RIS-enabled optimization method for precoding vectors and reflection coefficients in spatial modulation

Abstract

This invention discloses a method for optimizing precoding vectors and reflection coefficients in RIS-enabled spatial modulation, primarily addressing the high bit error rate problem in existing RIS-enabled SM systems. The solution includes: 1) constructing a framework and channel model for a RIS-enabled transmitter precoding spatial modulation system; 2) after receiving information, the receiver constructs a received power expression for a specified receiving antenna based on the information and maximizes this received power; 3) using an alternating optimization algorithm to obtain the optimal optimization variable corresponding to the target expression; 4) canceling the phase deviation generated by the optimal optimization variable at the receiver to obtain the final received signal vector; 5) employing the MLD algorithm to jointly detect and estimate the receiving antenna index and phase modulation symbol. This invention can significantly improve the detection performance of the system while balancing the spectral efficiency and energy efficiency of the communication system, and can be used in 5G mobile communication RIS-enabled precoding spatial modulation systems.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and further relates to RIS-enabled precoding spatial modulation, specifically a method for optimizing precoding vectors and reflection coefficients in RIS-enabled spatial modulation, which can be used in 5G mobile communication RIS-enabled precoding spatial modulation systems. Background Technology

[0002] Spatial Modulation (SM) is a multiple-input multiple-output (MIMO) transmission technology that combines traditional amplitude-and-phase modulation (APM) with antenna-indexed modulation, simultaneously achieving both spectral efficiency and energy efficiency in communication systems. Precoding techniques, by precoding information bits at the transmitter, significantly reduce the bit error rate (BER) of the communication system. By combining precoding with SM, and given perfect channel state information at the transmitter, precoding-SM (Precoding-SM) can improve the system's BER performance by selecting appropriate receiving antennas.

[0003] Reconfigurable Intelligent Surfaces (RIS) can effectively control the phase, amplitude, frequency, and even polarization of their array elements without complex decoding and encoding operations. Specifically, RIS is equipped with a large number of small, low-cost, controllable passive components that cancel out the phase of the transmitted signal by changing the reflection coefficient of the array elements, thereby significantly improving the communication quality of the wireless link. SM technology can carry additional information bits without consuming additional spectrum and energy; therefore, the combination of RIS and SM technology achieves high spectral efficiency and high energy efficiency.

[0004] In their paper "Large Intelligent Surface Assisted Wireless Communications With Spatial Modulation and Antenna Selection" (IEEE Journal on Selected Areas in Communications, 2020: 2562-2574), Teng M, Xia L, Ping Y, and others only considered a practical structure combining LIS with spatial modulation (LIS-SM). This structure can utilize both transmit and receive antenna indexes simultaneously, thereby achieving higher transmission efficiency. Although SM technology is rapidly developing and modulation frameworks based on RIS and SM have received widespread attention, current research on how to utilize precoding techniques to improve the bit error rate performance of RIS-assisted spatial modulation systems is still insufficient. Current research mainly considers the combination of RIS and SM or precoding and SM, which suffers from a relatively high bit error rate. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by proposing a method for optimizing the precoding vector and reflection coefficient in RIS-enabled spatial modulation. This method maximizes the received signal power of the receiver antenna to find the optimal transmitter precoding vector and the optimal phase design of the RIS. This effectively improves the detection performance of the system while taking into account both the spectral efficiency and energy efficiency of the communication system.

[0006] The basic idea of ​​this invention is as follows: In a system with RIS-enabled transmitter precoding spatial modulation, considering two-hop channels as Rician fading channel and Rayleigh fading channel models respectively, a receiver signal power maximization problem is constructed based on the two-hop channel model, and the optimal transmitter precoding vector and RIS optimal phase design are obtained by using an alternating optimization algorithm. Finally, the proposed optimization algorithm is simulated and analyzed using the Maximum Likelihood Detection (MLD) algorithm, and the feasibility of this invention is verified by comparing it with other methods.

[0007] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0008] (1) By configuring N T Transmitter with one transmitting antenna, N R The receiver with the root receiving antenna and N S A model of a RIS-enabled spatial modulation system is constructed using a reconfigurable smart surface (RIS) with N reflective array elements. T N R and N SThe number of all elements satisfies the condition that they are non-negative integer powers of 2, and N T ≥N R The distance between the horizontal and vertical array elements in the RIS is not less than half the signal wavelength; the transmitter controls the RIS through a controller;

[0009] (2) Based on the RIS-enabled space modulation system model, the received signal y of the r-th receiving antenna of the receiver is obtained. r :

[0010]

[0011] Where P represents the transmission power; Let represent the conjugate transpose of the channel vector from RIS to the r-th receiving antenna of the receiver; Let θ represent the reflection coefficient matrix of RIS, where θ l The phase shift introduced for the l-th RIS reflector element that takes continuous values ​​in the interval (0, 2π); This represents the channel matrix from the transmitter to the RIS. Represents the transmitter precoding vector. Represents the field of complex numbers; x m Let x be the m-th symbol in the amplitude-phase modulation symbol set, and x m satisfy m∈{1,2,…,M}, where M is the order of each phase modulation symbol in the symbol set; z r Let represent the Gaussian white noise at the r-th receiving antenna, with a mean of 0 and a variance of 1;

[0012] (3) Obtain the useful signal received power E of the r-th receiving antenna. r :

[0013]

[0014] (4) Maximize the useful signal received power E of the r-th receiving antenna. r The optimal variables for the RIS-enabled spatial modulation system are obtained, as follows:

[0015] (4.1) Construct the expression P1 for maximizing the useful signal received power of the r-th receiving antenna under the RIS-enabled space modulation system model:

[0016]

[0017] The optimization variables are the transmitter precoding vector w and the reflection coefficient matrix Θ of the RIS; the constraint is the conjugate transpose w of the transmitter precoding vector. H The product of the transmitter precoding vector w and the transmitter precoding vector w must be equal to the transmit power P, i.e., w H w = P;

[0018] (4.2) The optimal transmitter precoding vector w is obtained through the alternating optimization algorithm. * and the reflection coefficient matrix Θ of the optimal RIS * :

[0019] (4.2.1) With the transmitter precoding vector w fixed, the reflection coefficient matrix of the RIS is optimized to obtain the optimal reflection coefficient matrix Θ of the RIS. * ;

[0020] (4.2.2) Fix the reflection coefficient matrix Θ of the optimal RIS * The zero-forcing ZF constraint method is used to obtain the optimal transmitter precoding vector w by projecting the signals of all receiving antennas except the r-th receiving antenna onto the null space of the cascaded channel matrix from transmitter to receiver. * ;

[0021] (5) Based on the obtained optimal RIS reflection coefficient matrix Θ * and the optimal transmitter precoding vector w * The optimal received signal vector y at the receiver is obtained:

[0022]

[0023] Among them, H H This represents the conjugate transpose channel matrix from the RIS to the receiver;

[0024] (6) At the receiver, cancellation is performed based on the optimal transmitter precoding vector w. * and the reflection coefficient matrix Θ of the optimal RIS * The resulting phase deviation yields the final received signal vector y at the receiver. π :

[0025]

[0026] Where, Θ r and w r Represents the optimal RIS reflection coefficient matrix and the optimal transmitter precoding vector obtained from the specified r-th receiving antenna; π r Indicated based on Θ r and w r The resulting phase deviation factor;

[0027] (7) The maximum likelihood detection is used to jointly detect and estimate the receiving antenna index number and the phase modulation symbol to obtain the estimated receiving antenna index number. and estimated phase modulation symbols

[0028]

[0029] in,

[0030] The present invention has the following advantages compared with the prior art:

[0031] First, this invention employs the Zero Forcing (ZF) constraint method, which projects the signals from all receiving antennas except for a certain receiving antenna onto the null space of the cascaded channel matrix from the transmitter to the receiver, thereby obtaining a closed-form expression for the transmitter precoding vector. This maximizes the receiver's message reception capability and makes the system's bit error rate performance significantly better than other precoding methods.

[0032] Secondly, this invention combines precoding technology with RIS and SM, sacrificing a small amount of complexity to achieve a significant improvement in the reliability of the system detection results while ensuring the maximum received power at the selected receiving antenna. Attached Figure Description

[0033] Figure 1 This is a schematic diagram illustrating an application scenario of the method of the present invention;

[0034] Figure 2 This is a flowchart illustrating the implementation of the method of the present invention;

[0035] Figure 3 This is a graph showing the relationship between the bit error rate performance and the signal-to-noise ratio of the method of the present invention under different parameters;

[0036] Figure 4 This is a comparison of simulation results showing the impact of different Rician factor parameters on the bit error rate of the present invention;

[0037] Figure 5 The figure shows a comparison of simulation results of different precoding schemes under Rician fading channels and Rayleigh channels, respectively.

[0038] Figure 6 This is a comparison chart of simulation results between the present invention and LIS-SM and traditional uplink SIMO system frameworks;

[0039] Figure 7 This is a comparison chart of the receiver's three-dimensional constellation simulation results when the baseband modulation scheme is 4-QAM, K=1, and SNR=-5dB.

[0040] (a) is a comparison of the three-dimensional constellation simulation results of the received signals of each receiving antenna when the selected receiving antenna of the receiver is designated as the first antenna. (b) and (c) are comparison of the three-dimensional constellation simulation results of the received signals of each receiving antenna when the selected receiving antenna of the receiver is designated as the first antenna, based on the Alternate Null-space Beamforming (ANBE) transmitter preprocessing method and the ZF transmitter preprocessing method, respectively. Detailed Implementation

[0041] The implementation process of the technical solution of the present invention will be described in detail below with reference to the accompanying drawings:

[0042] Reference Figure 2 This invention provides a method for optimizing precoding vectors and reflection coefficients in RIS-enabled spatial modulation, with the specific implementation steps as follows:

[0043] Step 1: Refer to Figure 1 This invention constructs a RIS-enabled spatial modulation system model by configuring N T Transmitter with one transmitting antenna, N R The receiver with the root receiving antenna and N S The system consists of a reconfigurable smart surface RIS composed of N reflective array elements. T N R and N S The number of all elements satisfies the condition that they are non-negative integer powers of 2, and N T ≥N R In the RIS (Radio-Induced Signal Transmission System), the distance between the horizontal and vertical array elements is no less than half the signal wavelength. The transmitter controls the RIS through a controller. The transmitter, acting as the transmitting end, transmits the signal to the receiver at the receiving end through the RIS, thus completing the signal transmission. The channel modeling process in the RIS-enabled spatial modulation system model is as follows:

[0044] Consider the transmitter-to-RIS channel matrix G as Rician fading:

[0045]

[0046] Where K is the Rician factor; G NLOS The channel H from part of the RIS to the receiver is considered a Rayleigh fading channel; G LOS Part of it is a LOS fading channel:

[0047]

[0048] Where β represents the path gain; φ r and φ tLet a and b represent the angle of arrival at the RIS and the angle of departure at the transmitter, respectively; let a and b represent the angle of arrival at the RIS and the turning vector at the transmitter, respectively. N (φ r ) and a Nt (φ t ):

[0049]

[0050]

[0051] Where d is the antenna separation distance; λ is the wavelength, assuming...

[0052] Step 2: Based on the RIS-enabled spatial modulation system model, obtain the received signal y from the r-th receiving antenna of the receiver. r :

[0053]

[0054] Where P represents the transmission power; Let represent the conjugate transpose of the channel vector from RIS to the r-th receiving antenna of the receiver; Let θ represent the reflection coefficient matrix of RIS, where θ l The phase shift introduced for the l-th RIS reflector element that takes continuous values ​​in the interval (0, 2π); This represents the channel matrix from the transmitter to the RIS. Represents the transmitter precoding vector. Represents the field of complex numbers; x m Let x be the m-th symbol in the amplitude-phase modulation symbol set, and x m satisfy m∈{1,2,…,M}, where M is the order of each phase modulation symbol in the symbol set; z r Let represent the Gaussian white noise at the r-th receiving antenna, with a mean of 0 and a variance of 1.

[0055] The received signal y from the r-th receiving antenna of the receiver r Specifically, it is obtained as follows:

[0056] Assuming there is an obstacle between the transmitter and receiver, the channel from the transmitter to the RIS follows Rician fading, and the channel from the RIS to the receiver follows Rayleigh fading. The received signal vector y at the receiver is represented as follows:

[0057]

[0058] Among them, H HThe conjugate transpose of the channel matrix from RIS to the receiver is represented by the conjugate transpose of the channel vector from RIS to the r-th receiving antenna of the receiver. Replace H in the above formula H The received signal y from the r-th receiving antenna of the receiver is obtained. r .

[0059] Step 3: Obtain the useful signal received power E of the r-th receiving antenna. r :

[0060]

[0061] Step 4: Maximize the useful signal received power E of the r-th receiving antenna. r The optimal variables for the RIS-enabled spatial modulation system are obtained, as follows:

[0062] (4.1) Construct the expression P1 for maximizing the useful signal received power of the r-th receiving antenna under the RIS-enabled space modulation system model:

[0063]

[0064] The optimization variables are the transmitter precoding vector w and the reflection coefficient matrix Θ of the RIS; the constraint is the conjugate transpose w of the transmitter precoding vector. H The product of the transmitter precoding vector w and the transmitter precoding vector w must be equal to the transmit power P, i.e., w H w = P;

[0065] (4.2) Due to the strong coupling between variables w and Θ in the objective function, the objective function is a non-convex expression. To solve this expression, a two-step alternating optimization algorithm is proposed: First, fix the transmitter precoding vector w and optimize the reflection coefficient matrix Θ of the RIS to obtain its optimal value; Second, optimize the transmitter precoding vector w based on the optimal value of the RIS reflection coefficient matrix Θ obtained in the first step.

[0066] Here, the optimal transmitter precoding vector w is obtained through an alternating optimization algorithm. * and the reflection coefficient matrix Θ of the optimal RIS * It includes the following steps:

[0067] (4.2.1) With the transmitter precoding vector w fixed, the reflection coefficient matrix of the RIS is optimized to obtain the optimal reflection coefficient matrix Θ of the RIS. * The implementation is as follows:

[0068] From the channel model from the transmitter to the RIS, it can be seen that the visible link portion has a greater impact on the channel G than the non-visual link portion. When K >> 0, the channel G is approximated as the visible link portion. Based on this fact, it is assumed that the channel between the transmitter and the RIS is mainly LOS (Line of No Optical). In practice, given the location of the transmitter, the RIS is installed within the transmitter's line of sight. Since the power of the NLOS path is negligible compared to the power of the LOS path, the channel G from the transmitter to the RIS is converted into an equivalent channel G′:

[0069]

[0070] Where α is the path gain factor; and These represent the normalized array response vectors associated with the RIS and the transmitter, respectively; and

[0071] Based on the equivalent channel G′, the expression for maximizing the useful signal received power of the r-th receiving antenna is transformed as follows:

[0072]

[0073] Where μ=υ T w For Hadamah accumulation;

[0074] Rewrite the expression P1 in step (4.1) as follows:

[0075]

[0076] in, Constraints on the reflection coefficient matrix of RIS;

[0077] The phase shift introduced by the l-th RIS reflector element satisfies When the objective function reaches its maximum value ||Ω||1, the reflection coefficient matrix Θ of the optimal RIS is obtained. * :

[0078]

[0079] Among them, Ω l Let be the l-th component of Ω; arg(x) is the phase angle for calculating the complex scalar x;

[0080] (4.2.2) Fix the reflection coefficient matrix Θ of the optimal RIS * The zero-forcing ZF constraint method is used to obtain the optimal transmitter precoding vector w by projecting the signals of all receiving antennas except the r-th receiving antenna onto the null space of the cascaded channel matrix from transmitter to receiver. * .

[0081] The zero-forcing ZF constraint method maximizes the receiver's message reception capability by projecting the signals from all receiving antennas except the r-th receiving antenna onto the null space of the cascaded channel matrix from transmitter to receiver. Introducing the zero-forcing constraint into the objective function yields the following expression:

[0082]

[0083] In the formula, w H w = P; This means that the useful received power on all receiving antennas except the r-th receiving antenna is 0. Let RIS represent the channel matrix from the r-th receiving antenna to the remaining receiving antennas; the constraints are simplified as follows: Define Perform singular value decomposition on it:

[0084] F = [U S U ⊥ ][Λ 0] H V,

[0085] Among them, U ⊥ To cross the null space of the column space of matrix F, a new precoding vector w′ is introduced, let w = U ⊥ w′, and satisfying condition w H F = 0 1×(Nr-1) ;

[0086] Substituting the new precoded vector w′ into the objective function and constraints yields an unconstrained optimization form:

[0087]

[0088] Using the generalized Rayleigh-Ritz theorem, the new precoding vector w i ' is equal to the eigenvector corresponding to the largest eigenvalue of matrix Π, i.e., w' = η(Π), where If η(·) is the eigenvector corresponding to the largest eigenvalue of the matrix, then the optimal value of w is U. ⊥ η(Π).

[0089] Step 5: Based on the obtained optimal RIS reflection coefficient matrix Θ * and the optimal transmitter precoding vector w * The optimal received signal vector y at the receiver is obtained:

[0090]

[0091] Among them, H H This represents the conjugate transpose channel matrix from the RIS to the receiver;

[0092] Step 6: Based on the obtained optimal transmitter precoding vector w * and the reflection coefficient matrix Θ of the optimal RIS * This will produce a certain phase deviation. When the transmitter knows all the channel state information, the phase deviation is also known to the transmitter. Therefore, the receiver needs to consider canceling the phase deviation. This is achieved by canceling the phase deviation based on the optimal transmitter precoding vector w using the following formula. * and the reflection coefficient matrix Θ of the optimal RIS * A phase offset is generated, resulting in the final received signal vector y at the receiver. π :

[0093]

[0094] Where, Θ r and w r Represents the optimal RIS reflection coefficient matrix and the optimal transmitter precoding vector obtained from the specified r-th receiving antenna; π r Indicated based on Θ r and w r The resulting phase deviation factor;

[0095] Step 7: Perform joint detection and estimation of the receiving antenna index number and phase modulation symbol using maximum likelihood detection to obtain the estimated receiving antenna index number. and estimated phase modulation symbols

[0096]

[0097] in,

[0098] Example 2: Refer to Appendix Figure 3-7 The overall implementation steps of this embodiment are the same as those of Embodiment 1. The effectiveness of the method of the present invention will now be further described:

[0099] Reference Figure 3 It describes the system parameter configuration as K=1, N T ∈{2,4}、N R ∈{2,4}、N S The bit error rate performance comparison of the method of the present invention using the MLD algorithm when M ∈ {32, 64} and M ∈ {2, 4}. It can be observed from the figure that when the system parameter is N... T =4, N R =2, N SThe optimal bit error rate (BER) performance is achieved when M=64 and M=4. The receiver's BER performance improves with increasing SNR. Furthermore, the system performance of the proposed scheme is further enhanced with increasing RIS array elements. This is because more RIS array elements improve the signal-to-noise ratio (SNR) of the received signal. It can also be seen from the figure that the BER performance of the system under the MLD algorithm deteriorates with increasing number of receiving antennas. When the number of receiving antennas increases from 2 to 4, the system performance with 4 receiving antennas requires at least 17 dB of additional SNR to achieve the same 10 dB as with 2 receiving antennas. -3 The bit error rate is high. The reason is that adding a receiving antenna increases the spatial multiplexing gain at the cost of reduced transmission reliability.

[0100] Reference Figure 4 It describes the system parameter configuration as N T =2, N R =2, N S The impact of different Rician factors on the system bit error rate when K=64 and M=4. It can be seen that the larger the K value, the worse the system's bit error rate performance. When the K value increases from 1 to 10, the bit error rate is 10. -3 At that time, the system experiences a 6dB performance loss.

[0101] Reference Figure 5 It describes the system parameter configuration as N T =2, N R =2, N S The graph shows the comparison results of precoding schemes under different channel settings: M=64, M=4, K=1. It can be seen that the bit error rate performance of this invention is generally better than that of the Rayleigh channel when considering the Rician channel; furthermore, under the Rician channel, the transmitter precoding scheme optimized in this invention is superior to the ANBE and ZF schemes. This is because, in this invention, the signals from all receiving antennas except the selected antenna are projected onto the null space of the cascaded channel matrix from transmitter to receiver, maximizing the receiver's message reception capability.

[0102] Reference Figure 6 It describes the system parameter configuration as N T ∈{1,4,8}、N R =2, N SThe graph shows a comparison of the results of the RIS-enabled precoding spatial modulation application scenario and the LIS-SM application scenario in this invention when M=64, M=4, and K=1. As can be seen from the graph, the bit error rate performance of the proposed scheme is superior to that in the LIS-SM scenario. This is because, considering the JSM scenario, the simultaneous detection of transmitter and receiver indices reduces the system's detection reliability. Furthermore, the proposed scheme is compared with the traditional uplink SIMO scenario. It can be seen that the proposed scheme achieves better performance in N... T When the signal-to-noise ratio (SNR) is 8, the system exhibits high detection performance. This can be explained by the fact that, when using precoding techniques, the number of transmit antennas increases, and the transmitter and RIS form a sufficient number of multipath links, significantly improving the system's SNR.

[0103] Reference Figure 7 Taking a simulation of 200 points as an example, N T =4, N R =2, N S =64, M=4, K=1, SNR=0dB, and with 4-QAM modulation, the constellation dispersion of the received signal for different receiving antennas is as follows: Figure 7 (a) in the figure is a comparison of the three-dimensional constellation simulation results of the received signals of each receiving antenna when the selected receiving antenna of the receiver is specified as the first antenna; Figure 7 Figures (b) and (c) show a comparison of the 3D constellation simulation results of the received signals from each antenna when the transmitter precoding uses the ANBE and ZF methods, and the receiver's selected receiving antenna is designated as the first antenna. "+" and "□" represent the constellation diagram of the received signal from the first antenna and the constellation diagram of the received signals from the remaining antennas, respectively, when the first antenna is designated as the first antenna. Figure 7 As shown in (a) of the present invention, the received signal from the designated receiving antenna can effectively decode the baseband symbol, forming a regular constellation symbol; while the received signals from the other antennas exhibit a high degree of constellation cohesion, indicating that the signal reception at the designated antenna in this scheme has a certain degree of directionality. In comparison, the constellation... Figure 7 Although the constellation diagram of the received signal at the specified receiving antenna in (c) can form a regular constellation symbol, it has frequency deviation; and the constellation... Figure 7 The constellation diagram of the received signal at the specified receiving antenna in (b) has a serious phase deviation, which causes the constellation diagram to be unable to form a regular constellation symbol, further illustrating the feasibility of this scheme.

[0104] The effects of the present invention will be further illustrated below with simulation experiments:

[0105] A. Simulation conditions

[0106] A computer simulation tool was used to simulate the event, assuming that the transmitter obtained all channel state information. The specific simulation parameters were set as follows:

[0107] Simulation 1: Set N T ∈{2,4}、N R ∈{2,4}、N S ∈{32,64}, M∈{2,4}, K=1

[0108] Simulation 2: Setting N T =2, N R =2, N S =64, M=4, K∈{1,2,5,10}

[0109] Simulation 3: Setting N T =2, N R =2, N S =64, M=4, K=1

[0110] Simulation 4: N T ∈{1,4,8}、N R =2, N S =64, M=4, K=1

[0111] Simulation 5: Setting N T =4, N R =2, N S =64, M=4, K=1, SNR=0dB

[0112] B. Simulation Content

[0113] Simulation 1: The relationship between the bit error rate performance and signal-to-noise ratio of the method of the present invention under different parameters is shown in the following simulation results. Figure 3 As shown;

[0114] Simulation 2: A comparison of simulation results of the bit error rate of the present invention under different Rician factor parameters. The simulation results are as follows: Figure 4 As shown;

[0115] Simulation 3: A comparison of simulation results of different precoding schemes under Rician fading channels and Rayleigh channels, as shown in the figure. Figure 5 As shown;

[0116] Simulation 4: Comparison of simulation results of the present invention under different application scenarios. The simulation results are as follows: Figure 6 As shown;

[0117] Simulation 5: A comparison of receiver 3D constellation simulation results under different precoding methods when the baseband modulation scheme is 4-QAM, K=1, and SNR=-5dB. The simulation results are as follows: Figure 7 As shown;

[0118] C. Simulation Results

[0119] Depend on Figure 3 It is evident that as the number of receiving antennas gradually increases, the system bit error rate performance of the proposed method gradually decreases.

[0120] Depend on Figure 4 It is evident that, while keeping other system parameters constant, the system performance of the proposed method gradually decreases as the Rician factor increases.

[0121] Depend on Figure 5 It is evident that the method proposed in this invention exhibits superior performance under Rician channels, and is better than the ANBE and ZF schemes.

[0122] Depend on Figure 6 It is evident that the application scenarios described in this invention exhibit better detection performance compared to LIS-SM and traditional uplink SIMO scenarios.

[0123] Depend on Figure 7 As can be seen, using the method of the present invention, the received signal of the designated receiving antenna can effectively complete the decoding of the baseband symbol, while the received signal of the undesignated receiving antenna is almost zero, demonstrating the feasibility of the transmitter precoding design proposed in this invention.

[0124] The above simulation analysis proves the correctness and effectiveness of the method proposed in this invention.

[0125] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0126] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art, after understanding the content and principle of the present invention, may make various modifications and changes in form and detail without departing from the principle and structure of the present invention. However, these modifications and changes based on the concept of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing precoding vectors and reflection coefficients in RIS-enabled spatial modulation, characterized in that, Includes the following steps: (1) By configuring N T Transmitter with one transmitting antenna, N R The receiver with the root receiving antenna and N S A model of a RIS-enabled spatial modulation system is constructed using a reconfigurable smart surface (RIS) with N reflective array elements. T N R and N S The number of all elements satisfies the condition that they are non-negative integer powers of 2, and N T ≥N R The distance between the horizontal and vertical array elements in the RIS is not less than half the signal wavelength; the transmitter controls the RIS through a controller; (2) Based on the RIS-enabled space modulation system model, the received signal y of the r-th receiving antenna of the receiver is obtained. r : Where P represents the transmission power; Let represent the conjugate transpose of the channel vector from RIS to the r-th receiving antenna of the receiver; Let θ represent the reflection coefficient matrix of RIS, where θ l The phase shift introduced for the l-th RIS reflector element that takes continuous values ​​in the interval (0, 2π); This represents the channel matrix from the transmitter to the RIS. Represents the transmitter precoding vector. Represents the field of complex numbers; x m Let x be the m-th symbol in the amplitude-phase modulation symbol set, and x m satisfy M is the order of each phase modulation symbol in the symbol set; z r Let represent the Gaussian white noise at the r-th receiving antenna, with a mean of 0 and a variance of 1; (3) Obtain the useful signal received power E of the r-th receiving antenna. r : (4) Maximize the useful signal received power E of the r-th receiving antenna. r The optimal variables for the RIS-enabled spatial modulation system are obtained, as follows: (4.1) Construct the expression P1 for maximizing the useful signal received power of the r-th receiving antenna under the RIS-enabled space modulation system model: The optimization variables are the transmitter precoding vector w and the reflection coefficient matrix Θ of the RIS; the constraint is the conjugate transpose w of the transmitter precoding vector. H The product of the transmitter precoding vector w and the transmitter precoding vector w must be equal to the transmit power P, i.e., w H w = P; (4.2) The optimal transmitter precoding vector w is obtained through the alternating optimization algorithm. * and the reflection coefficient matrix Θ of the optimal RIS * : (4.2.1) With the transmitter precoding vector w fixed, the reflection coefficient matrix of the RIS is optimized to obtain the optimal reflection coefficient matrix Θ of the RIS. * ; (4.2.2) Fix the reflection coefficient matrix Θ of the optimal RIS * The zero-forcing ZF constraint method is used to obtain the optimal transmitter precoding vector w by projecting the signals of all receiving antennas except the r-th receiving antenna onto the null space of the cascaded channel matrix from transmitter to receiver. * ; (5) Based on the obtained optimal RIS reflection coefficient matrix Θ * and the optimal transmitter precoding vector w * The optimal received signal vector y at the receiver is obtained: Among them, H H This represents the conjugate transpose channel matrix from the RIS to the receiver; (6) At the receiver, cancellation is performed based on the optimal transmitter precoding vector w. * and the reflection coefficient matrix Θ of the optimal RIS * The resulting phase deviation yields the final received signal vector y at the receiver. π : Where, Θ r and w r Represents the optimal RIS reflection coefficient matrix and the optimal transmitter precoding vector obtained from the specified r-th receiving antenna; π r Indicated based on Θ r and w r The resulting phase deviation factor; (7) The maximum likelihood detection is used to jointly detect and estimate the receiving antenna index number and the phase modulation symbol to obtain the estimated receiving antenna index number. and estimated phase modulation symbols in, 2. The method according to claim 1, characterized in that: In step (1), the RIS-enabled spatial modulation system model is built. The channel modeling process in the RIS-enabled spatial modulation system model is as follows: The channel matrix G from the transmitter to the RIS exhibits Rician fading. Where K is the Rician factor; G NLOS The channel H from part of the RIS to the receiver is considered a Rayleigh fading channel; G LOS Part of it is a LOS fading channel: Where β represents the path gain; φ r and φ t Let a and b represent the angle of arrival at the RIS and the angle of departure at the transmitter, respectively; let a and b represent the angle of arrival at the RIS and the turning vector at the transmitter, respectively. N (φ r )and Where d is the antenna separation distance; λ is the wavelength, assuming...

3. The method according to claim 1, characterized in that: In step (2), the received signal y of the r-th receiving antenna of the receiver r It is obtained as follows: Assuming there is an obstacle between the transmitter and receiver, the channel from the transmitter to the RIS follows Rician fading, and the channel from the RIS to the receiver follows Rayleigh fading. The received signal vector y at the receiver is represented as follows: Among them, H H The conjugate transpose of the channel matrix from RIS to the receiver is represented by the conjugate transpose of the channel vector from RIS to the r-th receiving antenna of the receiver. Replace H in the above formula H The received signal y from the r-th receiving antenna of the receiver is obtained. r .

4. The method according to claim 1, characterized in that: The reflection coefficient matrix Θ of the optimal RIS in step (4.2.1) * It is obtained as follows: When K >> 0, channel G is approximated as a line-of-sight link; assuming the channel between the transmitter and RIS is primarily LOS, the RIS is installed within the transmitter's line of sight, and the transmitter-to-RIS channel G is converted into an equivalent channel G′: Where α is the path gain factor; and These represent the normalized array response vectors associated with the RIS and the transmitter, respectively; and Based on the equivalent channel G′, the expression for maximizing the useful signal received power of the r-th receiving antenna is transformed as follows: Where μ=υ T w For Hadamah accumulation; Rewrite the expression P1 in step (4.1) as follows: in, Constraints on the reflection coefficient matrix of RIS; The phase shift introduced by the l-th RIS reflector element satisfies When the objective function reaches its maximum value ||Ω||1, the reflection coefficient matrix Θ of the optimal RIS is obtained. * : Among them, Ω l Let be the l-th component of Ω; arg(x) is used to calculate the phase angle of the complex scalar x.

5. The method according to claim 1, characterized in that: The zero-forcing ZF constraint method described in step (4.2.2) maximizes the receiver's message reception capability by projecting the signals from all receiving antennas except the r-th receiving antenna onto the null space of the cascaded channel matrix from transmitter to receiver. Introducing the zero-forcing constraint into the objective function yields the following expression: In the formula, w H w = P; This means that the useful received power on all receiving antennas except the r-th receiving antenna is 0. Let RIS represent the channel matrix from the r-th receiving antenna to the remaining receiving antennas; the constraints are simplified as follows: Define Perform singular value decomposition on it: F=[U S U ⊥ ][Λ 0] H V, Among them, U ⊥ To cross the null space of the column space of matrix F, a new precoding vector w′ is introduced, let w = U ⊥ w′, and satisfying condition w H F = 0 1×(Nr-1) ; Substituting the new precoded vector w′ into the objective function and constraints yields an unconstrained optimization expression: Using the generalized Rayleigh-Ritz theorem, the new precoding vector w′ i The eigenvector corresponding to the largest eigenvalue of matrix Π is equal to w′=η(Π), where, If η(·) is the eigenvector corresponding to the largest eigenvalue of the matrix, then the optimal value of w is U. ⊥ η(Π).

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