Intelligent reflecting surface assisted spatial modulation system reflection coefficient optimization method

Abstract

The application discloses a kind of intelligent reflecting surface assisted spatial modulation system reflection coefficient optimization method, belong to wireless communication field, the information bits to be sent of sending end is divided into several information blocks with same length, according to each information block selects corresponding active antenna and sends specific signal;Optimize the coefficient of reflecting element on intelligent reflecting surface, maximize the Euclidean distance between different receiving signals;Maximum likelihood detection decoding is used at receiving end, and the original information bits are recovered.The application combines intelligent reflecting surface with spatial modulation scheme, reconstructs wireless channel using intelligent reflecting surface, increases the Euclidean distance between different receiving signals, improves the error performance of system, and can obtain better error performance than existing algorithm under the same condition.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method for optimizing the reflection coefficient of a spatial modulation system assisted by an intelligent reflector. Background Technology

[0002] In future sixth-generation (6G) wireless communication systems, wireless networks will use terahertz (THZ) or even higher frequency bands. Improving the system's spectral efficiency (SE) and energy efficiency (EE) is becoming increasingly important. Index modulation (IM) technology is one of the enabling technologies to meet these requirements of 6G. IM transmits information bits through spatial, frequency, or polarization indices, providing higher spectral and energy efficiency. Spatial modulation, as a technique within IM, has received increasing attention.

[0003] Spatial modulation is a modulation method based on a multi-antenna architecture. In each transmission, only one or a few antennas are activated to transmit signals. The activated antennas are called active antennas, and their indices are used to transmit information bits. Compared to traditional constellation modulation, spatial modulation technology introduces additional information bits to transmit in the spatial domain, greatly improving the system's spectral efficiency. Simultaneously, the number of RF links in a spatial modulation system can be far less than the number of transmit antennas, effectively reducing system hardware costs and power consumption. Furthermore, in a spatial modulation system, only one or a few antennas are activated to transmit signals within a transmission time slot, effectively reducing electromagnetic interference between adjacent antennas and lowering the requirement for strict synchronization of transmitted signals. Driven by design flexibility and the need to achieve higher transmission rates, numerous spatial modulation schemes have emerged. Typical spatial modulation schemes include: Space Modulation (SM), Space Shift Keying (SSK), Quadrature Spatial Modulation (QSM), and Successive Coded-Space Shift Keying (SC-SSK), etc.

[0004] A Reconfigurable Intelligent Surface (RIS) is a metasurface composed of numerous low-cost, low-complexity, and passive reflective elements. The amplitude and phase responses of these elements can be controlled in real-time by an external controller, thereby reconstructing the wireless transmission channel and improving transmission quality. Unlike relay-assisted communication systems, RIS does not require radio frequency (RF) links or power amplifiers to reshape the incident signal and does not amplify environmental noise. Currently, RIS reflection coefficient optimization is a hot research topic in RIS-assisted spatial modulation systems, and many typical algorithms have been proposed, such as the semi-definite relaxation (SDR) algorithm and low-complexity algorithms based on the cosine similarity theorem. In existing algorithms, the reflection coefficients on the RIS are solved with the goal of maximizing the received signal-to-noise ratio (SNR). However, when the system's bit error rate performance is the primary requirement and the receiver employs maximum likelihood detection, the Euclidean distance between different received signals is crucial to the system's bit error rate performance, leaving significant room for improvement in existing algorithms. Based on this, the present invention proposes a method for optimizing the reflection coefficient of a spatial modulation system assisted by an intelligent reflector, with the goal of maximizing the Euclidean distance between different received signals. Summary of the Invention

[0005] This invention provides a method for optimizing the reflection coefficient of a spatial modulation system assisted by an intelligent reflector. By using a RIS-assisted spatial modulation system, the reflection coefficient on the RIS is optimized to maximize the Euclidean distance between different received signals, thereby solving the technical problem of limited system error performance in traditional optimization algorithms.

[0006] A first aspect of the present invention provides a method for optimizing the reflection coefficient of a space modulation system assisted by a smart reflector. The space modulation system includes a transmitter, a smart reflector, and a receiver. The method for optimizing the reflection coefficient includes the following steps:

[0007] The information bits to be transmitted at the transmitting end are divided into multiple information blocks of the same length. Based on the principle of spatial modulation, an active antenna is selected for each information block to transmit modulation symbols. The information bits are transmitted through the active antenna index and modulation symbols to perform spatial modulation at the transmitting end.

[0008] The optimal target receiving signal is designed to maximize the Euclidean distance between the target receiving signals. The optimization objective is to minimize the Euclidean distance between the actual received signal and the target received signal. All reflection coefficients of the intelligent reflector are optimization variables. An optimization problem is established. By solving the optimization problem, the optimal reflection coefficient of the intelligent reflector is obtained. Based on the optimal reflection coefficient, the phase of the incident signal is changed by the intelligent reflector, and the incident signal is reflected to the receiving end.

[0009] Based on the received signal from the receiving end, the maximum likelihood detection algorithm is used, and the decoding is performed based on the spatial modulation scheme of the transmitting end to obtain the information bits to be transmitted.

[0010] Optionally, in one embodiment of the present invention, designing the target received signal includes:

[0011] The average power of the received signal obtained by the optimization algorithm based on the cosine similarity theorem is used as the average power of the target received signal. The normalized distribution form of the target received signal is designed with the criterion of maximizing the Euclidean distance between different received signals, and the target received signal is obtained.

[0012] Optionally, in one embodiment of the present invention, the optimization objective is to minimize the Euclidean distance between the actual received signal and the target received signal, and all reflection coefficients of the intelligent reflective surface are optimization variables. The optimization problem includes:

[0013] The i-th actually received signal is:

[0014] y i =G·Θ i ·H·x i

[0015] in, These are the channel matrices from the transmitter to the smart reflector and from the smart reflector to the receiver, respectively, N. t N represents the number of antennas equipped at the transmitting end. r The number of antennas equipped at the receiver, K is the number of reflective elements of the smart reflector, and Θ is the number of antennas equipped at the receiver. i =diag(θ) i ) corresponds to x i The reflection matrix of the intelligent reflective surface, yes The j-th element is the coefficient of the j-th reflective element on the intelligent reflective surface, and has... x i The i-th transmitted signal carries the bit information from the i-th information block;

[0016] With the objective of minimizing the Euclidean distance between the i-th actual received signal and the i-th target received signal, and with all reflection coefficients on the intelligent reflector surface as optimization variables, the optimization problem is as follows:

[0017]

[0018] in,(·) H To perform the conjugate transpose of the matrix, 1 represents a vector of all 1s with dimension K×1.

[0019] Optionally, in one embodiment of the present invention, the method for solving the optimization problem is to solve it using the primal-dual interior point method.

[0020] Optionally, in one embodiment of the present invention, the information bits to be transmitted are obtained by employing a maximum likelihood detection algorithm and decoding based on the spatial modulation scheme of the transmitting end, according to the received signal of the receiving end, including:

[0021] The received signal containing the noisy signal received by the receiving end is:

[0022]

[0023] in, denoted as the received signal containing noisy signal received by the receiver, x is the transmitted signal from the transmitter, and n is additive white Gaussian noise.

[0024] The maximum likelihood detection algorithm is:

[0025]

[0026] Where ||·||2 represents the 2-norm, It is x i Estimation under maximum likelihood detection.

[0027] The intelligent reflector-assisted spatial modulation system reflection coefficient optimization method of this invention divides the information bits to be transmitted at the transmitting end into several information blocks of equal length, selects a corresponding active antenna to transmit a specific signal according to each information block, optimizes the coefficients of the reflection elements on the intelligent reflector to maximize the Euclidean distance between different received signals, and uses maximum likelihood detection decoding at the receiving end to recover the original information bits. By combining the intelligent reflector with the spatial modulation scheme, the wireless channel is reconstructed using the intelligent reflector, increasing the Euclidean distance between different received signals and improving the system's bit error rate performance.

[0028] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0029] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0030] Figure 1 A flowchart illustrating a method for optimizing the reflection coefficient of a space modulation system assisted by an intelligent reflector, according to an embodiment of the present invention;

[0031] Figure 2 This is a schematic diagram of the reflection coefficient optimization structure of a space modulation system assisted by an intelligent reflector according to an embodiment of the present invention;

[0032] Figure 3 This is a schematic block diagram according to Embodiment 1 of the present invention;

[0033] Figure 4 This is a schematic block diagram according to Embodiment 2 of the present invention;

[0034] Figure 5 In accordance with Embodiment 1 of the present invention, N t =5,N r Simulation graph of bit error rate for cases where K=1, K=16, 32, R=4;

[0035] Figure 6 In embodiment 2 of the present invention, N t =5,N r Simulation diagram of bit error rate for cases where K = 2, K = 16, 32, and R = 4. Detailed Implementation

[0036] Embodiments of the present invention are described in detail below. Examples of these embodiments are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0037] Figure 1 This is a flowchart illustrating a method for optimizing the reflection coefficient of a spatial modulation system assisted by an intelligent reflector, according to an embodiment of the present invention.

[0038] The spatial modulation system includes a transmitter, a Reflection Array (RIS), and a receiver. The reflection coefficient optimization method includes the spatial modulation process at the transmitter, the target received signal design process, the reflection coefficient calculation process on the RIS, and the detection and decoding process at the receiver. Without loss of generality, it is assumed that the direct path between the transmitter and receiver is blocked, and the RIS can obtain ideal channel state information.

[0039] Based on the advantages of RIS, this invention combines RIS with spatial modulation technology, and improves the bit error rate performance of spatial modulation system by optimizing the coefficients of the reflection elements on RIS and reconstructing the wireless transmission channel.

[0040] like Figure 1 As shown, the method for optimizing the reflection coefficient of the intelligent reflector-assisted spatial modulation system includes the following steps:

[0041] In step S101, the information bits to be transmitted at the transmitting end are divided into multiple information blocks of the same length. The information blocks are loaded onto the transmitting end for transmission. Based on the principle of spatial modulation, an active antenna is selected for each information block to transmit modulation symbols. The information bits are transmitted through the active antenna index and modulation symbols to perform spatial modulation at the transmitting end.

[0042] like Figure 2 As shown, the sending end is equipped with N t One antenna, the receiver is equipped with N r There is a root antenna, and the RIS has K reflective elements. Let represent the channel matrices from the transmitter to the RIS and from the RIS to the receiver, respectively, where each element follows a complex Gaussian distribution with mean 0 and variance 1; the reflection matrix corresponding to the RIS is Θ = diag(θ), where θ j Let be the j-th element in θ, representing the coefficient of the j-th reflection element on RIS, and let |θ j |=1.

[0043] Transmit signal vector It can be represented as:

[0044]

[0045] in, Indicates the index of the active antenna at the transmitting end. Indicates the sender n t Signals transmitted from each of the active antennas.

[0046] In step S102, an optimal target received signal is designed to maximize the Euclidean distance between the target received signals. The optimization objective is to minimize the Euclidean distance between the actual received signal and the target received signal. All reflection coefficients of the intelligent reflector are optimization variables. An optimization problem is established. By solving the optimization problem, the optimal reflection coefficient of the intelligent reflector is obtained. Based on the optimal reflection coefficient, the phase of the incident signal is changed using the intelligent reflector, and the incident signal is reflected to the receiving end.

[0047] Optionally, in one embodiment of the present invention, designing the target received signal includes the following two steps: determining the average power of the target received signal and designing the normalized distribution form of the target received signal. Specifically, the average power of the received signal obtained by the optimization algorithm based on the cosine similarity theorem is used as the average power of the target received signal; the normalized distribution form of the target received signal is designed based on maximizing the Euclidean distance between different received signals; and finally, the target received signal is obtained.

[0048] The reflection coefficient on the RIS is optimized with the goal of maximizing the Euclidean distance between different received signals in order to obtain better bit error rate performance.

[0049] First, the average power of the received signal obtained by the optimization algorithm based on the cosine similarity theorem is used as the target average power of the received signal.

[0050] The cosine similarity theorem-based optimization algorithm optimizes the reflection coefficients on the RIS (Receiving Signal-to-Noise Ratio) with the goal of maximizing the received signal-to-noise ratio. Phase cancellation is a special case of this algorithm. When only one antenna is activated at the transmitter and receiver respectively, each reflection element on the RIS can cancel out the phase of the channel coefficients on both sides of that element, thus ensuring that all reflected signals received by the receiver are in phase, achieving the goal of maximizing the received signal-to-noise ratio. With unchanged parameter configuration, phase cancellation can reach the theoretical upper limit of the received power, which can be used as the average power of the target received signal.

[0051] Assume the m-th antenna at the transmitting end is selected as the active antenna, transmitting signal s, where E(s) H ·s)=1. Let α represent the channel coefficients from the m-th antenna at the transmitter to the k-th reflection element on the RIS, and from the k-th reflection element on the RIS to the n-th antenna at the receiver, respectively. Both coefficients follow a complex Gaussian distribution with mean 0 and variance 1. Therefore, α mk and β kn They are independent random variables, and all of them follow a mean of . variance is Rayleigh distribution.

[0052] The signal received by the nth antenna at the receiving end is:

[0053]

[0054] Among them, y (n) This represents the nth element in y.

[0055] According to the phase cancellation method, let The above formula can be rewritten as:

[0056]

[0057] The average power of the signal received on the nth antenna can be expressed as:

[0058]

[0059] When k1 = k2

[0060]

[0061] When k1≠k2

[0062]

[0063] The average power of the signal received on the nth antenna can be rewritten as:

[0064]

[0065] The receiver has N r With one antenna, the average received power is:

[0066]

[0067] Therefore, P y It can be used as the average power of the target received signal.

[0068] Secondly, the distribution of the target received signal is designed based on the criterion of maximizing the minimum Euclidean distance between different received signals.

[0069] Under the constraint of normalizing the average power of the received signal, design the distribution of the target received signal to maximize the minimum Euclidean distance between different received signals.

[0070] 1) When N r When = 1,

[0071] The received signal is a complex number, which can be viewed as a constellation point in a constellation diagram. In this case, the QAM scheme can be directly used as the design method for the target received signal.

[0072] For example, when N r When M=1 and the system transmission rate is Rbits / transmission, M=2 can be performed. R The average power of the M constellation points generated by the first-order QAM modulation is normalized and can then be used as the normalized target received signal.

[0073] 2) When N r ≥2

[0074] The received signal is N r Given a complex vector of size × 1, where each component is a complex number consisting of a real part and an imaginary part, then this complex vector contains a total of N components. r Each real part and Nr There is an imaginary part. Therefore, an N r ×1 received signal vector and 2N r This corresponds to a point in 3D space. When the system transmission rate is R bits / transmission, the design M = 2. R N r The ×1 received signal vector can be equivalent to a 2N... r Find M points in a 3D space and maximize the minimum Euclidean distance between these M points.

[0075] When N r When ≥2, 2N r A 3D space is a high-dimensional space. Finding M points in a high-dimensional space and maximizing the minimum Euclidean distance between these M points is a very complex problem. Here, we present a suboptimal method by observing the characteristics of low-dimensional spaces.

[0076] In two-dimensional space, we can find 2 2 Given four points, we want to maximize the Euclidean distance between them. The coordinates of these four points are (1,1), (1,-1), (-1,1), and (-1,-1). They are the four vertices of a unit square centered at the origin.

[0077] In three-dimensional space, 2 can be found 3 Given 8 points, and maximizing the Euclidean distance between them, we have the following coordinates: (1,1,1), (1,1,-1), (1,-1,1), (1,-1,-1), (-1,1,1), (-1,1,-1), (-1,-1,1), (-1,-1,1), (-1,-1,-1). These are the eight vertices of a unit cube centered at the origin.

[0078] In 2N r In 3D space, one can find Let P points be points, and maximize the Euclidean distance between these points. These P points can be determined by making 2N... r Each dimension in the dimensional space is obtained by traversing the set S = {1, -1}.

[0079] For example, when N r When = 2, the above method can be used to find 2 in four-dimensional space. 4= 16 points, and the Euclidean distance between these 16 points is maximized. The coordinates of these 16 points are: (1,1,1,1),(1,1,1,-1),(1,1,-1,1),(1,1,-1,-1),(1,-1,1,1),(1,-1,1,-1),(1,-1,-1,1),(1,-1,-1,-1),(-1,1,1,1),(-1,1,1,-1),(-1,1,-1,-1),(-1,-1,1,1),(-1,-1,-1,1),(-1,-1,-1,1),(-1,-1,-1,-1).

[0080] In summary, when N r ≥2, when the system transmission rate is R bits / transmission, find M=2. R N r The methods for handling ×1 complex value vectors are summarized as follows:

[0081] 1. When R = 2N r In this case, the method described above can be used directly to find M=2. R We have M complex-valued vectors, and we maximize the Euclidean distance between them. Normalizing the average power of these M complex-valued vectors gives us the normalized target received signal.

[0082] 2. When R > 2N r At that time, we can increase 2N. r The traversal range of each dimension in 3D space, that is, each dimension can carry more than one bit of information, and the number of information bits carried by each dimension should be as equal as possible. Let... V1 = R - 2N r ·U1, of which This indicates the floor function.

[0083] For 2N r The first V1-dimensional space in the V1-dimensional space, where each dimension carries (U1+1) bits of information. Let S1 denote the set traversed in each dimension of the first V1-dimensional space, including... With elements, S1 can be represented as:

[0084]

[0085] For 2N r The remaining (2N) in dimensional space r -V1) dimensional space, where each dimension carries U1 bits of information. Let S2 represent the remaining (2N) dimensional space. r The set traversed in each dimension of the -V1) dimensional space, including With elements, S2 can be represented as:

[0086]

[0087] 3. When R < 2N r At that time, dimensionality reduction operations can be used to transform 2N r The dimensionality reduction space is reduced to R-dimensional space, and then Solution 1 can be used. The strategy for dimensionality reduction is to reduce the 2N-dimensional space to R-dimensional space. r The dimensions are divided into R groups, and each group is considered a generalized dimension, where all dimensions within each group must have consistent values. The grouping strategy is to make the number of dimensions in each group as equal as possible.

[0088] make V2=2N r -R·(U2-1), where This indicates a round-up operation. 2N r The first U²V² dimensions in the dimensional space are divided into V² groups, each containing U² dimensions. Then, the remaining (2N² - U²V²) dimensions are divided into (R - V²) groups, each containing (U² - 1) dimensions, where 2N² - U²V² = (R - V²) * (U² - 1). In this way, 2N... r The dimensional space is reduced to an equivalent R-dimensional space, and Scheme 1 can be directly used to generate a normalized target received signal.

[0089] 4. By combining steps 2 and 3, the target received signal can be obtained.

[0090] When the system's transmission rate is R bits / transmission, M = 2 R Each transmitted signal vector can be represented as x1, x2, ..., x M The received signals from M targets can be represented as:

[0091] The i-th actually received signal is:

[0092] y i =G·Θ i ·H·x i

[0093] in, These are the channel matrices from the transmitter to the smart reflector and from the smart reflector to the receiver, respectively, N. t N represents the number of antennas equipped at the transmitting end. r The number of antennas equipped at the receiver, K is the number of reflective elements of the smart reflector, and Θ is the number of antennas equipped at the receiver. i =diag(θ) i ) corresponds to x i The reflection matrix of the intelligent reflective surface, yes The j-th element is the coefficient of the j-th reflective element on the intelligent reflective surface, and has... x i The i-th transmitted signal carries the bit information from the i-th information block.

[0094] With the objective of minimizing the Euclidean distance between the i-th actual received signal and the i-th target received signal, and with all reflection coefficients on the intelligent reflector surface as optimization variables, the optimization problem is as follows:

[0095]

[0096] in,(·) H This indicates the conjugate transpose of the matrix, and 1 represents a vector of dimension K×1 consisting entirely of 1s.

[0097] As a specific implementation method, the optimization problem is solved using the primal-dual interior-point method.

[0098] Specifically, the above optimization problem is solved using the fmincon function in Matlab, and the solution to the optimization problem is the reflection coefficient of RIS.

[0099] Solving the above optimization problem yields the coefficients of the reflection elements on the RIS. The RIS then changes the phase of the incident signal based on the calculated reflection coefficients and reflects the incident signal back to the receiver.

[0100] In step S103, based on the received signal from the receiving end, the maximum likelihood detection algorithm is used, and decoding is performed based on the spatial modulation scheme of the transmitting end to obtain the information bits to be transmitted.

[0101] The received signal containing the noisy signal at the receiving end is:

[0102]

[0103] in, It is the noisy signal vector received by the receiver, with dimension N. r ×1; x is the signal vector transmitted by the sender, with dimension N. t ×1; n is an additive white Gaussian noise vector with dimension N. r ×1, where each component follows a mean of zero and a variance of . The complex Gaussian distribution;

[0104] The maximum likelihood detection algorithm is:

[0105]

[0106] Where ||·||2 represents the 2-norm; x i This represents the i-th transmitted signal vector, carrying the bit information from the i-th information block; Θi Indicates with x i The corresponding RIS reflection matrix; It is x i Estimation under maximum likelihood detection.

[0107] After performing maximum likelihood detection at the receiver, based on the decoding principle of the corresponding spatial modulation scheme, and according to the estimated parameters... Restore the initial information bits.

[0108] The following detailed description of the intelligent reflective surface-assisted spatial modulation system reflection coefficient optimization method of the present invention is provided through specific embodiments.

[0109] Example 1

[0110] like Figure 3 As shown, the sending end is equipped with N t =5 antennas, receiver equipped with N r =1 antenna, RIS has K=32 reflective elements. This represents the channel matrix from the transmitter to the RIS. Let H and G1 represent the channel matrix from the transmitter to the receiver. Each element in H and G1 follows a complex Gaussian distribution with mean 0 and variance 1. Assume that the direct path from the transmitter to the receiver is blocked. The transmitter implements SC-SSK modulation. In each transmission, two antennas are selected as active antennas to transmit signals s1 and s2 respectively, where s1 ≠ s2.

[0111] A method for optimizing the reflection coefficient of a smart reflector-assisted spatial modulation system can be implemented through the following four processes:

[0112] (1) Spatial modulation process at the transmitting end

[0113] The transmitting end divides the information bits to be transmitted into several information blocks of equal length. Based on the information bits in the information blocks and the SC-SSK modulation principle, the transmitting end selects two active antennas to transmit s1 and s2 respectively.

[0114] According to the SC-SSK modulation principle, the transmitting modulation involves two steps. In each step, the transmitting end selects one antenna from four antennas as the active antenna. Therefore, there are a total of 4×4=16 transmission patterns, and each pattern is mapped to 4 bits of information, as shown in Table 1.

[0115] Table 1. Mapping relationship between information bits and transmission patterns

[0116]

[0117]

[0118] 2) Target Receiving Signal Design Process

[0119] The average power of the target received signal is:

[0120] When N r When R = 1, the QAM scheme can be used as a design method for the target received signal. In this case, R = 4, M = 2. 4 =16, the average power of the 16 constellation points obtained after 16-QAM modulation is normalized, and the normalized 16 constellation points can be used as the normalized target received signal of the current system. The normalized target received signal set S3 can be expressed as:

[0121] S3={c1,c2,c3,c4,c5,c6,c7,c8,c9,c 10 ,c 11 ,c 12 ,c 13 ,c 14 ,c 15 ,c 16}

[0122] Among them, c i This represents the i-th constellation point after the average power is normalized by 16-QAM modulation.

[0123] The average power of the joint target received signal and the normalized target received signal are shown in Table 2. The target received signal of the current system is shown in Table 2.

[0124] Table 2 Target Received Signal in Example 1

[0125]

[0126] (3) Solution process of reflection coefficient on RIS

[0127] When the information bits in the information block are 0000, as shown in Table 1, the transmitted signal vector... It can be represented as:

[0128] x1 = [s1, s2, 0, 0, 0] T

[0129] Actual received signal It can be represented as:

[0130] y1=G1·Θ1·H·x1

[0131] Where Θ1=diag(θ1),

[0132] As shown in Table 2, the target received signal It can be represented as:

[0133] With minimizing the Euclidean distance between the actual received signal and the target received signal as the optimization objective, and all reflection coefficients on the RIS as optimization variables, the following optimization problem can be established:

[0134]

[0135] in,(·) H This indicates the conjugate transpose of the matrix, and 1 represents a vector of all 1s with dimensions 32×1.

[0136] The above optimization problem is solved using the `fmincon` function in Matlab. The solution to the optimization problem is the coefficient of the reflection element on the RIS. The RIS changes the phase of the incident signal based on the obtained reflection coefficients and reflects the signal back to the receiver.

[0137] (4) Receiver detects decoding process

[0138] The noisy signal vector received by the receiver It can be expressed as:

[0139]

[0140] The maximum likelihood detection algorithm can be represented as follows:

[0141]

[0142] in: It is x i Estimation under maximum likelihood detection.

[0143] After performing maximum likelihood detection at the receiver, based on the decoding principle of the SC-SSK scheme, and according to the estimated parameters... Restore the initial information bits.

[0144] Example 2

[0145] like Figure 4 As shown, the receiver is equipped with N r =2 antennas, This represents the channel matrix from the RIS to the receiver, where each element follows a complex Gaussian distribution with a mean of 0 and a variance of 1. The remaining parameter configurations are the same as in Example 1.

[0146] A method for optimizing the reflection coefficient of a smart reflector-assisted spatial modulation system can be implemented through the following four processes:

[0147] (1) Spatial modulation process at the transmitting end

[0148] The transmitting end divides the information bits to be transmitted into several information blocks of equal length. Based on the information bits in the information blocks and the SC-SSK modulation principle, the transmitting end selects two active antennas to transmit s1 and s2 respectively. The mapping relationship between the transmission pattern and the information bits is shown in Table 1.

[0149] According to the SC-SSK modulation principle, the transmitting modulation involves two steps. In each step, the transmitting end selects one antenna from four antennas as the active antenna. Therefore, there are a total of 4×4=16 transmission patterns, and each pattern is mapped to 4 bits of information, as shown in Table 1.

[0150] (2) Target Receiving Signal Design Process

[0151] The average power of the target received signal is:

[0152] When N r =2, R=2N r When = 4, the proposed sub-optimization method can be used to obtain the normalized target received signal distribution. In four-dimensional space, 2 can be found 4 =16 points, and the Euclidean distance between these 16 points is maximized. The coordinates of these 16 points are: (1,1,1,1),(1,1,1,-1),(1,1,-1,1),(1,1,-1,-1),(1,-1,1,1),(1,-1,1,-1),(1,-1,-1,1),(1,-1,-1,-1),(-1,1,1,1),(-1,1,1,-1),(-1,1,-1,-1),(-1,-1,1,1),(-1,-1,1,1),(-1,-1,-1,1),(-1,-1,-1,-1). These 16 points are transformed into 16 complex vectors of dimension 2×1, and the average power is normalized to obtain 16 normalized target received signals.

[0153] The average power of the joint target received signal and the normalized target received signal are shown in Table 3. The target received signal of the current system is shown in Table 3.

[0154] Table 3 Target Received Signals in Example 2

[0155]

[0156] (3) Solution process of reflection coefficient on RIS

[0157] When the information bit in the information block is 0001, as shown in Table 1, the transmitted signal vector... It can be represented as:

[0158] x2 = [s1, 0, s2, 0, 0] T

[0159] Actual received signal It can be represented as:

[0160] y2=G2·Θ2·H·x2

[0161] Where Θ2=diag(θ2),

[0162] As shown in Table 3, the target received signal It can be represented as:

[0163] With minimizing the Euclidean distance between the actual received signal and the target received signal as the optimization objective, and all reflection coefficients on the RIS as optimization variables, the following optimization problem can be established:

[0164]

[0165] in,(·) H This indicates the conjugate transpose of the matrix, and 1 represents a vector of all 1s with dimensions 32×1.

[0166] The above optimization problem is solved using the `fmincon` function in Matlab. The solution to the optimization problem is the coefficient of the reflection element on the RIS. The RIS changes the phase of the incident signal based on the obtained reflection coefficients and reflects the signal back to the receiver.

[0167] (4) Receiver detects decoding process

[0168] The noisy signal vector received by the receiver It can be expressed as:

[0169]

[0170] The maximum likelihood detection algorithm can be represented as follows:

[0171]

[0172] in: It is x i Estimation under maximum likelihood detection.

[0173] After performing maximum likelihood detection at the receiver, based on the decoding principle of the SC-SSK scheme, and according to the estimated parameters... Restore the initial information bits.

[0174] Figure 5 and Figure 6Simulation comparison graphs are provided for the bit error rate performance of the proposed algorithm in Examples 1 and 2, comparing it with existing SDR algorithms and algorithms based on the cosine similarity theorem. As can be seen from the graphs, under the same system transmission rate, regardless of N... r =1 or N r When K=2, K=16, or K=32, the proposed algorithm achieves a lower bit error rate than the other two existing algorithms. For example, ... Figure 6 As shown, when N r =2, K=32, BER=10 -3 At the same time, the proposed algorithm achieves a signal-to-noise ratio gain of 9dB and 18dB compared to the SDR algorithm and the cosine similarity theorem-based algorithm, respectively. This is because the proposed algorithm optimizes the RIS coefficients with the goal of maximizing the Euclidean distance between different received signals, considering both the power and distribution of the received signals, thus maximizing the Euclidean distance between the received signals. In contrast, the other two algorithms optimize the RIS coefficients with the goal of maximizing the received signal-to-noise ratio, without considering the distribution of the received signals, resulting in a smaller Euclidean distance between the received signals, poorer noise resistance, and thus reduced bit error rate performance. Meanwhile, observation... Figure 5 and Figure 6 It can also be seen that as the number of reflective elements or the number of receiving antennas on the RIS increases, the bit error rate performance of all algorithms gradually improves.

[0175] The intelligent reflector-assisted spatial modulation system reflection coefficient optimization method proposed in this invention divides the information bits to be transmitted at the transmitting end into several information blocks of equal length, selects a corresponding active antenna to transmit a specific signal according to each information block, optimizes the coefficients of the reflection elements on the intelligent reflector to maximize the Euclidean distance between different received signals, and uses maximum likelihood detection decoding at the receiving end to recover the original information bits. This invention combines an intelligent reflector with a spatial modulation scheme, utilizes the intelligent reflector to reconstruct the wireless channel, increases the Euclidean distance between different received signals, and improves the system's bit error rate performance. Under the same conditions, it can achieve better bit error rate performance than existing algorithms.

[0176] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0177] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0178] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

Claims

1. A method for optimizing reflection coefficient of an intelligent reflecting surface-assisted spatial modulation system, the spatial modulation system comprising a transmitter, an intelligent reflecting surface and a receiver, characterized in that, The reflection coefficient optimization method comprises the following steps: Divide the information bits to be sent of the sending end into a plurality of information blocks with the same length, select active antenna transmission modulation symbols for each information block based on a spatial modulation principle, transmit information bits through active antenna indexes and modulation symbols, and perform spatial modulation of the sending end; Design optimal target received signals, maximize the Euclidean distance between the target received signals, take minimizing the Euclidean distance between actual received signals and the target received signals as an optimization target, take all reflection coefficients of the intelligent reflecting surface as optimization variables, establish an optimization problem, obtain the optimal reflection coefficients of the intelligent reflecting surface by solving the optimization problem, change the phase of an incident signal by using the intelligent reflecting surface based on the optimal reflection coefficients, and reflect the incident signal to the receiving end; According to the received signals of the receiving end, a maximum likelihood detection algorithm is adopted, and decoding is performed based on the spatial modulation scheme of the sending end to obtain the information bits to be sent. Designing the target received signals comprises: Take the received signal average power obtained based on the cosine similarity theorem optimization algorithm as the target received signal average power, design the normalized distribution form of the target received signals according to the criterion of maximizing the Euclidean distance between different received signals, and obtain the target received signals.

2. The method of claim 1, wherein, Taking minimizing the Euclidean distance between the actual received signals and the target received signals as an optimization target, all reflection coefficients of the intelligent reflecting surface as optimization variables, and establishing an optimization problem comprises: The i-th actual received signal is: y i = G Θ i · H x i wherein, Hs, Hrare channel matrices from the transmitter to the IRS and from the IRS to the receiver, respectively, N t is the number of antennas equipped at the transmitter, N r is the number of antennas equipped at the receiver, K is the number of reflecting elements of the IRS, Θ i = diag(θ i ) is the reflection matrix of the IRS corresponding to x i , is the jth element in , is the coefficient of the jth reflecting element on the IRS, and has x i is the ith transmitted signal, carrying the bit information in the ith information block; Taking minimizing the Euclidean distance between the i-th actual received signal and the i-th target received signal as an optimization target, all reflection coefficients on the intelligent reflecting surface as optimization variables, and the optimization problem established is: s.t. diag(θ i ·θ i H ) = 1 where (·) H For the conjugate transpose of a matrix, 1 denotes an all-ones vector of dimension K x 1.

3. The method according to claim 1 or 2, characterized in that, The method for solving the optimization problem is to solve by using a primal-dual interior point method.

4. The method of claim 2, wherein, According to the received signals of the receiving end, a maximum likelihood detection algorithm is adopted, and decoding is performed based on the spatial modulation scheme of the sending end to obtain the information bits to be sent, comprising: The received signal of the noisy signal received by the receiving end is: wherein, x is a received signal of a noise signal received by a receiving end, x is a sending signal of a sending end, and n is an additive white Gaussian noise. The maximum likelihood detection algorithm is: where || · ||2denotes the 2-norm, is x i Estimation under maximum likelihood detection.

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