Generalized water injection power distribution method of communication and inductance integrated system based on OFDM signals

Abstract

The invention relates to a generalized water injection power distribution method of a communication and sensing integrated system based on OFDM signals. The method comprises the following steps: establishing a communication model and a sensing model; obtaining a communication rate of the user based on the communication model; obtaining a posterior Cramer-Rao bound of the position estimation error of the target based on the perception model; under the condition of power threshold constraint and posterior Cramer-Rao bound threshold constraint, establishing an optimization problem by taking maximization of the total communication rate and guarantee of the sensing performance of the communication and inductance integrated system as an optimization target; the optimization problem is converted into a convex optimization problem, a semi-closed solution of the convex optimization problem is solved, and a power distribution strategy is obtained. The sensing performance of the system can be measured under the condition that the target position is unknown, the balance between the communication performance and the sensing performance can be quantified, the power distribution strategy obtained through the method is more suitable for actual use scenes, and the power distribution efficiency is improved. And the sensing performance of the system can be ensured while the total communication rate is maximized.

Description

Technical Field

[0001] The present disclosure relates to the field of radar communication technology, and in particular to a generalized water injection power allocation method for a synaesthesia integration system based on OFDM signals. Background Art

[0002] With the rapid development of radar communication technology, in order to meet users' requirements for high-speed and high-reliability communication performance, the concept of Integrated Sensing and Communication (ISAC) has been proposed. ISAC aims to use ISAC signals to realize radar perception and communication on the same device at the same time, thus achieving the ability of simultaneous communication and perception.

[0003] The base stations in the cellular system can transmit information to mobile users by transmitting orthogonal frequency division multiplexing (OFDM) signals, which can significantly reduce interference in multipath environments; the base stations are connected to each other through optical fiber networks and can share information for collaborative communications, such as cloud wireless access networks and collaborative beamforming. Therefore, inspired by the above cellular systems, the interawareness integrated system can also be further designed with networked perception, that is, multiple base stations share the perception information contained in the echo signals they receive to jointly locate the target, thereby improving the radar perception accuracy.

[0004] In the prior art, in terms of improving the perception performance and communication performance of the synaesthesia integrated system, the transmission waveform of the system is generally designed appropriately or the power allocation is performed on different transmission channels. However, on the one hand, the above-mentioned method of improving system performance usually assumes that the position of the target is determined and known, which is not only difficult to achieve in the actual system, but also makes the designed power allocation scheme unsuitable for the actual use scenario; on the other hand, the above-mentioned method of improving system performance cannot directly quantify the balance between communication performance and perception performance, and thus cannot obtain the optimal power allocation strategy between different subcarriers.

[0005] Therefore, it is necessary to provide a new technical solution to improve one or more problems existing in the above solutions.

[0006] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to ordinary technicians in the field. Summary of the invention

[0007] The purpose of the embodiments of the present disclosure is to provide a generalized water-filling power allocation method for a synaesthesia integration system based on OFDM signals, which is more suitable for actual usage scenarios and can also quantify the balance between communication performance and perception performance.

[0008] According to an embodiment of the present disclosure, a generalized water injection power allocation method for a synaesthesia integration system based on OFDM signals is provided, comprising:

[0009] Establish communication models and perception models;

[0010] Obtaining a communication rate of a user based on the communication model;

[0011] A posterior Cramer-Rao bound of a position estimation error of a target is obtained based on the perception model;

[0012] Under the conditions of power threshold constraint and a posteriori Cramer-Rao bound threshold constraint, the optimization problem is established with the optimization goal of maximizing the total communication rate and ensuring the perception performance of the synaesthesia integrated system.

[0013] The optimization problem is transformed into a convex optimization problem, a semi-closed solution of the convex optimization problem is solved, and a power allocation strategy is obtained.

[0014] In an exemplary embodiment of the present disclosure, in the step of obtaining the communication rate of the user based on the communication model, the communication model is:

[0015]

[0016] in, represents the signal received by the kth user on the nth subcarrier, Indicates that from the mth n The complex channel from the base station to the kth user on the nth subcarrier, Indicates the mth n The power allocated by a base station on its allocated nth subcarrier, Indicates the mth n The frequency domain signal transmitted by a base station on the nth subcarrier, Represents additive white Gaussian noise with a mean of 0 and a variance of Gaussian distribution of

[0017] The communication rate is:

[0018]

[0019] Among them, R k represents the communication rate of the kth user, represents the set of subcarriers allocated to the kth user.

[0020] In an exemplary embodiment of the present disclosure, the perception model is:

[0021]

[0022] in, represents the propagation attenuation coefficient, Δf represents the subcarrier spacing in the OFDM signal, j represents a complex number, Indicates that from the mth n base stations, the total transmission delay after being reflected by the target and received by the u-th base station, Indicates the mth n The frequency domain signal transmitted by a base station on the nth subcarrier, To satisfy the mean of 0, the variance is Additive white Gaussian noise.

[0023] In an exemplary embodiment of the present disclosure, the posterior Cramer-Rao bound of the position estimation error of the target obtained based on the perception model includes:

[0024] Calculate the Fisher information matrix of the target based on the perception model;

[0025] A posterior Cramer-Rao bound of the position estimation error of the target is derived based on the Fisher information matrix of the target.

[0026] In an exemplary embodiment of the present disclosure, the Fisher information matrix of the target is:

[0027]

[0028] Among them, f r|θ (r|θ) represents the probability density function of the vector r composed of the received signal, θ represents the vector composed of unknown numbers, including the position coordinates (x, y) of the target and the propagation attenuation coefficient, α represents the vector composed of the propagation attenuation coefficient, is the Fisher information matrix of the prior information, E[·] represents the expectation, Im(·) and Re(·) represent the imaginary and real parts of the complex number, respectively, and the matrix Λ=diag(λ 1,1 ,...,λM ,M ), matrix Γ = diag(γ 1,1 ,...,γ M,M ), matrix ∑=diag(σ 1,1 ,...,σ M,M ), diag(·) represents a diagonal matrix; τ M,M It represents the total transmission delay from the Mth base station to the Mth base station after being reflected by the target.

[0029] In an exemplary embodiment of the present disclosure, the a posteriori Cramer-Rao bound of the position estimation error of the target is:

[0030]

[0031] in,[·] 2×2 Represents the submatrix consisting of the first two rows and first two columns of the target matrix, l and Respectively represent the vector composed of the target position coordinates and the corresponding estimate, E l Expressing expectation.

[0032] In an exemplary embodiment of the present disclosure, the optimization problem is:

[0033]

[0034] in, represents the posterior Cramer-Rao bound threshold constraint, t represents the threshold of the posterior Cramer-Rao bound value, represents the inverse of the Fisher information matrix of the target, tr(·) represents the trace of the matrix, represents the power threshold constraint, p m is the set power threshold of the mth base station, p m,n represents the power allocated by the mth base station on its allocated nth subcarrier, R k represents the communication rate of the kth user, K represents the total number of users, represents the set of subcarriers of the mth base station.

[0035] In an exemplary embodiment of the present disclosure, converting the optimization problem into a convex optimization problem includes:

[0036] Auxiliary variables are introduced to decompose the posterior Cramer-Rao bound threshold constraint in the optimization problem into two sub-constraints, the two sub-constraints are:

[0037]

[0038] Where β represents an auxiliary variable, e1 represents the first column of the first identity matrix, and e2 represents the second column of the second identity matrix;

[0039] The two sub-constraints are transformed according to the properties of Schur complement to obtain two convex constraints.

[0040] In an exemplary embodiment of the present disclosure, the convex optimization problem is:

[0041]

[0042] Among them, F i ≥0,i=1,2 and 0≤β≤1 represents the expression of the convex constraint transformed from the posterior Cramer-Rao bound threshold constraint.

[0043] In an exemplary embodiment of the present disclosure, the semi-closed solution of the convex optimization problem is:

[0044]

[0045] in, are coefficients related to the parameters of the synaesthesia integration system and the Lagrange multipliers, Represents a set of subcarriers; (·) + Indicates that the values ​​in the brackets that are greater than 0 are retained, and the values ​​in the brackets that are less than 0 are set to 0; Indicates that from the mth n The complex channel from the base station to the kth user on the nth subcarrier, Indicates the mth n The power allocated by a base station on its allocated nth subcarrier, Represents variance.

[0046] The technical solution provided by the present disclosure may have the following beneficial effects:

[0047] In the embodiments of the present disclosure, on the one hand, this embodiment establishes a communication model and a perception model, and the communication rate of the user can be derived based on the constructed communication model, and the posterior Cramer-Rao bound of the target position estimation error can be obtained based on the constructed perception model, so as to measure the communication rate and perception performance of the communication and perception integrated system. This embodiment adopts the posterior Cramer-Rao bound to describe the limit of positioning the target, and can measure the perception performance of the system when the specific coordinate position of the target is unknown, so that the power allocation strategy obtained in this embodiment is more suitable for actual usage scenarios; on the other hand, this embodiment proposes the conditions of power threshold constraints and posterior Cramer-Rao bound threshold constraints, and establishes an optimization problem with maximizing the total communication rate and ensuring the perception performance of the synaesthesia integrated system as the optimization goal, so as to quantify the balance between communication performance and perception performance, so that the power allocation strategy obtained in this embodiment can maximize the total communication rate while ensuring the perception performance of the synaesthesia integrated system.

[0048] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0050] Figure 1 A flowchart showing the steps of a generalized water injection power allocation method for a synaesthesia integration system based on OFDM signals in an exemplary embodiment of the present disclosure;

[0051] Figure 2 A schematic diagram showing the variation of the a posteriori Cramer-Rao bound with the total transmission power under different power allocation modes in an exemplary embodiment of the present disclosure;

[0052] Figure 3 A schematic diagram showing the variation of mean square error and corresponding a posteriori Cramer-Rao bound with total transmission power under different power allocation strategies in an exemplary embodiment of the present disclosure is shown;

[0053] Figure 4 The communication rate of the synaesthesia integration system under different power allocation strategies in the exemplary embodiments of the present disclosure is shown;

[0054] Figure 5 The communication rates corresponding to different values ​​of the a posteriori Clamer-Rao bound in the exemplary embodiment of the present disclosure are shown. DETAILED DESCRIPTION

[0055] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0056] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0057] In this example implementation, a generalized water injection power allocation method for a synaesthesia integrated system based on OFDM signals is first provided. Figure 1 As shown in , the method may include the following steps:

[0058] Step S101: establishing a communication model and a perception model;

[0059] Step S102: obtaining the user's communication rate based on the communication model;

[0060] Step S103: obtaining a posterior Cramer-Rao bound of the target position estimation error based on the perception model;

[0061] Step S104: Under the conditions of power threshold constraint and a posteriori Cramer-Rao bound threshold constraint, an optimization problem is established with maximizing the total communication rate and ensuring the perception performance of the synaesthesia integration system as the optimization goal;

[0062] Step S105: converting the optimization problem into a convex optimization problem, solving a semi-closed solution of the convex optimization problem, and obtaining a power allocation strategy.

[0063] In the embodiments of the present disclosure, on the one hand, this embodiment establishes a communication model and a perception model, and the communication rate of the user can be derived based on the constructed communication model, and the posterior Cramer-Rao bound of the target position estimation error can be obtained based on the constructed perception model, so as to measure the communication rate and perception performance of the communication and perception integrated system. This embodiment adopts the posterior Cramer-Rao bound to describe the limit of positioning the target, and can measure the perception performance of the system when the specific coordinate position of the target is unknown, so that the power allocation strategy obtained in this embodiment is more suitable for actual usage scenarios; on the other hand, this embodiment proposes the conditions of power threshold constraints and posterior Cramer-Rao bound threshold constraints, and establishes an optimization problem with maximizing the total communication rate and ensuring the perception performance of the synaesthesia integrated system as the optimization goal, so as to quantify the balance between communication performance and perception performance, so that the power allocation strategy obtained in this embodiment can maximize the total communication rate while ensuring the perception performance of the synaesthesia integrated system.

[0064] It should be noted that although the prior art discloses the transmission signal waveform design of the synaesthesia integrated system or the power allocation on the transmission channel, it needs to be performed when the specific position coordinates of the target are known, and it is impossible to perform waveform design or power allocation when only the statistical information of the target position is available, and the specific position coordinates of the known target are difficult to meet in actual use scenarios. In this embodiment, the a posteriori Cramer-Rao bound is used to describe the limit of locating the target, so that the perception performance of the system can be measured when only the statistical information of the target position is available, and then power allocation can be achieved while considering the communication rate and perception performance.

[0065] Next, each step of the generalized water filling power allocation method for the OFDM signal-based synaesthesia integration system in this exemplary implementation will be described in more detail.

[0066] Before discussing this method, the following professional terms are explained first. In the prior art, water injection power allocation is a power control technology used in communication systems, which aims to optimize the balance between user received signal quality and system energy efficiency. It maximizes the received signal quality of user equipment by allocating more power to users with better channel conditions. Orthogonal frequency division multiplexing (OFDM) is a multi-carrier modulation technology that divides the channel into several orthogonal sub-channels, converts high-speed data signals into parallel low-speed sub-data streams, and modulates them to each sub-channel for transmission. Synaesthesia integration refers to the integration of communication and perception functions into one system or device, and the ability to communicate and perceive simultaneously by sharing hardware, signal processing and information resources.

[0067] In one embodiment, in the step of obtaining the user's communication rate based on the communication model, the communication model is:

[0068]

[0069] in, represents the signal received by the kth user on the nth subcarrier, Indicates that from the mth n The complex channel from the base station to the kth user on the nth subcarrier, Indicates the mth n The power allocated by a base station on its allocated nth subcarrier, Indicates the mth n The frequency domain signal transmitted by a base station on the nth subcarrier, Represents additive white Gaussian noise with a mean of 0 and a variance of Gaussian distribution of

[0070] The communication rate is:

[0071]

[0072] Among them, R k represents the communication rate of the kth user, represents the set of subcarriers allocated to the kth user.

[0073] The communication model established in this embodiment takes into account the complex channels between each base station and the corresponding user on the corresponding subcarrier, the power allocated by each base station on its corresponding subcarrier, and the frequency domain signal transmitted by each base station on the corresponding subcarrier, while also taking into account noise interference to ensure that the established communication model is more in line with the actual communication scenario of the synaesthesia integration system.

[0074] In one embodiment, the perception model is:

[0075]

[0076] in, represents the propagation attenuation coefficient, Δf represents the subcarrier spacing in the OFDM signal, j represents a complex number, Indicates that from the mth n base stations, the total transmission delay after being reflected by the target and received by the u-th base station, Indicates the mth n The frequency domain signal transmitted by a base station on the nth subcarrier, To satisfy the mean of 0, the variance is Additive white Gaussian noise;

[0077] The perception model established in this embodiment takes into account the influence of propagation attenuation, the spacing of subcarriers in the OFDM signal, the total transmission delay when the signal is transmitted between the base station and the target, the frequency domain signal transmitted by each base station on the corresponding subcarrier, and noise interference, to ensure that the established perception model is more in line with the actual usage scenarios of the synaesthesia integration system.

[0078] Furthermore, obtaining the a posteriori Cramer-Rao bound of the target position estimation error based on the perception model in step S103 may further include the following sub-steps:

[0079] Step S1031: calculating the Fisher information matrix of the target based on the perception model;

[0080] Step S1032: deriving a posterior Cramer-Rao bound of the position estimation error of the target according to the Fisher information matrix of the target.

[0081] This embodiment derives the Fisher information matrix of the target through the perception model, and then derives the posterior Cramer-Rao bound of the target position estimation error based on the Fisher information matrix of the target, thereby realizing the use of the posterior Cramer-Rao bound to describe the limit of locating the target, so as to measure the perception performance of the system when the specific coordinate position of the target is unknown.

[0082] Specifically, the Fisher information matrix of the target derived in this embodiment is:

[0083]

[0084] Among them, f r|θ (r|θ) represents the probability density function of the vector r composed of the received signal, θ represents the vector composed of unknown numbers, including the position coordinates (x, y) of the target and the propagation attenuation coefficient, α represents the vector composed of the propagation attenuation coefficient, is the Fisher information matrix of the prior information, E[·] represents the expectation, Im(·) and Re(·) represent the imaginary and real parts of the complex number, respectively, and the matrix Λ=diag(λ1,1 ,...,λ M,M ), matrix Γ = diag(γ 1,1 ,...,γ M,M ), matrix ∑=diag(σ 1,1 ,...,σ M,M ), diag(·) represents a diagonal matrix; τ M,M It represents the total transmission delay from the Mth base station to the Mth base station after being reflected by the target.

[0085] It should be noted that the specific parameters in the above matrix Λ, matrix Γ, and matrix ∑ can be further expressed by formulas (12) to (14):

[0086]

[0087] Among them, λ m,u is the expression of the specific parameters in the matrix Λ, γ m,u is the expression of the specific parameters in the matrix Γ, σ m,u is the expression of the specific parameters in the matrix Σ, represents the set of subcarriers of the mth base station, ξ m,u =4πΔfα m,u , Δf represents the subcarrier spacing in the OFDM signal, α m,u represents the propagation attenuation coefficient, p m,n represents the power allocated by the m-th base station on its allocated n-th subcarrier, Represents variance, and the values ​​of m and u are both [1,M].

[0088] Specifically, the a posteriori Cramer-Rao bound of the target position estimation error derived in this embodiment is:

[0089]

[0090] in,[·] 2×2 Represents the submatrix consisting of the first two rows and first two columns of the target matrix, l and Respectively represent the vector composed of the target position coordinates and the corresponding estimate, E l Expressing expectation.

[0091] In this embodiment, the communication performance and perception performance of the synaesthesia integration system can be measured based on the above-derived user communication rate and the posterior Cramer-Rao bounds of the target position estimation error. Next, the power threshold constraint in the optimization problem can be constructed based on the above-derived user communication rate, and the posterior Cramer-Rao bound threshold constraint in the optimization problem can be constructed based on the above-derived target position estimation error. Therefore, the optimization problem in this embodiment can be expressed as:

[0092]

[0093] in, represents the posterior Cramer-Rao bound threshold constraint, t represents the threshold of the posterior Cramer-Rao bound value, represents the inverse of the Fisher information matrix of the target, tr(·) represents the trace of the matrix, represents the power threshold constraint, P m is the set power threshold of the mth base station, p m,n represents the power allocated by the mth base station on its allocated nth subcarrier, R k represents the communication rate of the kth user, K represents the total number of users, represents the set of subcarriers of the mth base station.

[0094] In the optimization problem constructed above, it is necessary to ensure that the total communication rate of all users in the synaesthesia integrated system is maximized. At the same time, two constraints that need to be satisfied by the optimization problem are set. One constraint is the posterior Cramer-Rao bound threshold constraint. The posterior Cramer-Rao bound threshold constraint indicates that the upper limit of the posterior Cramer-Rao bound of the target position estimation error is less than or equal to the threshold of the posterior Cramer-Rao bound value set. Another constraint condition is the power threshold constraint. The power threshold constraint indicates that the power allocated by the mth base station on its allocated nth subcarrier is less than or equal to the set power threshold of the mth base station. It can be seen that the optimization problem constructed in this implementation can achieve the optimization goal of maximizing the total communication rate and ensuring the perception performance of the synaesthesia integration system.

[0095] It should be noted that the expression of the above-mentioned posterior Cramer-Rao bound threshold constraint is obtained based on the posterior Cramer-Rao bound of the target position estimation error.

[0096] It should also be noted that the difficulty in solving the above optimization problem lies in the complex expression of the posterior Cramer-Rao bound threshold constraint. This embodiment will use the properties of Schur complement to convert the posterior Cramer-Rao bound threshold constraint into a convex constraint, thereby achieving a semi-closed solution to the optimization problem.

[0097] In one embodiment, the step S105 of converting the optimization problem into a convex optimization problem may include the following sub-steps:

[0098] Step S1051: introducing auxiliary variables, decomposing the posterior Cramer-Rao bound threshold constraint in the optimization problem into two sub-constraints, the two sub-constraints are:

[0099]

[0100] Where β represents an auxiliary variable, e1 represents the first column of the first identity matrix, and e2 represents the second column of the second identity matrix;

[0101] Step S1052: transform the two sub-constraints according to the properties of the Schur complement to obtain two convex constraints.

[0102] Specifically, in step S1051, the expression in the posterior Cramer-Rao bound threshold constraint is Split into and Target-based Fisher Information Matrix J θ (α) is a semi-positive definite matrix, which can be confirmed and The values ​​of are all non-negative. Therefore, based on the introduction of the auxiliary variable β, the posterior Cramer-Rao bound threshold constraint Decomposed into the two sub-constraints mentioned above.

[0103] Specifically, in step S1052, the two sub-constraints are transformed according to the properties of Schur complement, and can be transformed into F i ≥0,i=1,2 form of convex constraints, where F1 and F2 are:

[0104]

[0105] Among them, J θ (α) represents the Fisher information matrix of the target, e1 represents the first column of the first identity matrix, represents the inverse of the first identity matrix, e2 represents the second column of the second identity matrix, represents the inverse of the second identity matrix, β represents the auxiliary variable, and t represents the threshold of the posterior Cramer-Rao bound.

[0106] By decomposing the posterior Cramer-Rao bound threshold constraint in the optimization problem into two sub-constraints and converting the two sub-constraints into two convex constraints according to the properties of Schur complement, the optimization problem can be converted into a convex optimization problem. Therefore, the optimization problem can be solved by solving the semi-closed solution of the convex optimization problem, thereby obtaining the power allocation strategy.

[0107] In one embodiment, the convex optimization problem converted into the optimization problem can be expressed as:

[0108]

[0109] Among them, F i ≥0,i=1,2 and 0≤β≤1 represents the expression of the convex constraint transformed from the posterior Cramer-Rao bound threshold constraint.

[0110] Furthermore, the Lagrange dual method can be used to solve the above convex optimization problem, thereby obtaining a semi-closed solution to the convex optimization problem, where the semi-closed solution to the convex optimization problem can be expressed as:

[0111]

[0112] in, are coefficients related to the parameters of the synaesthesia integration system and the Lagrange multipliers, Represents a set of subcarriers; (·) + Indicates that the values ​​in the brackets that are greater than 0 are retained, and the values ​​in the brackets that are less than 0 are set to 0; Indicates that from the mth n The complex channel from the base station to the kth user on the nth subcarrier, Indicates the mth n The power allocated by a base station on its allocated nth subcarrier, Represents variance.

[0113] It should be explained that the semi-closed solution obtained above shows that when the balance between communication rate and perception performance needs to be considered, the water level of the generalized water filling power allocation algorithm is There will be different values ​​on different subchannels. The threshold t of the posterior Cramer-Rao threshold can reflect the requirements for the perceptual performance of the synaesthesia integration system. Different perceptual performance requirements will change The value of , thus affecting the power distribution on the sub-channel.

[0114] In the embodiment of the present application, in order to further verify the effect of the generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system proposed in the present application, the following simulation experiment was carried out:

[0115] In the simulation experiment, a synaesthesia integrated system consisting of M = 4 base stations, a target and K = 4 users is set. They are distributed in a square area of ​​80m×80m, and the base stations are located at the four vertices of the square area. The number of subcarriers is set to N = 256, and the interval of the subcarriers is 30KHz, so the total bandwidth is 7.68MHz. It is assumed that each user is allocated N / K = 64 subcarriers. The noise power spectral density of all users and base stations is -169dBm / Hz. For the random coordinates of the target, it is assumed that the horizontal coordinate x and the vertical coordinate y are uniformly distributed in this square area.

[0116] refer to Figure 2 As shown in Figure 2 The figure shows the variation of the a posteriori Cramer-Rao bound with the total transmission power under different power allocation modes. Figure 2The horizontal axis P represents the total transmission power, and the vertical axis PCRB represents the posterior Cramer-Rao bound. Figure 2 The solid blue line in the middle is the minimum value of the posterior Cramer-Rao bound solved by CVX, a tool conventionally used in the art for solving optimization problems. Once the solution is completed, the corresponding power allocation solution can be obtained. Figure 2 The red dashed line in the middle is the variation trend of the a posteriori Cramer-Rao bound derived in this embodiment with the total transmission power. It can be seen that the a posteriori Cramer-Rao bound (blue solid line) solved by CVX and the a posteriori Cramer-Rao bound (red dashed line) derived in this embodiment are highly consistent, which can verify the correctness of the a posteriori Cramer-Rao bound expression (Formula 6) derived in this embodiment. In addition, Figure 2 The figure also gives the variation trend of the a posteriori Cramer-Rao bound with the total transmission power under the average power allocation scheme (green dotted line). It can be seen that the a posteriori Cramer-Rao bound under the average power allocation scheme is much higher than the minimum value of the a posteriori Cramer-Rao bound solved by CVX. Therefore, it can be seen that by improving the power allocation scheme, the a posteriori Cramer-Rao bound can be effectively reduced and the perception performance of the synaesthesia integrated system can be improved.

[0117] refer to Figure 3 As shown in Figure 3 The figure shows the variation of the mean square error and the corresponding posterior Cramer-Rao bound with the total transmission power under different power allocation strategies. Figure 3 The horizontal axis P represents the total transmission power, and the vertical axis MSE represents the mean square error, which is respectively obtained by setting the threshold of the posterior Cramer-Rao bound t = 2t min and t = 1.5t min , and solve the optimization problem to obtain strategy I and strategy II, where t min Indicates that when setting the power threshold P m Specifically, given a power threshold P m , first calculate the minimum achievable posterior Cramer-Rao bound t min . After obtaining t min Then, the threshold t of the posterior Cramer-Rao bound is set to 2t min , and set the power threshold P m Substitute into the optimization problem to obtain the allocation strategy I; set the threshold t of the posterior Cramer-Rao bound to 1.5t min , and set the power threshold P m Substitute it into the optimization problem to obtain allocation strategy II, and then allocation strategy I and allocation strategy II can be used to estimate the position of the target.

[0118] It should also be noted that Figure 3The water injection algorithm in the paper is a traditional water injection power allocation algorithm. It can remove the a posteriori Cramer-Rao bound threshold constraint in the optimization problem and use different power threshold constraints (for example, setting the power threshold P m The optimization problem is solved under the range of 3W to 10W) ​​to obtain the traditional water injection power allocation strategy.

[0119] refer to Figure 3 As shown in , the average power allocation strategy and the water injection algorithm show similar mean square errors when estimating the position of the target. Compared with the average power allocation strategy and the water injection algorithm, the power allocation strategy (allocation strategy I and allocation strategy II) obtained by using the generalized water injection power allocation method proposed in this embodiment can obtain lower posterior Cramer-Rao bounds and mean square errors. In addition, reference Figure 3 As shown in , in terms of perception performance, allocation strategy II is better than allocation strategy I. It can be seen that in the synaesthesia integration system considered in this embodiment, the power allocation strategy obtained by using a relatively low threshold t of the posterior Cramer-Rao boundary value will show better perception performance.

[0120] refer to Figure 4 As shown in Figure 4 The communication rate of the synaesthesia integrated system under different power allocation strategies is shown to evaluate the balance between perception performance and communication performance. Figure 4 The abscissa P represents the total transmission power.

[0121] pass Figure 4 It can be seen that the communication rate corresponding to the allocation strategy I is less than 1% lower than the communication rate corresponding to the water injection algorithm; the communication rate corresponding to the allocation strategy II proposed in the simulation experiment is less than 1% lower than the communication rate corresponding to the water injection algorithm. Figure 3 As shown in , compared with the water filling algorithm, the mean square error of allocation strategy I and allocation strategy II in estimating the position of the target is reduced by about 30% and 44% respectively. This shows that the power allocation strategy (allocation strategy I and allocation strategy II) obtained by the generalized water filling power allocation method proposed in this embodiment can significantly improve the perception performance of the synaesthesia integrated system on the basis of sacrificing very little communication performance.

[0122] refer to Figure 5 As shown in Figure 5 The communication rates corresponding to different values ​​of the posterior Cramer-Rao bound are shown. It should be noted that Figure 5 The abscissa PCRB represents the posterior Cramer-Rao bound, T SC and T CS are two boundary points, representing the minimum achievable Cramer-Rao bound and the maximum achievable total communication rate obtained by solving the optimization problem.

[0123] refer to Figure 5 As shown in , the performance outer bounds of the power allocation strategy proposed in this embodiment are consistent with the performance outer bounds obtained by CVX, which verifies the effectiveness of the generalized water injection power allocation method proposed in this embodiment. In addition, Figure 5 The performance inner bound obtained by the time sharing algorithm is also introduced as the performance benchmark. The performance outer bound of the power allocation strategy proposed in this embodiment is compared with the performance inner bound. It can be seen that the power allocation strategy obtained by the generalized water injection power allocation method proposed in this embodiment is used to jointly design the perception performance and communication performance, which can significantly improve the performance of the synaesthesia integrated system.

[0124] refer to Figure 5 As shown in , when the value of the posterior Cramer-Rao bound changes from 0.120m 2 Reduced to 0.050m 2 When , the communication rate of the system only slightly decreases. This shows that the power allocation strategy proposed in this embodiment can significantly improve the perception performance of the system without affecting the communication performance. However, when the Cramer-Rao bound is lower than 0.040m 2 When the sensory performance is slightly reduced, the communication performance of the system will be significantly degraded, which can be attributed to the power allocation strategy adopted by the integrated system.

[0125] It can be seen that for the power allocation strategy obtained by adopting the generalized water filling power allocation method proposed in this embodiment, when good perception performance is required, a higher water level needs to be set at the edge of the bandwidth. Therefore, in order to achieve a very low a posteriori Cramer-Rao bound, the synaesthesia integration system concentrates most of the transmission power at the edge of the bandwidth to meet the perception performance requirements of the synaesthesia integration system, although these sub-channels may have severe channel attenuation in terms of communication performance; and the consequence of this is that only a small amount of power is allocated to the remaining sub-channels, which has an adverse effect on the overall communication performance.

[0126] It should be understood that since achieving a lower a posteriori Cramer-Rao bound requires concentrating more power at the edge of the bandwidth, when the communication rate of the synaesthesia integration system is maximized, in order to ensure that the water level on all subcarriers remains balanced, this will cause the perceptual performance of the synaesthesia integration system to be significantly reduced.

[0127] Through the above simulation experiment analysis, it can be proved that the power allocation strategy obtained by the generalized water injection power allocation method proposed in this embodiment can ensure that the synaesthesia integrated system can achieve good perception performance while ensuring the communication performance of the synaesthesia integrated system when the water level changes moderately.

[0128] In the synaesthesia integration system proposed in the present invention, the base station uses OFDM signals for passive target positioning and provides communication services for multiple users. The communication performance and perception performance of the synaesthesia integration system are evaluated by the communication rate and the a posteriori Cramer-Rao bound respectively. The communication rate and the a posteriori Cramer-Rao bound are expressed as functions of the transmission power of the base station, and based on this, this embodiment also proposes an optimization problem for power allocation to explore the balance between perception performance and communication performance. Through the above simulation experiment analysis, it can be proved that the power allocation strategy obtained in this embodiment conforms to the generalized water injection rule. In the traditional water injection power control scheme, the goal is to maximize the total capacity without considering the perception performance. At this time, the water level of the subcarriers of all OFDM signals is the same, and more power will be allocated to the subcarriers with better channel conditions. However, in the generalized water injection power allocation method adopted by the synaesthesia integration system in this embodiment, the water level of all subcarriers is no longer the same, and specifically, the subcarriers suitable for perception performance have a higher water level. Therefore, the power allocated to each subcarrier depends on its effectiveness in perception performance and communication performance. By adopting the power allocation strategy obtained by the generalized water injection power allocation method proposed in this embodiment, the perception performance and communication performance of the synaesthesia integration system can be jointly designed, and compared with the traditional power allocation scheme, the performance of the synaesthesia integration system can be significantly improved.

[0129] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A generalized water injection power allocation method for a synaesthesia integrated system based on OFDM signals, characterized in that: include: Establish communication models and perception models; Obtaining a communication rate of a user based on the communication model; A posterior Cramer-Rao bound of a position estimation error of a target is obtained based on the perception model; Under the conditions of power threshold constraint and a posteriori Cramer-Rao bound threshold constraint, the optimization problem is established with the optimization goal of maximizing the total communication rate and ensuring the perception performance of the synaesthesia integrated system. The optimization problem is transformed into a convex optimization problem, a semi-closed solution of the convex optimization problem is solved, and a power allocation strategy is obtained.

2. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 1 is characterized in that: In the step of obtaining the user's communication rate based on the communication model, the communication model is: in, represents the signal received by the kth user on the nth subcarrier, Indicates that from the mth n The complex channel from the base station to the kth user on the nth subcarrier, Indicates the mth n The power allocated by a base station on its allocated nth subcarrier, Indicates the mth n The frequency domain signal transmitted by a base station on the nth subcarrier, Represents additive white Gaussian noise with a mean of 0 and a variance of Gaussian distribution of The communication rate is: Among them, R k represents the communication rate of the kth user, represents the set of subcarriers allocated to the kth user.

3. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 1 is characterized in that: The perception model is: in, represents the propagation attenuation coefficient, Δf represents the subcarrier spacing in the OFDM signal, j represents a complex number, Indicates that from the mth n base stations, the total transmission delay after being reflected by the target and received by the u-th base station, Indicates the mth n The frequency domain signal transmitted by a base station on the nth subcarrier, To satisfy the mean of 0, the variance is Additive white Gaussian noise.

4. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 1 is characterized in that: The a posteriori Cramer-Rao bound of the target position estimation error obtained based on the perception model includes: Calculate the Fisher information matrix of the target based on the perception model; A posterior Cramer-Rao bound of the position estimation error of the target is derived based on the Fisher information matrix of the target.

5. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 4 is characterized in that: The Fisher information matrix of the target is: Among them, f r|θ (r|θ) represents the probability density function of the vector r composed of the received signal, θ represents the vector composed of unknown numbers, including the position coordinates (x, y) of the target and the propagation attenuation coefficient, α represents the vector composed of the propagation attenuation coefficient, is the Fisher information matrix of the prior information, E[·] represents the expectation, Im(·) and Re(·) represent the imaginary and real parts of the complex number, respectively, and the matrix Λ=diag(λ 1,1 ,...,λ M,M ), matrix Γ = diag(γ 1,1 ,...,γ M,M ), matrix ∑=diag(σ 1,1 ,...,σ M,M ), diag(·) represents a diagonal matrix; τ M,M It represents the total transmission delay from the Mth base station to the Mth base station after being reflected by the target.

6. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 5 is characterized in that: The a posteriori Cramer-Rao bound for the target position estimation error is: in,[·] 2×2 Represents the submatrix consisting of the first two rows and first two columns of the target matrix, l and Respectively represent the vector composed of the target position coordinates and the corresponding estimate, E l Expressing expectation.

7. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 1 is characterized in that: The optimization problem is: in, represents the posterior Cramer-Rao bound threshold constraint, t represents the threshold of the posterior Cramer-Rao bound value, represents the inverse of the Fisher information matrix of the target, tr(· represents the trace of the matrix, represents the power threshold constraint, P m is the set power threshold of the mth base station, p m,n represents the power allocated by the mth base station on its allocated nth subcarrier, R k represents the communication rate of the kth user, K represents the total number of users, represents the set of subcarriers of the mth base station.

8. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 7 is characterized in that: The step of converting the optimization problem into a convex optimization problem comprises: Auxiliary variables are introduced to decompose the posterior Cramer-Rao bound threshold constraint in the optimization problem into two sub-constraints, the two sub-constraints are: Where β represents an auxiliary variable, e1 represents the first column of the first identity matrix, and e2 represents the second column of the second identity matrix; The two sub-constraints are transformed according to the properties of Schur complement to obtain two convex constraints.

9. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 8, characterized in that: The convex optimization problem is: Among them, F i ≥0,i=1,2 and 0≤β≤1 represents the expression of the convex constraint transformed from the posterior Cramer-Rao bound threshold constraint.

10. The generalized water injection power allocation method of the OFDM signal-based synaesthesia integrated system according to claim 9, characterized in that: The semi-closed form solution of the convex optimization problem is: in, are coefficients related to the parameters of the synaesthesia integration system and the Lagrange multipliers, a, b, c represent the Lagrange variables, Represents a set of subcarriers; (·) + Indicates that the values ​​in the brackets that are greater than 0 are retained, and the values ​​in the brackets that are less than 0 are set to 0; Indicates that from the mth n The complex channel from the base station to the kth user on the nth subcarrier, Indicates the mth n The power allocated by a base station on its allocated nth subcarrier, Represents variance.

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