Robust design method for IRS-assisted IWSPT system

Abstract

The invention discloses a robust design method of an IRS-assisted IWSPT system, which proposes a typical model of the IRS-assisted IWSPT system, maximizes the total receiving power of all EHDs under transmitting power constraint, IRS phase shift and detection target direction radar beam gain constraint by jointly optimizing a beam forming vector and IRS phase shift under the condition of an imperfect channel, and improves the robustness of the IRS-assisted IWSPT system. A corresponding optimization model is established; meanwhile, an SDR algorithm and a low-complexity algorithm are respectively used for solving a non-convex problem, so that the method is suitable for different calculation scenes and is more practical; experimental results prove that the total receiving power of the EHDs can be optimal on the basis of ensuring constraint conditions such as transmitting power, IRS phase shift and radar beam gain in the detection target direction under the condition that parameters such as the number of IRS reflection units and channel estimation error factors are changed.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless sensing and energy transmission, and in particular relates to a robust design method of an IRS-assisted IWSPT system. Background Art

[0002] In recent years, the new smart Internet of Things (IoT) has been identified as an important direction for the sixth generation (6G) wireless network and is considered suitable for supporting scenarios such as smart homes, smart health, and smart transportation. The new network integrates sensing and positioning functions while retaining the ability to communicate, compute, and control a large number of low-power IoT devices. At the same time, due to hardware and size limitations, these low-power sensors are usually battery-powered. Therefore, RF-based wireless power transmission (WPT) is used in IoT systems to effectively solve the energy shortage problem faced by low-power devices.

[0003] It is worth noting that the hardware structure, frequency band and signal of traditional radar sensing and wireless energy transfer are different. The recently proposed integrated wireless sensing and power transfer system (IWSPT) can effectively improve the hardware efficiency and spectrum utilization by integrating radar sensing and wireless energy transfer functions on the same hardware platform. However, similar to independent radar and wireless energy transfer systems, the path loss of the wireless channel significantly affects the energy harvesting efficiency of the device, and direct link blocking may cause sensing failure. To solve these problems, a reconfigurable intelligent surface (IRS) is introduced. IRS is a programmable subwavelength planar array composed of multiple independently controllable passive electromagnetic reflectors. It can individually adjust the phase, amplitude, frequency and polarization of the incident signal and strategically weight the reflected signals on other paths according to the channel parameters. This capability makes it possible to intelligently manipulate the wireless propagation environment. Therefore, IRS can provide strong support in IWSPT systems to alleviate path loss and blocking problems. At the same time, in real scenarios, the wireless channel will change due to the influence of the surrounding environment. In channel estimation, there will be an error between the real channel and the estimated channel. This error usually directly affects wireless perception and energy transmission. Therefore, it is necessary to fully consider the impact of channel changes on the performance of the IWSPT system during the system design process to ensure that the system can achieve the goal of optimizing performance under different channel conditions. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a robust design method for an IRS-assisted IWSPT system.

[0005] The present invention discloses a robust design method of an integrated wireless sensing and power transfer system (IWSPT) assisted by an intelligent reflection surface (IRS), comprising the following steps:

[0006] S1. Establish the overall model of IRS-assisted IWSPT system. In this model, there are obstacles between the transmitter and multiple detection targets. The transmitter detects the target through the IRS reflection channel. The transmitter transmits energy to multiple energy harvesting devices (EHDs) through the line-of-sight channel and the IRS reflection channel. Based on the actual situation of wireless channels in real environments, the wireless channels in this model are all imperfect channels, and there are channel estimation errors.

[0007] S2. Under the constraints of transmitter power, IRS phase shift and radar beam gain in the detection target direction, the total received power of all EHDs is maximized by jointly optimizing the beamforming vector and IRS phase shift, and a mathematical model for system optimization is established. The optimization problem in this mathematical model is a non-convex problem.

[0008] S3. For scenarios where computing devices have strong computing power, the present invention is designed to use a semi-definite relaxation (Semi-Definite Relaxation, SDR) method to solve the non-convex problem, that is, first decompose the target problem into two independently solvable sub-problems of optimizing the transmitter beamforming vector and the IRS reflection phase shift, and then use the SDR method to relax the two sub-problems into standard convex semi-definite programming (Semi-Definite Programming, SDP) problems respectively, and then obtain the optimal solutions of the beamforming vector and the IRS reflection phase, and finally use the alternating iterative algorithm to obtain the optimal solution of the total received power of EHDs;

[0009] S4. Aiming at the scenario where the computing power of the computing device is weak, the present invention comprehensively utilizes the first-order Taylor expansion and Riemann manifold optimization ideas to design a low-complexity algorithm, that is, on the basis of decomposing the target problem into two independently solvable sub-problems of optimizing the transmitter beamforming vector and the IRS reflection phase shift, the problem is converted into a convex second-order cone form by the first-order Taylor expansion method, and then the second-order cone relaxation (Second-Order Cone Programming, SOCP) method is used in combination with the Riemann manifold optimization idea to obtain the optimal solutions of the beamforming vector and the IRS reflection phase respectively, and finally the alternating iterative algorithm is used to obtain the optimal solution of the total received power of EHDs;

[0010] S5. Verification experiment. The IRS-assisted IWSPT system was simulated using simulation software, and the performance of the two algorithms was experimentally verified when the number of IRS reflection units, channel estimation error factor and other parameters were changed. The experimental results show that the two algorithms can achieve the optimal total EHDs received power on the basis of satisfying the constraints when the parameters are changed.

[0011] The IWSPT system model includes a multi-antenna transmitter with N antennas, K EHDs with single antennas, M point targets, and a uniform linear IRS array consisting of L reflective elements;

[0012] The system model is:

[0013]

[0014]

[0015]

[0016] In the formula, represents the real channel coefficient from the transmitter to the IRS, represents the real channel coefficient from the transmitter to the EHD, represents the real channel coefficient from IRS to EHD, and represents the estimated channel, represents the uncertainty of the channel, and Among them, ψ tk , rk and ψ tr is the channel estimation error factor, and

[0017] In the system model, the line-of-sight channel between the transmitter and the detection target is blocked by obstacles, and a virtual line-of-sight channel needs to be constructed after IRS reflection to realize the perception of the detection target; the pointing angle θ of the mth detection target m The radar beam pattern can be expressed as:

[0018] P(θ m )=E(|m(θ m )ΘH tr x| 2 )=|h m x| 2 ,(2)

[0019] In the formula, represents the wireless channel from the transmitter to the sensing target after being reflected by the IRS, Θ represents the phase offset matrix of all reflection units of the IRS, E(|m(θ m )ΘH tr x| 2 ) represents the strength of the radar beam at the corresponding angle, and x represents the signal transmitted by the transmitter.

[0020] In the system model, energy is transmitted between the transmitter and the EHDs via the line-of-sight link and the IRS reflection link. The power received at the kth EHD is expressed as

[0021] E k =ηP0|(h rk ΘH tr +h tk )w| 2 =ηP0|h k w| 2 (3)

[0022] In the formula, h k =h rk ΘH tr +h tk , represents the wireless channel from the transmitter line of sight and the reflection through the IRS to the EHDs, η represents the energy harvesting efficiency, and P0 represents the total power of the transmitter.

[0023] Under the constraints of the transmitter power, IRS phase shift and radar beam gain in the detection target direction, the total received power of all EHDs is maximized by jointly optimizing the beamforming vector w and the IRS phase shift matrix Θ. The optimization problem is constructed as follows:

[0024]

[0025]

[0026]

[0027]

[0028] In the formula, Γ m represents the predefined minimum radar beam intensity at the mth target, (4c) represents the transmission power constraint of each antenna of the transmitter, and (4d) is the phase offset constraint of the IRS reflection unit; in this problem, since the beamforming vector w and the IRS phase offset matrix Θ are coupled with each other, problem (4) is non-convex.

[0029] In step S3, for scenarios where the computing device has strong computing power, the SDR algorithm is used to convert problem (4) into the SDP form for solution; given the IRS phase offset matrix Θ, the beamforming vector w is optimized, and the SDR method can be used to convert problem (4) into the SDP form:

[0030]

[0031]

[0032]

[0033] By relaxing the rank-one constraint of rank(W)=1 in problem (5c), problem (5) is transformed into a convex optimization problem, which can be directly solved using standard convex optimization tools to obtain the optimal solution for the matrix W, h k represents the wireless channel from the transmitter directly to the energy harvesting device and reflected by the IRS, h k =h rk ΘH tr +h tk ,h m represents the wireless channel through which the signal is reflected by the IRS and reaches the sensing target. Defining the Matrix Yes k The conjugate transpose operation of

[0034]

[0035] In step S3, based on the optimized beamforming vector w, the IRS phase offset matrix Θ is optimized using the SDR algorithm. The problem (4) can be converted into the SDP form using the SDR method:

[0036]

[0037] In the formula, in

[0038] By relaxing the rank-one constraint of rank(V)=1 in problem (8d), problem (4) is converted into a convex optimization problem, and the optimal solution of the matrix V can be obtained using standard convex optimization tools. Finally, the optimal solution of the IRS phase offset matrix Θ under the current conditions is obtained through diagonalization transformation.

[0039] In step S4, for the scenario where the computing power of the computing device is weak, a low-complexity algorithm is designed by comprehensively utilizing the first-order Taylor expansion and Riemann manifold optimization ideas to solve the problem; given the IRS phase offset matrix Θ, the beamforming vector w is optimized, and problem (4) is equivalently transformed as follows:

[0040]

[0041]

[0042]

[0043] In the formula, w (n) represents the optimal value of the previous round of iterative calculation,

[0044] Problem (10) is a typical second order cone programming (SOCP) problem, which can be solved directly using standard convex optimization tools to obtain the optimal solution of the beamforming vector w under the current conditions.

[0045] In step S4, based on the optimized beamforming vector w, the IRS phase offset matrix Θ is optimized, and after performing a matrix equivalent transformation on problem (4), a first-order Taylor expansion is performed to reconstruct the problem as follows:

[0046]

[0047]

[0048]

[0049] in, represents the optimal value of the previous round of iterative calculation. Since the constraint (11c) is a constant modulus constraint and cannot be directly solved using standard convex optimization tools, the vector is obtained based on the Riemann manifold optimization idea. The optimal value of is obtained, and then the optimal solution of the IRS phase offset matrix Θ under the current conditions is obtained.

[0050] The beneficial effect of the present invention is that the present invention proposes a typical model of the IRS-assisted IWSPT system. Aiming at the characteristics of the wireless channel in the real scene, the error in channel estimation is first considered. At the same time, assuming that there are obstacles between the detection target and the transmitter, it is difficult to detect directly. The virtual line-of-sight channel between the transmitter and the detection target is established through IRS assistance to achieve target perception. Based on the above model, by jointly optimizing the beamforming vector and the IRS phase offset, the total received power of all EHDs is maximized under the constraints of the transmission power constraint, the IRS phase shift and the radar beam gain in the detection target direction, and a corresponding optimization model is established. At the same time, SDR and low-complexity algorithms are used to solve non-convex problems, so that the method is suitable for different computing scenarios and is more practical; experimental results confirm that the method proposed by the present invention can achieve the optimal total received power of EHDs on the basis of ensuring the constraints of transmission power, IRS phase shift and radar beam gain in the detection target direction when the parameters such as the number of IRS reflection units and the channel estimation error factor change. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a schematic diagram of the IRS-assisted IWSPT system of the present invention.

[0052] Figure 2 It is a convergence comparison between the SDP algorithm of the present invention and the LC algorithm.

[0053] Figure 3 It is the influence of the number of IRS reflection units of the present invention on the total received power.

[0054] Figure 4 3 is a beam pattern comparison between the SDP algorithm and the LC algorithm of the present invention.

[0055] Figure 5 This is the influence of the channel estimation error factor Ψ of the present invention on the beam pattern. DETAILED DESCRIPTION

[0056] Embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to be used to explain the present invention, but should not be understood as limiting the present invention.

[0057] The robust design method of the IRS-assisted IWSPT system of the present invention comprises the following steps:

[0058] S1. Establish an IWSPT system model. In the model, there are obstacles between the transmitter and the detection target. The target is detected through the IRS reflection channel. Energy is transmitted between the transmitter and multiple EHDs through the IRS reflection channel and the line-of-sight channel. Referring to the actual situation, the wireless channels in the model are all imperfect channels, and there are channel estimation errors.

[0059] S2. Under the constraints of transmitter power, IRS phase shift and radar beam gain in the detection target direction, the total received power of all EHDs is maximized by jointly optimizing the beamforming vector and IRS phase shift, and a mathematical model for system optimization is established. The optimization problem in this mathematical model is a non-convex problem.

[0060] S3. For scenarios with strong computing power of computing devices, the semidefinite relaxation method is used to solve the non-convex problem. That is, the target problem is first decomposed into two independently solvable sub-problems of optimizing the transmitter beamforming vector and the IRS reflection phase shift. Then, the two sub-problems are relaxed into standard convex semidefinite programming problems using the SDR method respectively. Then, the optimal solutions of the beamforming vector and the IRS reflection phase under the current conditions are obtained. Finally, the optimal solution of the total received power of EHDs is obtained using the alternating iterative algorithm.

[0061] S4. Aiming at the scenario where the computing power of computing equipment is weak, a low-complexity algorithm is designed by using the first-order Taylor expansion and Riemann manifold optimization ideas. That is, on the basis of decomposing the target problem into two independently solvable sub-problems of optimizing the transmitter beamforming vector and the IRS reflection phase shift, the problem is transformed into a convex second-order cone form by the first-order Taylor expansion method. Then, the second-order cone relaxation method is used in combination with the Riemann manifold optimization idea to respectively obtain the optimal solutions of the beamforming vector and the IRS reflection phase under the current conditions. Finally, the alternating iterative algorithm is used to obtain the optimal solution of the total received power of EHDs.

[0062] S5. Validation experiments.

[0063] Example

[0064] S1. This paper proposes an IRS-assisted IWSPT system that jointly optimizes the beamforming vector and IRS phase shift to maximize the total received power of all EHDs while satisfying the constraints of transmitter power, IRS phase shift, and radar beam gain in the direction of the detected target.

[0065] like Figure 1 The IWSPT system includes a multi-antenna transmitter with N antennas, K EHDs with single antennas, M point targets and a uniform linear IRS array consisting of L reflection units. The IRS phase is expressed as a l ∈[-π,π], l=1,...,L. The IRS reflection surface has L reflection units in total, each element represents the reflection phase of a different reflection unit, a l It means that the phase variation range of the IRS element is plus or minus 180 degrees.

[0066] The transmitter senses the target by transmitting radar signals and transmits energy to the EHD at the same time. In the IWSPT system, there is no difference between radar and WPT signals. Therefore, the transmitted signal can be described as x = ws, where is the beamforming vector used for radar sensing and energy reception, and the symbol s represents an independent and uncorrelated radar symbol, satisfying According to the definition of the signal, the matrix of the covariance transmission signal is

[0067] Considering the transmit power constraint of each antenna, the transmit covariance matrix W should satisfy W n，n ≤P0 / N, where P0 is the total transmitter power.

[0068] Based on the actual situation of wireless channels in real environments, the wireless channels in this model are all imperfect channels and there are channel estimation errors.

[0069] The channel model can be modeled as:

[0070]

[0071] In the formula, represents the real channel coefficient from the transmitter to the IRS, represents the real channel coefficient from the transmitter to the EHD, represents the real channel coefficient from IRS to EHD, and represents the estimated channel coefficient, l∈[1,L] represents the uncertainty of the channel, and Among them, ψ tk , rk and ψ tr is the channel estimation error factor, and

[0072] In the system model, the line-of-sight channel between the transmitter and the detection target is blocked by obstacles, and a virtual line-of-sight channel needs to be constructed after IRS reflection to achieve perception of the detection target; in order to evaluate the impact of IRS on radar perception performance, we use perception beam pattern gain as a metric.

[0073] Steering vector of IRS towards the mth target Where j is an imaginary unit, L represents the number of reflectors, and λ is the spacing between two adjacent reflectors in the IRS. Therefore, the pointing angle θ of the mth detected target is m The radar beam pattern can be expressed as:

[0074] P(θm )=E(|m(θ m )ΘH tr x| 2 )=|h m x| 2 ,(2)

[0075] In the formula, represents the wireless channel from the transmitter to the sensing target after being reflected by the IRS, Θ represents the phase offset matrix of all reflection units of the IRS, E(|m(θ m )ΘH tr x| 2 ) represents the strength of the radar beam at the corresponding angle, and x represents the signal transmitted by the transmitter.

[0076] In the system model, energy is transmitted between the transmitter and the EHDs via the line-of-sight link and the IRS reflection link. The power received at the kth EHD is expressed as

[0077] E k =ηP0|(h rk ΘH tr +h tk )w| 2 =ηP0|h k w| 2 (3)

[0078] In the formula, h k =h rk ΘH tr +h tk represents the wireless channel from the transmitter line of sight and reaching the EHDs through the IRS reflection, η represents the energy harvesting efficiency, and P0 represents the total power of the transmitter.

[0079] S2. Under the constraints of transmitter power, IRS phase shift and radar beam gain in the direction of the detected target, the total received power of all EHDs is maximized by jointly optimizing the beamforming vector w and the IRS phase shift matrix Θ. The optimization problem is formulated as follows:

[0080]

[0081] In the formula, Γ m represents the predefined minimum intensity of radar beam gain at the mth target, (4c) represents the transmission power constraint of each antenna of the transmitter, and (4d) is the phase offset constraint of the IRS reflection unit.

[0082] In this problem, since the beamforming vector w and the IRS phase offset matrix Θ are coupled with each other, problem (4) is non-convex. In order to solve this problem, the target problem (4) is decomposed into two independently solvable sub-problems of optimizing the transmitter beamforming vector w and the IRS phase offset matrix Θ. The optimal solution of the sub-problems is obtained by solving the two sub-problems separately, and then the optimal solution of the EHDs total received power is obtained by using the alternating iterative algorithm.

[0083] S3. For scenarios where computing devices have strong computing power, the SDR algorithm is designed to convert problem (4) into SDP form for solution;

[0084] S301. Given the IRS phase offset matrix Θ, optimize the beamforming vector w and use the SDR method to transform formula (4a) to obtain

[0085] The matrix is ​​defined in simplified formula form. Yes k The conjugate transpose operation of , similarly, formula (4b) can be transformed into Therefore, the SDR method can be used to transform problem (4) into SDP form:

[0086]

[0087] By relaxing the rank-one constraint of rank(W)=1 in problem (5c), problem (5) is converted into a convex optimization problem, which can be directly solved using standard convex optimization tools to obtain the optimal solution of the matrix W. The Gaussian randomization method can be used to decompose the matrix W into the optimal solution of the beamforming vector w under the current conditions.

[0088] S302. Based on the optimized beamforming vector w, optimize the IRS phase offset matrix Θ. Using the SDR method, perform equivalent transformations on formulas (4a) and (4b) to obtain

[0089] and P(θ m )=|vdiag(m H (θ m ))H tr w| 2 =|vd m | 2 , where the vector Each element in represents the phase offset of each reflection unit of IRS, a k =h tk w,c k =diag(h rk )H tr w and d m =diag(m H (θm ))H tr w, so problem (4) can be equivalently transformed into

[0090]

[0091] definition in, Problem (6) can be equivalently transformed as follows:

[0092]

[0093] in definition Using the SDR method, problem (7) can be reconstructed as follows:

[0094]

[0095] By relaxing the rank-one constraint of rank(V)=1 in problem (8d), problem (7) is transformed into a convex optimization problem. Standard convex optimization tools can be used to directly find the optimal solution for matrix V. Then, the Gaussian randomization method can be used to decompose matrix V into Then, the optimal solution of the IRS phase offset matrix Θ under the current conditions is obtained through diagonal transformation.

[0096] S303. Based on S301 and S302, the optimal solution of the beamforming vector w and the IRS phase offset matrix Θ under the current conditions is obtained, and the alternating iterative method is used to jointly obtain the maximum total received power when EHDs meets the constraints.

[0097] S4. For scenarios with weak computing power of computing devices, a low-complexity algorithm is designed to solve the problem by combining the first-order Taylor expansion and Riemann manifold optimization ideas.

[0098] S401. Given the IRS phase offset matrix Θ, optimize the beamforming vector w, and perform an equivalent transformation of problem (4a) through basic matrix operations to obtain the following formula:

[0099]

[0100] Similarly, after equivalent transformation of problem (4b), we can obtain in Therefore, problem (4) is equivalently transformed as follows:

[0101]

[0102] The first-order Taylor expansion of problem (9a) is as follows: H H k w≥2Re(w (n)H H k w)-w(n)H H k w (n) , where w (n) Represents the optimal value of the previous round of iterative calculation, Re is the operation of finding the real part of a complex number, which represents energy here, and H k It is equivalent to the wireless channel from the transmitter to the energy harvesting device. Similarly, after the first-order Taylor expansion of problem (9b), we can get in Therefore, problem (9) can be reconstructed as follows:

[0103]

[0104] Problem (10) is a typical second-order cone programming problem, which can be directly solved using standard convex optimization tools to obtain the optimal solution of the beamforming vector w under the current conditions.

[0105] S402. Based on the optimized beamforming vector w, optimize the IRS phase offset matrix Θ. Similar to S401, after performing matrix equivalent transformation on problem (4), a first-order Taylor expansion is performed to reconstruct the problem as follows:

[0106]

[0107] in, represents the optimal value of the previous round of iterative calculation, Since constraint (11c) is a constant modulus constraint and cannot be solved directly using standard convex optimization tools, it is solved based on the Riemann manifold optimization idea and introduces the variable Refactoring problem (11) into

[0108]

[0109] Where μ>0 represents the penalty term, and the Taylor first-order expansion of problem (12) is transformed as follows:

[0110]

[0111] in c is a constant representing the penalty parameter, which decreases with iterations to tighten the penalty term.

[0112] Problem (13) is a typical SOCP problem, which can be solved directly using standard convex optimization tools to obtain the vector under the current conditions. The optimal solution of the IRS phase offset matrix Θ under the current conditions is obtained through diagonal transformation.

[0113] S403. Based on S401 and S402, the optimal solution of the beamforming vector w and the IRS phase offset matrix Θ under the current conditions is obtained, and the alternating iterative method is used to jointly obtain the maximum total received power when EHDs meets the constraints.

[0114] Complexity Analysis:

[0115] The computational complexity of solving problems (5) and (8) is O(N 6.5 ) and O(L 6.5 ), the problem is transformed into an SDP problem through the SDR method, and then solved using existing convex optimization tools. Therefore, the total complexity of the SDR algorithm is O(I SDR (N 6.5 +L 6.5 )), where I SDR represents the number of iterations. In contrast, the complexity of the SOCP algorithm for solving problems (9) and (10) is affected by the worst-case time complexity of each step. SOCP uses an interior point method for solution, and its complexity depends on the number of nonlinear constraints, the number of variables, and the dimension of each quadratic cone (SOC) constraint. Ignoring linear constraints, the computational complexity of solving problems (9) and (10) is O(N 2 ) and O(L 2 ). Therefore, the total complexity of the low-complexity algorithm is O(I socp N 2 L 2 ), where I socp is the maximum number of iterations at which the algorithm terminates.

[0116] S5. Validation experiments.

[0117] The advantages of the IRS-assisted IWSPT system are verified by simulation experiments. In the simulation, we assume that the transmitter is equipped with N = 15 antennas with half-wavelength spacing, and uses L IRS reflection units to detect M = 3 point targets. The detection targets are located at -40°, 0°, and +40° angles of the IRS. At the same time, the transmitter transmits energy to K = 5 single-antenna EHDs.

[0118] The physical distances between the transmitter and IRS, IRS and EHDs, and transmitter and EHDs are 30 m, 30 m, and 50 m, respectively. The channel path loss is modeled as K1 is the Rice factor, set to 6dB, P0 = 40dBm, η = 0.8, and the channel estimation error factor ψ tk , rk and ψ tr The experiment was conducted under three conditions: 0, 0.02 and 0.06.

[0119] Convergence analysis of SDP and LC algorithms, such as Figure 2 As shown in the figure, both algorithms achieve fast convergence on different IRS reflection units, usually within 2 to 4 iterations, and show consistent performance, indicating the effectiveness of the algorithm design.

[0120] Verify the impact of the number of IRS elements and the channel estimation error factor on the total received power of EHDs. In order to better compare the algorithm performance, two scenarios, an IRS scenario with random phase offset and a scenario without IRS, are introduced for comparison. Figure 3 As shown in the figure, as the number of IRS reflection units increases, the total received power of EHDs also increases; while in the absence of IRS, the power remains unchanged, which shows that the introduction of IRS can significantly improve the energy transmission capacity. At the same time, as the channel estimation error factor increases, the total received power of EHDs decreases, which shows that when the channel quality decreases, the transmitter beamforming vector and IRS phase shift optimization need to meet more constraints, resulting in a decrease in the total received power of EHDs.

[0121] Verify the effect of the number of IRS elements on the radar beam pattern. Figure 4 As shown, both algorithms effectively enhance the beam pattern gain at the target angle, and as the number of IRS reflection units increases, not only the gain in the target direction is improved, but also the resolution of the radar beam is increased, thereby achieving more accurate target positioning.

[0122] Verify the influence of the channel estimation error factor ψ on the radar beam pattern. Figure 5 As shown in the figure, with the increase of channel estimation error, the resolution and gain of the radar beam are reduced, but the impact is relatively limited. At the same time, with the increase of the number of IRS reflection units, the impact of channel error will be further reduced. This is because in perception, the beam pattern represents the radiation characteristics of the radar antenna or array, reflecting the intensity distribution of the signal in different directions, which is mainly affected by the antenna or array design, operating frequency and beamforming technology. Therefore, the channel error ψ from the transmitter to the IRS may affect the quality of the reflected signal of the IRS, thereby affecting the beam pattern performance. Since the target is perceived by the IRS in the IWSPT model, increasing the IRS reflection unit will improve the gain and resolution of the beam pattern.

[0123] In summary, a typical model of the IRS-assisted IWSPT system is proposed. In the case of imperfect channels, the total received power of all EHDs is maximized under the constraints of transmit power, IRS phase shift and ensuring radar detection effect by jointly optimizing the beamforming vector and IRS phase shift, and a corresponding optimization model is established. At the same time, SDR and low-complexity algorithms are used to solve non-convex problems, making the method suitable for different computing scenarios and more practical; experimental results confirm that the method proposed in the present invention can achieve the optimal total received power of EHDs on the basis of ensuring the radar beam gain in the detection target direction when the number of IRS reflection units and channel estimation error factors and other parameters change.

[0124] Although the above embodiments have been shown and described, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. Changes, modifications, substitutions and variations of the above embodiments by those of ordinary skill in the art are all within the scope of protection of the present invention.

Claims

1. A robust design method for an IRS-assisted IWSPT system, characterized in that: The following steps are involved: S1. Establish an IWSPT system model. In the model, there are obstacles between the transmitter and the detection target. The target is detected through the IRS reflection channel. Energy is transmitted between the transmitter and multiple EHDs through the IRS reflection channel and the line-of-sight channel. Based on the actual situation of wireless channels in real environments, the wireless channels in the model are all imperfect channels, and there are channel estimation errors. S2. Under the constraints of transmitter power, IRS phase shift and radar beam gain in the detection target direction, the total received power of all EHDs is maximized by jointly optimizing the beamforming vector and IRS phase shift, and a mathematical model for system optimization is established. The optimization problem in this mathematical model is a non-convex problem. S3. For scenarios with strong computing power of computing devices, the semidefinite relaxation method is used to solve the non-convex problem, and the optimal solution of the beamforming vector and IRS reflection phase is obtained. Then, the alternating iterative algorithm is used to obtain the optimal solution of the total received power of EHDs. S4. For scenarios where computing power of computing devices is weak, a low-complexity algorithm is designed using the first-order Taylor expansion and Riemann manifold optimization ideas to obtain the optimal solutions of the beamforming vector and IRS reflection phase, respectively. Finally, an alternating iterative algorithm is used to obtain the optimal solution of the total received power of EHDs. S5. Validation experiments.

2. The robust design method of the IRS-assisted IWSPT system according to claim 1, characterized in that: The IWSPT system model includes a multi-antenna transmitter with N antennas, K EHDs with single antennas, M point targets, and a uniform linear IRS array consisting of L reflective elements; The system model is: In the formula, represents the real channel coefficient from the transmitter to the IRS, represents the real channel coefficient from the transmitter to the EHD, represents the real channel coefficient from IRS to EHD, and represents the estimated channel, l∈[1,L] represents the uncertainty of the channel, and Among them, ψ tk , rk and ψ tr is the channel estimation error factor, and 3. The robust design method of the IRS-assisted IWSPT system according to claim 2, characterized in that: In the system model, the line-of-sight channel between the transmitter and the detection target is blocked by obstacles, and a virtual line-of-sight channel needs to be constructed after IRS reflection to realize the perception of the detection target; the pointing angle θ of the mth detection target m The radar beam pattern can be expressed as: In the formula, represents the wireless channel from the transmitter to the sensing target after being reflected by the IRS, Θ represents the phase offset matrix of all reflection units of the IRS, E(|m(θ m )ΘH tr x| 2 ) represents the calculation of the intensity of the radar beam at the corresponding angle, and x represents the signal transmitted by the transmitter.

4. The robust design method of the IRS-assisted IWSPT system according to claim 3, characterized in that: In the system model, energy is transmitted between the transmitter and the EHDs via the line-of-sight link and the IRS reflection link. The power received at the kth EHD is expressed as E k =ηP0|(h rk ΘH tr +h tk )w| 2 =ηP0|h k w| 2 (3) In the formula, h k =h rk ΘH tr +h tk , represents the wireless channel from the transmitter line of sight and the reflection through the IRS to the EHDs, η represents the energy harvesting efficiency, and P0 represents the total power of the transmitter.

5. The robust design method of the IRS-assisted IWSPT system according to claim 4, characterized in that: Under the constraints of the transmitter power, IRS phase shift and radar beam gain in the detection target direction, the total received power of all EHDs is maximized by jointly optimizing the beamforming vector w and the IRS phase shift matrix Θ. The optimization problem is constructed as follows: In the formula, Γ m represents the predefined minimum radar beam intensity at the mth target, (4c) represents the transmission power constraint of each antenna of the transmitter, and (4d) is the phase offset constraint of the IRS reflection unit; in this problem, since the beamforming vector w and the IRS phase offset matrix Θ are coupled with each other, problem (4) is non-convex.

6. The robust design method of the IRS-assisted IWSPT system according to claim 5, characterized in that: In step S3, for scenarios where the computing device has strong computing power, the SDR algorithm is used to convert problem (4) into the SDP form for solution; given the IRS phase offset matrix Θ, the beamforming vector w is optimized, and the SDR method can be used to convert problem (4) into the SDP form: By relaxing the rank-one constraint of rank(W)=1 in problem (5c), problem (5) is transformed into a convex optimization problem, which can be directly solved using standard convex optimization tools to obtain the optimal solution for the matrix W, h k represents the wireless channel from the transmitter directly to the energy harvesting device and reflected by the IRS, h k =h rk ΘH tr +h tk ,h m represents the wireless channel through which the signal is reflected by the IRS and reaches the sensing target. Defining the Matrix Yes k The conjugate transpose operation of 7. The robust design method of the IRS-assisted IWSPT system according to claim 6, characterized in that: In step S3, based on the optimized beamforming vector w, the IRS phase offset matrix Θ is optimized using the SDR algorithm. The problem (4) can be converted into the SDP form using the SDR method: [V] l,l =1,l=1,...,L+1, (8c) rank(V)=1,V≥0. (8d) In the formula, in By relaxing the rank-one constraint of rank(V)=1 in problem (8d), problem (4) is converted into a convex optimization problem, and the optimal solution of the matrix V can be obtained using standard convex optimization tools. Finally, the optimal solution of the IRS phase offset matrix Θ under the current conditions is obtained through diagonalization transformation.

8. The robust design method of the IRS-assisted IWSPT system according to claim 5, characterized in that: In step S4, for the scenario where the computing power of the computing device is weak, a low-complexity algorithm is designed by comprehensively utilizing the first-order Taylor expansion and Riemann manifold optimization ideas to solve the problem; given the IRS phase offset matrix Θ, the beamforming vector w is optimized, and problem (4) is equivalently transformed as follows: In the formula, w (n) represents the optimal value of the previous round of iterative calculation, Problem (10) is a typical second-order cone programming problem, which can be directly solved using standard convex optimization tools to obtain the optimal solution of the beamforming vector w under the current conditions.

9. The robust design method of the IRS-assisted IWSPT system according to claim 8, characterized in that: In step S4, based on the optimized beamforming vector w, the IRS phase offset matrix Θ is optimized, and after performing a matrix equivalent transformation on problem (4), a first-order Taylor expansion is performed to reconstruct the problem as follows: in, represents the optimal value of the previous round of iterative calculation. Since the constraint (11c) is a constant modulus constraint and cannot be directly solved using standard convex optimization tools, the vector is obtained based on the Riemann manifold optimization idea. The optimal value of is obtained, and then the optimal solution of the IRS phase offset matrix Θ under the current conditions is obtained.

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