Mirage search-based optimization algorithm for communication-sensing-energy integrated system

Abstract

The invention discloses an optimization algorithm of a mirage search-based communication-sensing-energy integrated system, and the algorithm comprises the steps: building an optimization problem of a system objective function on a point target model and an extended target model, and optimizing the objective function through simulating the propagation behavior of light in mirage; in a search space, an objective function of each search individual corresponds to a potential solution, global exploration is performed on the position of the potential solution through a mirage strategy, local search is performed on the position of the potential solution through a mirage strategy, and boundary check is performed on the solution with the updated position, so that the search process is guided to gradually approach a global optimal solution. According to the method, the optimal performance is achieved in the aspects of basic performance balance and average objective function value among the three aspects of expansion power, communication and perception under a system framework, and the provided MSO provides a reliable and energy-saving solution for simultaneously optimizing the rate, the detection performance and the energy supply for next-generation mobile communication.

Description

Technical Field

[0001] This invention relates to the field of technology, and specifically to an optimization algorithm for a synesthetic energy integration system based on mirage search. Background Technology

[0002] With the rapid development of IoT technology, future 6G networks are expected to support a large number of new smart applications, including smart logistics, smart homes, industrial automation, and smart healthcare. To realize this vision, cellular systems need to connect billions of low-power IoT devices and continuously meet their multi-dimensional needs for sensing, communication, computing, control, and positioning throughout their entire lifecycle. According to predictions, 6G systems for low-power IoT devices need to achieve a battery life of up to 20 years, positioning accuracy of 1cm indoors and 50cm outdoors, and peak user rates of 1Tbps and actual service rates in the 10–100Gbps range.

[0003] To meet the aforementioned stringent key performance indicators (KPIs), a completely new wireless network architecture and key technologies are urgently needed. Synchronous Wireless Message and Power Transfer (SWIPT) is one such example, organically combining wireless communication with radio frequency (RF)-based wireless power transfer (WPT). In recent years, SWIPT has been considered a feasible solution for providing ubiquitous power supply to large-scale IoT nodes, enabling terminals to operate continuously without battery replacement or even without batteries. In a SWIPT system, the same RF signal is used for both energy harvesting (EH) and message decoding (MD), thereby achieving synchronous transmission of information and energy.

[0004] On the other hand, Integrated Sensing and Communication (ISAC) is considered an important way to support the integration of sensing and communication in 6G networks. ISAC allows the use of the same set of wireless signals to achieve environmental and target perception through echo signals while transmitting information. It is foreseeable that future 6G networks will simultaneously integrate SWIPT and ISAC, evolving into a multifunctional wireless system with sensing, communication, and power supply capabilities. By jointly designing sensing, communication, and WPT, such multifunctional systems are expected to significantly improve the utilization efficiency of limited hardware and spectrum resources, especially for highly dense base station (BS) deployment scenarios.

[0005] With the evolution of IoT networks, the number of mobile sensor devices is constantly increasing. Existing technology has designed a SWIPT system for powering mobile devices worn by walkers. However, SWIPT research for mobile electronic health record (EHR) devices is still in its early stages and faces many new challenges. Especially in precise energy transfer scenarios, obtaining accurate location information of mobile EHRs is even more difficult. A natural approach is to first locate the EHR through sensing capabilities and then transmit information and energy to it. The recently proposed ISAC framework offers a promising solution to this problem: by integrating sensing and communication services on a single platform, ISAC can reuse hardware, spectrum, and signal processing modules.

[0006] In emerging IoT applications such as industrial automation and smart cities, multi-functional wireless solutions are particularly attractive. These scenarios typically deploy a large number of IoT or sensor nodes to continuously monitor environmental conditions. To reliably transmit the sensed data back to the base station in the uplink direction, these devices require a stable power supply; simultaneously, the base station needs to locate the data for further processing and transmit control information in the downlink direction. In these applications, integrating ISAC and SWIPT into a unified multi-functional wireless system can effectively simplify the data acquisition and location process for large-scale low-power terminals, reducing the overall network complexity. Conversely, the awareness of IoT devices or environmental targets helps achieve adaptive resource allocation, reducing the signaling overhead of the SWIPT system when acquiring channel state information. Summary of the Invention

[0007] The purpose of this invention is to address the above-mentioned problems by providing an optimization algorithm for a synesthetic energy integrated system based on mirage search, thereby achieving algorithm optimization for the synesthetic energy integrated system based on mirage search.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] An optimization algorithm for a synesthetic energy integrated system based on mirage search is proposed. The optimization problem of the system objective function is based on a point objective model and an extended objective model. The objective function is optimized by simulating the propagation behavior of light in a mirage.

[0010] In the search space, the objective function of each search entity corresponds to a potential solution. Its position is explored globally using the upper mirage strategy and searched locally using the lower mirage strategy. Boundary checks are performed on the solutions whose positions are updated to guide the search process to gradually approach the global optimum.

[0011] As an improvement to the above technical solution, the integrated sensing and energy system includes a base station, an energy harvesting receiver, a message decoding receiver, and a target to be sensed; the base station S is equipped with M Tx One transmitting antenna and M Rx One receiving antenna for sensing; the energy harvesting receiver and the message decoding receiver are each equipped with M EH With M MD One receiving antenna.

[0012] As an improvement to the above technical solution, M Rx >M Tx .

[0013] As an improvement to the above technical solution, the system operates under quasi-static narrowband channel conditions. During a transmission block containing N symbols, the channel matrices from the base station to the energy harvesting receiver, the message decoding receiver, and the sensing target are denoted as follows: and target response matrix At the nth symbol time (n = 1, ..., N), the base station's transmitted signal vector is denoted as... The transmit signal matrix of the entire transmission block is as follows

[0014] set up Then R is the emission covariance matrix, satisfying

[0015] Sample covariance matrix When N is sufficiently large, it can be approximately equal to the statistical covariance matrix R;

[0016] The message decoding receiver receives signal z. MD (n)=G MD y(n)+v MD (n); where This represents additive white Gaussian noise; the achievable rate per unit bandwidth of the MD receiver is written as:

[0017]

[0018] The energy formula for the energy harvesting receiver is:

[0019] The echo signal received by the base station sensing receiver is represented as Z. S =G S Y+V S ;in This represents the equivalent noise matrix, which includes background noise and clutter interference generated during full-duplex operation.

[0020] As an improvement to the above technical solution, under the point target model, the target response matrix is ​​written as follows: in The complex-valued reflection coefficient, θ∈[0,2π), represents the target's arrival / departure angle. and These are the steering vectors for the transmitter and receiver, respectively.

[0021] Assuming the element spacing of the base station is half the wavelength, and denoted by λ, the array response vector can be written as:

[0022]

[0023] Using the Cramér–Rao lower bound (CRB) as an index of the direction angle θ, the Fisher information matrix with respect to θ is derived, and the corresponding scalar CRB1(R) is obtained as follows:

[0024]

[0025] in It's about b r (θ), b t Differentiate (θ);

[0026]

[0027] Under the extended target model, the target response matrix is ​​written as

[0028] Where P is the number of scatterers. Indicates the Nth p AoA / AoD of each scatterer This corresponds to the complex-valued reflection coefficient;

[0029] Based on Gaussian noise, construct a function for G. S The Fisher Information Matrix (FIM) is expressed as follows:

[0030] in Represents the Kronecker product;

[0031] Therefore, the CRB matrix is ​​obtained as CRB = J. -1 ;

[0032] If the trace of the CRB matrix is ​​used as the perception performance metric for the extended target scene, then:

[0033]

[0034] As an improvement to the above technical solution, based on It is known that the reach rate AR(R) is a function of R. Furthermore, based on both the point target model and the extended target model, to ensure sensing accuracy and energy supply quality, constraints on the CRB and energy harvesting must be satisfied simultaneously.

[0035] The minimization problem of maximizing the rate in R is defined as follows: constraints in the formula This ensures that the covariance matrix is ​​positive semi-definite, thus its eigenvalues ​​are non-negative;

[0036] For the above objective function to be feasible in a practical system, the following constraints must also be satisfied.

[0037]

[0038] CRB i (R)≤Γ R ;

[0039] tr(R)≤ω;

[0040] in To receive at least Γ EH The minimum energy, CRB i (R)≤Γ R The perceptual error is specified to not exceed a given threshold Γ R This ensures that the positioning or parameter estimation accuracy is within an acceptable range; tr(R)≤ω limits the total transmit power to not exceed the budget ω, thereby ensuring that the system meets hardware capabilities and regulatory requirements.

[0041] As an improvement to the above technical solution, the steps to optimize the objective function by simulating the propagation behavior of light in a mirage are as follows: For each search individual Mx i (The i-th candidate solution) is randomly initialized to Mx within the allowed range of values ​​for the design variables. i =[Mx i1 ,Mx i2 ,…,Mx iD ],Mx id ∈[LB d UB d ]; where i = 1, 2, ..., N x For individual indices, D is the number of decision variables (problem dimension), and LB is the index. d and UB d Let represent the lower and upper bounds of the d-th dimension variable, respectively;

[0042] Generate a random initial solution Mx within the interval. i =LB i +r1×(UB i -LB i ), i = 1, 2, ..., N xWhere r1 is a uniformly random number in the interval [0,1], and N x Indicates population size;

[0043] For each search entity, calculate its corresponding objective function value as: F i =f(Mx i ), i = 1, 2, ..., N x ;

[0044] Based on the fitness (objective function) value, select the optimal solution from the current population:

[0045] As an improvement to the above technical solution, the method of the mirage strategy is as follows:

[0046] Determine the number n individuals that employ the mirage strategy. SMS : Where T and T max These are the current iteration count and the maximum iteration count, respectively.

[0047] The influence factor σ is calculated based on the individual's fitness value. i : Where r2 is a random number, F Best This represents the current optimal fitness value, where ε is a very small positive constant introduced to avoid the denominator being zero;

[0048] After obtaining the impact factor, the top n values ​​are updated using the mirage strategy. SMS Individual location:

[0049] Where r3 and r4 are random numbers that follow a uniform distribution, and R1 is a vector consisting of random variables that follow a normal distribution.

[0050] As an improvement to the above technical solution, the method of the Mirage Strategy is:

[0051] Calculate the influence factor θ based on fitness value i : Where r5 is a random number;

[0052] For the remaining individuals (i.e., index i = n) SMS +1,…,N x The position is updated using a mirage strategy: Where r6 and r7 are uniformly random numbers, and R2 is a normally distributed random vector.

[0053] As an improvement to the above technical solution, the method for lower boundary control is:

[0054] For each individual, boundary control can be represented as: In the formula, max(·) and min(·) act on the vector in a dimension-wise manner, thereby truncating each component to [LB]. i UB i Within the interval;

[0055] For the updated individual Recalculate its objective function value:

[0056] If the fitness of the new individual is better than that of the original individual, then the new solution replaces the old solution:

[0057] At the same time, if the new individual is better than the global optimum, then the global optimum is updated:

[0058]

[0059] Compared with the prior art, the advantages and positive effects of this invention are:

[0060] The optimization algorithm for an integrated sensing and energy system based on mirage search, as presented in this invention, demonstrates through simulation results that the Mirage Search Algorithm (MSO) achieves a lower objective function value and higher communication rate while maintaining sensing accuracy and energy harvesting performance. Furthermore, it exhibits the lowest transmit power overhead, the most concentrated result distribution, and the best robustness. This optimization algorithm for an integrated sensing and energy system based on mirage search demonstrates significant comprehensive advantages and practical value in the joint optimization problem of "rate-sensing-energy". Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 This is a schematic diagram of the system model architecture of the present invention;

[0063] Figure 2 This is a schematic diagram illustrating the iterative performance of the present invention;

[0064] Figure 3 This is a schematic diagram comparing the effects of the present invention and existing algorithms. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art to all other embodiments obtained without creative effort should be included within the protection scope of the present invention.

[0066] Figure 1 As shown, consider a class of multi-functional MIMO wireless systems where the estimation-rate-energy (ERE) functions are jointly performed by a multi-mode base station (MM-BS), an energy harvesting (EH) receiver, a message decoding (MD) receiver, and a target to be sensed. The MM-BS employs a uniform linear antenna array (ULAA) structure and is equipped with M... Tx One transmitting antenna and M Rx >M Tx One receiving antenna for sensing. The EH and MD receivers are each equipped with an M... EH With M MD There are 1 receiving antenna. Assuming the system operates under quasi-static narrowband channel conditions, the channel remains constant during a transmission block containing N symbols. The channel matrices from the MM-BS to the EH receiver, the MD receiver, and the sensing target are denoted as follows: and target response matrix The transmit signal vector of MM-BS at the nth symbol time (n=1,…,N) is denoted as... The transmit signal matrix of the entire transmission block is then:

[0067]

[0068] To maximize capacity, assume Where R is the emission covariance matrix, satisfying:

[0069]

[0070] Sample covariance matrix When N is sufficiently large, it can be approximated by the statistical covariance matrix R. In subsequent optimization, R will be used as the primary design variable. At the MD receiver, the received signal is:

[0071] z MD (n)=G MD y(n)+v MD (n)(3)

[0072] in This represents additive white Gaussian noise. Based on this, the achievable data rate (bps / Hz) per unit bandwidth of the MD receiver can be written as:

[0073]

[0074] Next, we consider the wireless power transfer process from the base station to the EH receiver. The EH receiver typically uses a rectifier circuit for power harvesting; generally, the relationship between its DC output power and the received RF power is not a simple linear one. For ease of analysis, in this system, it takes the following form:

[0075]

[0076] Finally, consider target detection and parameter estimation. The echo signal received by the MM-BS sensing receiver can be expressed as:

[0077] Z S =G S Y+V S (6)

[0078] in This represents the equivalent noise matrix, including background noise and clutter interference generated during full-duplex operation. The goal of sensing is to utilize the known transmitted signal Y and received signal Z. S Target-related parameters, such as orientation angle and reflection coefficient, are estimated. This paper considers two perception scenarios: point targets and extended targets.

[0079] I. Point Target Model:

[0080] For point targets, the target response matrix can be written as:

[0081]

[0082] in The complex-valued reflection coefficient, θ∈[0,2π), represents the target's arrival / departure angle (AoA / AoD). and These are the steering vectors for the transmitter and receiver, respectively. Assuming the element spacing of the ULAA is half the wavelength, and denoted by λ, the array response vector can be written as:

[0083]

[0084] In point target scenarios, perception performance is typically characterized by the lower bound of the estimation error of the orientation angle θ, i.e., the Cramér–Rao lower bound (CRB) is used as the metric. Based on the constructed observation model, the Fisher information matrix with respect to θ can be derived, and the corresponding scalar CRB (denoted as CRB1(R) in this paper) can be obtained. Its specific expression depends on the steering vector and its derivative with respect to θ, which will not be elaborated here, but will only be used as a perception performance constraint in subsequent optimizations.

[0085]

[0086] in It's about b r (θ), b t Differentiate (θ). Where:

[0087]

[0088] II. Extending the target model:

[0089] For an extended target scenario, the target consists of multiple scatterers. In this case, the target response matrix can be expressed as:

[0090]

[0091] Where P is the number of scatterers. Indicates the Nth p AoA / AoD of each scatterer These are the corresponding complex-valued reflection coefficients. At this point, the goal of MM-BS is to estimate the entire matrix G. S The set of unknown parameters in G. Based on the Gaussian noise assumption, we can construct a parameter for G. S The Fisher Information Matrix (FIM) is expressed as follows:

[0092]

[0093] in This represents the Kronecker product. Therefore, the CRB matrix can be obtained as CRB = J. -1 To facilitate scalarization, this paper uses the trace of the CRB matrix as the perception performance metric for the extended target scenario, i.e.:

[0094]

[0095] In summary, in a multifunctional MIMO system, a joint trade-off needs to be made between the achievable rate given by Equation (4), the energy harvesting performance corresponding to Equation (5), and the sensing accuracy described by Equation (15) in order to characterize the achievable region of the system in the three-dimensional performance space of estimation-rate-energy (ERE).

[0096] III. Optimization of Problem Establishment

[0097] To improve the data rate and overall performance of the communication system, the transmit covariance matrix R needs to be designed rationally to efficiently utilize power and channel resources. According to equation (4), the achievable rate AR(R) is a function of R. On the other hand, to ensure sensing accuracy and energy supply quality, the constraints on CRB and energy acquisition must be satisfied simultaneously. For the two scenarios of point targets and extended targets (denoted as (i∈{1,2})), under the premise of satisfying energy and CRB constraints, maximizing the rate can be equivalently written as the following minimization problem of R:

[0098]

[0099] constraints in the formula The covariance matrix is ​​guaranteed to be positive semi-definite, thus its eigenvalues ​​are non-negative. To make the above objective function feasible in a practical system, the following constraints must also be satisfied:

[0100]

[0101] CRB i (R)≤Γ R (18)

[0102] tr(R)≤ω (19)

[0103] Where constraint (14) is that the receiver must obtain at least Γ EH The minimum energy, constraint (15) stipulates that the perception error cannot exceed a given threshold Γ. R To ensure that the positioning or parameter estimation accuracy is within an acceptable range; constraint (16) limits the total transmit power to not exceed the budget ω, thereby ensuring that the system meets hardware capabilities and regulatory requirements.

[0104] The proposed MSO algorithm:

[0105] The Mirage Search Optimizer (MSO) optimizes the objective function by simulating the propagation of light in a mirage. In the search space, each agent corresponds to a potential solution, and its position is updated using two strategies: the Superior Mirage Strategy (SMS) and the Inferior Mirage Strategy. These two strategies respectively handle global exploration and local development, thus jointly guiding the search process to gradually approach the global optimum.

[0106] Step 1: Initialization

[0107] For each search individual Mx i (The i-th candidate solution) is randomly initialized within the allowed range of values ​​for the design variables.

[0108] Initialization:

[0109] Mx i =[Mx i1 ,Mx i2 ,…,Mx iD ],Mx id ∈[LB d UB d (20)

[0110] Where i = 1, 2, ..., N x For individual indices, D is the number of decision variables (problem dimension), and LB is the index. d and UB d Let represent the lower and upper bounds of the d-th dimension variable, respectively.

[0111] In practical implementation, a random initial solution can be generated within the interval as follows:

[0112] Mx i =LB i +r1×(UB i -LB i ), i = 1, 2, ..., N x (twenty one)

[0113] Where r1 is a uniformly random number in the interval [0,1], and N x This represents the population size. Then, for each individual being searched, the corresponding objective function value is calculated:

[0114] F i =f(Mx i ), i = 1, 2, ..., N x (twenty two)

[0115] Based on the fitness (objective function) value, select the optimal solution from the current population and record its corresponding solution vector:

[0116]

[0117] Among them, Mx Best This represents the best solution found so far.

[0118] Step 2: Implement the Superior Mirage Strategy (SMS)

[0119] This stage corresponds to global exploration, where a subset of individuals are primarily responsible for searching distant regions in the early stages of the algorithm to prevent it from prematurely getting trapped in local optima. First, it is necessary to determine the number n individuals, which will employ the mirage strategy. SMS :

[0120]

[0121] Where T and T max These represent the current iteration count and the maximum iteration count, respectively. It can be seen that as the iteration count T increases, n... SMS The number of individuals participating in the global exploration gradually decreases over time. Next, the influence factor σ is calculated based on the individual's fitness value. i :

[0122]

[0123] Where r2 is a random number, F Best This represents the current optimal fitness value, where ε is a very small positive constant introduced to avoid the denominator being zero.

[0124] After obtaining the impact factor, the top n values ​​are updated using the mirage strategy. SMS Individual location:

[0125]

[0126] Where r3 and r4 are random numbers that follow a uniform distribution, and R1 is a vector composed of random variables that follow a normal distribution. Equation (24) describes the behavior of an individual "seeing" a better solution in the distance and jumping toward it, thereby achieving global exploration.

[0127] Step 3: Inferior Mirage Strategy

[0128] This stage corresponds to local development. The remaining individuals not participating in the upper mirage strategy perform a detailed search near the current excellent solution using the lower mirage strategy to further improve the solution's accuracy. First, the influence factor θ is calculated based on the fitness value. i :

[0129]

[0130] Where r5 is a random number. This factor gives individuals with better fitness a greater search weight, thus allowing them to move more accurately along the preferred direction. For the remaining individuals (i.e., those with index i = n) SMS +1,…,N x The position is updated using a mirage strategy:

[0131]

[0132] Where r6 and r7 are uniformly random numbers, and R2 is a normally distributed random vector. This update formula guides individuals toward the current optimal solution while retaining a certain degree of randomness through a distance-related perturbation term, thereby avoiding getting trapped in local optima and improving local search capabilities.

[0133] Step 4: Boundary Control

[0134] After updating the location, a boundary check needs to be performed on the new solution to ensure that all decision variables remain within the predefined feasible region. For each individual, the boundary control can be represented as:

[0135]

[0136] In the formula, max(·) and min(·) act on the vector in a dimension-wise manner, thereby truncating each component to [LB]. i UB i Within the range.

[0137] For the updated individual Recalculate its objective function value:

[0138]

[0139] If the fitness of the new individual is better than that of the original individual, then the new solution replaces the old solution:

[0140]

[0141] At the same time, if the new individual is better than the global optimum, then the global optimum is updated:

[0142]

[0143] In the MSO algorithm, steps 2 through 4 are executed iteratively until the maximum number of iterations is reached or the given convergence condition is met. The final output is Mx. Best This is the optimal solution obtained, and its corresponding objective function value is denoted as F. Best .

[0144] Numerical simulation and performance analysis

[0145] To verify the effectiveness of the proposed MSO in a multifunctional MIMO inductive power supply system, MSO was compared with two other representative metaheuristic algorithms: the Artificial Hummingbird Algorithm (AHA) and the Draco Lizard Optimizer (DLO). In the simulation, each algorithm was run independently 50 times, and the combined objective function value was statistically obtained.

Claims

1. An optimization algorithm for a synesthetic energy integrated system based on mirage search, characterized in that: The optimization problem of the system objective function is based on the point objective model and the extended objective model. The objective function is optimized by simulating the propagation behavior of light in a mirage. In the search space, the objective function of each search entity corresponds to a potential solution. Its position is explored globally using the upper mirage strategy and searched locally using the lower mirage strategy. Boundary checks are performed on the solutions with updated positions to guide the search process to gradually approach the global optimum.

2. The optimization algorithm for the synesthetic energy integrated system based on mirage search as described in claim 1, characterized in that... The integrated sensing and energy system includes a base station, an energy harvesting receiver, a message decoding receiver, and a target to be sensed; the base station S is equipped with M Tx One transmitting antenna and M Rx One receiving antenna for sensing; the energy harvesting receiver and the message decoding receiver are each equipped with M EH With M MD One receiving antenna.

3. The optimization algorithm for the synesthetic energy integrated system based on mirage search as described in claim 2, characterized in that... :M Rx >M Tx 。 4. The optimization algorithm for the synesthetic energy integrated system based on mirage search as described in claim 2, characterized in that... The system operates under quasi-static narrowband channel conditions. During a transmission block containing N symbols, the channel matrices from the base station to the energy harvesting receiver, the message decoding receiver, and the sensing target are denoted as follows: and target response matrix At the nth symbol time (n = 1, ..., N), the base station's transmitted signal vector is denoted as... The transmit signal matrix of the entire transmission block is as follows set up Then R is the emission covariance matrix, satisfying Sample covariance matrix When N is sufficiently large, it can be approximately equal to the statistical covariance matrix R; The message decoding receiver receives signal z. MD (n)=G MD y(n)+v MD (n); where This represents additive white Gaussian noise; the achievable rate per unit bandwidth of the MD receiver is written as: The energy formula for the energy harvesting receiver is: The echo signal received by the base station sensing receiver is represented as Z. S =G S Y+V S ;in This represents the equivalent noise matrix, which includes background noise and clutter interference generated during full-duplex operation.

5. The optimization algorithm for the synesthetic energy integrated system based on mirage search as described in claim 2, characterized in that... In the point target model, the target response matrix is ​​written as in The complex-valued reflection coefficient, θ∈[0,2π), represents the target's arrival / departure angle. and These are the steering vectors for the transmitter and receiver, respectively. Assuming the element spacing of the base station is half the wavelength, and denoted by λ, the array response vector can be written as: Using the Cramér–Rao lower bound, i.e., CRB, as the orientation angle θ index, the Fisher information matrix with respect to θ is derived, and the corresponding scalar CRB1(R) is obtained as follows: in It's about b r (θ), b t Differentiate (θ); Under the extended target model, the target response matrix is ​​written as Where P is the number of scatterers. Indicates the Nth p AoA / AoD of each scatterer This corresponds to the complex-valued reflection coefficient; Based on Gaussian noise, construct a function for G. S The Fisher information matrix is ​​expressed as follows: in Represents the Kronecker product; Therefore, the CRB matrix is ​​obtained as CRB = J. -1 ; If the trace of the CRB matrix is ​​used as the perception performance metric for the extended target scene, then:

6. The optimization algorithm for the synesthetic energy integration system based on mirage search as described in claim 5, characterized in that... :based on It is known that the reach rate AR(R) is a function of R. Furthermore, based on both the point target model and the extended target model, to ensure sensing accuracy and energy supply quality, constraints on the CRB and energy harvesting must be satisfied simultaneously. The minimization problem of maximizing the rate in R is defined as P. i : Constraints in the formula This ensures that the covariance matrix is ​​positive semi-definite, thus its eigenvalues ​​are non-negative; For the above objective function to be feasible in a practical system, the following constraints must also be satisfied. CRB i (R)≤Γ R ; tr(R)≤ω; in To receive at least Γ EH The minimum energy, CRB i (R)≤Γ R The perceptual error is specified to not exceed a given threshold Γ R This ensures that the positioning or parameter estimation accuracy is within an acceptable range; tr(R)≤ω limits the total transmit power to not exceed the budget ω, thereby ensuring that the system meets hardware capabilities and regulatory requirements.

7. The optimization algorithm for the synesthetic energy integrated system based on mirage search as described in claim 6, characterized in that... The steps to optimize the objective function by simulating the propagation behavior of light in a mirage are as follows: For each search individual Mx i That is, the i-th candidate solution is randomly initialized Mx within the allowed range of values ​​for the design variables. i =[Mx i1 ,Mx i2 ,...,Mx iD ],Mx id ∈[LB d UB d ]; where i = 1, 2, ..., N x For individual indices, D is the number of decision variables, and LB is the index. d and UB d Let represent the lower and upper bounds of the d-th dimension variable, respectively; Generate a random initial solution Mx within the interval. i =LB i +r1×(UB i -LB i ), i = 1, 2, ..., N x Where r1 is a uniformly random number in the interval [0,1], and N x Indicates population size; For each search entity, calculate its corresponding objective function value as: F i =f(Mx i ), i = 1, 2, ..., N x ; Based on the fitness objective function value, select the optimal solution from the current population:

8. The optimization algorithm for the synesthetic energy integrated system based on mirage search as described in claim 7, characterized in that... The method of the mirage strategy is: Determine the number n individuals that employ the mirage strategy. SMS : Where T and T max These are the current iteration count and the maximum iteration count, respectively. The influence factor σ is calculated based on the individual's fitness value. i : Where r2 is a random number, F Best This represents the current optimal fitness value, where ε is a very small positive constant introduced to avoid the denominator being zero; After obtaining the impact factor, the top n values ​​are updated using the mirage strategy. SMS Individual location: Where r3 and r4 are random numbers that follow a uniform distribution, and R1 is a vector consisting of random variables that follow a normal distribution.

9. The optimization algorithm for the synesthetic energy integrated system based on mirage search as described in claim 8, characterized in that... The method of using the Mirage Strategy is: Calculate the influence factor θ based on fitness value i : Where r5 is a random number; For the remaining individuals, i.e., index i = n SMS +1,…,N x Update its position using a mirage strategy: Where r6 and r7 are uniformly random numbers, and R2 is a normally distributed random vector.

10. The optimization algorithm for the synesthetic energy integrated system based on mirage search as described in claim 2, characterized in that... The method for lower boundary control is: For each individual, boundary control can be represented as: In the formula, max(·) and min(·) act on the vector in a dimension-wise manner, thereby truncating each component to [LB]. i UB i Within the interval; For the updated individual Recalculate its objective function value: If the fitness of the new individual is better than that of the original individual, then the new solution replaces the old solution: At the same time, if the new individual is better than the global optimum, then the global optimum is updated:

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