A method for using a double-irs assisted passive beamforming and information transmission system

Abstract

The application discloses a kind of Double-IRS auxiliary passive beam forming and information transmission system's use method, comprising: S1: constructing a kind of Double-IRS auxiliary passive beam forming and information transmission system, by a multi-antenna base station, 1 single antenna user, 2 cascaded IRS are constituted, wherein each IRS contains N reflecting elements;S2: communication scenario is considered as two links, a kind of straight-through link, another user passes through Double-IRS and transmits information to the base station in system;S3: reduce the error rate of system, construct the optimization equation based on the switch of reflecting element and passive beam forming design to adjust the switch of reflecting element and IRS phase shift parameter decoupling optimization solution;S4: given the switch parameter of reflecting element and one of IRS parameter, to optimization equation: using semi-definite limit relaxation to make optimization equation become homogeneous quadratic constraint quadratic programming.This Double-IRS auxiliary system proposed in the application, especially the system of optimized passive beam forming, is obviously superior to Single-IRS system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless communication, and particularly relates to a use method of a Double-IRS assisted passive beam forming and information transmission system. BACKGROUND

[0002] The current 5G communication technology is developed by China first, and has been commercially used at home and abroad. With the accelerated deployment of 5G commercial use, the research of 6G is gradually carried out. Compared with 5G, 6G network will accelerate the digitalization of economy and society. The development of communication changes the progress of the whole society, and also brings more challenges and requirements for the innovation and development of communication technology. Metamaterials can be used to make antenna covers to improve the ability of antenna transceiver signals and reduce the height of the antenna. Information metamaterial has a great use, which is to make intelligent reflecting surface (IRS, Intelligent Reflecting Surface), which has the advantages of flexible deployment and energy saving, and can also expand the coverage of the network, improve the network capacity, and suppress electromagnetic interference. The joint optimization of the active beam forming of the base station BS and the passive beam forming of the IRS is considered. The capacity maximization of the single-user MIMO system under the assistance of single IRS is researched, and an alternating optimization algorithm for finding local optimum is proposed. The above IRS only studies the scene of one IRS or multiple non-cooperative IRSs (each independently serving its related users). There is a lack of research on the reflection channel between IRSs and the cooperation ability between IRSs. SUMMARY

[0003] The application aims at the defects and deficiencies of the prior art, and provides a use method of a Double-IRS assisted passive beam forming and information transmission system, wherein the cascade IRSs simultaneously enhance the main communication (through passive beam forming), and when the receiver receives the data transmitted by the transmitter correctly, the received signal-to-noise ratio (SNR) of the Double-IRS is lower, so that the system can use the passive beam forming method to improve the average received signal-to-noise ratio (SNR). The numerical results show that the proposed Double-IRS assisted system, especially the system with optimized passive beam forming, is obviously better than the Single-IRS system.

[0004] The application adopts the technical scheme that a use method of a Double-IRS assisted passive beam forming and information transmission system is provided, and the method comprises the following steps:

[0005] Step 1: constructing a Double-IRS assisted passive beam forming and information transmission system, which is composed of a multi-antenna base station, a single-antenna user and two cascade IRSs, wherein each IRS contains N reflecting elements;

[0006] Step 2: The communication scenario is considered as two links, one is a direct link (from the base station to the user), and the other is that the user transmits information to the base station in the system through Double-IRS;

[0007] Step 3: In order to reduce the bit error rate of the system, an optimization equation is constructed based on the switching of the reflective element and the passive beamforming design to adjust the IRS phase shift parameters. The switching of the reflective element and the IRS phase shift parameters are decoupled and optimized based on the alternating optimization algorithm.

[0008] Step 4: Given the switching parameters of the reflector and one of the IRS parameters, the optimization equation is transformed into a homogeneous quadratic constrained quadratic program (QCQP) by using semi-definite relaxation (SDR). The optimization is then iteratively optimized to solve the IRS phase shift parameter.

[0009] Step 5: Using two methods, namely singular value decomposition (SVD) and bilinear generalized approximate message passing (BiG-AMP), the signal-to-noise ratio of the Double-IRS auxiliary system is reduced to the same bit error rate at the receiver.

[0010] Furthermore, step 1 includes:

[0011] Assuming each transmission block consists of L time slots, the receiver observes the signal in the first time slot as follows:

[0012]

[0013] Where G represents the equivalent baseband channel vector between the base station and the l-th IRS, H II h represents the channel vector between the l-th IRS and the 2nd IRS. r h represents the channel vector between the second IRS and the user. d Θ represents the channel vector between the base station and the user. u =diag{θ u}, |θ μ，Ν |=1, u∈{1,2} represents the phase shift matrix of IRS u, where θ μ，Ν Let s represent the Nth phase shift of the u-th IRS. For IRS u, let s ui It is the state of the i-th reflecting element of IRS u, where sui = 1 means the state of the i-th element is "on", otherwise s ui = 0 for the first smart reflector S ui = diag{s ui} is the diagonal on / off state matrix of LIS, where s ui = [s u1 , s u2 ,..., s uN ] T ∈ R N×1 carries the LIS data, assuming each s ui independently takes value 1 ("on") with probability p u and value 0 ("off") with probability 1 - p u , i.e.

[0014]

[0015] Then s n of IRS 1 and IRS 2 both independently take value 1 ("on") with probability p1p2, and at least one takes value 0 ("off") with probability 1 - p1p2, i.e.,

[0016]

[0017] Then, the observed signal matrix of the transmitted blocks, denoted by Y = [yl,..., yL], can be expressed as Y = (G Θ1S a H II S b Θ2h r + h d ) x T + W (Eq. 2)

[0018] From information theory, the total capacity of the system in Eq. 2 is given by the mutual information rate I(x, s; Y), then the design problem can be decoupled into two sub-problems: one is the passive beamforming design, i.e., maximizing I(x, s; Y) over the phase shift matrix Θ u ; the other is the transceiver design, i.e., designing (x, s) and the signal of the receiver to achieve the maximum I(x, s; Y) obtained. We first consider the passive beamforming design. I(x, s; Y) is difficult to evaluate because Eq. 2: Y = (G Θ1S a H II S b Θ2h r + h d ) x T + W is a complex model, to avoid this difficulty, a heuristic design metric is proposed as follows:

[0019]

[0020] where formula 3-1 follows the mutual information rule; formula 3-2 follows the assumption of I(s;Y) << I(x,Y|s), we use Jensen inequality and the concavity of the logarithmic function to approximate formula 3-4 to formula 3-5.

[0021] Further, in the step 2, in order to improve the total safety rate of the system, an optimization problem is proposed:

[0022] In order to maximize the signal-to-noise ratio of the receiving end, an optimization problem is proposed:

[0023]

[0024] s.t. |θ u,m |=1,for m=1,...,N (formula 4-2)

[0025] In formula 4-1, the intelligent reflecting surface switching probability and the IRS phase shift parameter are decoupled by using an alternating optimization algorithm, one of the IRS phase shift parameters is optimized, and the other vector is fixed. Specifically, for given Θ1 and S a , and Q=Θ1S a , D h =diag{h d}, problem formula 4-1 is equivalent to:

[0026]

[0027] Further, in the step 3, the intelligent reflecting surface switching probability and the IRS phase shift parameter are decoupled by using an alternating optimization algorithm, wherein, denotes the real part of complex number a, according to formula 1: the probability distribution of s b is obtained:

[0028] E[s b ]=ρ21and E[s b s b H ]=ρ21·1 T +ρ2(1-ρ2)I (formula 6)

[0029] Where 1 is an n-dimensional all-1 vector, and I is a unit matrix with appropriate size. Insert formula 6 into formula 5 to obtain:

[0030]

[0031] Let

[0032]

[0033] Further, in the step 4, SDP is employed to make the optimization equation into a homogeneous QCQP, and the optimization is solved by constantly alternating iteration optimization for IRS phase shift parameters;

[0034] For formula 8, it can be seen that the problem in formula 4-1 and formula 4-2 is a non-convex quadratic constraint quadratic program (QCQP), first by introducing an auxiliary variable t, the optimization problem is re-expressed as a homogeneous QCQP, and formula 8 is obtained:

[0035]

[0036]

[0037] Wherein, And

[0038] Ψ2 is a semi-definite matrix, that is, Ψ2≥0 and rank(Ψ2)=1, by relaxing the rank 1 constraint on Q, formula 9-1 and formula 9-2 are converted to:

[0039]

[0040]

[0041] The above problem is a standard SDP, which can be optimized and solved by existing convex optimization solver such as CVX;

[0042] Next, let Q'=Θ1S b ,D h =diag{h d} with the solved Θ2 and given S b , the problem of formula 4-1 is converted to:

[0043]

[0044] After the above problem is converted in formula 6-formula 11, θ1 can also be optimized and solved by using the existing convex optimization solver CVX.

[0045] Further, in the step 5, the received target is to retrieve information from the user x, in order to solve this problem, formula 2 is rewritten to obtain:

[0046] Y=(A+h d )x T +W=zx T +W (formula 12)

[0047] Let A=GΘ1S a HII S b Θ2h r , z = [z1, z2,..., z M ], z m = a m + hm, given the algebraic structure between Y and x in equation 12, we propose to retrieve x by the following method: first recover x from Y, recovering z and x from the observation matrix Y can be seen as a rank-1 matrix factorization problem. Two methods are proposed, namely singular value decomposition (SVD) method and bilinear generalized approximate message passing (BiG-AMP).

[0048] Advantages:

[0049] 1. The application provides a Double-IRS assisted communication system model, which solves the communication problem of remote mountainous areas blocked by high buildings.

[0050] 2. The application provides a Double-IRS assisted communication and information technology combination scheme, which maximizes the average received signal-to-noise ratio.

[0051] 3. The application provides an optimization method for Double-IRS assisted communication and information technology, which is proved to be better than Single-IRS system through algorithm optimization.

[0052] 4. The application is based on a Double-IRS assisted passive beamforming and information transmission technology single-user uplink wireless system, in which two IRSs are respectively deployed near a multi-antenna BS and a user to assist their communication. Each IRS is composed of an IRS module equipped with N passive reflecting elements and a controller that can adaptively adjust the on / off state and phase shift of each reflecting element. At the same time, the controller adjusts the phase shift of the open element according to the passive beamforming design to optimize system performance. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 The system model diagram of the application.

[0054] Figure 2 The algorithm flowchart of the application.

[0055] Figure 3 The comparison diagram of Double-IRS system and Single-IRS three algorithms of the application.

[0056] Figure 4A comparison chart of the Double-IRS system and the Single-IR in different IRS quantities. DETAILED DESCRIPTION

[0057] The application will be further described in detail below in combination with the accompanying drawings.

[0058] As shown in the figure, the use method of the Double-IRS auxiliary passive beam forming and information transmission system of the application comprises the following steps: Figure 2

[0059] Step 1: Construct a Double-IRS auxiliary passive beam forming and information transmission system, which is composed of a multi-antenna base station, a single-antenna user and two cascaded IRSs, wherein each IRS contains N reflecting elements.

[0060] Step 2: The communication scenario is considered as two links, one is a direct link (base station to user), and the other is that the user transmits information to the base station in the system through the Double-IRS.

[0061] Step 3: In order to reduce the bit error rate of the system, an optimization equation for adjusting the IRS phase shift parameters is constructed based on the switch of the reflecting element and the passive beam forming design, and the switch of the reflecting element and the IRS phase shift parameters are decoupled and optimized based on the alternating optimization algorithm.

[0062] Step 4: Given the switch parameters of the reflecting element and one of the IRS parameters, the optimization equation is changed into a homogeneous quadratic constraint quadratic program (QCQP) by using semi-definite relaxation (SDR), and the IRS phase shift parameters are iteratively optimized.

[0063] Step 5: By using two methods, i.e. singular value decomposition (SVD) method and bilinear generalized approximate message passing (BiG-AMP), the Double-IRS auxiliary system has a smaller signal-to-noise ratio under the condition that the receiving end has the same signal bit error rate.

[0064] The above step 1 of the application comprises:

[0065] We assume that each transmission block is composed of L time slots, and the receiver observation signal of the first time slot is

[0066] ​

[0067] where G denotes the equivalent baseband channel vector between the base station and the lth IRS, H II denotes the channel vector between the lth IRS and the 2nd IRS, h r denotes the channel vector between the 2nd IRS and the user, h d denotes the channel vector between the base station and the user, Θ u = diag{θ u},

[0068] |θ μ，Ν | = 1, u e {1, 2} denotes the phase shift matrix of IRS u, where θ μ，Ν denotes the Nth phase shift of the u-th IRS, and for IRS u, let s ui be the state of the i-th reflecting element of IRS u, where s ui = 1 means the state of the i-th element is “on”, otherwise s ui = 0, for the first smart reflecting surface S ui = diag{s ui} is the diagonal on / off state matrix of LIS, where s ui = [s u1 , s u2 ,..., s uN ] T e R N×1 carries the LIS data, assuming each s ui independently takes value 1 (“on”) with probability p u and value 0 (“off”) with probability 1-p u , i.e.

[0069]

[0070] Then s n of IRS 1 and IRS 2 both independently take value 1 (“on”) with probability p1p2, and at least one takes value 0 (“off”) with probability 1-p1p2, i.e.

[0071]

[0072] Then, the observed signal matrix of the transmission block, denoted by Y = [yl,..., yL], can be represented as Y = (G Θ1 S a H II S b Θ2 h r + h d ) x T + W (Equation 2)

[0073] From information theory, the total capacity of the system in equation 2 is given by the mutual information rate I(x,s;Y), then the design problem can be decoupled into two sub-problems: one is the passive beamforming design, i.e., maximizing I(x,s;Y) with respect to the phase shift matrix Θ u max I(x,s;Y) with respect to the phase shift matrix Θ a H II S b Θ2h r +h d )x T +W is a complex model, to avoid this difficulty, a heuristic design metric is proposed as follows:

[0074]

[0075] where equation 3-1 follows the mutual information rule; equation 3-2 follows the assumption that I(s;Y) << I(x,Y|s), we use the Jensen inequality and the concavity of the logarithmic function to approximate equation 3-4 to equation 3-5.

[0076] In step 2 of the above invention, to improve the total security rate of the system, an optimization problem is proposed:

[0077] To maximize the signal-to-noise ratio at the receiving end, an optimization problem is proposed:

[0078]

[0079] s.t.|θ u,m |=1,for m=1,...,N (equation 4-2)

[0080] In equation 4-1, an alternating optimization algorithm is used to decouple the IRS switch probability and the IRS phase shift parameter, one IRS phase shift parameter is optimized alternately, and the other vector is fixed. Specifically, for given Θ1 and S a , and Q=Θ1S a ,D h =diag{h d}, the problem equation 4-1 is equivalent to:

[0081]

[0082]

[0083] In the step 3 of the above application, an alternating optimization algorithm is used to decouple the IRS reflection probability and the IRS phase shift parameter, wherein, represents the real part of a complex number a, according to formula 1: s b The probability distribution of s

[0084] E[s b ] = ρ21 and E[s b s b H ] = ρ21·1 T + ρ2(1-ρ2)I (formula 6)

[0085] Where 1 is an n-dimensional all-1 vector, I is a unit matrix with appropriate size, and formula 6 is inserted into formula 5 to obtain:

[0086]

[0087] Let

[0088]

[0089] In the step 4 of the above application, SDP is used to make the optimization equation a homogeneous QCQP, and the IRS phase shift parameter is continuously alternately iterated and optimized to solve;

[0090] For formula 8, it can be seen that the problem in formula 4-1 and formula 4-2 is a non-convex quadratic constraint quadratic program (QCQP), first by introducing an auxiliary variable t, the optimization problem is re-expressed as a homogeneous QCQP, and formula 10 is obtained:

[0091]

[0092]

[0093] Wherein, and

[0094] Ψ2 is a semi-definite matrix, that is, Ψ2 ≥ 0 and rank(Ψ2) = 1, by relaxing the rank 1 constraint on Q, formula 9-1 and formula 9-2 are converted to:

[0095]

[0096]

[0097] The above problem is a standard SDP, which can be optimized by existing convex optimization solvers such as CVX to solve θ2;

[0098] Next, let Q' = Θ1S b ,D h = diag{h d} with Θ2 solved above and given S b , the problem, i.e., equation 4-1, is transformed to:

[0099]

[0100] After the above problem is transformed similarly in equations 6-11, θ1 can also be solved by existing convex optimization solver CVX.

[0101] In step 5 above, the goal is to retrieve x from Y, in order to solve this problem, equation 2 is rewritten to get:

[0102] Y = (A + h d )x T + W = zx T + W (equation 12)

[0103] Let A = GΘ1S a H II S b Θ2h r , z = [z1, z2,..., z M ], z m = a m + hm, given the algebraic structure between Y and x in equation 12, the method for retrieving x is proposed as follows: first, recover x from Y, recovering z and x from the observation matrix Y can be seen as a rank-1 matrix factorization problem. Two methods are proposed, namely singular value decomposition (SVD) method and bilinear generalized approximate message passing (BiG-AMP).

[0104] As Figure 1 shown, the Double-IRS assisted communication system in the present application includes a multi-antenna base station and a single-antenna user, wherein the base station contains M antennas, each IRS contains M reflecting elements, and the uplink transmission mode is adopted. The channel coefficients between the base station and the IRS, IRS1 and IRS2, IRS2 and the user, and the base station and the user are respectively: G ∈ C M*N , H II ∈ C N*N , h r ∈ C N , h d ∈ C MAll channels follow the Rayleigh fading model. Assume the bandwidth of each channel in the system is unit bandwidth. Θ u =diag{θ u}, |θ μ，Ν |=1, u∈{1,2} represents the phase shift matrix of IRS u, where θ μ，Ν This represents the Nth phase shift of the u-th IRS.

[0105] This invention discloses a method for using a Double-IRS-assisted passive beamforming and information transmission system, the method comprising the following steps:

[0106] Step 1: Construct a Double-IRS assisted passive beamforming and information transmission system. The system consists of a multi-antenna base station, a single-antenna user, and two cascaded IRSs, where each IRS contains N reflection units.

[0107] Step 2: The communication scenario is considered as two links, one is a direct link (from the base station to the user), and the other is that the user transmits information to the base station in the system through Double-IRS;

[0108] Step 3: In order to reduce the bit error rate of the system, an optimization equation is constructed based on the switching of the reflective element and the passive beamforming design to adjust the IRS phase shift parameters. The switching of the reflective element and the IRS phase shift parameters are decoupled and optimized based on the alternating optimization algorithm.

[0109] Step 4: Given the switching parameters of the reflector and one of the IRS parameters, the optimization equation is transformed into a homogeneous quadratic constrained quadratic program (QCQP) by using semi-definite relaxation (SDR). The optimization is then iteratively optimized to solve the IRS phase shift parameter.

[0110] Step 5: Using two methods, namely singular value decomposition (SVD) and bilinear generalized approximate message passing (BiG-AMP), the signal-to-noise ratio of the Double-IRS auxiliary system is reduced to the same bit error rate at the receiver.

[0111] Furthermore, step 1 includes:

[0112] We assume that each transmission block consists of L time slots, and the receiver observes the signal in the first time slot as follows:

[0113]

[0114] Where G represents the equivalent baseband channel vector between the base station and the l-th IRS, H II h represents the channel vector between the l-th IRS and the 2nd IRS. r h represents the channel vector between the second IRS and the user. d Θ represents the channel vector between the base station and the user. u =diag{θ u}, |θ μ，Ν |=1, u∈{1,2} represents the phase shift matrix of IRS u, where θ μ，Ν Let s represent the Nth phase shift of the u-th IRS. For IRS u, let s ui It is the state of the i-th reflecting element of IRS u, where s ui =1 indicates that the state of the i-th element is "on", otherwise it is s. ui =0, for the first intelligent reflective surface S ui =diag{s ui} is the diagonal on / off state matrix of the LIS, where s ui =[s u1 ,s u2 ,...,s uN ] T ∈R N×1 Carrying LIS data, assuming each s ui It independently takes the value 1 ("on"), with a probability of ρ. u The value is 0 ("off"), with a probability of 1-ρ. u ,Right now

[0115]

[0116] So, what are the s values ​​of IRS 1 and IRS 2? n All values ​​independently take the value 1 ("on") with a probability of ρ1ρ2, and at least one value takes the value 0 ("off") with a probability of 1-ρ1ρ2, that is,

[0117]

[0118] Then, the observed signal matrix of the transport block, denoted by Y = [y1, ..., yL], can be expressed as Y = (GΘ1S a H II S b Θ2h r +h d )x T +W (Equation 2)

[0119] From an information theory perspective, the total capacity of the system in Equation 2 is given by the mutual information rate I(x,s;Y). Then, the design problem can be decoupled into two sub-problems: one is the passive beamforming design, i.e., in the phase shift matrix Θ... u One approach is to maximize I(x,s;Y); the other is transceiver design, which involves designing the signals (x,s) and receiver to achieve the maximum I(x,s;Y). We first consider the passive beamforming design. I(x,s;Y) is difficult to evaluate because Equation 2: Y=(GΘ1S a H II S b Θ2h r +h d )x T +W is a complex model. To avoid this difficulty, a heuristic design metric is proposed as follows:

[0120]

[0121]

[0122] Equation 3-1 follows the mutual information rule; Equation 3-2 follows the assumption that I(s;Y) << I(x,Y|s). We use Jensen's inequality and the concavity of the logarithmic function to approximate Equation 3-4 as Equation 3-5.

[0123] Furthermore, in step 2, to improve the overall system security rate, an optimization problem is proposed:

[0124] To maximize the signal-to-noise ratio at the receiver, an optimization problem is proposed:

[0125]

[0126] st|θ u,m |=1, for m=1,...,N (Equation 4-2)

[0127] In Equation 4-1, an alternating optimization algorithm is used to decouple the smart reflector switching probability and the IRS phase shift parameter. One of the IRS phase shift parameters is optimized alternately while the other vector is fixed. Specifically, for a given Θ1 and S... a And Q = Θ1S a D h =diag{h d Problem 4-1 is equivalent to:

[0128]

[0129] Further, in the step 3, an alternating optimization algorithm is adopted to decouple the IRS reflection probability and the IRS phase shift parameters, wherein, denotes the real part of a complex number a, according to formula 1: b The probability distribution of s

[0130] E[s b ] = ρ21and E[s b s b H ] = ρ21·1 T + ρ2(1-ρ2)I (formula 6)

[0131] Where 1 is an n-dimensional all-1 vector, I is a unit matrix with appropriate size, and formula 6 is inserted into formula 5 to obtain:

[0132]

[0133] Let

[0134]

[0135] Further, in the step 4, SDP is used to make the optimization equation a homogeneous QCQP, and the IRS phase shift parameters are alternately iterated and optimized to solve;

[0136] For formula 8, it can be seen that the problem in formula 4-1 and formula 4-2 is a non-convex quadratic constraint quadratic program (QCQP), first by introducing an auxiliary variable t, the optimization problem is re-expressed as a homogeneous QCQP, to obtain:

[0137]

[0138]

[0139] Wherein, and

[0140] Ψ2 is a semi-definite matrix, that is, Ψ2≥0 and rank(Ψ2)=1, by relaxing the rank 1 constraint on Q, formula 9-1 and formula 9-2 are converted to:

[0141]

[0142]

[0143] The above problem is a standard SDP, which can be optimized by existing convex optimization solvers such as CVX to solve θ2; ​

[0144] Next, let Q' = Θ1S b ,D h = diag{h d} with Θ2 solved above and given S b , the problem, i.e., equation 4-1, is transformed to:

[0145]

[0146] After the above problem is transformed similarly in equations 6-11, θ1 can also be solved by existing convex optimization solver CVX.

[0147] Further, in the step 5, the goal is to retrieve x from the received Y. To solve this problem, equation 2 is rewritten to get:

[0148] Y = (A + h d )x T + W = zx T + W (equation 12)

[0149] Let A = GΘ1S a H II S b Θ2h r , z = [z1, z2,..., z M ], z m = a m + hm

[0150] Given the algebraic structure between Y and x in equation 12, we propose to retrieve x by the following method: first recover x from Y, recovering z and x from the observation matrix Y can be seen as a rank-1 matrix factorization problem. Two methods are proposed, namely singular value decomposition (SVD) method and bilinear generalized approximate message passing (BiG-AMP).

[0151] To decouple the IRS reflection probability and the IRS phase shift parameters, we propose to alternate optimizing one of the IRS phase shift parameters, first fix Θ1 and S a of IRS1, and Q = Θ1S a , D h = diag{h d},

[0152]

[0153] According to s bThe probability distribution E[s] b ]=ρ21 and E[s b s b H ]=ρ21·1 T +ρ2(1-ρ2)I.

[0154] The above expression can then be transformed into...

[0155]

[0156] Let v = D h H Q H G H GQD h

[0157] =ρ2 2 θ2 H D h H H II H Q H G H GQH II D h θ2+2ρ2Re(θ2 H D h H H II H Q H G H h d )+ρ2(1-ρ2)θ2 H diag{v}θ2

[0158] The above problem is a standard SDP, which can be solved by existing convex optimization solvers such as CVX. However, the optimal Ψ² of the SDP problem in the above equation is generally not guaranteed to be first-order. To obtain from Q... The suboptimal solution is to decompose the eigenvalues ​​of Q into Ψ² = ΦTΦ. H ,,in It is a unitary matrix. It is a diagonal matrix. Then, we obtain the suboptimal solution for θ2 as θ2 = ΦΤ. 12 r, where It is a random vector, each element of which is generated by a circularly symmetric complex Gaussian (CSCG) distribution CN(0,1). Then, the suboptimal of θ2 is... Where [θ2] (1:N) This represents a vector containing the first N elements of θ2.

[0159] SVD method: Y = UΛV H , where U=[u1,u2,...,uM ] and V = [v1, v2,..., v M ] are unitary matrices, A = [a1, a2,..., a M ] is a diagonal matrix, whose elements are arranged in descending order, i.e. a1≥ a2≥... ≥ a M We simply take the first column of V as the estimate of x. That is The corresponding estimate of z is given by

[0160] BiG-AMP method: The BiG-AMP algorithm is used to solve Y for x and z. Note that the BiG-AMP algorithm requires the prior distribution of x and z. We assume that the entries of x are independent and uniformly distributed For z, we approximate z m , as a CSCG random variable whose mean and variance are given by p1p2a m 1+ hm and respectively, where denotes the 2-norm of vector a. Similar to the SVD method, we denote the output estimates of x and z by and respectively.

[0161] There is a scalar offset γ in and because if is a solution of (3), then is also a valid solution of (3). The scalar offset can be eliminated by inserting a reference symbol at the first position of x. Given the knowledge of the reference symbol x1, γ can be estimated by Then, the estimates of z and x are corrected to and Finally, we map to x as

[0162]

[0163] The practical effect of the present application is described in detail below in combination with simulation.

[0164] 1) Simulation conditions

[0165] In the simulation, x is generated by gray mapping modulation of quadrature phase shift keying (QPSK). We set the transmission power to P = 50 db. The signal-to-noise ratio is defined as SNR = P / σ 2 ω ​The maximum number of iterations of BiG-AMP is set to 200. For M = 32, for Double-IRS system IRS1N = IRS2N = 32, for Single-IRS system IRSN = 64, L = 100, p1 = p2 = 0.5.

[0166] As shown in Figure 1 , the system is provided with a base station containing 32 antennas, two IRSs, each IRS having 32 smart reflecting units, the distance from the base station to the user being 90, the loss being channel path 3, the distance from the base station to IRS1 being 1, the distance from IRS2 to the user being 1, and the path loss being 2.2. The distance between the two smart reflecting surfaces is 98, and the loss is channel path 3; for the Single-IRS system, the distance from the base station to the IRS is 50, the distance from IRS2 to the user is 50, and the loss is channel path 3. The channel path loss related to the distance is modeled as y = y0 / d, where y0 represents the reference path loss at a reference distance of 1 m, and for all individual links, y0 = -30 db is set.

[0167] For the recovery of x, we compare the following methods under the Double-IRS system and the Single-IRS system:

[0168] 1. The proposed SVD-based method.

[0169] 2. The proposed BiG-AMP-based method.

[0170] 3. The proposed lower bound LB-x method: is S a and S b In the case of perfect knowledge, the lower bound of x is estimated as for i = 1,..., N.

[0171] 2) Simulation results

[0172] In this embodiment, it can be seen from Figure 3 that the average bit error rate of x and the signal-to-noise ratio of the three methods SVD method, BiG-AMP method and lower bound LB-x method are compared under the Double-IRS system and the Single-IRS system, and for the Double-IRS system, the average bit error rate of the above three methods is 10 -4 , the performance of the system can be improved by about 10 dB signal-to-noise ratio. We also found that when the average bit error rate of x is 10 -4 , the performance of the Double-IRS system can be improved by about 30 dB, 29 dB and 25 dB respectively in the LB-x method, the SVD method and the BiG-AMP method compared with the Single-IRS system. From Figure 4It can be seen that the figure compares the Double-IRS system with the Single-IRS in the lower bound LB-x method and the average bit error rate of x is 10 -4 The relationship between the number of intelligent reflecting surface reflecting units and the signal-to-noise ratio is shown below. As the number of intelligent reflecting surface reflecting units N increases, the signal-to-noise ratio of the Double-IRS system and the Single-IRS system is improved. The performance of the Double-IRS system is better than that of the Single-IRS system.

[0173] The above only describes the preferred embodiments of the present application and is not used to limit the present application. Any modification, equivalent replacement and improvement within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for using a Double-IRS assisted passive beamforming and information transmission system, the method comprising: The method comprises the following steps: Step 1: a Double-IRS assisted passive beamforming and information transmission system is constructed, the system is composed of a multi-antenna base station, a single-antenna user and two cascaded IRSs, each IRS contains N reflecting elements; Step 2: the communication scenario is considered as two links, one is a direct link from the base station to the user, and the other is that the user transmits information to the base station in the system through the Double-IRS; Step 3: in order to reduce the bit error rate of the system, a switch based on the reflecting element and a passive beamforming design are constructed to adjust the optimization equation of the IRS phase shift parameter, and the switch parameter and the IRS phase shift parameter are decoupled and optimized based on the alternating optimization algorithm (AO algorithm); Step 4: given the switch parameter of the reflecting element and one of the IRS parameters, the semi-definite relaxation (SDR) is used to make the optimization equation into a homogeneous quadratic constraint quadratic programming (QCQP), and the IRS phase shift parameter is alternately and iteratively optimized and solved; Step 5: under the condition that the bit error rate of the received signal is the same, the signal-to-noise ratio of the Double-IRS assisted system is reduced through two methods, namely singular value decomposition (SVD) method and bilinear generalized approximate message passing (BiG-AMP); The step 1 comprises: It is assumed that each transmission block is composed of L time slots, and the receiver observation signal of the first time slot is: where G represents an equivalent baseband channel vector between the base station and the lth IRS, H II represents a channel vector between the lth IRS and the 2nd IRS, h r represents a channel vector between the 2nd IRS and the user, h d represents a channel vector between the base station and the user, Θ u = diag{θ u}, denotes the phase shift matrix of IRS u, where θ μ,Ν denotes the Nth phase shift of the u-th IRS, for IRS u, let s ui is the state of the i-th reflecting element of IRS u, where s ui = 1 indicates that the state of the i-th element is "on", otherwise s ui = 0, for the first smart reflecting surface S ui = diag{s ui} is the diagonal on / off state matrix of LIS, where s ui = [s u1 , s u2 ,..., s uN ] T ∈ R N×1 carries the LIS data, assuming each s ui independently takes value 1 ("on") with probability p u and value 0 ("off") with probability 1-p u , i.e. where s n all independently take the value 1 ("on") with probability p1p2and at least one takes the value 0 ("off") with probability 1 - p1p2, i.e., The signal matrix of the observed transmission blocks, denoted Y = [yl,..., yL], is then expressed as Y = (G Θ1S a H II S b Θ2h r +h d )x T +W (Equation 2) Starting from information theory, the total capacity of the system in Equation 2 is given by the mutual information rate I(x, s; Y). Then, the design problem is decoupled into two sub-problems: one is the passive beamforming design, i.e., maximizing I(x, s; Y) with respect to the phase shift matrix Θ u H II S b Θ2h r +h d )x T +W over the set of all possible phase shift matrices Θ a H II S b Θ2h r +h d )x T +W is a complex model, in order to avoid this difficulty, a heuristic design metric is proposed as follows: I(x, s; Y) = H(Y) - H(Y | x, s) = H(Y) - H(X | Y) = H(Y) - H(X | s) In the step 3, in order to improve the total safety rate of the system, an optimization problem is proposed: In order to maximize the signal-to-noise ratio of the receiver, an optimization problem is proposed: s.t. | θ u,m = 1, for m = 1,..., N (Equation 4-2) In formula 4-1, the smart reflector switch probability and the IRS phase shift parameter are decoupled by using an alternating optimization algorithm, one of the IRS phase shift parameters is optimized, and the other vector is fixed. Specifically, for given Θ1 and S a , and Q = Θ1S a ,D h = diag{h d}, the problem formula 4-1 is equivalent to:

2. The method of using a Double-IRS aided passive beamforming and information transmission system according to claim 1, wherein, In the step 3, the alternating optimization algorithm is used to decouple the switch probability of the intelligent reflecting surface and the IRS phase shift parameter: wherein represents the real part of the complex number a, according to equation 1: The probability distribution of the middle s b is obtained as: E[s b ] = p21and E[s b s b H ] = p21·1 T + p2(1 - p2)I (Equation 6) Where 1 is an n-dimensional all-1 vector, I is a unit matrix with appropriate size, formula 6 is inserted into formula 5, and formula 7 is obtained: Let 3. The method of using a Double-IRS aided passive beamforming and information transmission system according to claim 1, wherein, In the step 4, the SDP is used to make the optimization equation into a homogeneous QCQP, and the IRS phase shift parameter is alternately and iteratively optimized and solved: For formula 8, it is seen that the problem in formula 4-1 and formula 4-2 is a non-convex QCQP, first, an auxiliary variable t is introduced, the optimization problem is re-expressed as a homogeneous QCQP, and formula 9-1 and formula 9-2 are obtained: wherein and Ψ2 is a semi-definite matrix, that is, Ψ2 ≥ 0 and rank (Ψ2) = 1, by relaxing the rank 1 constraint on Q, formula 9-1 and formula 9-2 are converted into formula 10-1 and formula 10-2: The above optimization problem is a standard SDP, and the existing convex optimization solver CVX is used to optimize and solve θ2; Next, let Q' = Θ1S b ,D h = diag{h d}, with Θ2 solved above and given S b , the problem, i.e. equation 4-1, is transformed into: After the above problem is converted by formula 6-11, the existing convex optimization solver CVX is used to optimize and solve θ1.

4. The method of using a Double-IRS aided passive beamforming and information transmission system according to claim 1, wherein, In the step 5, the target of the receiver is to retrieve information from the user x, in order to solve this problem, formula 2 is rewritten to obtain formula 11. Y = (A + h d )x T + W = zx T + W (Equation 12) Let A = GΘ1S a H II S b Θ2h r , z = [z1, z2,..., z M ], z m = a m + hm, given the algebraic structure between Y and x in equation 12, we propose to retrieve x by the following method: first recover x from Y, recovering z and x from the observation matrix Y is treated as a rank-1 matrix factorization problem, two methods are proposed, namely singular value decomposition (SVD) method and bilinear generalized approximate message passing (BiG-AMP).

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