Cross_add(x,y) is the new vector generated Is and The result elements of cross addition operation on all elements of ; S516: based on the expected signal strength ρ of user k k PDF expressions and formulas The SER expression of M-PAM for designed user k is: in, 2F1(α,β;γ;x) represents Gaussian hypergeometric function; S517. When 2PAM is used for signal modulation, the SER of user k can be simplified to: S52. According to the designed probability density function of the desired signal, an analytical expression of the SER of M-QAM is designed, including: S521, in a cellular-free network enabled by a smart metasurface, M-ary quadrature amplitude modulation (QAM) is used, and each user selects from the set {Cross_add(Amplitude QAM ,i×Amplitude QAM )} select its transmission signal, where M QAM represents the modulation order of M-QAM, and S522, analytical formula The expected signal strength ρ k ~Ga(θ mk ,ω mk ) and calculate the PDF expression of the formula For all The error terms of the real and imaginary parts of The PDF is as follows: S523, based on the equivalent noise ε of user k k and formula For all The error term ε k The PDF expressions for the real and imaginary parts of are: in, express The jth row of S524, based on formula and formula The SER expression of M-QAM for user k is designed as: Among them, c1=1.09500814703333, c2=0.75651138383854, D p (x) represents the parabolic cylindrical function, S525. Simplify the SER of 4QAM of user k to: in, S53. According to the designed probability density function of the desired signal, an analytical expression of the SER of M-PSK is designed, including: S531. In a cellular-free network enabled by a smart metasurface, when M-ary phase modulation PSK is used, all users are from the set Select its transmission signal, where M PSK represents the modulation order of PSK, and obtains the error term of M-PSK The PDFs of the real and imaginary parts of in S532, using formula and the error term ε k The PDF expressions of the real and imaginary parts of , the SER expression of M-PSK of user k is:

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