Resource allocation method for IRS-assisted MISO system based on index modulation

Abstract

The present invention relates to a resource allocation method for an IRS-assisted MISO system based on index modulation, and belongs to the field of wireless communications. This method uses an index-modulated IRS to assist a downlink MISO system. The IRSs are grouped, and the activated IRS element groups increase the received signal power through passive beamforming, while simultaneously transmitting spatial information through reflection. The optimization problem is to maximize the system sum rate by jointly optimizing the beamforming at the access point and the phase shift matrix at the IRS, assuming known channel information. An alternating optimization method is employed to solve the non-convex problem. The present invention can achieve higher rate performance than conventional fully-reflective IRS-assisted systems.

Description

Technical Field

[0001] The invention belongs to the field of wireless communications and relates to an IRS-assisted MISO system resource allocation method based on index modulation. Background Art

[0002] Extensive research has confirmed that intelligent reflecting surfaces (IRS) used in wireless communication systems can improve wireless network channel environments, enhance system received power, and improve system energy efficiency. They consist of several low-power passive components that form the reflective elements required for signal reflection. Deploying an IRS in a channel modifies the channel gain, and the IRS reflected signal can be combined with other signals to enhance signal power or suppress co-channel interference. Compared to current advanced wireless technologies such as millimeter wave, MIMO, and ultra-dense deployment, IRS, as a passive component, does not require a radio frequency link. This significantly reduces system energy consumption and hardware costs, while offering unique advantages in energy and cost efficiency, leading to its widespread adoption.

[0003] Index modulation transmits information by selecting different index numbers. While the use of multi-antenna technology brings higher data rates, its various solutions, such as spatial division multiplexing, spatial diversity, or smart antennas, also introduce issues such as channel crosstalk, antenna synchronization, and multi-radio transmission, increasing system complexity and cost. To address these issues, index modulation (IM) has been introduced. For example, spatial modulation (SM) divides the transmitted information bits into two parts: one for modulation symbol mapping and the other for transmitting antenna selection. This offers the advantage of transmitting additional information bits via independent channels. Generalized spatial modulation (GSM) builds on SM by activating multiple antennas, allowing them to transmit different modulation symbols simultaneously, further improving spectral efficiency. Index modulation builds on multi-antenna technology, addressing its shortcomings while retaining its advantages. Using index resources to transmit information bits increases data rates and energy efficiency without consuming any energy. The large number of reflective elements that make up a smart reflector can be considered a large-scale passive antenna array, naturally suited for implementing index modulation.

[0004] IRS-assisted MISO systems have been widely studied. Because MISO systems use active beamforming, they require expensive hardware such as digital-to-analog converters, resulting in high costs. In smart reflector systems, the low-power array gain of IRSs replaces the more expensive antenna array gain of MISO systems, reducing both cost and design complexity. Index modulation in smart reflector systems utilizes active index units to transmit information while simultaneously optimizing the reflected phase shift to increase the system transmission rate and improve the quality of the received signal. To further improve system spectral efficiency, some research has shifted to IRS-assisted SM. Okan Yurduseven et al. have also studied the feasibility of implementing SM on IRSs from an electromagnetic perspective. While preliminary exploration of index modulation has been conducted on the transmitter side, applying indexing exclusively at the transmitter side inevitably results in a loss of beamforming at the transmitter side. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide an IRS-assisted MISO system resource allocation method based on index modulation. Combining the advantages of IM and IRS-MISO systems, it is proposed to use IM technology for smart reflective surfaces, called IM-IRS-MISO system. The information to be transmitted by the IRS is embedded in the selection of activated reflective units, and the information is transmitted through the index of the activated units. At the same time, with the goal of maximizing multi-user and rate, the transmitting end beamforming and IRS phase shift matrix are designed, and alternately optimized and solved. Simulation results show that compared with the traditional IRS-assisted system with full reflection, the IM-based IRS-assisted multi-antenna communication system can achieve a compromise between received signal power and achievable rate performance.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] An IRS-assisted MISO system resource allocation method based on index modulation specifically includes the following steps:

[0008] S1: Build an index-modulated IRS to assist the MISO system: Group the IRS reflectors according to their number. To further reduce channel overhead, set the reflection coefficients of each group of IRS reflectors to be the same. Then determine the number of additional transmitted bits and the spatial mapping between the transmitted bits and the sequence number of the activated IRS units.

[0009] S2: Based on the mapping relationship determined in step S1, the transmitter signal is divided into two parts. One part is used to implement the mapping of the IRS activation part, and the other part sends the transmitter modulated signal to the IRS. The IRS unit group is activated through spatial mapping. The IRS then transmits the signal carrying the amplitude and phase modulation symbols and the reflector element sequence number to the legitimate receiver. Under the premise of phase shift constraints and transmit power constraints, the goal is to maximize the system sum rate.

[0010] S3: Use the alternating optimization method to transform the non-convex objective function into a convex optimization problem, and design the IRS phase shift matrix and transmit beamforming. This includes the following steps:

[0011] S31: Based on the optimization objective of step S2, the initial beamforming value is given and the IRS phase shift matrix is ​​optimized. Since the phase shift constraint is a non-convex constraint with a modulus of 1, this constraint can be regarded as the problem being defined on an n-dimensional space sphere. That is, the IRS phase shift matrix is ​​solved using a popular optimization method.

[0012] S32: Based on the result of step S31, a set of phase shift matrices are given to optimize the beamforming matrix. This problem is still a non-convex problem, that is, the WMMSE algorithm is used to transform the problem into a convex problem for iterative solution; wherein the WMMSE algorithm represents the weighted minimum mean square error algorithm.

[0013] Furthermore, in step S1, a downlink communication system model of an IRS-assisted MISO system based on index modulation, referred to as an IM-IRS-MISO system, is constructed. Specifically, a downlink IRS-assisted multi-user MISO downlink wireless system is considered, in which an IRS consisting of N reflective elements is deployed to assist transmission from an AP equipped with M transmitting antennas to K nearby single-antenna users; in order to reduce the channel estimation overhead and implementation complexity, the N IRS elements are divided into G groups, each of which consists of G elements with the same reflection coefficient. The IRS is connected to the intelligent controller. The transmitter divides the data stream into two parts. One part is used to implement the mapping of the IRS activation part, and the other part sends the transmitter modulated signal to the IRS. The IRS then transmits the signal carrying the amplitude and phase modulation symbols and the reflector element sequence number to the legitimate receiver.

[0014] The information bits of the IRS are transmitted by the index of the open state group. For an IRS with G groups, there are L groups of IRS elements in the open state, L≤G, and the activation mode of the reflector has a total of The information bits transmitted by the index are log2(N c ),Other represents the index of L open state groups, for Given open state group The switching state of the IRS element group can be represented as a vector with each item being:

[0015]

[0016] The reflection coefficient of the IRS element group can be expressed as a vector, denoted as Each item is:

[0017]

[0018] Among them, β g ∈[0,1],φ g ∈(0,2π], respectively, represent the reflection amplitude and reflection phase shift of the on-state group; to enhance the hardware design of the reflected power mitigation of the IRS, the reflection amplitude of the on-state group is set to the maximum value, that is:

[0019] make They represent the baseband channels from AP to IRS, from IRS to user, and from AP directly to IRS, respectively. and They represent the corresponding channels associated with the g-th group of IRS elements. In addition, due to the severe path loss and high attenuation, the power of the signal reflected twice or more by the IRS is very small and can be ignored.

[0020] Further, step S2 specifically includes: using s k represents the data symbol sent to user k, which is an independent random variable with zero mean and unit variance; then, the signal sent at the AP can be expressed as:

[0021]

[0022] Where, is the transmit beamforming vector of the kth user, K represents the total number of users;

[0023] The received signal at the kth user is:

[0024]

[0025] in, represents the baseband channel from the AP directly to the kth user; represents the baseband channel from the AP through the IRS to the kth user; θ = Φs, n k represents the additive white Gaussian noise (AWGN) at the kth user receiver, with mean 0 and variance σ 2Gaussian random distribution; the kth user treats all signals from other users as interference; therefore, s at user k k The decoding signal-to-interference-noise ratio γ k for:

[0026]

[0027] in, represents the noise power;

[0028] Additionally, the transmission power is limited to:

[0029]

[0030] Among them, P T Indicates the total power of the transmitter;

[0031] The system and rate problem (i.e., the objective function) is:

[0032]

[0033]

[0034]

[0035] Where W represents the transmitting end beamforming matrix.

[0036] Although the formula of the sum rate problem P(1) is very simple, the joint beamforming and phase optimization problem is much more difficult because the optimization variables W and θ are deeply coupled in the non-convex objective function, and the constraint (7b) is a non-convex constraint with a modulus of 1. Below we use the idea of ​​alternating optimization to solve the optimization variables W and θ separately.

[0037] Furthermore, in step S31, the IRS phase shift matrix is ​​solved using a popular optimization method. Specifically, for a given W, the objective function for solving θ is expressed as:

[0038]

[0039] Then, equation (8) is differentiated with respect to θ to obtain the gradient of the function f(θ) with respect to θ in Euclidean space. After obtaining the Euclidean gradient, the required Riemann gradient is the orthogonal projection of the Euclidean gradient on the complex circle. The search direction involved in the Riemann gradient is the tangent vector conjugate with the Riemann gradient. The objective function f(θ) descends along the η direction. After obtaining the search direction and search step size, the point θ outside the manifold is reduced by the contraction factor. (t+1) Contract back to the manifold, and the update of the IRS reflection coefficient θ is completed.

[0040] Furthermore, in step S32, when θ is fixed, problem (P1) is also a non-convex problem for W. For such a non-convex problem, the WMMSE algorithm is used to transform the non-convex downlink and rate problem in problem (P1) into a convex problem for iterative solution; according to the definition of MMSE, there is a mean square error E k , expressed as:

[0041]

[0042] Among them, u k is a gain factor on the power generated by the channel, is the received signal at user k, h k is the channel matrix of the kth user; u is obtained by equation (9) k Take the derivative to find the value of u k The extreme point of is expressed as:

[0043]

[0044] Next, we solve the weights in WMMSE; specifically, each downlink single-antenna user corresponds to a weight coefficient η k , expressed as:

[0045]

[0046] So we get w in each iteration k Stable solution of :

[0047]

[0048] Where λ represents the dual variable of the transmit power constraint, I M represents the M-order identity matrix.

[0049] In an IM-IRS-assisted multi-user MISO system, this paper designs active beamforming at the base station and passive beamforming at the IRS with the goal of maximizing the system sum rate. However, the sum rate maximization problem is non-convex, so an alternating optimization algorithm is used to iteratively optimize the objective functions. When the active beamforming is fixed, a manifold optimization method is used to solve the constraints of the reflector unit. When the phase is given, a minimum mean square error (MMSE) beamforming algorithm is used to solve the active beamforming at the base station from the perspective of inter-user interference suppression. The optimization is iteratively optimized until the objective function converges.

[0050] The beneficial effects of the present invention are:

[0051] 1) The present invention introduces index modulation at the IRS end in the traditional IRS-MISO system, so that the system can additionally transmit spatial domain information and increase the system spectrum efficiency.

[0052] 2) Compared with the traditional index modulation at the transmitting end, the present invention adopts beamforming technology at the transmitting end to control the signal power in a specific direction, increase the array gain, and improve the system and rate.

[0053] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0055] Figure 1 This is a flowchart of the system resource allocation method of the present invention;

[0056] Figure 2 Constructing a graph for the system model problem of the present invention;

[0057] Figure 3 This is the convergence diagram of the algorithm proposed in the present invention;

[0058] Figure 4 The comparison diagram of sum rate and power change;

[0059] Figure 5 The figure shows the comparison of the sum rate with the signal-to-noise ratio. DETAILED DESCRIPTION

[0060] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0061] See also Figures 1 to 5The present invention provides an IRS-assisted MISO system resource allocation method based on index modulation, in which the IRS based on index modulation is used to assist the downlink multi-user (MISO) system, wherein the IRS is grouped, and the activated IRS element group improves the received signal power through passive beamforming, while transmitting spatial information through reflection. The optimization problem is to maximize the system sum rate by jointly optimizing the beamforming at the access point and the phase shift matrix at the IRS under the assumption that the channel information is known. Since the problem is non-convex, it is difficult to optimize and solve, so the present invention proposes an efficient algorithm based on alternating optimization technology to obtain a high-quality solution. Figure 1 As shown, the method specifically includes the following steps:

[0062] 1) Build the IM-IRS-MISO downlink communication system model, such as Figure 2 As shown in Figure 2 . Consider a multi-user MISO downlink wireless system assisted by a downlink IRS, in which an IRS consisting of 100 reflective elements is deployed to assist transmission from an AP equipped with four transmit antennas to four nearby single-antenna users. To reduce channel estimation overhead and implementation complexity, the 100 IRS elements are divided into four groups, each consisting of 25 adjacent elements with the same reflection coefficient. The IRS is connected to an intelligent controller, and the transmitter divides the data stream into two parts: one part is used to implement the mapping of the IRS active part, and the other part sends the transmitter modulated signal to the IRS. The IRS then transmits the signal carrying the amplitude and phase modulation symbols and the reflective element sequence number to the receiver.

[0063] The information bits of IRS are transmitted through the index of the open state group. For an IRS with 4 groups, there is 1 group open, and there are 4 ways to activate the reflector. The information bits transmitted through the index are 2 bits. represents the index of L open state groups, for Given open state group The switching state of the IRS element group can be expressed as a vector, and the reflection coefficient of the IRS element group can be expressed as a vector, which is recorded as Each item is:

[0064]

[0065] Among them, β g ∈[0,1],φ g ∈(0,2π], respectively, represent the reflection amplitude and reflection phase shift of the on-state group. To enhance the hardware design of reflected power mitigation of IRS, the reflection amplitude of the on-state group is set to the maximum value, that is:

[0066] make They represent the baseband channels from AP to IRS, from IRS to user, and from AP directly to IRS, respectively. and They represent the corresponding channels associated with the g-th group of IRS elements. In addition, due to the severe path loss and high attenuation, the power of the signal reflected twice or more by the IRS is very small and can be ignored.

[0067] 2) Use s k represents the data symbol sent to user k, which is an independent random variable with zero mean and unit variance. The received signal at the kth user is

[0068]

[0069] in, n k represents the additive white Gaussian noise (AWGN) at the kth user receiver, with mean 0 and variance σ 2 The kth user treats all signals from other users as interference. Therefore, s at user k is k The decoding signal-to-drying ratio is

[0070]

[0071] In addition, the transmission power limit

[0072]

[0073] The sum rate problem of the system is

[0074]

[0075]

[0076]

[0077] Although the P(1) and rate problem formulations are simple, the joint beamforming and phase optimization problem is much more difficult because the optimization variables W and θ are deeply coupled in the non-convex objective function, and the phase constraint is a non-convex constraint with a modulus of 1. Below we use the idea of ​​alternating optimization to solve the optimization variables W and θ separately.

[0078] 3) IRS passive beamforming solution based on manifold optimization. For a given W, the objective function for solving θ is expressed as

[0079]

[0080] Further, let Taking the derivative of θ, we get the gradient of the function f(θ) with respect to θ in Euclidean space:

[0081]

[0082] The Riemann gradient is the orthogonal projection of the Euclidean gradient on the complex circle. Therefore, the Riemann gradient corresponding to the objective function is

[0083]

[0084] The search direction is the tangent vector conjugate to the Riemann gradient

[0085]

[0086] The conversion factor is

[0087]

[0088] The objective function f(θ) descends along the direction of η. After obtaining the search direction and search step, the point θ outside the manifold is reduced by the contraction factor. (t+1) Contracting back to the manifold, there is an iterative

[0089]

[0090] At this point, the update of the IRS reflection coefficient θ is completed, where the update iterative formula for the change β in the search direction is:

[0091]

[0092] where r θ(t+1) =-grad θ(t+1) f(θ),

[0093] 4) Solution of base station active beamforming based on minimum mean square error algorithm. When θ is fixed, problem (P1) is also a non-convex problem for W. For such a non-convex problem, the invention adopts WMMSE algorithm to solve it. The non-convex downlink and rate problem is converted into a convex problem for iterative solution. According to the definition of MMSE, there is a mean square error

[0094]

[0095] Among them, u k is a gain factor on the power generated by the channel. k Take the derivative to find the value of u k The extreme point of

[0096]

[0097] Each downlink single antenna user corresponds to a weight coefficient η k , expressed as

[0098]

[0099] So we get w in each iteration k Stable solution of

[0100]

[0101] In the IM-IRS-MISO system, active beamforming at the base station and passive beamforming at the IRS are designed with the goal of maximizing the system sum rate. However, the sum rate maximization problem is non-convex, so an alternating optimization algorithm is used to iteratively optimize the objective functions. When the active beamforming is fixed, the constraints of the reflector unit are solved using a manifold optimization method. When the phase is given, the minimum mean square error (MMSE) beamforming algorithm is used to solve the active beamforming at the base station from the perspective of inter-user interference suppression. The optimization is iteratively optimized until the objective function converges.

[0102] Outputs base station beamforming, IRS phase shift matrix, and downlink multi-user sum rate.

[0103] 5) Comparative Experimental Setup

[0104] Figure 3 In this paper, the number of smart reflector elements N is 100, the number of transmitting antennas M is set to 4, and there are 4 single-antenna users on the receiving end. The comparison is made between the case where all IRS elements are used to reflect signals and the case where index modulation is used in the IRS element group. The index modulation here is the GSM case. The 100 IRS elements are divided into 4 groups, each with 25 elements sharing a reflection coefficient, and 3 groups are opened at a time.

[0105] Figure 4 In the figure, the three simulation performance curves are from bottom to top: without IRS assistance, only one antenna is activated at the transmitter for spatial modulation; with IRS assistance, there are 25 IRS reflective elements, and one antenna is activated at the transmitter for spatial modulation; all four antennas at the transmitter are used to transmit modulated signals, and the 25 turned-on IRS reflective elements transmit signals carrying amplitude and phase modulation symbols and reflective element serial numbers to the receiver, which is the invention proposed in this article.

[0106] Figure 5In this paper, the number of smart reflector elements N is 100, the number of transmitting antennas M is set to 4, the receiving end has four single-antenna users, and the signal-to-noise ratio is set in the range of 0-20dB. The three comparison cases are, from bottom to top: without IRS assistance, only one transmitting antenna is activated for spatial modulation; with IRS assistance, one transmitting antenna is activated for spatial modulation; and all four transmitting antennas are used to transmit modulated signals. The IRS transmits signals carrying amplitude and phase modulation symbols and reflector element numbers to the receiving end, which is the invention proposed in this paper.

[0107] 6) Simulation results analysis

[0108] like Figure 3 As shown in the figure, according to the above algorithm design, the algorithm shows a convergence trend. Since the IRS is grouped for index modulation in this paper, the components of the IRS are not all turned on. Compared with the state where the IRS is fully turned on, the received power is relatively weak, and there is a certain loss in the weighted rate. Figure 4 The performance curve of the sum rate versus total power is shown in Figure 1. IRSM represents the solution adopted by the present invention, and 100 reflective elements are deployed on the IRS, but only 25 reflective elements are activated at a time. Its performance curve is higher than that of the other two solutions that perform spatial modulation at the transmitter. This is because the IRSM solution uses beamforming technology at the transmitter to control the signal power in a specific direction, thereby increasing the array gain. Figure 5 As shown, due to the IRS grouping, the transmitter can implement spatial domain mapping of the IRS element group through index modulation to send more information bits. The receiver can achieve a certain degree of improvement in rate compared to the case where only spatial modulation is performed at the transmitter or the IRS assists the transmitter in performing spatial modulation.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. An IRS-assisted MISO system resource allocation method based on index modulation, characterized in that: The method specifically comprises the following steps: S1: Build an index-modulated IRS to assist the MISO system: Group the IRS reflectors according to their number, set the reflection coefficients of each group of IRS reflectors to be the same, and then determine the number of additional transmitted bits and the spatial mapping between the transmitted bits and the sequence number of the activated IRS units. S2: Based on the mapping relationship determined in step S1, the transmitter signal is divided into two parts. One part is used to implement the mapping of the IRS activation part, and the other part sends the transmitter modulated signal to the IRS. The IRS unit group is activated through spatial mapping. The IRS then transmits the signal carrying the amplitude and phase modulation symbols and the reflector element sequence number to the legitimate receiver. Under the premise of phase shift constraints and transmit power constraints, the goal is to maximize the system sum rate. S3: Use the alternating optimization method to transform the non-convex objective function into a convex optimization problem, and design the IRS phase shift matrix and transmit beamforming. This includes the following steps: S31: According to the optimization goal of step S2, the initial beamforming value is first given and the IRS phase shift matrix is ​​optimized, that is, the IRS phase shift matrix is ​​solved using a popular optimization method; S32: Based on the result of step S31, a set of phase shift matrices are given, and the beamforming matrix is ​​optimized. That is, the problem is converted into a convex problem and solved iteratively using the WMMSE algorithm. The WMMSE algorithm stands for weighted minimum mean square error algorithm. In step S1, a downlink communication system model of an IRS-assisted MISO system based on index modulation, referred to as an IM-IRS-MISO system, is constructed. Specifically, a downlink IRS-assisted multi-user MISO downlink wireless system is considered, in which an IRS consisting of N reflective elements is deployed to assist transmission from an AP equipped with M transmitting antennas to K nearby single-antenna users; the N IRS elements are divided into G groups, each of which has the same reflection coefficient. The IRS is connected to the intelligent controller. The transmitter divides the data stream into two parts. One part is used to implement the mapping of the IRS activation part, and the other part sends the transmitter modulated signal to the IRS. The IRS then transmits the signal carrying the amplitude and phase modulation symbols and the reflector element sequence number to the legitimate receiver. The information bits of the IRS are transmitted by the index of the on-state group. For an IRS with G groups of IRS elements, there are L groups of IRS elements in the on state, L≤G, and the activation mode of the reflector has a total of The information bits transmitted by the index are log2(N c ),Other represents the index of L open state groups, for Given open state group The switching state of the IRS element group is represented by a vector s, each of which is: The reflection coefficient of the IRS element group is represented by a vector, denoted as Each item is: Among them, β g ∈[0,1],φ g ∈(0,2π], respectively representing the reflection amplitude and reflection phase shift of the open state group; the reflection amplitude of the open state group is set to the maximum value, that is: β g =1, make They represent the baseband channels from AP to IRS, from IRS to user, and from AP directly to IRS, respectively. and represent the corresponding channels associated with the g-th group of IRS elements; Step S2 specifically includes: k represents the data symbol sent to user k, which is an independent random variable with zero mean and unit variance; then, the signal sent at the AP is expressed as: Among them, w k represents the transmit beamforming vector of the kth user, and K represents the total number of users; The received signal at the kth user is: in, represents the baseband channel from the AP directly to the kth user; represents the baseband channel from the AP through the IRS to the kth user; θ = Φs, n k represents the additive white Gaussian noise at the kth user receiver, with mean 0 and variance σ 2 Gaussian random distribution; the kth user takes all signals from other users as interference; s at user k k The decoding signal-to-interference-noise ratio γ k for: in, represents the noise power; Additionally, the transmission power is limited to: Among them, P T Indicates the total power of the transmitter; The objective function is: Where W represents the transmitting end beamforming matrix.

2. The IRS-assisted MISO system resource allocation method according to claim 1, characterized in that: In step S31, the IRS phase shift matrix is ​​solved using a popular optimization method. Specifically, for a given W, the objective function for solving θ is expressed as: Then, equation (8) is derived with respect to θ to obtain the gradient of the function f(θ) with respect to θ in Euclidean space. After obtaining the Euclidean gradient, the orthogonal projection of the Euclidean gradient on the complex circle is the Riemann gradient. The search direction involved in the Riemann gradient is the tangent vector conjugate with the Riemann gradient. The objective function f(θ) descends along the direction of η. After obtaining the search direction and search step size, the point θ outside the manifold is reduced by the contraction factor. (t+1) Contract back to the manifold, and the update of the IRS reflection coefficient θ is completed.

3. The IRS-assisted MISO system resource allocation method according to claim 2, characterized in that: In step S32, when θ is fixed, the WMMSE algorithm is used to transform the non-convex downlink and rate problem in problem (P1) into a convex problem for iterative solution; according to the definition of MMSE, there is a mean square error E k , expressed as: Among them, u k is a gain factor on the power generated by the channel, is the received signal at user k, h k is the channel matrix of the kth user; u is obtained by equation (9) k Take the derivative to find the value of u k The extreme point of is expressed as: Next, we solve the weights in WMMSE; specifically, each downlink single-antenna user corresponds to a weight coefficient η k , expressed as: So we get w in each iteration k Stable solution of : Where λ represents the dual variable of the transmit power constraint, I M represents the M-order identity matrix.

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