Hardware impairment based energy efficiency optimization method for mobile antenna sensing system

Abstract

This invention discloses an energy efficiency optimization method for a mobile antenna sensing system based on hardware impairments. It primarily addresses the technical problems of poor robustness in energy efficiency optimization under non-ideal hardware characteristics and channel errors in existing systems, and the failure to consider the impact of antenna movement overhead. The solution includes: 1) configuring multiple mobile antennas at the base station transmitter to construct an integrated sensing system; 2) introducing hardware impairments at the transceiver end and channel state information errors to construct communication, sensing, and non-ideal signal models; 3) establishing a system energy efficiency model including positioning time, movement energy consumption, transmission energy consumption, and circuit energy consumption; 4) jointly optimizing the transmission beamforming matrix, mobile antenna positions, and positioning time with the goal of maximizing system energy efficiency; and 5) using fractional programming and alternating optimization methods to obtain the optimal result. This invention can significantly improve system energy efficiency while meeting communication service quality and sensing accuracy constraints, and is applicable to wireless sensing integrated scenarios.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and further relates to communication and sensing integration, movable antennas, beamforming, and energy efficiency optimization technology. Specifically, it is a method for optimizing the energy efficiency of a movable antenna sensing system based on hardware impairment, which can be used in scenarios that require simultaneous wireless communication and target perception, such as sixth-generation mobile communication networks, intelligent transportation, low-altitude sensing, UAV monitoring, and industrial Internet of Things. Background Technology

[0002] Integrated Sensing and Communication (ISAC) technology, by sharing spectrum resources, hardware platforms, and signal processing flows, simultaneously achieves information transmission and target perception within the same system, and is considered one of the key technologies for future sixth-generation mobile communication networks. Existing ISAC systems typically employ fixed-position antenna arrays and coordinate communication and sensing performance through beamforming, power allocation, or time-frequency resource allocation. Movable antenna (MA) technology overcomes the limitations of fixed antenna structures, enabling the adjustment of the antenna's physical position within a preset area to alter the array response and wireless channel phase relationship, thereby providing the system with additional spatial degrees of freedom. Existing research has shown that movable antennas can improve communication link quality and can be used to enhance the performance of integrated sensing and communication systems.

[0003] Lyu W et al., in their paper "Movable Antenna Enabled Integrated Sensing and Communication" (DOI 10.1109 / TWC.2025.3525631), proposed a mobile antenna-assisted integrated sensing and communication system, which enhances communication and sensing performance by adjusting the antenna position. However, it mainly focuses on improving communication and sensing performance, and does not adequately consider practical factors such as hardware impairment, imperfect channel state information, mobile positioning time, and mobile energy consumption. Chen G et al., in their paper "Energy Efficiency Maximization for Multiuser CommunicationsWith Movable Antennas: Joint Beamforming and Antenna Position Design" (DOI10.1109 / JIOT.2025.3626139), studied the energy efficiency maximization problem of mobile antenna communication systems, improving the energy efficiency of multi-user communication by jointly optimizing beamforming and antenna position. This method can effectively utilize the positional freedom of mobile antennas, but it is mainly geared towards a single communication scenario and does not consider the sensing accuracy constraints in the integrated sensing and communication system.

[0004] Furthermore, while existing research on robust beamforming under non-ideal hardware and imperfect channel state information has improved the reliability of traditional communication systems under practical conditions, it primarily focuses on fixed antenna arrays or single communication tasks. It fails to incorporate optimization of movable antenna positions and cannot simultaneously address the coupling relationship between communication service quality, sensing accuracy, mobility time, and mobility energy consumption. Therefore, current technologies still struggle to achieve energy efficiency optimization for mobile antenna-assisted integrated sensing systems under conditions of non-ideal hardware characteristics and imperfect channel state information. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing an energy efficiency optimization method for movable antenna sensing systems based on hardware impairments. It aims to solve the technical problems in existing integrated sensing systems where the fixed antenna structure has limited spatial freedom, insufficient adaptability to hardware non-ideal characteristics and channel state information errors, and does not fully consider the impact of movable antenna positioning time and mobility energy consumption, thus failing to achieve high-efficiency optimization while ensuring communication and sensing performance. This invention improves system energy efficiency under conditions of hardware non-ideal characteristics and channel state information errors by jointly optimizing the transmit beamforming matrix and the movable antenna position, while meeting the requirements of communication service quality and sensing accuracy.

[0006] The basic idea behind this invention is as follows: Multiple movable antennas are configured at the base station transmitter, allowing them to adjust their positions within a preset two-dimensional area. This alters the antenna array response and the phase relationship of the wireless channel, enabling spatial reconstruction of the communication and sensing channels. Simultaneously, hardware impairments at the transmitter and receiver, as well as channel state information errors, are incorporated into the communication and sensing models, making the optimization process more consistent with real-world non-ideal systems. Furthermore, the positioning time and energy consumption of the movable antennas are included in the system energy efficiency model, avoiding the reduction of effective transmission time or increase in total energy consumption due to solely pursuing channel gain, thus achieving energy-saving effects. Finally, the system energy efficiency maximization problem is decomposed into two sub-problems: beamforming optimization and antenna position optimization. These are solved jointly using fractional programming and alternating optimization to obtain the optimal result.

[0007] To achieve the above objectives, the technical solution of the present invention includes the following:

[0008] (1) Constructing a mobile antenna-assisted integrated sensing system:

[0009] A mobile antenna-assisted sensing integrated system is constructed, comprising a base station, multiple mobile transmitting antennas, a fixed sensing receiver, multiple single-antenna communication users, and a sensing target. The mobile transmitting antennas move within a preset two-dimensional area to change the array response in the directions of the communication users and the sensing target.

[0010] (2) Establish a communication channel based on the location of the movable transmitting antenna. and sensing channels The communication channel adopts the multipath Ricean fading model, and the sensing channel adopts the line-of-sight path model.

[0011] (3) Construct a model of the synesthetic system under non-ideal conditions and establish performance constraints:

[0012] (3.1) Introduce communication channel state information error into the communication channel to obtain the actual communication channel. Simultaneously, sensing channel state information error is introduced into the sensing channel to obtain the actual sensing channel. ;

[0013] (3.2) Based on the actual communication channel and the actual sensing channel, hardware impairments are introduced to establish models of the actual transmitted signal, the received signal of the communication user and the sensing echo signal, and the signal-to-interference-plus-noise ratio and reachability of the communication user, as well as the Cramerlow lower bound of the sensing target.

[0014] (3.3) Establish communication service quality based on the signal-to-interference-plus-noise ratio and reachable rate of communication users. Constraints are established by using the Cramero lower bound of the perceived target to determine the perception accuracy. constraint;

[0015] (4) Combining antenna mobility characteristics and system energy consumption model, construct the energy efficiency expression of the integrated sensing system:

[0016] (4.1) Based on the communication service quality constraints and perception accuracy constraints established in step (3), the position optimization of the movable transmitting antenna is completed, and the antenna positioning time is determined according to the initial position, optimized position and preset moving speed of the movable transmitting antenna. ;

[0017] (4.2) From the total time slot length of the system The effective sensing transmission time is obtained by subtracting the antenna positioning time from the input. The effective sensing transmission time is not less than the minimum transmission time required to achieve the target communication service quality and sensing accuracy;

[0018] (4.3) Using the number of communication users and the rate during the effective inductive transmission time as the system throughput, and combining the transmission energy consumption, antenna movement energy consumption and circuit energy consumption, establish the system energy efficiency expression;

[0019] (5) Using the system energy efficiency expression as the objective function, the transmit beamforming matrix, the position of the movable transmit antenna and the antenna positioning time are used as optimization variables; the communication service quality constraints and sensing accuracy constraints mentioned in step (3) and the duration requirements of effective sensing transmission time in step (4) are introduced to construct a joint optimization model with the goal of maximizing system energy efficiency.

[0020] (6) Solve the joint optimization model, including using the fractional programming method to transform the model into a parameterized subtractive optimization model to eliminate the fractional form of the objective function; and using the alternating optimization method to iteratively update the transmit beamforming matrix and the position of the movable transmit antenna until the algorithm converges and outputs the optimal transmit beamforming matrix and the optimal position of the movable transmit antenna.

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] First, because this invention introduces a movable antenna at the base station transmitter and jointly optimizes its position with the transmit beamforming matrix, compared to the traditional fixed antenna integrated sensing system which only relies on beamforming to control the signal direction, this invention can adjust the array response phase by changing the physical position of the movable antenna, thereby reconstructing the communication channel and sensing channel. This design increases the spatial degree of freedom of the system, which is beneficial to improving the effective received signal quality of communication users and enhancing the availability of echo signals in the direction of the sensing target.

[0023] Secondly, this invention simultaneously introduces transmit hardware impairments, receive hardware impairments, and channel state information errors in the modeling of the communication signal-to-interference-plus-noise ratio and the lower bound of sensing Cramer-Rao. Compared with methods that only optimize under ideal hardware and perfect channel state information conditions, the transmit beamforming matrix and movable antenna position obtained by this invention can reflect the distortion noise and channel uncertainty in the actual system, thereby reducing the impact of hardware non-ideal characteristics and channel estimation errors on communication service quality and sensing accuracy.

[0024] Third, this invention incorporates the positioning time and mobile energy consumption of the movable antenna into the system energy efficiency model. During the optimization process, it simultaneously constrains the mobile distance, effective transmission time, and mobile energy consumption, so that the movable antenna will not incur excessive time or energy loss in order to obtain a small channel gain improvement, thereby helping to improve the overall energy efficiency of the system.

[0025] Fourth, this invention aims to maximize system energy efficiency while simultaneously setting constraints on transmit power, mobile area, minimum antenna spacing, communication signal-to-interference-plus-noise ratio, and sensing Cramer-Rao lower bound. Compared to methods that only optimize communication rate or only optimize sensing performance, this invention can optimize energy efficiency while ensuring communication service quality and sensing accuracy, thereby achieving coordination between communication performance, sensing performance, and energy consumption.

[0026] Fifth, this invention employs a solution method combining fractional programming and alternating optimization. It decomposes the originally coupled optimization problems of transmit beamforming matrix, movable antenna position, and positioning time into beamforming optimization sub-problems and antenna position optimization sub-problems. For the beamforming sub-problem, a weighted minimum mean square error transformation and a continuous convex approximation are used for solution. For the antenna position sub-problem, a quadratic penalized near-end gradient projection method is used for solution. This approach significantly reduces the difficulty of solving the original non-convex fractional optimization problem and improves the feasibility of the method in practical systems. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the movable antenna-assisted integrated sensing system constructed in this invention;

[0028] Figure 2 This is a flowchart illustrating the overall implementation of the method of the present invention;

[0029] Figure 3 This is a comparison chart of the system energy efficiency convergence performance provided in the embodiments of the present invention;

[0030] Figure 4 This is a comparison chart of system energy efficiency performance under different launch hardware quality factors provided in the embodiments of the present invention;

[0031] Figure 5 This is a comparison chart of system energy efficiency performance under different receiving hardware quality factors provided in the embodiments of the present invention;

[0032] Figure 6 This is a comparison chart of system energy efficiency performance under different channel state information errors provided in the embodiments of the present invention. Detailed Implementation

[0033] The present invention will now be further described with reference to the accompanying drawings.

[0034] Example 1: Refer to Figure 1-2 This invention proposes an energy efficiency optimization method for a movable antenna sensing system based on hardware impairment, the specific implementation steps of which are as follows:

[0035] Step 1) Refer to Figure 1 Construct a mobile antenna-assisted integrated sensing system:

[0036] A mobile antenna-assisted sensing integrated system is constructed, comprising a base station, multiple movable transmitting antennas, a fixed sensing receiver, multiple single-antenna communication users, and a sensing target. The movable transmitting antennas move within a preset two-dimensional area to alter the array response in the directions of the communication users and the sensing target. The multiple movable transmitting antennas are configured at the transmitting end of the base station, and each movable antenna can adjust its position within the preset two-dimensional area. The sensing receiver is used to receive reflected echoes from the target; the communication users are used to receive downlink communication signals. By jointly adjusting the transmitting beamforming matrix and the positions of the movable antennas, the system energy efficiency is improved while meeting the requirements for communication service quality and sensing accuracy.

[0037] Step 2) Establish a communication channel based on the location of the movable transmitting antenna. and sensing channels The communication channel adopts the multipath Ricean fading model, and the sensing channel adopts the line-of-sight path model.

[0038] Step 3) Construct a model of the synesthetic system under non-ideal conditions and establish performance constraints:

[0039] (3.1) Introduce communication channel state information error into the communication channel to obtain the actual communication channel. Simultaneously, sensing channel state information error is introduced into the sensing channel to obtain the actual sensing channel. ;

[0040] (3.2) Based on the actual communication channel and the actual sensing channel, hardware impairments are introduced to establish models of the actual transmitted signal, the received signal of the communication user and the sensing echo signal, and the signal-to-interference-plus-noise ratio and reachability of the communication user, as well as the Cramerlow lower bound of the sensing target.

[0041] In this embodiment, the aforementioned hardware impairments include both transmitter hardware impairments and receiver hardware impairments; the actual transmitted signal model is as follows:

[0042]

[0043] in, Indicates the launch hardware quality factor. Represents the transmitted beamforming matrix. Represents a communication symbol vector. This indicates transmission hardware distortion noise;

[0044] The above-mentioned sensing echo signal model is as follows:

[0045] ,

[0046] in, Indicates the receive hardware quality factor. This indicates the conjugate transpose. This indicates received hardware distortion noise. Indicates perceived thermal noise;

[0047] In this embodiment, the signal-to-interference-plus-noise ratio (SIR) of the aforementioned communication users is calculated by simultaneously including multi-user interference, interference caused by channel state information errors, transmission hardware distortion noise, and communication thermal noise; the Cramer-Rao lower bound of the aforementioned sensing target is calculated by introducing transmitter hardware impairment, receiver hardware impairment, and sensing channel state information errors.

[0048] (3.3) Establish communication service quality based on the signal-to-interference-plus-noise ratio and reachable rate of communication users. Constraints are established by using the Cramero lower bound of the perceived target to determine the perception accuracy. constraint;

[0049] Step 4) Combining antenna mobility characteristics with the system energy consumption model, construct the energy efficiency expression for the integrated sensing and communication system:

[0050] (4.1) Based on the communication service quality constraints and perception accuracy constraints established in step (3), the position optimization of the movable transmitting antenna is completed, and the antenna positioning time is determined according to the initial position, optimized position and preset moving speed of the movable transmitting antenna. ;

[0051] (4.2) From the total time slot length of the system The effective sensing transmission time is obtained by subtracting the antenna positioning time from the input. The effective sensing transmission time is not less than the minimum transmission time required to achieve the target communication service quality and sensing accuracy;

[0052] (4.3) Using the number of communication users and the rate during the effective inductive transmission time as the system throughput, and combining the transmission energy consumption, antenna movement energy consumption, and circuit energy consumption, establish the system energy efficiency expression:

[0053] ;

[0054] in, Indicates the first Signal-to-interference-plus-noise ratio for each communication user Indicates the total number of communication users; The total energy consumption of the system is determined according to the following formula:

[0055]

[0056] in, Indicates the power amplifier efficiency. Indicates the transmission power; Indicates energy consumption per unit distance traveled. Indicates the first The location of a movable transmitting antenna Indicates the first The initial position of a movable transmitting antenna. Indicates the power of the radio frequency link circuit. This indicates the static circuit power.

[0057] Step 5) Using the system energy efficiency expression as the objective function, the transmit beamforming matrix, the position of the movable transmit antenna, and the antenna positioning time are used as optimization variables; introducing the communication service quality constraints and sensing accuracy constraints mentioned in Step 3), as well as the duration requirement of effective sensing transmission time in Step 4), a joint optimization model is constructed with the goal of maximizing system energy efficiency:

[0058]

[0059] The constraints include:

[0060]

[0061] in, Indicates the maximum transmission power. Indicates the area where the antenna moves. Indicates the minimum spacing between antennas. and These represent the minimum and maximum movement distances, respectively. This represents the signal-to-interference-plus-noise ratio (SIR) threshold for communication. This represents the lower bound threshold for perceiving Clamello.

[0062] Step 6) Solve the joint optimization model, including using a fractional programming method to transform the model into a parameterized subtractive optimization model to eliminate the fractional form of the objective function; and using an alternating optimization method to iteratively update the transmit beamforming matrix and the position of the movable transmit antenna until the algorithm converges and outputs the optimal transmit beamforming matrix and the optimal position of the movable transmit antenna.

[0063] In this embodiment, solving the joint optimization model specifically includes:

[0064] (6.1) The system energy efficiency optimization objective function is transformed into a parameterized subtractive optimization objective function using fractional programming:

[0065]

[0066] in This represents the total effective throughput of the system. Represents the total system energy consumption parameters in the form of Represent the parameters of the fractional programming;

[0067] (6.2) Given the location of the movable antenna and the antenna positioning time, the communication rate optimization problem is transformed into a weighted mean square error optimization problem using the weighted minimum mean square error transformation. The continuous convex approximation method is used to process the non-convex terms in the communication signal-to-interference-plus-noise ratio constraint and the sensing Cramer-Rao lower bound constraint to obtain the updated transmit beamforming matrix. In this embodiment, the update process of the transmit beamforming matrix is ​​implemented in the following way: Given the location of the movable transmit antenna and the antenna positioning time, the receiving filter coefficient and weight coefficient of the communication user are introduced to transform the communication rate optimization objective into the weighted minimum mean square error optimization objective. The expected signal power term in the communication signal-to-interference-plus-noise ratio constraint is approximated by a first-order lower bound, and the non-convex term in the sensing Cramer-Rao lower bound constraint is approximated by a first-order lower bound. A convex quadratic constraint quadratic programming is constructed to iteratively update the transmit beamforming matrix.

[0068] The above-mentioned introduction of the receiving filter coefficients and weighting coefficients of communication users transforms the communication rate optimization objective into a weighted minimum mean square error optimization objective, including updating the receiving filter coefficients in the weighted minimum mean square error according to the following formula:

[0069] ;

[0070] The weighting coefficients in the weighted minimum mean square error are updated according to the following formula:

[0071] ;

[0072] in, Indicates the first Beamforming vectors for each communication user Indicates the first The mean square error of each communication user Indicates the first Interference and noise term for each communication user.

[0073] (6.3) Given the transmit beamforming matrix, determine the antenna positioning time based on the position of the movable antenna:

[0074] ;

[0075] in, Indicates the moving speed of the movable antenna;

[0076] (6.4) The communication signal-to-interference-plus-noise ratio constraint, the sensing Cramer-Rao lower bound constraint, the minimum spacing constraint of the movable antenna, and the minimum moving distance constraint of the movable antenna are transformed into penalty terms, and the position of the movable antenna is updated using the near-end gradient projection method; wherein, the position of the movable transmitting antenna is projected onto the feasible set jointly determined by the antenna moving area and the maximum moving distance:

[0077] ;

[0078] in, Represents the set of position vectors for all movable transmitting antennas;

[0079] (6.5) After completing the alternating updates of the transmit beamforming matrix and the position of the movable transmit antenna, update the fractional programming parameters based on the current effective throughput and total energy consumption:

[0080] ;

[0081] in, This indicates the current iteration number. When the change in the objective function value or fractional programming parameter between two adjacent iterations is less than a preset threshold, the iteration stops, and the optimal transmit beamforming matrix and the optimal movable transmit antenna position are output.

[0082] Example 2: The overall implementation steps of the energy efficiency optimization method proposed in this example are the same as in Example 1, and will now be referred to... Figure 2 The implementation process of the method of the present invention will be further described in detail with specific parameter settings:

[0083] Step 1: Construct a downlink movable antenna-assisted sensing integrated system, including a base station, A movable transmitting antenna, A single-antenna communication user, a sensing target, and a fixed sensing receiver. The base station connects via... One movable transmitting antenna simultaneously transmits to Each communication user sends downlink communication signals and transmits sensing signals to the sensing target; a fixed sensing receiver is used to receive the echo signals reflected back from the sensing target.

[0084] The All movable transmitting antennas are deployed at the base station transmitter; the first The positions of the movable transmitting antennas are denoted as:

[0085] ;

[0086] The set of locations of all movable antennas is represented as:

[0087] ;

[0088] Step 2: Consider that the position of the movable antenna will affect the antenna array response, thereby changing the communication channel and the sensing channel; for the first... The first communication user's The response vector of the movable antenna array for each propagation path is expressed as:

[0089] ;

[0090] in, Indicates the carrier wavelength. Indicates the first The communication user The propagation direction vector of each path.

[0091] The first The estimated communication channel for each communication user is represented as follows:

[0092] ;

[0093] in, Represents Rice factor, Indicates path gain. This indicates the number of propagation paths.

[0094] Considering the error in communication channel state information, the actual communication channel is represented as follows:

[0095] ;

[0096] in, Indicates the first The communication channel state information error for each communication user can be modeled as follows:

[0097] ;

[0098] For the sensing link, the sensing channel adopts the line-of-sight path model, and the estimated sensing channel is represented as:

[0099] ;

[0100] in, Indicates the reflectance coefficient of the perceived target. This represents the array response vector corresponding to the direction of the perceived target.

[0101] Considering the error in the sensing channel state information, the actual sensing channel is represented as follows:

[0102] ;

[0103] in, Indicates the error in sensing channel state information:

[0104] .

[0105] Step 3: Establish the transmitted signal model, the communication received signal model, and the sensing echo signal model under non-ideal hardware conditions:

[0106] Let the transmitted beamforming matrix be:

[0107] ;

[0108] in, Indicates the first Beamforming vectors corresponding to each communication user.

[0109] The communication symbol vector is represented as:

[0110] ;

[0111] And satisfy:

[0112] ;

[0113] Considering hardware defects at the transmitting end, the actual transmitted signal is represented as follows:

[0114] ;

[0115] in, ∈[0,1], This indicates hardware distortion noise at the transmitting end.

[0116] No. The signal received by a communication user is represented as follows:

[0117] ;

[0118] in This indicates thermal noise in communication.

[0119] Therefore, the first number is calculated. The signal-to-interference-plus-noise ratio (SIR) of a single communication user is expressed as:

[0120] ;

[0121] in, Indicates the first The total interference plus noise term for each communication user specifically includes multi-user interference, interference caused by channel state information errors, transmission hardware distortion noise, and communication thermal noise.

[0122] The quality of service constraints are expressed as follows:

[0123] ;

[0124] For a sensing link, considering hardware impairments at the receiving end, the echo signal received by the sensing receiver is represented as:

[0125] ;

[0126] in, ∈[0,1], This indicates hardware distortion noise at the receiving end. This indicates perceived thermal noise.

[0127] Based on the sensed echo signal, the lower bound of the sensed Cramer-Rao (CRB) is calculated and used as an evaluation index for sensed accuracy.

[0128] The perception accuracy constraint is expressed as:

[0129] ;

[0130] in, This represents the signal-to-interference-plus-noise ratio (SIR) threshold for communication. This represents the perception accuracy threshold.

[0131] Step 4: Establish the positioning time and effective sensing transmission time of the movable antenna:

[0132] Within a system time slot, the movable antenna first adjusts its position, and then the base station performs communication and sensing transmission; let the total system time slot length be... The positioning time is The effective inductive transmission time is:

[0133] ;

[0134] And it meets the positioning time constraint:

[0135] ;

[0136] Step 5: Construct the system energy efficiency maximization optimization problem.

[0137] The total system energy consumption includes transmission energy consumption, mobile antenna energy consumption, and circuit energy consumption, expressed as:

[0138] ;

[0139] in, Indicates the power amplifier efficiency. Indicates energy consumption per unit distance traveled. Indicates the power of the radio frequency link circuit. This indicates the static circuit power.

[0140] System energy efficiency is defined as the ratio of the sum of achievable speeds of all communication users during the effective inductive transmission time to the total system energy consumption:

[0141] ;

[0142] This invention aims to maximize system energy efficiency by jointly optimizing the transmit beamforming matrix. Movable antenna position and positioning time The following optimization problem is established:

[0143] ;

[0144] ;

[0145] Among them, it means Minimum safe distance between movable antennas and These represent the minimum and maximum movement distances, respectively.

[0146] Step 6: Solve the system energy efficiency maximization problem using fractional programming and alternating optimization methods:

[0147] Define the effective transmission rate function:

[0148] ;

[0149] Define the total energy consumption function:

[0150] ;

[0151] The Dinkelbach fractional programming method is used to transform the system energy efficiency maximization problem into a parameterized subtractive optimization problem:

[0152] ;

[0153] in, Indicates the Dinkelbach parameter; This represents the total effective throughput of the system, corresponding to the total reachable rate of communication users. This represents the total system energy consumption, which includes transmit power energy consumption, antenna movement energy consumption, and circuit static energy consumption.

[0154] In the In the next outer iteration, the Dinkelbach parameter is updated according to the following formula:

[0155] ;

[0156] in, The first The next iteration's transmit beamforming matrix, set of movable transmit antenna positions, and antenna positioning time. Given... In this case, the alternating optimization method is used to solve the transmit beamforming subproblem and the movable antenna position subproblem respectively.

[0157] Step 7: Iterate through the two subproblems until convergence:

[0158] Given a movable antenna location and positioning time In the case where the communication channel and sensing channel are fixed, this invention uses the weighted minimum mean square error method and the continuous convex approximation method to update the transmit beamforming matrix;

[0159] Introducing the first Received filtering coefficients for each communication user and weighting coefficients , No. The mean square error of a communication user is expressed as:

[0160] ;

[0161] The received filter coefficients are updated as follows:

[0162] ;

[0163] The weighting coefficients are updated as follows:

[0164] ;

[0165] Then, a first-order approximation is made to the non-convex terms in the communication signal-to-interference-plus-noise ratio constraint and the sensing Cramer-Rao lower bound constraint, transforming the transmit beamforming subproblem into a convex quadratic constraint quadratic programming problem. Solving this convex quadratic constraint quadratic programming problem yields the updated transmit beamforming matrix. .

[0166] Given a transmit beamforming matrix In this case, the movable antenna position The determination of communication and sensing channels affects both positioning time and mobile energy consumption. This invention employs a quadratic penalized near-end gradient projection method to update the position of the movable antenna.

[0167] First, the positioning time is calculated based on the current location of the movable antenna:

[0168]

[0169] Then, the communication signal-to-interference-plus-noise ratio constraint, the sensing Cramer-Rao lower bound constraint, the minimum spacing constraint of movable antennas, and the minimum moving distance constraint are transformed into quadratic penalty terms, thus transforming the position optimization problem into a composite optimization problem.

[0170] The feasible set of movable antenna locations is represented as follows:

[0171] ;

[0172] In a single location update, gradient descent is first performed on the smooth target portion, then near-end update is performed on the moving energy consumption term, and finally the updated movable antenna position is projected onto the feasible set. Inside.

[0173] The updated position of the movable antenna is obtained through the above steps. and the corresponding positioning time .

[0174] After completing one update of the transmit beamforming matrix and the movable antenna position, calculate the current system energy efficiency. and parameterized subtractive objective function value .

[0175] If the change in the objective function between two consecutive alternating optimizations is less than the first preset threshold, the inner alternating optimization is considered to have converged; if the change in the Dinkelbach parameter between two consecutive optimizations is less than the second preset threshold, the outer fractional programming is considered to have converged iteratively.

[0176] When the convergence condition is met, the variable is output; if the convergence condition is not met, the alternating update of the transmit beamforming matrix and the position of the movable antenna continues.

[0177] The effects of the present invention will be further explained below with reference to simulation experiments.

[0178] 1. Simulation conditions:

[0179] The simulation experiments of this invention are performed using Monte Carlo simulation in the MATLAB simulation environment, and the convex optimization subproblems generated during beamforming optimization are solved using the CVX toolbox. The simulation considers a downlink movable antenna-assisted sensing integrated system, which includes a base station, multiple movable transmit antennas, multiple single-antenna communication users, a sensing target, and a fixed sensing receiver. The base station performs downlink communication and target sensing tasks simultaneously through the movable transmit antennas, and the system optimization objective is to maximize system energy efficiency.

[0180] In one embodiment, the number of movable antennas is set to N=4, the number of communication users is K=2, the maximum transmit power is 30dBm, the system time slot length is 2s, and the movable antenna speed is 0.1m / s. The communication users are 40m and 50m away from the base station, respectively, and the sensing target is 30m away from the base station. The communication channel adopts the Ricean fading model, including one line-of-sight path and multiple non-line-of-sight paths; the sensing link is modeled using the array response corresponding to the target direction. Regarding hardware non-ideal characteristics, the default transmit hardware quality factor and receive hardware quality factor are both set to 0.95. Regarding movable antenna constraints, the movable antennas are restricted to a preset two-dimensional movement area and satisfy the minimum antenna spacing constraint, minimum movement distance constraint, and maximum movement distance constraint. The system also sets a communication signal-to-interference-plus-noise ratio threshold and a sensing Cramer-Rao lower bound threshold to ensure communication service quality and sensing accuracy, respectively. Except for the parameters specifically changed in the figure, all other system parameters remain consistent.

[0181] 2. Simulation content:

[0182] To verify the effectiveness of the method of the present invention, the following comparison scheme was set up:

[0183] (a) Fixed-position antenna scheme: In this scheme, the position of the transmitting antenna remains fixed, and only the transmitting beamforming matrix is ​​optimized. This scheme is used to characterize a traditional fixed antenna integrated sensing system.

[0184] (b) Random movable antenna location scheme: This scheme randomly generates movable antenna locations that satisfy the constraints of the moving area and antenna spacing, and optimizes the transmit beamforming matrix at these locations to characterize movable antenna schemes without joint location optimization.

[0185] (c) The method of the present invention: The scheme simultaneously optimizes the transmit beamforming matrix and the position of the movable antenna, and takes into account hardware impairment, channel state information error, mobile positioning time and mobile energy consumption during the optimization process.

[0186] Simulation 1: Under default parameter settings, the system energy efficiency of the proposed method, the fixed-position antenna scheme, and the random movable antenna position scheme is compared with the number of iterations. This is used to verify the convergence of the proposed fractional programming and alternating optimization algorithms, as well as the effect of jointly optimizing beamforming and movable antenna position on improving system energy efficiency. The simulation results are as follows: Figure 3 As shown.

[0187] Simulation 2: Under the conditions of fixed number of movable antennas, number of communication users, transmit power, channel state information error parameters, and sensing constraints, the transmit hardware quality factor is changed. The simulation results compare the changes in system energy efficiency under different schemes to verify the impact of transmitter hardware defects on communication link quality and system energy efficiency. Figure 4 As shown.

[0188] Simulation 3: Under the conditions of fixed number of movable antennas, number of communication users, transmit power, channel state information error parameters, and communication constraints, the receiver hardware quality factor is changed. The simulation results compare the changes in system energy efficiency under different schemes to verify the impact of receiver hardware impairments on sensing echo quality, sensing constraint satisfiesability, and system energy efficiency. Figure 5 As shown.

[0189] Simulation 4: Under the conditions of fixed number of movable antennas, number of communication users, transmit power, and hardware quality factor, the channel state information error parameters are changed, and the system energy efficiency changes of different schemes are compared. This is used to verify the adaptability of the proposed method under imperfect channel state information conditions. The simulation results are as follows: Figure 6 As shown.

[0190] 3. Simulation results:

[0191] Depend on Figure 3 As can be seen, the system energy efficiency of the method of this invention gradually improves and tends to stabilize with the increase of the number of iterations, indicating that the Dinkelbach outer iteration and AO alternating optimization method adopted has good convergence. Compared with other schemes, the overall system energy efficiency of the method of this invention is higher than that of the fixed-position antenna scheme and the random movable antenna position scheme. This is because the antenna position of the comparative schemes remains unchanged, and the system can only adjust the signal distribution in the direction of the communication user and the sensing target by transmitting the beamforming matrix, thus limiting the available spatial degrees of freedom and restricting the improvement of system energy efficiency. In contrast, the method of this invention can make fuller use of spatial degrees of freedom by adjusting the position of the movable antenna to change the array response and channel phase relationship, thus achieving higher system energy efficiency. This result shows that jointly optimizing the transmitting beamforming matrix and the movable antenna position can effectively improve the energy efficiency of the movable antenna-assisted sensing integrated system.

[0192] Depend on Figure 4 It is evident that, with the improvement of the launch hardware quality factor... With the increase in [specific energy level], the overall system energy efficiency of each scheme shows an upward trend. This is because [the energy level] is significantly higher. This indicates that reduced hardware impairment at the transmitting end leads to lower transmission distortion and noise, and improved quality of the effective signal received by communication users, thereby enabling the system to achieve higher communication rates and energy efficiency. Under different transmitting hardware quality factors, the method of this invention outperforms both fixed-position antenna schemes and randomly movable antenna position schemes, demonstrating that this invention can maintain good energy efficiency performance even under non-ideal transmitting hardware conditions by jointly optimizing beamforming and antenna position.

[0193] Depend on Figure 5 It can be seen that with the improvement of the receiving hardware quality factor The increase in size leads to an overall improvement in system energy efficiency. This is because the larger size... This indicates that reduced hardware impairment at the receiving end leads to lower distortion and noise at the sensing receiver, making it easier to satisfy the lower bound constraint of the sensing Cramer-Rao equation. The system can allocate more degrees of freedom to improve energy efficiency while meeting sensing accuracy requirements. The method of this invention achieves higher system energy efficiency under different receiving hardware quality factors, demonstrating its ability to effectively adapt to the impact of non-ideal characteristics of the receiving end hardware on sensing performance and energy efficiency.

[0194] Depend on Figure 6As can be seen, the system energy efficiency of all schemes decreases with the increase of the channel state information error parameter. This is because the channel state information error leads to a mismatch between the transmit beamforming matrix and the position of the movable antenna and the actual channel, thereby reducing the signal-to-interference-plus-noise ratio and affecting the degree to which the sensing constraints are met. Compared with the fixed-position antenna scheme and the random movable antenna position scheme, the method of this invention can still maintain high energy efficiency when the channel state information error increases, indicating that by introducing channel uncertainty in the modeling and optimization process, it can improve the system's adaptability under imperfect channel state information conditions.

[0195] The simulation results above show that the method of the present invention can improve the system energy efficiency while meeting the requirements of communication service quality and sensing accuracy, and maintain good performance under the conditions of non-ideal hardware characteristics and imperfect channel state information.

[0196] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties. Furthermore, the collection, use and processing of the relevant data must comply with the laws, regulations and standards of the relevant countries and regions, and corresponding operation portals are provided for users to choose to authorize or refuse.

[0197] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0198] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art, after understanding the content and principle of the present invention, may make various modifications and changes in form and detail without departing from the principle and structure of the present invention. However, these modifications and changes based on the concept of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing the energy efficiency of a movable antenna sensing system based on hardware impairments, characterized in that, Includes the following steps: (1) Constructing a mobile antenna-assisted integrated sensing system: A mobile antenna-assisted sensing integrated system is constructed, comprising a base station, multiple mobile transmitting antennas, a fixed sensing receiver, multiple single-antenna communication users, and a sensing target. The mobile transmitting antennas move within a preset two-dimensional area to change the array response in the directions of the communication users and the sensing target. (2) Establish a communication channel based on the location of the movable transmitting antenna. and sensing channels The communication channel adopts the multipath Ricean fading model, and the sensing channel adopts the line-of-sight path model. (3) Construct a model of the synesthetic system under non-ideal conditions and establish performance constraints: (3.1) Introduce communication channel state information error into the communication channel to obtain the actual communication channel. Simultaneously, sensing channel state information error is introduced into the sensing channel to obtain the actual sensing channel. ; (3.2) Based on the actual communication channel and the actual sensing channel, hardware impairments are introduced to establish models of the actual transmitted signal, the received signal of the communication user and the sensing echo signal, and the signal-to-interference-plus-noise ratio and reachability of the communication user, as well as the Cramerlow lower bound of the sensing target. (3.3) Establish communication service quality based on the signal-to-interference-plus-noise ratio and reachable rate of communication users. Constraints are established by using the Cramero lower bound of the perceived target to determine the perception accuracy. constraint; (4) Combining antenna mobility characteristics and system energy consumption model, construct the energy efficiency expression of the integrated sensing system: (4.1) Based on the communication service quality constraints and perception accuracy constraints established in step (3), the position optimization of the movable transmitting antenna is completed, and the antenna positioning time is determined according to the initial position, optimized position and preset moving speed of the movable transmitting antenna. ; (4.2) From the total time slot length of the system The effective sensing transmission time is obtained by subtracting the antenna positioning time from the input. The effective sensing transmission time is not less than the minimum transmission time required to achieve the target communication service quality and sensing accuracy; (4.3) Using the number of communication users and the rate during the effective inductive transmission time as the system throughput, and combining the transmission energy consumption, antenna movement energy consumption and circuit energy consumption, establish the system energy efficiency expression; (5) Using the system energy efficiency expression as the objective function, the transmit beamforming matrix, the position of the movable transmit antenna and the antenna positioning time are used as optimization variables; the communication service quality constraints and sensing accuracy constraints mentioned in step (3) and the duration requirements of effective sensing transmission time in step (4) are introduced to construct a joint optimization model with the goal of maximizing system energy efficiency. (6) Solve the joint optimization model, including using the fractional programming method to transform the model into a parameterized subtractive optimization model to eliminate the fractional form of the objective function; and using the alternating optimization method to iteratively update the transmit beamforming matrix and the position of the movable transmit antenna until the algorithm converges and outputs the optimal transmit beamforming matrix and the optimal position of the movable transmit antenna.

2. The method according to claim 1, characterized in that: The hardware damage mentioned in step (3.2) includes hardware damage at the transmitting end and hardware damage at the receiving end; The actual transmitted signal model is as follows: ， in, Indicates the launch hardware quality factor. Represents the transmit beamforming matrix. Represents a communication symbol vector. This indicates transmission hardware distortion noise; The sensing echo signal model is as follows: ， in, Indicates the receive hardware quality factor. This indicates the conjugate transpose. This indicates the received hardware distortion noise. Indicates perceived thermal noise; The signal-to-interference-plus-noise ratio of the communication user is calculated by simultaneously including multi-user interference, interference caused by channel state information errors, transmission hardware distortion noise, and communication thermal noise. The calculation of the Cramerlow lower bound of the sensing target introduces transmitter hardware impairment, receiver hardware impairment, and sensing channel state information error.

3. The method according to claim 2, characterized in that: The system energy efficiency expression described in step (4.3) is as follows: ； in, Indicates the first Signal-to-interference-plus-noise ratio for each communication user Indicates the total number of communication users; This represents the total energy consumption of the system.

4. The method according to claim 3, characterized in that: The total energy consumption of the system is determined according to the following formula: ， in, Indicates the power amplifier efficiency. Indicates the transmission power; Indicates energy consumption per unit distance traveled. Indicates the first The location of a movable transmitting antenna Indicates the first The initial position of a movable transmitting antenna. Indicates the power of the radio frequency link circuit. This indicates the static circuit power.

5. The method according to claim 4, characterized in that: The joint optimization model described in step (5), which aims to maximize system energy efficiency, is expressed as follows: ， The constraints include: ， in, Indicates the maximum transmission power. Indicates the area where the antenna moves. Indicates the minimum spacing between antennas. and These represent the minimum and maximum movement distances, respectively. This represents the signal-to-interference-plus-noise ratio (SIR) threshold for communication. This represents the lower bound threshold for perceiving Clamello.

6. The method according to claim 5, characterized in that: Step (6) involves solving the joint optimization model, specifically including: (6.1) The system energy efficiency optimization objective function is transformed into a parameterized subtractive optimization objective function using fractional programming: ， in Represents the total effective throughput of the system. Represents the total system energy consumption parameters in the form of Represent the parameters of the fractional programming; (6.2) Given the location of the movable antenna and the antenna positioning time, the communication rate optimization problem is transformed into a weighted mean square error optimization problem by using the weighted minimum mean square error transformation. The non-convex terms in the communication signal-to-interference-plus-noise ratio constraint and the sensing Cramer-Rao lower bound constraint are processed by the continuous convex approximation method to obtain the updated transmit beamforming matrix. (6.3) Given the transmit beamforming matrix, determine the antenna positioning time based on the position of the movable antenna: ； in, Indicates the moving speed of the movable antenna; (6.4) The communication signal-to-interference-plus-noise ratio constraint, the sensing Cramer-Rao lower bound constraint, the minimum spacing constraint of the movable antenna, and the minimum moving distance constraint of the movable antenna are transformed into penalty terms, and the position of the movable antenna is updated using the near-end gradient projection method; wherein, the position of the movable transmitting antenna is projected onto the feasible set jointly determined by the antenna moving area and the maximum moving distance: ； in, Represents the set of position vectors for all movable transmitting antennas; (6.5) After completing the alternating updates of the transmit beamforming matrix and the position of the movable transmit antenna, update the fractional programming parameters based on the current effective throughput and total energy consumption: ； in, This indicates the current iteration number. When the change in the objective function value or fractional programming parameter between two adjacent iterations is less than a preset threshold, the iteration stops, and the optimal transmit beamforming matrix and the optimal movable transmit antenna position are output.

7. The method according to claim 6, characterized in that: The transmit beamforming matrix described in step (6.2) is updated in the following way: given the location of the movable transmit antenna and the antenna positioning time, the receiving filter coefficient and weight coefficient of the communication user are introduced, and the communication rate optimization objective is equivalently transformed into the weighted minimum mean square error optimization objective; A first-order lower bound approximation is made for the expected signal power term in the communication signal-to-interference-plus-noise ratio constraint, and a first-order lower bound approximation is made for the non-convex term in the sensing Cramer-Rao lower bound constraint. A convex quadratic constraint quadratic programming is constructed to iteratively update the transmit beamforming matrix.

8. The method according to claim 7, characterized in that: The introduction of the receiving filter coefficients and weighting coefficients of communication users transforms the communication rate optimization objective into a weighted minimum mean square error optimization objective, including updating the receiving filter coefficients in the weighted minimum mean square error according to the following formula: ； The weighting coefficients in the weighted minimum mean square error are updated according to the following formula: ； in, Indicates the first Beamforming vectors for each communication user Indicates the first The mean square error of each communication user Indicates the first Interference and noise term for each communication user.

Images