A RIS-IM-NOMA system design method based on channel distribution information

Abstract

The present invention relates to a RIS‑IM‑NOMA system design method based on channel distribution information, and belongs to the field of communication technology. The method comprises the following steps: S1: establishing a channel model constructed using a channel correlation matrix; S2: establishing a RIS‑IM‑NOMA‑CDI system model, defining a reflection coefficient matrix and a detection method; S3: deriving and analyzing the theoretical upper limit of the bit error rate of the system model; S4: theoretically analyzing the spectrum efficiency performance of the system model, introducing an interruption probability limit to propose the fairness problem of spectrum efficiency between users; S5: optimizing the power allocation method. The present invention utilizes channel distribution information to construct a channel for data transmission through the channel correlation matrix observed by the transmitting end, adopts a greedy detection method to perform signal detection at the receiving end and derives the theoretical upper limit of the bit error rate, and discusses the optimal power allocation method under the fairness problem.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology and relates to a RIS-IM-NOMA system design method based on channel distribution information. Background Art

[0002] Fifth-generation mobile communication (5G) networks aim to realize the vision of "the Internet of Everything," encompassing a range of new communication modes, including machine-to-person, machine-to-machine, and person-to-person communications. These new modes are expected to connect a large number of heterogeneous, data-hungry devices with diverse needs, leading to a spectrum shortage crisis and increased energy consumption. The anticipated large number of users, along with spectrum scarcity and power resource constraints, are among the key challenges facing future communication systems. Although the initial 5G standard was completed in 2018, researchers have begun exploring potential alternative technologies for subsequent versions of 5G. These technologies include reconfigurable intelligent surfaces (RIS), index modulation (IM), and non-orthogonal multiple access (NOMA).

[0003] Among emerging technologies, RIS has garnered widespread attention from both industry and academia for its ability to create intelligent radio environments, enabling control over previously uncontrollable wireless environments and enhancing wireless communications. Unlike traditional Multiple-Input Multiple-Output (MIMO) arrays that integrate a large number of standard antenna elements, novel antenna modules are deployed within a limited aperture to form a spatially continuous surface. By incorporating reflective elements and jointly programming them, RIS manipulates impinging electromagnetic waves to perform various functions, such as wave reflection, refraction, absorption, steering, and focusing. This novel design enables RIS to possess powerful electromagnetic wave manipulation capabilities, theoretically enabling the entire wireless communication environment to become intelligent. Consequently, optimizing RIS design and integrating it with existing technologies has become a major research hotspot.

[0004] Meanwhile, IM was proposed at the beginning of this century as a technology to mitigate issues such as inter-subchannel interference and inter-antenna synchronization associated with MIMO technology. In IM, data blocks are transmitted between two communicating nodes not only using traditional complex constellation points but also using the index of the transmitting entity (e.g., transmitting antenna, operating frequency, or occupied time slot). This significantly improves spectral efficiency and error performance. Since its inception, IM has been widely applied in various technologies, such as Orthogonal Frequency Division Multiple Access (OFDMA), MIMO, wireless sensor networks, cooperative and cognitive networks, and signal polarization. As can be seen from the above, while regulating the wireless environment through RIS, whether using RIS as a new index entity in IM or using RIS to implicitly convey index information for other entities, RIS and IM technology demonstrate a strong compatibility. In recent years, many researchers have explored this technology, but most existing research focuses solely on directly transmitting M-order modulated signals to a single user and has not explored channel multiplexing in multi-user scenarios. In order to make the Reconfigurable Intelligent Surface-assisted Index Modulation (RIS-IM) system suitable for the vision of "Internet of Everything", research should be conducted on combining multiple access technologies to enable limited bandwidth to serve multiple users.

[0005] Multiple access technology, as one of the foundational technologies for wireless mobile communications, is essential for enabling simultaneous communication between multiple users in wireless networks. NOMA, a key technology for 5G and future wireless communications, can reduce latency, enhance connectivity and reliability, and improve energy and spectral efficiency. Its fundamental principle is to employ superposition coding at the base station, classifying users based on their channel gain. Signals are then multiplexed in the power domain to further partition the minimum resource units (time-frequency resource blocks) used by OFDMA. In a NOMA environment, the RIS-IM system can optimize the propagation environment to meet specific user needs, thereby enabling efficient deployment of the NOMA system. By effectively utilizing RIS-IM, user order can be altered based on specific user priorities to meet specific system performance requirements, rather than relying on the random propagation environment of the wireless channel. Therefore, applying NOMA technology to the RIS-IM system holds significant research value in the context of future "Internet of Everything" wireless communication scenarios.

[0006] To achieve maximum throughput and reliability in a communication system, all nodes require complete CSI for all links in the network. Leveraging this knowledge, technologies such as smart beamforming can minimize interference and achieve optimal rates. However, in practical communication systems, obtaining real-time CSI is difficult due to limitations such as errors and limited feedback information. Therefore, further analysis of system performance in scenarios with incomplete CSI is necessary. Summary of the Invention

[0007] In view of this, the object of the present invention is to provide a RIS-IM-NOMA system design method based on channel distribution information.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] A RIS-IM-NOMA system design method based on channel distribution information, the method comprising the following steps:

[0010] S1: Establish a channel model using the channel correlation matrix;

[0011] S2: Establish the RIS-IM-NOMA-CDI system model and define the reflection coefficient matrix and detection method;

[0012] S3: Derive and analyze the theoretical upper bound of the bit error rate of this system model;

[0013] S4: Conduct theoretical analysis on the spectrum efficiency performance of the system model, introduce outage probability constraints and propose the issue of spectrum efficiency fairness among users;

[0014] S5: Optimize the power allocation method to improve system fairness.

[0015] Optionally, the S1 specifically includes:

[0016] Assume that the correlation Rayleigh fading model is adopted, and the channel Z obeys a zero-mean circularly symmetric complex Gaussian distribution. The channel correlation matrix is defined as:

[0017] R=E[vec(Z)vec H (Z)]

[0018] Where vec(·) means stacking the columns of the matrix in the brackets into a long column vector; vec H (·) represents the conjugate transpose of the vector in the brackets. Since the base station has a large enough space, it is assumed that the transmitting antennas are uncorrelated and only the receiving antennas are correlated. The total correlation matrix is expressed as follows:

[0019]

[0020] where R (m) Refers to the receiving correlation matrix observed by antenna numbered m; 0 K×K Represents a matrix of all zeros with K rows and K columns; in actual scenarios, the observed R (m) Multiply by the mth column Σ of a matrix Σ with the same dimensions as Z and a standard complex Gaussian distribution m to replace Z, eliminating the need for real-time CSI feedback on Z, R (m) ×Σ m The expanded form is as follows:

[0021]

[0022] in It represents the modulus and phase of the corresponding element in the channel matrix generated by the receiving correlation matrix observed by antenna numbered m.

[0023] Optionally, the S2 specifically includes:

[0024] Total transmitted data includes (log2N t +Klog2M) bits of information, the first part log2N t bits convey the transmit antenna index information and enable the RIS controller to adjust the reflection parameters accordingly; the second part Klog2Mbits conveys the user data information, which is multiplied by the respective power allocation coefficients and mapped to the constellation diagram for transmission; using the above correlation channel matrix, the channel estimation overhead of knowing the perfect CSI is avoided, and the total received signal expression is as follows

[0025]

[0026]

[0027] That is, the data received by the kth user from the antenna numbered m is expressed as:

[0028]

[0029] Each RIS sub-surface improves signal quality and implicitly transmits transmit antenna index information by appropriately and independently adjusting its phase shift matrix. Assuming that each reflective element reaches its maximum reflection coefficient, and since the modulus and phase of each element of the correlation channel matrix in the above formula are obtained by observation, and setting all RIS reflection amplitudes to 1, the received signal-to-noise ratio when using the mth transmit antenna is:

[0030]

[0031] Where N0 represents the noise energy; when determining the transmit antenna index m and user k, take Maximize the receive signal-to-noise ratio:

[0032]

[0033] The receiving end uses the detected transmitting antenna index m and user information x k Demodulate the received signal sequentially, that is, first demodulate the signal estimation value of the user with the worst channel condition Then by In descending order of user power allocation coefficients, the signal with the largest power allocation coefficient is demodulated from the original received signals of each user and removed one by one until all user signals are demodulated;

[0034] Transmit antenna index information The test is performed as follows:

[0035]

[0036] Determine the transmit antenna index information After that, send symbol x k The test is performed as follows:

[0037]

[0038] Then select the transmitting antenna m that maximizes the received signal-to-noise ratio, that is, the transmitting antenna index information, and then demodulate the u1 signal estimation value Then by The remaining signals are demodulated in sequence to complete data transmission.

[0039] Optionally, the S3 specifically includes:

[0040] Upper bound P of the bit error rate of system user k bk as follows:

[0041]

[0042] Among them, P e (m) Using PEP, the upper bound is:

[0043]

[0044] in It refers to the average PEP when all index information detect errors, which is consistent for each user; when sending M-QAM modulated signals, And E[|x| 2 ]=E s , the calculation is as follows:

[0045]

[0046] in The index information is detected as m or When the total user channel is in All obey Gaussian distribution, then B1 and Analyze the statistical characteristics of

[0047] The channel correlation matrix is obtained from observations, and when generating the channel, it is multiplied by the channel that obeys the Rayleigh distribution, so and According to the central limit theorem, B and All obey the Gaussian distribution, so we have for Also need to consider and The same is the uniform distribution of (0,2π), so we have and Considering the symmetry of the sine and cosine functions, we finally have

[0048] Then let Q1 = x1 T Ax1, where x1 = [X1, X2, X3, X4], A = diag{1, 1, -1, -1}; then the mean V1 and covariance matrix C1 of x1 are:

[0049] V1=

[0000] T

[0050] Represents the correlation coefficient between X5 and X6; Combined with the above formula, we can get the moment generating function Ψ of Q1 Q (w), and then find

[0051]

[0052] For the left side of the equation, consider P sk , that is, the average symbol error probability under the condition of correct index information detection, the corresponding moment generating function is:

[0053]

[0054] where α k E s / N0 represents the signal-to-noise ratio of each user. When using M-QAM modulation signals under CDI conditions, the bit error rates of each user are as follows:

[0055]

[0056] Where det(·) means to find the determinant of the matrix in the brackets; I NtK Indicates dimension N t×K identity matrix; g QAM =3 / 2(M-1) is defined as the signal correlation constant when using M-QAM modulation; using α k E s / N0 replaces E in the above process s / N0, and obtain the upper bound of the theoretical bit error rate of users in the RIS-IM-NOMA-CDI system.

[0057] Optionally, the S4 specifically includes:

[0058] Assume that the total spectrum efficiency of RIS-IM-NOMA-CDI is SE NC , according to the demodulation process, the signal-to-interference-and-noise ratio (SINR) at the user decoding time is obtained and the spectrum efficiency is calculated using the following formula:

[0059]

[0060] where β k represents the total channel coefficient from the RIS-IM-NOMA system base station to the kth user, SE NCk represents the spectrum efficiency of the kth user in the RIS-IM-NOMA system. Meanwhile, the difference in power allocation coefficients will cause the problem of spectrum efficiency fairness among users. The user with smaller power coefficient has lower spectrum efficiency. Next, the appropriate power allocation method is designed in conjunction with the outage probability constraint to ensure system fairness.

[0061] Optionally, the S5 specifically includes:

[0062] Whether error-free reception can be achieved depends on the signal-to-noise ratio at that time, and we define γ min Indicates the minimum receive signal-to-noise ratio without error. If the receive signal-to-noise ratio is greater than γ min There will be no bit error if it is less than γ min Correct decoding cannot be guaranteed, which is called an interruption; the corresponding interruption probability is:

[0063] P out =P(γ<γ min )

[0064] When the transmitter sends data at the maximum rate corresponding to the signal-to-noise ratio, there is P out The possibility of bit error occurs, in other words, if γ min If the value is extremely small, the outage capacity approaches the Shannon capacity. In the above scenario, the power allocation optimization problem is redefined as follows:

[0065]

[0066] α1>α2>…>α K

[0067] SINRk represents the received SINR of the kth user; the optimization problem is then re-described using SINR as follows:

[0068]

[0069] α1>α2>…>α K

[0070] where β k represents the total channel coefficient for the received signal of user k; r min That is, the predefined minimum γ min The spectrum efficiency requirement is determined in combination with the corresponding business requirements; k is any real number greater than 0 to ensure the limit on the interruption probability;

[0071] Then the outage probability is transformed to simplify its expression as follows:

[0072]

[0073] The left side of the above equation is defined as:

[0074]

[0075] Then order:

[0076]

[0077] where a i =α i 、b i =E s 、Z i =|β i | 2 ; Z i Independent entities are identically distributed in a chi-square distribution with 2 degrees of freedom; let X = Z1, τ i =(a i b i ) / (a1b1), we get:

[0078]

[0079] Since the chi-square distribution with 2 degrees of freedom is an exponential distribution with parameter 1 / 2, we have:

[0080]

[0081] According to the definition of moment generating function, the integral term is the moment generating function of Y, denoted as ψ Y (t), due to It is formed by adding the elements of the chi-square distribution with 2 degrees of freedom, so:

[0082]

[0083] And because Z i It obeys the chi-square distribution with 2 degrees of freedom, and its moment generating function is:

[0084]

[0085] So we have:

[0086]

[0087] The outage probability is finally written as follows:

[0088]

[0089] Then, we use the complement of the interruption probability to redefine the constraint conditions as follows:

[0090]

[0091] in B=N0 / E s C=1 / (1-ε k ); Using the logarithmic function without changing the monotonicity, we get:

[0092]

[0093] To use the Lagrange multiplier method to solve the extreme value of a multivariate function under conditional constraints, it is written as follows:

[0094]

[0095] Where θ is any real number, which ensures that the left side of the equality is divided by θ. 2 The sum of the remaining terms is strictly less than or equal to 0; the original problem is finally described as follows:

[0096]

[0097] α1>α2>…>α K

[0098] Then build the auxiliary function as follows:

[0099]

[0100] z1(α1,α2,…,α K )=1-α1-α2-…-α K

[0101]

[0102] Then set the Lagrangian factor μ and construct the following system of equations:

[0103]

[0104] The following (K+2) expressions are obtained:

[0105]

[0106] Let α1,α2,…,α K Substitute z1(α1,α2,…,α K )=0 and z2(α1,α2,…,α K )=0 to obtain μ1 and μ2; then μ1,μ2,α1,α2,…,α K-1 Substitute α in sequence K =g K (μ1,μ2,α1,…,α K-1 ) Solve for α K ; Obtain the optimal power allocation coefficients one by one under the spectrum efficiency fairness maximization problem considering the outage probability limit.

[0107] The beneficial effects of the present invention are as follows: the present invention designs and implements the RIS-IM-NOMA-CDI system for downlink scenarios in densely populated urban environments. Channel distribution information (CDI) is used to construct a channel for data transmission through the channel correlation matrix observed by the transmitter. Greedy detection is used at the receiver to detect the signal and derive the theoretical upper limit of the bit error rate. Combined with the interruption probability limit introduced by the channel model, the optimal power allocation method under the fairness issue is discussed. Finally, a comparison and analysis of spectrum efficiency and bit error rate performance is made through simulation with the RIS-IM-CDI system to verify the effectiveness of the proposed scheme.

[0108] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0110] Figure 1 This is a diagram of the RIS-IM-NOMA system model of the present invention;

[0111] Figure 2This is a comparison chart of the bit error rates of the RIS-IM-NOMA-CDI, RIS-IM-NOMA, and RIS-IM systems of the present invention;

[0112] Figure 3 This is a comparison diagram of bit error rates after changing the number of reflective elements of the present invention;

[0113] Figure 4 This is a comparison diagram of spectrum efficiency before and after the improved power allocation method of the present invention. DETAILED DESCRIPTION

[0114] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0115] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0116] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0117] See also Figures 1 to 4 The present invention is mainly divided into three parts: the RIS-IM-NOMA-CDI system model, the derivation of the theoretical upper bound of the RIS-IM-NOMA-CDI system bit error rate, and the RIS-IM-NOMA-CDI system power allocation method under the problem of maximizing fairness with the interruption probability constraint. Specifically, it includes the following steps:

[0118] 1. Explain the channel model constructed using the channel correlation matrix;

[0119] 2. Propose a RIS-IM-NOMA-CDI system model and explain the reflection coefficient matrix setting and detection method;

[0120] 3. Derive and analyze the theoretical upper limit of the system's bit error rate;

[0121] 4. Conduct theoretical analysis on the spectrum efficiency performance of the system and introduce interruption probability constraints to address the issue of spectrum efficiency fairness among users;

[0122] 5. Improve system fairness by optimizing the design of power distribution methods.

[0123] Furthermore, in said step 1, it specifically includes:

[0124] In real-world communication scenarios, factors such as large numbers of users, mobility, and dynamic operating environments cause the channel to change rapidly, resulting in outdated or inaccurate CSI. Another approach to obtaining channel information is to leverage channel statistics or distribution information to enhance communication. Because CDI accounts for channel randomness, it is more robust against interference with shorter channel coherence times and therefore remains effective for much longer than CSI. Furthermore, given the trend toward more location-based services, statistics based on node location can also be collected and stored a priori. This location-based data eliminates the need for real-time channel feedback.

[0125] Assuming the correlation Rayleigh fading model, assuming that the channel Z obeys a zero-mean circularly symmetric complex Gaussian distribution, the channel correlation matrix is defined as:

[0126] R=E[vec(Z)vec H (Z)]

[0127] Where vec(·) means stacking the columns of the matrix in the brackets into a long column vector; vec H (·) represents the conjugate transpose of the vector in the brackets. Since the base station has a large enough space, it is assumed that the transmitting antennas are uncorrelated, so only the receiving antennas are correlated. The total correlation matrix can be expressed as follows:

[0128]

[0129] where R (m) Refers to the receiving correlation matrix observed by antenna numbered m; 0 K×K represents a matrix of all zeros with K rows and K columns. In actual scenarios, the observed R (m) Multiply by the mth column Σ of a matrix Σ with the same dimensions as Z and a standard complex Gaussian distribution mto replace Z, thus eliminating the need for real-time CSI feedback on Z, R (m) ×Σ m The expanded form is as follows:

[0130]

[0131] in It represents the modulus and phase of the corresponding element in the channel matrix generated by the receiving correlation matrix observed by antenna numbered m.

[0132] In the step 2, it specifically includes:

[0133] Total transmitted data includes (log2N t +Klog2M) bits of information, the first part log2N t bits convey the transmit antenna index information and enable the RIS controller to adjust the reflection parameters accordingly; the second part Klog2Mbits conveys the user data information, which is multiplied by the respective power allocation coefficients and mapped to the constellation diagram for transmission. Using the above correlation channel matrix, the channel estimation overhead of knowing perfect CSI is avoided, and the total received signal expression is as follows

[0134]

[0135] That is, the data received by the kth user from the antenna numbered m is expressed as:

[0136]

[0137] Each RIS sub-surface improves signal quality and implicitly conveys transmit antenna index information by appropriately and independently adjusting its phase shift matrix. Assuming that each reflective element achieves its maximum reflection coefficient, and since the modulus and phase of each element of the correlation channel matrix in the above equation are obtained from observations, and setting all RIS reflection amplitudes to 1 because no additional adjustment of user signal energy is required, the received signal-to-noise ratio when using the mth transmit antenna is:

[0138]

[0139] Where N0 represents the noise energy. So we can know that when determining the transmit antenna index m and user k, we can take Maximize the receive signal-to-noise ratio:

[0140]

[0141] The receiving end uses the detected transmitting antenna index m and user information x k Demodulate the received signal sequentially, that is, first demodulate the signal estimation value of the user with the worst channel condition Then by In descending order of the user power allocation coefficients, the signal with the largest power allocation coefficient is demodulated from the original received signals of each user and removed one by one until all user signals are demodulated.

[0142] Transmit antenna index information The test is performed as follows:

[0143]

[0144] Determine the transmit antenna index information After that, send symbol x k The test is performed as follows:

[0145]

[0146] Then select the transmitting antenna m that maximizes the received signal-to-noise ratio, that is, the transmitting antenna index information, and then demodulate the u1 signal estimation value Then by The remaining signals are demodulated in sequence to complete data transmission.

[0147] In the step 3, it specifically includes:

[0148] Upper bound P of the bit error rate of system user k bk as follows:

[0149]

[0150] Among them, P e (m) can be expressed as an upper bound using PEP:

[0151]

[0152] in It refers to the average PEP when all index information detect errors, which is consistent for each user. When sending M-QAM modulated signals, consider And E[|x| 2 ]=E s , the calculation is as follows:

[0153]

[0154] in The index information is detected as m or When the total user channel is in All obey Gaussian distribution, then B1 and Analyze the statistical characteristics of .

[0155] From the above model, we can see that the channel correlation matrix is obtained by observation, and when generating the channel, it is multiplied by the channel that obeys the Rayleigh distribution, so we have and According to the central limit theorem, B and All obey the Gaussian distribution, so we have for Also need to consider and The same is the uniform distribution of (0,2π), so we have and Considering the symmetry of the sine and cosine functions, we finally have

[0156] Then let Q1 = x1 T Ax1, where x1 = [X1, X2, X3, X4] and A = diag{1, 1, -1, -1}. Then the mean V1 and covariance matrix C1 of x1 are:

[0157] V1=

[0000] T

[0158] Indicates the correlation coefficient between X5 and X6. Combining the above formula, we can get the moment generating function Ψ of Q1 Q (w), and then find

[0159]

[0160] For the left side of the right side of the equal sign, we mainly consider P sk , that is, the average symbol error probability under the condition of correct index information detection, the corresponding moment generating function is:

[0161]

[0162] where α k E s / N0 represents the signal-to-noise ratio (SNR) for each user. When using M-QAM modulated signals under known CDI conditions, the bit error rates for each user are as follows:

[0163]

[0164] Where det(·) means finding the determinant of the matrix in the brackets; Indicates dimension N t ×K identity matrix; g QAM =3 / 2(M-1) is defined as the signal correlation constant when using M-QAM modulation. k E s / N0 replaces E in the above process s / N0, we can get the upper bound of the theoretical bit error rate of users in the RIS-IM-NOMA-CDI system.

[0165] In said step 4, it specifically includes:

[0166] Assume that the total spectrum efficiency of RIS-IM-NOMA-CDI is SE NC The signal-to-interference-plus-noise ratio (SINR) at the user decoding time is obtained from the demodulation process, and the spectrum efficiency is calculated using the following formula:

[0167]

[0168] where β k represents the total channel coefficient from the RIS-IM-NOMA system base station to the kth user, SE NCk represents the spectral efficiency of the kth user in the RIS-IM-NOMA system. Simultaneously, differences in power allocation coefficients can lead to spectral efficiency fairness issues among users: users with smaller power coefficients experience lower spectral efficiency. Next, we combine the combined outage probability constraint to design an appropriate power allocation scheme to ensure system fairness.

[0169] In said step 5, it specifically includes:

[0170] When only CDI is known, interruption probability limits must be considered. Interruption probability is derived from interruption capacity, a concept that corresponds to Shannon capacity. Intuitively, Shannon capacity guarantees the fastest error-free transmission rate under a certain capacity, while interruption capacity refers to allowing a certain percentage of bit errors in exchange for a higher rate, even if this reduces capacity. In actual communication systems, interruption capacity is important because some services require faster rates but do not require guaranteed capacity. Accordingly, some bit errors at the receiver do not affect service needs. For example, in live sports broadcasts, in order to obtain real-time game progress, clarity can be sacrificed, or even only voice signals can be received, in exchange for the real-time availability of key information such as the image or "game status."

[0171] Whether error-free reception can be achieved depends on the signal-to-noise ratio at that time, and we define γ min Indicates the minimum receive signal-to-noise ratio without error. If the receive signal-to-noise ratio is greater than γ min There will be no bit error if it is less than γ min Correct decoding cannot be guaranteed, which is called an interruption. The corresponding interruption probability is:

[0172] P out =P(γ<γ min )

[0173] When the transmitter sends data at the maximum rate corresponding to the signal-to-noise ratio, there is Pout The possibility of bit error occurs, in other words, if γ min If the value is extremely small, the outage capacity approaches the Shannon capacity. In the above scenario, the power allocation optimization problem is redefined as follows:

[0174]

[0175] α1>α2>…>α K

[0176] SINR k Denotes the received SINR of the kth user. Then, the optimization problem is re-described as follows using SINR:

[0177]

[0178] α1>α2>…>α K

[0179] where β k represents the total channel coefficient for the received signal of user k; r min That is, the predefined minimum γ min The spectrum efficiency requirement can be determined in combination with the corresponding business requirements; k is any real number greater than 0 to ensure the limit on the outage probability.

[0180] Then the outage probability is transformed to simplify its expression as follows:

[0181]

[0182] The left side of the equation is defined as:

[0183]

[0184] Then order:

[0185]

[0186] where a i =α i 、b i =E s 、Z i =|β i | 2 It can be seen that Z i The independent entities are identically distributed in a chi-square distribution with 2 degrees of freedom. So we can let X = Z1, τ i =(a i b i ) / (a1b1), we get:

[0187]

[0188] Since the chi-square distribution with 2 degrees of freedom is an exponential distribution with parameter 1 / 2, we have:

[0189]

[0190] According to the definition of moment generating function, the integral term is the moment generating function of Y, denoted as ψ Y (t), due to It is formed by adding the elements of the chi-square distribution with 2 degrees of freedom, so:

[0191]

[0192] And because Z i It obeys the chi-square distribution with 2 degrees of freedom, and its moment generating function is:

[0193]

[0194] So we have:

[0195]

[0196] The outage probability is finally written as follows:

[0197]

[0198] Then, we use the complement of the interruption probability to redefine the constraint conditions as follows:

[0199]

[0200] in B=N0 / E s C=1 / (1-ε k ). Note that there are complex multiplication forms and exponential functions on both sides of the inequality. To facilitate derivation, we use the logarithmic function without changing the monotonicity to obtain:

[0201]

[0202] Furthermore, in order to use the Lagrange multiplier method to solve the extreme value of a multivariate function under conditional constraints, it can be written as follows:

[0203]

[0204] Where θ is any real number, which ensures that the left side of the equality is divided by θ. 2 The sum of the remaining terms is strictly less than or equal to 0. The original problem is finally described as follows:

[0205]

[0206] α1>α2>…>α K

[0207] Then build the auxiliary function as follows:

[0208]

[0209] z1(α1,α2,…,α K )=1-α1-α2-…-α K

[0210]

[0211] Then set the Lagrangian factor μ and construct the following system of equations:

[0212]

[0213] The solution can be obtained as follows (K+2) expressions:

[0214]

[0215] Let α1,α2,…,α K Substitute z1(α1,α2,…,α K )=0 and z2(α1,α2,…,α K )=0, we can solve for μ1 and μ2. Then we can solve for μ1,μ2,α1,α2,…,α K-1 Substitute α in sequence K =g K (μ1,μ2,α1,…,α K-1 ) can be solved to get α K By analogy, the optimal power allocation coefficients for the problem of maximizing spectrum efficiency fairness with consideration of outage probability constraints can be obtained one by one.

[0216] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A RIS-IM-NOMA system design method based on channel distribution information, characterized by: The method comprises the following steps: S1: Establish a channel model using the channel correlation matrix, specifically including: Assume that the correlation Rayleigh fading model is adopted, and the channel Z obeys a zero-mean circularly symmetric complex Gaussian distribution. The channel correlation matrix is defined as: R=E[more(Z)more H (W)] Where vec(·) means stacking the columns of the matrix in the brackets into a long column vector; vec H (·) represents the conjugate transpose of the vector in the brackets. Since the base station has a large enough space, it is assumed that the transmitting antennas are uncorrelated and only the receiving antennas are correlated. The total correlation matrix is expressed as follows: where R (m) Refers to the receiving correlation matrix observed by antenna numbered m; 0 K×K Represents a matrix of all zeros with K rows and K columns; in actual scenarios, the observed R (m) Multiply by the mth column Σ of a matrix Σ with the same dimensions as Z and a standard complex Gaussian distribution m to replace Z, eliminating the need for real-time CSI feedback on Z, R (m) ×Σ m The expanded form is as follows: in represents the modulus and phase of the corresponding element in the channel matrix generated by the receive correlation matrix observed by antenna numbered m; S2: Establish the RIS-IM-NOMA-CDI system model and define the reflection coefficient matrix and detection method, including: Total transmitted data includes (log2N t +Klog2M) bits of information, the first part log2N t bits convey the transmit antenna index information and enable the RIS controller to adjust the reflection parameters accordingly; the second part Klog2Mbits conveys the user data information, which is multiplied by the respective power allocation coefficients and mapped to the constellation diagram for transmission; using the above correlation channel matrix, the channel estimation overhead of knowing the perfect CSI is avoided, and the total received signal expression is as follows Y=R (m) Σ m DX+ω That is, the data received by the kth user from the antenna numbered m is expressed as: Each RIS sub-surface improves signal quality and implicitly transmits transmit antenna index information by appropriately and independently adjusting its phase shift matrix. Assuming that each reflective element reaches its maximum reflection coefficient, and since the modulus and phase of each element of the correlation channel matrix in the above formula are obtained by observation, and setting all RIS reflection amplitudes to 1, the received signal-to-noise ratio when using the mth transmit antenna is: Where N0 represents the noise energy; when determining the transmit antenna index m and user k, take Maximize the receive signal-to-noise ratio: The receiving end uses the detected transmitting antenna index m and user information x k Demodulate the received signal sequentially, that is, first demodulate the signal estimation value of the user with the worst channel condition Then by In descending order of user power allocation coefficients, the signal with the largest power allocation coefficient is demodulated from the original received signals of each user and removed one by one until all user signals are demodulated; Transmit antenna index information The test is performed as follows: Determine the transmit antenna index information After that, send symbol x k The test is performed as follows: Then select the transmitting antenna m that maximizes the received signal-to-noise ratio, that is, the transmitting antenna index information, and then demodulate the u1 signal estimation value Then by Demodulate the remaining signals in sequence to complete data transmission; S3: Derive and analyze the theoretical upper bound of the bit error rate of this system model; S4: Conduct theoretical analysis on the spectrum efficiency performance of the system model, introduce outage probability constraints and propose the issue of spectrum efficiency fairness among users; S5: Optimize the power allocation method to improve system fairness.

2. The RIS-IM-NOMA system design method based on channel distribution information according to claim 1, characterized in that: The S3 specifically includes: Upper bound P of the bit error rate of system user k bk as follows: Among them, P e (m) Using PEP, the upper bound is: in It refers to the average PEP when all index information detect errors, which is consistent for each user; when sending M-QAM modulated signals, And E[|x| 2 ]=E s , the calculation is as follows: in The index information is detected as m or When the total user channel is in All obey Gaussian distribution, then B1 and Analyze the statistical characteristics of The channel correlation matrix is obtained from observations, and when generating the channel, it is multiplied by the channel that obeys the Rayleigh distribution, so and According to the central limit theorem, B and All obey the Gaussian distribution, so we have for Also need to consider and The same is the uniform distribution of (0,2π), so we have and Considering the symmetry of the sine and cosine functions, we finally have Then let Q1 = x1 T Ax1, where x1 = [X1, X2, X3, X4], A = diag{1, 1, -1, -1}; then the mean V1 and covariance matrix C1 of x1 are: V1＝[0 0 0 0] T Represents the correlation coefficient between X5 and X6; Combined with the above formula, we can get the moment generating function Ψ of Q1 Q (w), and then find For the left side of the equation, consider P sk , that is, the average symbol error probability under the condition of correct index information detection, the corresponding moment generating function is: where α k E s / N0 represents the signal-to-noise ratio of each user. When using M-QAM modulation signals under CDI conditions, the bit error rates of each user are as follows: Where det(·) means finding the determinant of the matrix in the brackets; Indicates dimension N t ×K identity matrix; g QAM =3 / 2(M-1) is defined as the signal correlation constant when using M-QAM modulation; using α k E s / N0 replaces E in the above process s / N0, and obtain the upper bound of the theoretical bit error rate of users in the RIS-IM-NOMA-CDI system.

3. The RIS-IM-NOMA system design method based on channel distribution information according to claim 2 is characterized in that: The S4 specifically includes: Assume that the total spectrum efficiency of RIS-IM-NOMA-CDI is SE NC , according to the demodulation process, the signal-to-interference-and-noise ratio (SINR) at the user decoding time is obtained and the spectrum efficiency is calculated using the following formula: where β k represents the total channel coefficient from the RIS-IM-NOMA system base station to the kth user, SE NCk represents the spectrum efficiency of the kth user in the RIS-IM-NOMA system. Meanwhile, the difference in power allocation coefficients will cause the problem of spectrum efficiency fairness among users. The user with smaller power coefficient has lower spectrum efficiency. Next, the appropriate power allocation method is designed in conjunction with the outage probability constraint to ensure system fairness.

4. The RIS-IM-NOMA system design method based on channel distribution information according to claim 3 is characterized by: The S5 specifically includes: Whether error-free reception can be achieved depends on the signal-to-noise ratio at that time, and we define γ min Indicates the minimum receive signal-to-noise ratio without error. If the receive signal-to-noise ratio is greater than γ min There will be no bit error if it is less than γ min Correct decoding cannot be guaranteed, which is called an interruption; the corresponding interruption probability is: P out =P(γ<γ min ) When the transmitter sends data at the maximum rate corresponding to the signal-to-noise ratio, there is P out The possibility of bit error occurs, in other words, if γ min If the value is extremely small, the outage capacity approaches the Shannon capacity. In the above scenario, the power allocation optimization problem is redefined as follows: α1＞α2＞…＞α K SINR k represents the received SINR of the kth user; the optimization problem is then re-described using SINR as follows: α1＞α2＞…＞α K where β k represents the total channel coefficient for the received signal of user k; r min That is, the predefined minimum γ min The spectrum efficiency requirement is determined in combination with the corresponding business requirements; k is any real number greater than 0 to ensure the limit on the interruption probability; Then the outage probability is transformed to simplify its expression as follows: The left side of the above equation is defined as: Then order: where a i =α i 、b i =E s 、Z i =|β i | 2 ; Z i Independent entities are identically distributed in a chi-square distribution with 2 degrees of freedom; let X = Z1, τ i =(a i b i ) / (a1b1), we get: Since the chi-square distribution with 2 degrees of freedom is an exponential distribution with parameter 1 / 2, we have: According to the definition of moment generating function, the integral term is the moment generating function of Y, denoted as ψ Y (t), due to It is formed by adding the elements of the chi-square distribution with 2 degrees of freedom, so: And because Z i It obeys the chi-square distribution with 2 degrees of freedom, and its moment generating function is: So we have: The outage probability is finally written as follows: Then, we use the complement of the interruption probability to redefine the constraint conditions as follows: in B=N0 / E s C=1 / (1-ε k ); Using the logarithmic function without changing the monotonicity, we get: To use the Lagrange multiplier method to solve the extreme value of a multivariate function under conditional constraints, it is written as follows: Where θ is any real number, which ensures that the left side of the equality is divided by θ. 2 The sum of the remaining terms is strictly less than or equal to 0; the original problem is finally described as follows: α1＞α2＞…＞α K Then build the auxiliary function as follows: z1(α1,α2,…,α K )＝1-α1-α2-…-α K Then set the Lagrangian factor μ and construct the following system of equations: The following (K+2) expressions are obtained: Let α1,α2,…,α K Substitute z1(α1,α2,…,α K )=0 and z2(α1,α2,…,α K )=0 to obtain μ1 and μ2; then μ1,μ2,α1,α2,…,α K-1 Substitute α in sequence K =g K (μ1,μ2,α1,…,α K-1 ) Solve for α K ; Obtain the optimal power allocation coefficients one by one under the spectrum efficiency fairness maximization problem considering the outage probability limit.

Images