A reconfigurable surface-aided index modulation method based on non-orthogonal multiple access

Abstract

The application relates to a reconfigurable surface-assisted index modulation method based on non-orthogonal multiple access, and belongs to the technical field of communication. The method comprises the following steps: S1, establishing an RIS-IM-NOMA system model, and defining a reflection coefficient matrix and a detection mode; S2, deducing and analyzing a theoretical upper limit of the bit error rate of the system model; S3, theoretically analyzing the performance of the spectral efficiency of the system model and putting forward a user-to-user spectral efficiency fairness problem; and S4, optimizing and designing a power distribution mode to improve system fairness.

Description

Technical Field

[0001] This invention belongs to the field of communication technology and relates to a reconfigurable surface-assisted index modulation method based on non-orthogonal multiple access. Background Technology

[0002] Intelligent Reflector (RIS) technology utilizes low-cost passive reflective devices to alter the wireless propagation environment, while Indexed Modulation (IM) technology transmits data by indexing transmitting entities. By using RIS to regulate the wireless environment, whether RIS is used as a new indexing entity in IM or implicitly transmits index information to other entities, the compatibility of RIS and IM technologies is demonstrated. The RIS-IM technology, combining both, has been the subject of various studies in the literature. In 2020, two schemes were first proposed: RIS-based Spatial Shift Keying (RIS-SSK) and RIS-based Spatial Modulation (RIS-SM). RIS-SSK directly transmits unmodulated subcarriers to select the antenna with the highest signal-to-noise ratio at the receiving time, while RIS-SM simultaneously transmits M-order modulated signals to improve spectral efficiency. Based on this, related literature has studied its performance in various aspects, including spectral efficiency, bit error rate, and detection algorithms. Existing literature has made preliminary explorations of RIS-assisted IM systems from different perspectives, but only considers the direct transmission of M-order modulated signals to a single user, without discussing channel multiplexing in multi-user scenarios. For RIS-IM to be suitable for the vision of the "Internet of Everything," limited bandwidth should serve multiple users. Current 4G mobile communication systems use Orthogonal Frequency Division Multiple Access (OFDMA) technology to achieve multi-user access, dividing channels into time-frequency resource blocks to improve spectrum efficiency. Non-Orthogonal Multiple Access (NOMA) technology, on the other hand, can access more users under the same conditions, achieving more efficient use of time-frequency resources. In a NOMA environment, the RIS-IM system regulates the radio channel to ensure the needs of specific users; by effectively utilizing RIS-IM, user order can be changed according to priority rather than relying on random propagation. However, issues such as the impact of inter-user interference on bit error rate performance and the fairness of spectrum efficiency in multi-user scenarios require further exploration of NOMA-based RIS-IM systems. Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide a reconfigurable surface-assisted index modulation method based on non-orthogonal multiple access. To achieve the above objective, this invention provides the following technical solution:

[0004] A reconfigurable surface-assisted index modulation method based on non-orthogonal multiple access, the method comprising the following steps:

[0005] S1: Establish the RIS-IM-NOMA system model and define the reflection coefficient matrix and detection method;

[0006] S2: The theoretical upper bound of the bit error rate of the system model is derived and analyzed;

[0007] S3: The theoretical analysis of the spectral efficiency performance of the system model is conducted, and the issue of spectral efficiency fairness among users is raised;

[0008] S4: Optimize the power allocation method to improve system fairness.

[0009] Optionally, S1 specifically includes:

[0010] Let the number of BS antennas be N t The number of REs is L, and K single-antenna users are sorted by channel quality, with the worst being u1 and the best being u. k The RIS controller exchanges information with the BS via a feedback link to adjust reflection parameters and transmit transmit antenna index information to achieve index modulation.

[0011] Total transmitted data includes (log2N) t +Klog2M) bits of information, the first part is log2N t The first part, Klog2Mbits, transmits the transmit antenna index information and causes the RIS controller to adjust the reflection parameters accordingly; the second part, Klog2Mbits, transmits user data information, where each user data is multiplied by its respective power allocation coefficient and mapped to the constellation diagram before transmission; the overall received signal expression is as follows:

[0012]

[0013] In the formula, H represents the BS to RIS channel matrix, and D represents the RIS phase shift matrix; x k For the transmission signal after user k data is mapped to the constellation diagram, p k For the corresponding power distribution coefficient, G = {g k}(k=1,2,...,K) is the channel matrix from RIS to user k, and w is the channel noise; the receiver uses greedy detection to obtain the transmit antenna index information, and the received signal-to-noise ratio when using the m-th transmit antenna is:

[0014]

[0015] In the formula E s β and N0 represent the energy of the transmitted signal and noise, respectively. m,l and These represent the magnitude and phase of the channel coefficient when transmitting to the l-th reflection element using the m-th antenna, respectively. The reflection coefficient is set using the following formula:

[0016]

[0017] When the RIS reflection amplitude is 1, the reflection phase satisfies At that time, the maximum received signal-to-noise ratio is obtained as follows:

[0018]

[0019] Next, the transmitting antenna m that maximizes the received signal-to-noise ratio is selected, i.e., the transmitting antenna index information. Then, the estimated value of the u1 signal is demodulated. Then by The remaining signals are demodulated sequentially to complete the data transmission.

[0020] Optionally, S2 specifically includes:

[0021] The upper bound of the bit error rate of the RIS-IM system is approximated as follows:

[0022]

[0023] In the formula P c (m) represents the probability of correct detection of index information, P e (m)=1-P c (m) represents the probability of index information error detection under the same conditions, P s The average symbol error probability of user data when the index information is correctly detected; therefore, the upper bound P of the bit error rate of user k in the RIS-IM-NOMA system. bk as follows:

[0024]

[0025] In the formula P e The upper bound of (m) is represented as:

[0026]

[0027] Average error detection probability when using MQAM modulation in the formula as follows:

[0028]

[0029]

[0030] In the formula Represents the RIS reflection matrix; from equation (8), it is known that to calculate the bit error rate, the characteristic function of Q must first be found. X1 and X2 are correlated. Q is written as a quadratic form to derive its statistic; let Q = x T Given Ax, x = X1, X2, X3, X4, and A = diag{1, 1, -1, -1}, then the mean m and covariance matrix C of x are:

[0031]

[0032]

[0033] Combining the above equation, we obtain the characteristic function Ψ of Q. Q (w), and then calculate

[0034]

[0035]

[0036] On the other hand, P s The average sign error probability under the condition that the index information is correctly detected is given by the moment generating function:

[0037]

[0038] Bit error rate P under MQAM s for:

[0039]

[0040] The signal-to-noise ratio p of each user k E s Substituting / N0 into the above process, we obtain the upper bound of the theoretical bit error rate for the RIS-IM-NOMA system.

[0041] Optionally, S3 specifically includes:

[0042] Let the total spectral efficiency of RIS-IM-NOMA be ηN, and the total spectral efficiency of RIS-IM be ηI, then the following formulas apply:

[0043]

[0044]

[0045] In the formula β k η represents the total channel coefficient from BS to user k. k Indicates the user k-spectral efficiency of the RIS-IM-NOMA system; using a proportional fairness approach. Perform power distribution, d i Let denot represent the distance from user i to RIS; assuming two users, d1 = 100m and d2 = 30m, then p1 = 0.9578 and p2 = 0.2873, indicating that the power of user i is much smaller than that of user i; as the signal-to-noise ratio gradually increases, since β1 < β2, and user i considers user i as noise during demodulation, while user i only needs to consider channel noise, η2 and its increase both rise compared to η1; the smaller the power coefficient of a user, the lower the spectral efficiency obtained.

[0046] Optionally, S4 specifically includes:

[0047] To address the issue of fairness in system spectral efficiency, the Jain fairness index is introduced. This index measures system fairness; when the fairness index approaches 1, the system tends towards absolute fairness; when the index approaches 0, the system tends towards complete unfairness. The problem is described as follows:

[0048]

[0049]

[0050] p1>p2>…>p K

[0051] Considering that the objective function has a complex logarithmic form, based on the concept and properties of logarithmic functions, spectral efficiency fairness is equivalent to signal-to-interference-plus-noise ratio fairness. Therefore, the optimization problem is transformed into the following form:

[0052]

[0053]

[0054] p1>p2>…>p K

[0055] Next, construct the helper function as follows:

[0056]

[0057] z(x1,x2,…,x K ) = 1 - x1 - x2 - ... - x K

[0058] Set the Lagrange factor λ and construct the following system of equations:

[0059]

[0060] Solving the above system of (K+1) linear equations yields the following expression:

[0061]

[0062] The obtained x1,x2,…,x K Substituting the expression into z(x1,x2,…,x) in sequence K Solving for λ, we get λ = 0; then we set λ, x1, x2, ..., x... K-1 Substitute x K =f K (λ,x1,x2,…,x K-1 Solving for x, we get x K By analogy, the optimal power allocation coefficient under the problem of maximizing spectral efficiency fairness is obtained one by one; in the case of two users, x2=(1-x1) is directly substituted into the original optimization problem and then solved.

[0063] The beneficial effects of this invention are as follows: A greedy detection method is used at the receiver for signal detection, and a theoretical upper limit for the bit error rate is derived. The system's spectral efficiency is theoretically analyzed, and a power allocation method is proposed to address the issue of spectral efficiency fairness among users. Finally, simulations and comparisons of spectral efficiency and bit error rate performance with a RIS-IM system are conducted to verify the effectiveness of the proposed scheme.

[0064] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0065] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0066] Figure 1 This is a model diagram of the RIS-IM-NOMA system of the present invention;

[0067] Figure 2 This is a comparison chart of the bit error rates of the RIS-IM-NOMA and RIS-IM systems of the present invention;

[0068] Figure 3 This is a comparison chart of bit error rates after changing the number of reflective elements according to the present invention;

[0069] Figure 4 This is a comparison chart of spectral efficiency before and after the improved power allocation method of the present invention. Detailed Implementation

[0070] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed 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 representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0071] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0072] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship 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 orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0073] Please see Figures 1-4 This invention is mainly divided into three parts: the RIS-IM-NOMA system model, the theoretical upper bound derivation of the RIS-IM-NOMA system bit error rate, and the power allocation method for the RIS-IM-NOMA system under the problem of maximizing fairness. Specifically, it includes the following steps:

[0074] 1. A RIS-IM-NOMA system model is proposed, and the setting of the reflection coefficient matrix and the detection method are explained;

[0075] 2. Derive and analyze the theoretical upper limit of the bit error rate of this system;

[0076] 3. Theoretical analysis of the spectral efficiency performance of the system is conducted, and the issue of spectral efficiency fairness among users is raised;

[0077] 4. Improve system fairness by optimizing the power allocation method.

[0078] Furthermore, step 1 specifically includes:

[0079] Considering the blocked line-of-sight (LoS) links between the BS and users in densely built-up urban environments, data transmission can be performed using a Reliable Information System (RIS) deployed near the user side, such as... Figure 1 As shown. Let the number of BS antennas be N. t The number of REs is L, and K single-antenna users are sorted by channel quality, with the worst being u1 and the best being u. k The RIS (Radio Reflector System) exchanges information with the BS (Base Station) via a feedback link to adjust reflection parameters and transmit antenna index information to achieve index modulation.

[0080] Total transmitted data includes (log2N) t +Klog2M) bits of information, the first part is log2N t The first part, Klog2Mbits, transmits the transmit antenna index information and causes the RIS controller to adjust the reflection parameters accordingly. The second part, Klog2Mbits, transmits user data information. Each user's data is multiplied by its respective power allocation coefficient and mapped to a constellation diagram before transmission. The overall received signal expression is as follows:

[0081]

[0082] In the formula, H represents the BS to RIS channel matrix, and D represents the RIS phase shift matrix. k For the transmission signal after user k data is mapped to the constellation diagram, p k For the corresponding power distribution coefficient, G = {g k}(k=1,2,...,K) is the channel matrix from RIS to user k, and w is the channel noise. The receiver uses greedy detection to obtain the transmit antenna index information. When using the m-th transmit antenna, the received signal-to-noise ratio is:

[0083]

[0084] In the formula E s β and N0 represent the energy of the transmitted signal and noise, respectively. m,l and These represent the magnitude and phase of the channel coefficient when transmitting to the l-th reflection element using the m-th antenna, respectively. The reflection coefficient is set using the following formula:

[0085]

[0086] It can be seen that when the RIS reflection amplitude is 1, the reflection phase satisfies At that time, the maximum received signal-to-noise ratio is obtained as follows:

[0087]

[0088] Next, the transmitting antenna m that maximizes the received signal-to-noise ratio is selected, i.e., the transmitting antenna index information. Then, the estimated value of the u1 signal is demodulated. Then by The remaining signals are demodulated sequentially to complete the data transmission.

[0089] Step 2 specifically includes:

[0090] The upper bound of the bit error rate of the RIS-IM system is approximated as follows:

[0091]

[0092] In the formula Pc (m) represents the probability of correct detection of index information, P e (m)=1-P c (m) represents the probability of index information error detection under the same conditions, P s The average symbol error probability of user data when the index information is correctly detected is given. Therefore, the upper bound P of the bit error rate for user k in the RIS-IM-NOMA system is calculated. bk as follows:

[0093]

[0094] In the formula P e The upper bound of (m) is represented as:

[0095]

[0096] Average error detection probability when using MQAM modulation in the formula as follows:

[0097]

[0098]

[0099] In the formula Let represent the RIS reflection matrix. From equation (8), we know that to calculate the bit error rate, we first need to find the characteristic function of Q. Since X1 and X2 are correlated, Q needs to be written as a quadratic form to derive its statistics. Let Q = x T Given Ax, x = X1, X2, X3, X4, and A = diag{1, 1, -1, -1}, then the mean m and covariance matrix C of x are:

[0100]

[0101]

[0102] Combining the above equation, we obtain the characteristic function Ψ of Q. Q (w), and then calculate

[0103]

[0104]

[0105] On the other hand, P s The average sign error probability under the condition that the index information is correctly detected is given by the moment generating function:

[0106]

[0107] At this point, the bit error rate P under MQAM is... s for:

[0108]

[0109] The signal-to-noise ratio p of each user k E s Substituting / N0 into the above process, we can obtain the upper bound of the theoretical bit error rate for users of the RIS-IM-NOMA system.

[0110] Step 3 specifically includes:

[0111] Let the total spectral efficiency of RIS-IM-NOMA be η. N The total spectral efficiency of RIS-IM is η I The following formula exists:

[0112]

[0113]

[0114] In the formula β k η represents the total channel coefficient from BS to user k. k Let represent the spectral efficiency of user k in the RIS-IM-NOMA system. Assuming only path loss is considered, comparing (15) and (16), RIS-IM-NOMA achieves a higher overall spectral efficiency, but the difference in power allocation coefficients can cause fairness issues in spectral efficiency among users. A proportional fairness approach could be used instead. Power allocation is a common power allocation method in NOMA systems. i Let ηi represent the distance from user i to RIS. Assuming two users, d1 = 100m and d2 = 30m, then p1 = 0.9578 and p2 = 0.2873, indicating that user i's power is much lower than user i's. However, as the signal-to-noise ratio gradually increases, since β1 < β2, and user i treats user i as noise during demodulation, while user i only needs to consider channel noise, η2 and its increase are significantly higher than η1.

[0115] The above analysis shows that users with smaller power coefficients receive lower spectral efficiency, and a suitable power allocation method needs to be designed to ensure system fairness.

[0116] Step 4 specifically includes:

[0117] To address the issue of fairness in system spectral efficiency, the Jain fairness index is introduced. This index measures system fairness; a value close to 1 indicates absolute fairness, while a value close to 0 indicates complete unfairness. The problem is described as follows:

[0118]

[0119]

[0120] p1>p2>…>p K

[0121] Considering that the objective function has a complex logarithmic form, based on the concept and properties of logarithmic functions, spectral efficiency fairness is equivalent to signal-to-interference-plus-noise ratio fairness. Therefore, the optimization problem is transformed into the following form:

[0122]

[0123]

[0124] p1>p2>…>p K

[0125] Next, construct the helper function as follows:

[0126]

[0127] z(x1,x2,…,x K ) = 1 - x1 - x2 - ... - x K

[0128] Set the Lagrange factor λ and construct the following system of equations:

[0129]

[0130] Solving the above system of (K+1) linear equations yields the following expression:

[0131]

[0132] The obtained x1,x2,…,x K Substituting the expression into z(x1,x2,…,x) in sequence K Solving for l by finding x1, x2, ..., x... K-1 Substitute x K =f K (l,x1,x2,…,x K-1 x can be solved by ) K By analogy, the optimal power allocation coefficients under the problem of maximizing spectral efficiency fairness can be obtained one by one. In particular, in the case of two users, x2=(1-x1) can be directly substituted into the original optimization problem and solved.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A reconfigurable surface-assisted index modulation method based on non-orthogonal multiple access, characterized in that: The method includes the following steps: S1: Establish a RIS-IM-NOMA system model and define the reflection coefficient matrix and detection method; specifically including: Let the number of BS antennas be The number of REs is , Single-antenna users are ranked by channel quality, with the worst being... It is best to be The RIS controller exchanges information with the BS via a feedback link to adjust reflection parameters and transmit transmit antenna index information to achieve index modulation. Total transmitted data includes Bit information, Part 1 The bits transmit the transmit antenna index information and cause the RIS controller to adjust the reflection parameters accordingly; Part Two Bits transmit user data information. Each user multiplies their own power allocation coefficient and maps it to a constellation diagram before transmission. The overall received signal expression is as follows: In the formula This represents the BS to RIS channel matrix. Represents the RIS phase shift matrix; For users The transmitted signal after the data is mapped onto the constellation diagram, For the corresponding power allocation factor, , k =1,2,..., K For RIS to users The channel matrix, For channel noise; the receiver uses greedy detection to obtain the transmit antenna index information, and uses the first... The received signal-to-noise ratio when using the transmit antenna is: In the formula and These represent the energy of the transmitted signal and the energy of the noise, respectively. and They respectively represent the use of the first The root antenna transmits to the first The channel coefficient magnitude and phase for each reflection unit; the following formula is considered for setting the reflection coefficient: When the RIS reflection amplitude is 1, the reflection phase satisfies At that time, the maximum received signal-to-noise ratio is obtained as follows: Next, select the transmitting antenna that maximizes the received signal-to-noise ratio. That is, to send antenna index information, and then demodulate it. Signal estimation Then by The remaining signals are demodulated sequentially to complete the data transmission. S2: The theoretical upper bound of the bit error rate of the system model is derived and analyzed; S3: The theoretical analysis of the spectral efficiency performance of the system model is conducted, and the issue of spectral efficiency fairness among users is raised; S4: Optimize the power allocation method to improve system fairness.

2. The reconfigurable surface-assisted index modulation method based on non-orthogonal multiple access according to claim 1, characterized in that: S2 specifically includes: The upper bound of the bit error rate of the RIS-IM system is approximated as follows: In the formula To determine the probability of correctly detecting index information. Given the probability of index information error detection under the same conditions, The average symbol error probability of user data when the index information is correctly detected; therefore, the RIS-IM-NOMA system user Upper bound of bit error rate as follows: In the formula The upper bound is represented as: Average error detection probability when using MQAM modulation in the formula as follows: In the formula , This represents the RIS reflection matrix; to calculate the bit error rate, we first need to find... , characteristic function , Having relevance, Write it as a quadratic form to derive its statistic; let , , ,but mean Covariance Matrix for: Combining the above equations, we get characteristic function And then find : on the other hand, The average sign error probability under the condition that the index information is correctly detected is given by the moment generating function: Bit error rate under MQAM for: Signal-to-noise ratio of each user Substituting into the above equation, we obtain the upper bound of the theoretical bit error rate for users of the RIS-IM-NOMA system.

3. The reconfigurable surface-assisted index modulation method based on non-orthogonal multiple access according to claim 2, characterized in that: S3 specifically includes: Let the total spectral efficiency of RIS-IM-NOMA be... The overall spectral efficiency of RIS-IM is The following formula exists: In the formula Indicates BS to user Total channel coefficient, Indicates RIS-IM-NOMA system users Spectral efficiency; using proportional fairness Perform power distribution. Indicates user Distance to RIS; assuming two users m、 m, has User 2's power is much lower than User 1's; as the signal-to-noise ratio gradually increases, due to Furthermore, when demodulating, User 1 treats User 2 as noise, while User 2 only needs to consider channel noise. Compared with its growth rate All increase; users with smaller power coefficients receive lower spectral efficiency.

4. The reconfigurable surface-assisted index modulation method based on non-orthogonal multiple access according to claim 3, characterized in that: S4 specifically includes: To address the issue of fairness in system spectral efficiency, the Jain fairness index is introduced. This index measures system fairness; when the fairness index approaches 1, the system tends towards absolute fairness; when the index approaches 0, the system tends towards complete unfairness. The problem is described as follows: Considering that the objective function has a complex logarithmic form, based on the concept and properties of logarithmic functions, spectral efficiency fairness is equivalent to signal-to-interference-plus-noise ratio fairness. Therefore, the optimization problem is transformed into the following form: Next, construct the helper function as follows: Set the Lagrange factor And construct the following system of equations: Solve the above The system of linear equations in the unknowns can be expressed as follows: The results Substitute the expressions sequentially Solving Next, Substitution Solving By analogy, the optimal power allocation coefficient under the problem of maximizing spectral efficiency fairness is obtained one by one; in the case of two users, the coefficient is directly... Substitute the original optimization problem into the solution.

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