CN115085774A

CN115085774A - Joint sensation fusion hybrid beam forming method based on Cramer-Lo boundary

Info

Publication number: CN115085774A
Application number: CN202210449241.9A
Authority: CN
Inventors: 王新奕; 张嘉慧; 费泽松; 匡镜明
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2022-04-26
Filing date: 2022-04-26
Publication date: 2022-09-20
Anticipated expiration: 2042-04-26
Also published as: CN115085774B

Abstract

The invention discloses a joint-sensing fusion hybrid beam forming method based on a Cramer-Lo junction, and belongs to the field of communication sensing integration. The invention adopts CrB which can more intuitively reflect the estimation performance of the perception parameter, and minimizes the CRB estimated by the DOA of the target arrival angle under the condition that the base station meets the communication of the service user; the transmitter of the MU-MISO ISAC system forms the HAD wave beam by adopting a partial connection mode, thereby reducing the hardware cost and complexity. A digital beam former and an analog beam former of a MU-MISO ISAC system communication and perception shared beam are optimized through combined design, namely, analog beams and digital beams are directly optimized in an iterative mode through manifold alternate optimization, CRB of target DOA estimation is minimized under the condition that signal-to-noise ratio constraint and transmitter power constraint of a user are met, perception performance of HAD beams in the ISAC system is improved on the premise that communication between a base station and the user is guaranteed, and complexity of a hybrid beam forming system can be reduced.

Description

Joint sensation fusion hybrid beam forming method based on Cramer-Lo boundary

Technical Field

The invention relates to a joint-sensing fusion hybrid beam forming method based on a Cramer-Lo junction, and belongs to the field of communication sensing integration.

Background

Integrated Sensing and Communications (ISAC) is one of the candidates for 6G mobile networks. With the development of millimeter wave communication, characteristics of sensing and communication in terms of channels and signal processing tend to be similar, and thus it is possible to simultaneously perform sensing and communication functions using an integrated beam and platform, thereby reducing hardware costs. In addition, the fusion of sensing and communication information also facilitates cooperation between sensing and communication, thereby improving spectral efficiency.

Based on the above advantages, there have been many efforts to study ISAC beamforming to improve ISAC system perception and communication performance. Liu researches the beam forming in a Multi-User Multi-Input-Single-Output (MU-MISO) ISAC system, aims to approach a target perception beam diagram while meeting the Signal to Interference plus Noise Ratio (SINR) constraint of a Single communication User, and simultaneously shows that when the number of users approaches the number of antennas, the mechanism can synthesize the beam diagram. Liu proposes to minimize the squared error between the designed beam pattern and the desired beam pattern under the quality of service requirements of the communication users. Wang has studied reconfigurable intelligent surface-assisted ISAC systems to mitigate multi-user interference, improving the overall rate of the entire system under the constraint of the perceptual beam pattern.

In addition to the beam pattern, the accuracy of the perceptual parameter estimation is also used as a perceptual performance indicator. Cheng investigated the bit emission sequence design problem of minimum MUI under the crammel bound (CRB) constraint in ISAC systems to estimate the angle of arrival (DOA). Ni studies the communication performance optimization problem under the radar aware CRB constraint. Wang studied joint ISAC beam and passive beamforming using CRB as the perceptual metric.

The above work has focused on a full Radio Frequency (RF) chain architecture, i.e., a unique RF chain is connected to each antenna, which results in high hardware cost and power consumption, especially for large antenna arrays in millimeter wave systems. To address this problem, researchers have studied Hybrid Analog-Digital (HAD) beamforming for ISAC systems. Liu pioneers the joint design of analog and digital beamformers in a Single-User multiple-input Single-output (Single-User MISO) ISAC system to balance communication and radar beamforming errors. Cheng then investigated the sum-rate maximization problem under the perceptual beam-pattern mismatch constraint, using the alternating direction multiplier mechanism and weighted mean square error minimization in single-user and multi-user scenarios, respectively. Dai performs HAD beamforming in ISAC systems using SINR as a performance indicator for sensing and communication. Considering the potential application of the ISAC technology in the terahertz waveband, a.m. elbir researches the design of the HAD beamformer of an ultra-large capacity multiple-input multiple-output antenna ISAC system, and develops model-based and model-free technologies to realize the trade-off between a communication beamformer and a required sensing beamformer.

However, in the existing research method for HAD beamforming, the performance of perceptual parameter estimation cannot be directly reflected by adopting a beam pattern matching error to approach a predefined beam pattern or adopting radar SINR as a perceptual performance index. For unbiased (or asymptotic unbiased) parameter estimation in radar perception, the cramer-circle CRB provides a lower bound of the mean square error of the target estimation, which can directly reflect the perceptual performance. By minimizing CRB in a particular direction, we can improve perceptual capability and perceptual accuracy in a desired perceptual direction. The invention aims to solve the problem of HAD beam forming of an MU-MISO ISAC system by adopting CRB as a target estimation performance index.

Disclosure of Invention

Aiming at the problems that the existing HAD beam forming method lacks an index for directly reflecting the estimation performance of perception parameters and the perception performance needs to be improved in the communication and perception shared beam forming of a multi-user multi-input single-output and general-perception integrated MU-MISO ISAC system, the invention mainly aims to provide a general-perception fusion hybrid beam forming method based on the Clarithromol boundary. The transmitter of the MU-MISO ISAC system forms the HAD wave beam by adopting a partial connection mode, thereby reducing the hardware cost and complexity. Through manifold alternate optimization, analog beams and digital beams are directly optimized in an iterative mode, the sensing performance of the HAD beams in the system can be improved, and the complexity of a hybrid beam forming system can be reduced.

The purpose of the invention is realized by the following technical scheme.

The invention discloses a joint-sense fusion hybrid beam forming method based on a Cramer-Lo junction, which comprises the following steps:

step one, a multi-user multi-input single-output general-purpose integrated MU-MISO ISAC system model with a partial connection hybrid analog-digital HAD wave beam framework is established, wherein a base station serves a plurality of communication users by using designed HAD wave beams, and senses a target by using echoes of the HAD wave beams, so that the base station senses the target while serving the plurality of communication users, and the hardware cost and the complexity are reduced.

Step 1. A: the MU-MISO ISAC system consists of one base station and K single antenna users. Base station using partially connected N _t A hybrid array of antennas, the array being divided into N _RF A plurality of non-overlapping sub-arrays, each sub-array comprising M-N _t /N _RF Each sub-array is connected to the radio frequency chain through the analog phase shifter, and a partial connection structure is adopted, so that the hardware cost and the complexity are reduced. And the base station serves K users and simultaneously carries out target tracking according to the echo signals. Receiver equipment N _r An all-digital ULA antenna is used to receive the echo signal to improve DOA estimation performance.

Step 1.B, according to the MU-MISO ISAC system model given in the step 1.A, the emission signal of the base station in the MU-MISO ISAC system model is expressed as

X＝F _RF F _BB S (1)

Wherein,

representing the baseband data stream, L being the number of symbols contained in a communication frame, S _k,l The l information symbols corresponding to the k user are subject to an independently identically distributed Circularly Symmetric Complex Gaussian (CSCG) distribution, i.e.

The data streams being independent of each other, i.e.

Is a digital precoding matrix;

is an analog precoding matrix; since a partial connection structure is adopted, F _RF Represented as a block diagonal matrix

And each element is an M-dimensional vector with a constant modulus value, i.e.

|f _i (j)|＝1,j＝1,…,M。

Step 1.C, according to the system model given in step 1.A and the transmitted signal model in step 1.B, the signal stream received at the k-th user is represented as

Wherein,

represents that the variance at the k-th user is sigma ² The additive white gaussian noise AWGN of (1),

representing the channel vector between the base station and the kth user, since the millimeter wave channel usually consists of one line-of-sight, LOS, path and multiple non-line-of-sight, NLOS, paths, h _k Is shown as

Where ρ represents the reference distance d ₀ 1m path loss, d _k Denotes the distance, n, between the base station and the k-th user _NL Indicating the number of non-line-of-sight paths, psi _k Indicates the angle, alpha, at which the k-th user is located _ki Representing a small scale fading of the corresponding path,

is the antenna direction vector and δ represents the normalized antenna spacing.

Step 1.D, obtaining an SINR expression at the k-th user according to the signal flow expression received at the k-th user in the step 1.C, wherein the SINR expression is expressed as

Step 1.E, according to the emission signal X of the base station in the step 1.B, the echo signal received by the base station is expressed as follows

Wherein psi ₀ Signal-dependent interference, psi, such as clutter from trees and buildings may be present in the MIMO radar for the angle of the target _j ≠ψ ₀ J e {1, …, J } represents the angle at which J mutually independent signal interferences lie. Xi ₀ And xi _j Path loss and complex reflection coefficient corresponding to the target and jth interferer, respectively;

is a mean of zero and a covariance matrix of R _N The AWGN of (a) is a function of,

step 1.F, according to the echo signal Y received by the base station in step 1.E, the angle psi of the target is shown ₀ Cramer de Roche CRB as follows

Wherein,

the derivative of the steering vector is represented as,

a _i the i-th item of a (ψ) is represented.

And step 1, G, realizing the perception of the target while the base station serves a plurality of communication users by establishing an MU-MISO ISAC system model shown in formulas (1), (2), (4), (5) and (7).

Step two, optimizing the digital beam former F based on the optimization method of semi-definite relaxation SDR or the suboptimal method of second-order cone planning SOCP according to the MU-MISO ISAC system model established in the step one _BB (ii) a Optimizing digital beam former F based on semi-definite relaxation SDR optimization method _BB Obtaining a digital beam former F _BB The optimal solution of (a); second-order cone programming-based SOCP suboptimal method optimization digital beam former F _BB Capable of reducing the digital beam former F _BB The complexity is resolved.

Step 2. A: given unit mode partially connected analog beamformer F _RF Minimizing the CRB of the target DOA estimate while satisfying the user SINR constraint and the transmitter power constraint, the digital beamformer optimization problem expression being

Wherein | · | purple sweet _F Representing norm, P transmitter power, Γ _th Representing a lower bound on the SINR for guaranteed user communications.

Step 2. B: reformulating the digital beamformer optimization problem (8) as a function of the SINR expression at the kth user in step 1.D and the CRB expression in step 1.F

Wherein,

further re-expression of (9) as

Step 2. C: for the digital beamformer optimization problem (10) in step 2.B, the choice is made to proceed to step 2.D using a semi-deterministic relaxation (SDR) based optimization method, and the choice of a Second Order Cone Programming (SOCP) based suboptimal method of reducing complexity jumps to step 2. F.

Step 2. D: introduction of

By removing T _k Relaxing the digital beamformer optimization problem (10) in step 2.B to the semi-definite programming SDP problem

Step 2. E: solving the SDP problem in the step 2.C to obtain an optimal solution

When in use

In order 1, decomposition by eigenvalues

Get the optimal solution

According to step 1.B

Thus obtaining the digital beam former F _BB And jumping to the third step.

Step 2.F: using hyperbolic constraint z ² Equal to or less than xy is equivalent to | | [2z, x-y]The digital beam former optimization problem (10) in the second step is expressed as x + y with | | < x > 0 and y > 0

Wherein,

step 2.G: based on the principle of the continuous convex approximation SCA technology, the optimization problem objective function in the step 2.F is subjected to given point

Instead of the first-order Taylor expansion, the conversion is to the following SOCP form

Step 2. H: approximating (13) in the step 2.G to obtain a solution f _BB,k According to step 1.B

To obtain the digital beam former F _BB And jumping to the third step.

Step three, according to the MU-MISO ISAC system model established in the step one and the digital beam former F calculated in the step two _BB Optimization of the analog beamformer F based on the exact penalty function method and the manifold optimization method _RF And the sensing performance of the HAD wave beam in the MU-MISO ISAC system is improved.

Step 3.A digital beam former F given based on step two _BB The optimization problem of the analog beamformer is shown as follows

Wherein,

step 3.B, expressing the optimization problem in step 3.A as

Step 3.D extraction of F _RF Of the non-zero elements of (a),

and extracting

The extraction rule for the element corresponding to d is as follows

Simultaneous definition of

Wherein m is 1, …, N _RF ，n＝1,…,N _RF 。

Step 3. E-based on the extraction operation in step 3.D, the optimization problem (15) in step 3.B is represented as

Step 3. F: introduction of relaxation variable kappa ═ kappa ₁ ,…,κ _K ](18) in step 3.E is represented by

Step 3. G: conversion of the problem (19) in step 3.F into a problem based on the exact penalty function method

Wherein,

λ _k is a penalty factor.

Step 3. H: solving (20) in step 3.G by using a manifold optimization algorithm, and calculating the Euclidean gradient of the target function (20)

And have the same

When the temperature of the water is higher than the set temperature,

otherwise,' _k (d)＝0。

Step 3. I: calculating a Riemann gradient of the H objective function (21) based on the Euclidean gradient thereof in step 3

Step 3. J: judgment of

Whether or not it is greater than or equal to threshold value epsilon ₁ If yes, t is t +1, the step 3.K is continued, and if no, the step 3.L is skipped.

Step 3. K: introducing superscripts t and t +1 to represent values of t iteration and t +1 iteration variables, adopting a Riemann steepest descent RSD algorithm, selecting the opposite direction of a Riemann gradient as the descent direction of the t iteration, and updating d to be

Wherein beta is _k Representing a pull-back operation in the manifold optimization,

the tangent space of d

The feasible region manifold of points in (1) mapped to (d)

The pull-back operation expression is

Step 3. L: judgment of phi _k (d ^(t+1) ) K is 1, …, and K is less than or equal to threshold value epsilon ₂ Or a maximum number of iterations I _max If yes, let d ^* ＝d ^(t) And output d ^* Jumping to the step four, if not, making lambda _k ＝δ _λ λ _k ，δ _λ And (4) increasing, and returning to the step 3.H for iterative calculation.

According to step 3.D

Obtaining an analog beamformer F _RF And the perception performance of the HAD wave beam in the MU-MISO ISAC system is improved.

Step four: based on the repeated iteration of the second step and the third step, the digital beam former and the analog beam former of the MU-MISO ISAC system communication and perception shared beam are jointly optimized, namely, the digital beam former F is directly and iteratively optimized through the manifold alternative optimization _BB And an analog beamformer F _RF Under the condition of meeting the signal-to-noise ratio constraint of a user and the power constraint of a transmitter, the CRB of the target DOA estimation is minimized, the perception performance of the HAD wave beam in the MU-MISO ISAC system is improved on the premise of ensuring the communication between the base station and the user, and the complexity of a hybrid wave beam forming system can be reduced.

Judgment of

Whether the value of (A) converges or whether the maximum number of iterations I is reached _max If not, jumping to the step two to carry out iteration, if yes, ending the iteration, and outputting a mixed beam former of the MU-MISO ISAC system, namely a digital beam former F _BB And an analog beamformer F _RF Namely, under the condition of meeting the signal-to-noise ratio constraint of a user and the power constraint of a transmitter, optimizing to obtain the CRB estimated by the minimized target DOA, improving the perception performance of the HAD wave beam in the MU-MISO ISAC system on the premise of ensuring the communication between the base station and the user, and reducing the complexity of a hybrid wave beam forming system.

Has the advantages that:

1. the invention discloses a joint-sensing fusion hybrid beam forming method based on a Clarithromol boundary, which is based on an established MU-MISO ISAC model, adopts a CRB (CrB) which can more intuitively reflect sensing performance, and optimizes an HAD (Had beam) of an MU-MISO ISAC system under the constraint of a user communication signal-to-noise ratio), so that the CRB estimated by a target DOA (direction of arrival) is minimized, and the sensing performance of a beam is improved on the premise that a base station meets the user communication.

2. The invention discloses a joint-sensing fusion hybrid beam forming method based on a Clarithrome bound, which jointly designs and optimizes a digital beam former and an analog beam former of an MU-MISO ISAC system communication and sensing common beams, namely directly and iteratively optimizes analog beams and digital beams through manifold alternative optimization, minimizes CRB of target DOA estimation under the condition of meeting the signal-to-noise ratio constraint of a user and the power constraint of a transmitter, improves the sensing performance of HAD beams in the ISAC system on the premise of ensuring the communication between a base station and the user, and can reduce the complexity of a hybrid beam forming system.

3. The invention discloses a joint-sensing fusion hybrid beam forming method based on a Clarithrome bound.A base station uses designed HAD beams to serve communication of a plurality of users and simultaneously senses a target based on echo signals, wherein an MU-MISO ISAC system model with a partially connected HAD beam architecture is established. The base station transmitter adopts a partially connected HAD beam forming structure, reducing hardware cost and complexity.

4. The invention discloses a Kelmelo bound-based synergetics mixed beam forming method, which optimizes a digital beam former F by using an optimization method based on semi-definite relaxation SDR or a suboptimal method based on second-order cone programming SOCP (self-adaptive beamforming) according to the requirements of beam forming precision, resolving complexity, optimization efficiency and the like for an established MU-MISO ISAC (multiple user-input single-output) system model _BB . Digital beam former F optimized based on semi-definite relaxation SDR optimization method _BB Obtaining a digital beam former F _BB The optimal solution of (2); second-order cone programming-based SOCP suboptimal method optimization digital beam former F _BB Capable of reducing the digital beam former F _BB The complexity is resolved.

5. The invention discloses a joint-sensing fusion hybrid beam forming method based on a Claritrol bound, which is based on an MU-MISO ISAC system model and a digital beam former F _BB Optimization of the analog beamformer F based on the method of exact penalty functions and manifold optimization _RF And the perceptual performance of the HAD beam in the ISAC system is improved.

Drawings

Fig. 1 is a flow chart of a method for forming a combined beam based on the clarmero bound common-sense fusion and establishing a MU-MISO ISAC system model with a partially connected HAD beam architecture according to the method of the present invention and embodiment 1;

FIG. 2 is a flow chart of a method for forming a combined beamforming by joint-sensing fusion based on Cramer-Lo junction and an optimized digital beamformer in embodiment 1;

FIG. 3 is a flow chart of a method for forming a combined beamforming by joint sensing based on Cramer-Lo and an optimized analog beamformer in embodiment 1;

FIG. 4 is a flow chart of a method for forming a combined beamforming by joint-sense fusion based on Cramer-Lo junction and an integrally iteratively optimized analog and digital beamformer in embodiment 1 according to the present invention;

FIG. 5 is a diagram of simulation results of a beam pattern after the method of the present invention and the method of the embodiment 1;

fig. 6 is a diagram of a root mean square error RMSE simulation result of a crosssense fusion hybrid beamforming method based on cramer-circle and DOA estimation performed in embodiment 1.

Detailed Description

The present invention provides a method for beamforming a coherent and fused hybrid beam based on cramer-law, which is described in detail below with reference to the accompanying drawings and specific embodiments.

Example 1

This embodiment details the steps of the implementation of the method for forming a hybrid beamforming by joint-sensing fusion based on the clarmero bound.

In the scheme, an MU-MISO ISAC system is considered, in order to reduce hardware cost and complexity, a base station transmitter adopts a partially connected HAD forming structure, and a base station provides communication service for users by using designed HAD wave beams and senses targets according to echo signals. The existing HAD beam forming adopts beam pattern matching error or radar SINR as a performance index of perception, lacks visual evaluation, adopts CrB as a target estimation performance index, can directly reflect the performance of perception parameter estimation, and simultaneously improves the perception capability and the perception precision in the expected perception direction by minimizing the CRB in a specific direction. Therefore, the method for forming the through-sensing fusion hybrid beam based on the Kramer-Lo boundary is adopted, the problem of HAD beam forming of the MU-MISO ISAC system is solved, the communication performance is ensured, and the sensing performance is improved.

Fig. 1 is a flow chart of a method for forming a combined beam forming by joint-sense fusion based on cramer-circle and a method for establishing a MU-MISO ISAC system model with a partially connected HAD beam architecture in embodiment 1.

As can be seen from fig. 1, a multi-user multi-input single-output and multi-sense integrated MU-MISO ISAC system model with a partially connected hybrid analog-digital HAD beam architecture is established, wherein a base station uses a designed HAD beam to serve a plurality of communication users, and simultaneously senses a target by using echoes of the HAD beam, so that the base station can serve the plurality of communication users and sense the target at the same time, and hardware cost and complexity are reduced.

The method for forming a through-sensing fusion hybrid beam based on the cramer-melalo bound disclosed by the embodiment comprises the following specific operation steps:

step 1. A: the MU-MISO ISAC system consists of one base station and K single antenna users. Base station using partially connected N _t A hybrid array of antennas, the array being divided into N _RF A plurality of non-overlapping sub-arrays, each sub-array comprising M-N _t /N _RF Each sub-array is connected to the radio frequency chain through the analog phase shifter, and a partial connection structure is adopted, so that the hardware cost and the complexity are reduced. And the base station serves K users and simultaneously carries out target tracking according to the echo signals. Receiver equipment N _r An all-digital ULA antenna is used for receiving echo signals to improve DOA estimation performance.

In particular, in this embodiment, K is 4, N _t ＝N _r ＝4，N _RF ＝4/8/16/32

Step 1.B, according to the MU-MISO ISAC system model given in step 1.A, the transmission signal of the base station in the system is expressed as

X＝F _RF F _BB S (1)

Wherein,

Assuming that the data streams are independent of each other i.e.

Is a digital precoding matrix;

is an analog precoding matrix; due to the partial connection structure, F _RF Can be expressed as a block diagonal matrix

And each element is an M-dimensional vector with a constant modulus value, i.e.

|f _i (j)|＝1,j＝1,…,M。

Specifically, in the present embodiment, L is 20.

Wherein,

represents that the variance at the k-th user is sigma ² Additive White Gaussian Noise (AWGN),

representing the channel vector between the base station and the kth user, since the millimeter wave channel usually consists of one line-of-sight (LOS) path and multiple non-line-of-sight (NLOS) paths, h _k Can be expressed as

Specific to this embodiment, σ ² ＝-110dBm，ρ＝-60dB，ψ ₁ ＝-45°，ψ ₂ ＝-15°，ψ ₃ ＝15°，ψ ₄ ＝60°，d ₁ ＝d ₂ ＝d ₃ ＝d ₄ ＝50m。

Wherein psi ₀ Signal-dependent interference, psi, such as clutter from trees and buildings may be present in the MIMO radar for the angle of the target _j ≠ψ ₀ J e {1, …, J } represents J mutually exclusiveThe angle at which the standing signal interferes. Xi shape ₀ And xi _j Path loss and complex reflection coefficient corresponding to the target and jth interferer, respectively;

specific to the embodiment,. psi ₀ ＝0°，J＝2，ψ ₁ ＝-30°，ψ ₂ ＝30°，ξ ₀ ＝ξ _j ＝0dB

Wherein,

the derivative of the steering vector is represented as,

a _i the i-th item of a (ψ) is represented.

In particular to the present embodiment, | a _i | ² Is [ -10dB, -5 dB)]With uniformly distributed random numbers.

So far, from step 1.A to step 1.F, the establishment of the MU-MISO ISAC system model with the partially connected HAD beam architecture is completed in the embodiment.

Fig. 2 is a flowchart of a method for forming a combined beamforming based on a clarmero boundary and an optimized digital beamformer in embodiment 1.

As can be seen from FIG. 2, the digital beamformer F is optimized based on the optimization method of the semi-definite relaxation SDR or the suboptimal method of the second order cone programming SOCP according to the MU-MISO ISAC system model established in the step one _BB (ii) a Optimization method optimization digital beam former F based on semi-definite relaxation SDR _BB Obtaining a digital beam former F _BB The optimal solution of (a); second-order cone programming SOCP-based suboptimal method optimization digital beam former F _BB Capable of reducing the digital beam former F _BB Resolving complexity, and the specific operation steps are as follows:

In particular, in this embodiment, P is 30dBm, Γ _th ＝5,7,9,11,13,15,17dB。

Wherein,

further re-expression of (9) as

Step 2. C: for the digital beamformer optimization problem (10) in step 2.B, the selection continues with step 2.D using a semi-deterministic relaxation (SDR) based optimization method, and the selection of a Second Order Cone Programming (SOCP) based suboptimal method of complexity reduction jumps to step 2. F.

Step 2. D: introduction of

When in use

In order 1, decomposition by eigenvalues

Get the optimal solution

According to step 1.B

To obtain the digital beam former F _BB And jumping to the third step.

Step 2.F, hyperbolic constraint z is utilized ² Equal to or less than xy is equivalent to | | [2z, x-y]The digital beam former optimization problem (10) in the second step is expressed as x + y with | | < x > 0 and y > 0

Wherein,

step 2.G, based on the principle of the continuous convex approximation (SCA) technology, using a given point for the objective function of the optimization problem in the step 2.F

Thus obtaining the digital beam former F _BB And jumping to the third step.

To this end, from step 2.A to step 2.E, the connection of the analog beamformer F at a given unit mode portion is completed _RF To the digital beam former F _BB And (4) optimizing.

Fig. 3 is a flowchart of a method for forming a combined beamforming by joint sensing based on cramer-circle and optimizing an analog beamformer in embodiment 1.

As can be seen from FIG. 3, the MU-MISO ISAC system model built according to step one and the digital beamformer F calculated according to step two _BB Optimization of the analog beamformer F based on the exact penalty function method and the manifold optimization method _RF The method improves the sensing performance of the HAD wave beam in the MU-MISO ISAC system, and comprises the following specific operation steps:

Wherein,

step 3. B-expressing the optimization problem in step 3.A by applying a matrix transformation as

Step 3.D extraction of F _RF Is a non-zero element of (a),

and extracting

The extraction rule for the element corresponding to d is as follows

Simultaneous definition of

Wherein m is 1, …, N _RF ，n＝1,…,N _RF

Step 3. F: introduction of relaxation variable kappa ═ kappa ₁ ,…,κ _K ]Will be(18) in step 3.E is represented by

Step 3. G: converting the question (19) in step 3.F into a question based on an exact penalty method

Wherein,

λ _k is a penalty factor.

Step 3. H: solving (20) in step 3.G by using a manifold optimization algorithm, and calculating the Euclidean gradient of the objective function (20)

And have the same

When the temperature of the water is higher than the set temperature,

otherwise,' _k (d)＝0

Step 3. J: judgment of

Whether or not it is greater than or equal to threshold value epsilon ₁ If yes, continuing to execute step 3.K, otherwise, jumping to step 3. L.

Specifically to this embodiment, the threshold e ₁ ＝0.001。

Step 3. K: introducing superscripts t and t +1 to represent values of t iteration and t +1 iteration variables, adopting Riemann Steepest Descent (RSD) algorithm, selecting the opposite direction of Riemann gradient as the descent direction of the t iteration, and updating d to be

Wherein, beta _k Representing a pull-back operation in the manifold optimization,

the tangent space of d

The feasible region manifold of points in (1) mapped to (d)

K is 1, …, K, and the pullback operation expression is

Step 3. L: judgment of phi _k (d ^(t+1) ) K is 1, …, and K is less than or equal to threshold value epsilon ₂ Or to a maximum number of iterations I _max If yes, let d ^* ＝d ^(t) And output d ^* Jumping to the step four, if not, making lambda _k ＝δ _λ λ _k ，δ _λ And (4) increasing, and returning to the step 3.H for iterative calculation.

In particular to this embodiment, the maximum number of iterations I _max Set to 15, the threshold ∈ ₂ ＝0.001，δ _λ ＝2。

To this end, from step 3.A to step 3.K, the given digital beamformer F is completed _BB Optimizing the simulated beams based on the method of precise penalty function and manifold optimizationFormer F _RF 。

According to step 3.D

Obtaining an analog beamformer F _RF And the sensing performance of the HAD wave beam in the MU-MISO ISAC system is improved.

Fig. 4 is a flowchart of a method for forming a combined beamforming by joint-sensing fusion based on cramer-circle and an integrated iterative optimization analog and digital beamformer in embodiment 1.

As can be seen from fig. 4, the digital beamformer and the analog beamformer for the MU-MISO ISAC system communication and sensing shared beam are jointly optimized based on the iterative iteration of step two and step three, i.e. the digital beamformer F is directly iteratively optimized by the manifold alternating optimization _BB And an analog beamformer F _RF Under the condition of meeting the signal-to-noise ratio constraint of a user and the power constraint of a transmitter, the CRB of the target DOA estimation is minimized, the perception performance of the HAD wave beam in the MU-MISO ISAC system is improved on the premise of ensuring the communication between the base station and the user, and the complexity of a hybrid wave beam forming system can be reduced.

Judgment of

So far, the procedure of the perceptual fusion hybrid beamforming method based on the cramer-circle of the present embodiment is completed from step one to step four.

FIG. 5 is a diagram of simulation results of a beam pattern after a method of applying a flux-fusion hybrid beamforming method based on Clarithrome boundary and the method of embodiment 1 according to the present invention;

the abscissa of fig. 5 is the user SINR threshold, which takes values of [ -30:0.2:30 []The unit is degree, the ordinate is normalized beam gain, the unit is dB, and the simulation experiment carries out comparative analysis on three conditions of ISAC mixed analog digital HAD beam forming: n is a radical of _RF 8CRB minimization design method, N _RF 64CRB minimization design method, N _RF As can be seen from fig. 4, the method provided by the present invention has higher beam gain in the target direction, and can obtain higher sensing accuracy, that is, the sensing capability of the beam is improved;

fig. 6 is a diagram of a root mean square error RMSE simulation result of a crosssense fusion hybrid beamforming method based on cramer-circle and an angle of arrival DOA estimation performed in embodiment 1.

In FIG. 6, the abscissa represents the SNR of the radar signal, which is [ -18:1:2] in dB, and the ordinate represents the RMSE of the angle estimation in degrees. The simulation experiment carries out comparative analysis on four conditions: the RMSE of DOA estimation based on multi-signal classification MUSIC estimation and the RMSE of DOA estimation based on maximum likelihood estimation MLE are both used in the CRB minimization method and the beam pattern approximation method, and fig. 5 shows that the RMSE of DOA estimation based on MUSIC or MLE is lower than that of the beam pattern approximation method, that is, the target estimation performance is better than that of the beam pattern approximation method, that is, the sensing performance of the beam is improved.

While the foregoing is directed to the preferred embodiment of the present invention, it is not intended that the invention be limited to the embodiment and the drawings disclosed herein. Equivalents and modifications may be made without departing from the spirit of the disclosure, which is to be considered as within the scope of the invention.

Claims

1.A common-sense fusion hybrid beam forming method based on a Cramer-Lo boundary is characterized in that: comprises the following steps of (a) carrying out,

establishing a multi-user multi-input single-output general-purpose integrated MU-MISO ISAC system model with a partial connection hybrid analog-digital HAD beam architecture, wherein a base station serves a plurality of communication users by using a designed HAD beam, and simultaneously senses a target by using an echo of the HAD beam, so that the base station can sense the target while serving the plurality of communication users, and the hardware cost and the complexity are reduced;

step two, optimizing the digital beam former F based on the optimization method of semi-definite relaxation SDR or the suboptimal method of second-order cone planning SOCP according to the MU-MISO ISAC system model established in the step one _BB (ii) a Optimizing digital beam former F based on semi-definite relaxation SDR optimization method _BB Obtaining a digital beam former F _BB The optimal solution of (2); second-order cone programming-based SOCP suboptimal method optimization digital beam former F _BB Capable of reducing the digital beam former F _BB Resolving complexity;

step three, according to the MU-MISO ISAC system model established in the step one and the digital beam former F calculated in the step two _BB Optimization of the analog beamformer F based on the exact penalty function method and the manifold optimization method _RF The sensing performance of the HAD wave beam in the MU-MISO ISAC system is improved;

2. The method of claim 1, wherein the method comprises: the first implementation method comprises the following steps of,

step 1. A: the MU-MISO ISAC system consists of a base station and K single-antenna users; base station using partially connected N _t A hybrid array of antennas, the arrayIs divided into N _RF A plurality of non-overlapping sub-arrays, each sub-array comprising M-N _t /N _RF Each subarray is connected to the radio frequency chain through the analog phase shifter, and a partial connection structure is adopted, so that the hardware cost and complexity are reduced; the base station serves K users and simultaneously carries out target tracking according to the echo signals; receiver equipment N _r The all-digital ULA antenna is used for receiving echo signals so as to improve DOA estimation performance;

X＝F _RF F _BB S (1)

Wherein,

The data streams being independent of each other, i.e.

Is a digital precoding matrix;

And each element is an M-dimensional vector with a constant modulus value, i.e.

|f _i (j)|＝1,j＝1,…,M；

Wherein,

represents that the variance at the k-th user is sigma ² White gaussian noise

is the antenna direction vector, δ represents the normalized antenna spacing;

Wherein psi ₀ Signal-dependent interference, psi, such as clutter from trees and buildings may be present in the MIMO radar for the angle of the target _j ≠ψ ₀ J ∈ {1, …, J } represents the angle at which J mutually independent signal interferences lie; xi ₀ And xi _j Path loss and complex reflection coefficient corresponding to the target and jth interferer, respectively;

Wherein,

the derivative of the steering vector is represented as,

a _i item i representing a (ψ);

and step 1, G, realizing that the base station serves a plurality of communication users and simultaneously senses the target by establishing an MU-MISOISAC system model shown in formulas (1) (2) (4) (5) (7).

3. The method of claim 2, wherein the method comprises: the second step is realized by the method that,

Wherein | · | purple sweet _F Representing norm, P transmitter power, Γ _th A lower bound representing the SINR guaranteeing user communications;

Wherein,

further re-expression of (9) as

Step 2. C: for the digital beamformer optimization problem (10) in step 2.B, selecting and using an optimization method based on semi-definite relaxation (SDR) to continue with step 2.D, selecting a sub-optimal method based on Second Order Cone Programming (SOCP) to reduce complexity to jump to step 2. F;

step 2. D: introduction of

When in use

In order 1, decomposition by eigenvalues

Get the optimal solution

According to step 1.B

To obtain the digital beam former F _BB And jumping to the third step;

Wherein,

To obtain the digital beam former F _BB And jumping to the third step.

4. The method of claim 3, wherein the method comprises: the third step is to realize the method as follows,

Wherein,

Step 3.D extraction of F _RF Is a non-zero element of (a),

and extracting

The extraction rule for the element corresponding to d is as follows

Simultaneous definition of

Wherein m is 1, …, N _RF ，n＝1,…,N _RF ；

Step 3. F: introducing relaxation variables

(18) in step 3.E is represented by

Wherein,

λ _k is a penalty factor;

step 3. H: solving (20) in step 3.G by using a manifold optimization algorithm, calculating the Euclidean of the objective function (20)

Gradient of gradient

And have the same

When the temperature of the water is higher than the set temperature,

otherwise,' _k (d)＝0；

Step 3. I: calculating the Riemann gradient of the H objective function (21) based on the Euclidean gradient in step 3

Step 3. J: judgment of

Whether or not it is greater than or equal to threshold value epsilon ₁ If yes, continuing to execute the step 3.K, otherwise, jumping to the step 3. L;

the tangent space of d

The feasible region manifold of points in (1) mapped to (d)

The pull-back operation expression is

Step 3. L: judgment of phi _k (d ^(t+1) ) K is 1, …, and K is less than or equal to threshold epsilon ₂ Or a maximum number of iterations I _max If yes, let d ^* ＝d ^(t) And output d ^* Jumping to the step four, if not, making lambda _k ＝δ _λ λ _k ，δ _λ And (4) adding the quantity, and returning to the step (3. H) for iterative calculation;

according to step 3.D

5. The method of claim 4, wherein the method comprises: the implementation method of the fourth step is that,

judgment of