A method and system for MIMO transmission using fluid antennas

Abstract

The application discloses a kind of MIMO transmission method and system using fluid antenna, and multiple fluid antennas that can freely move in given area are respectively arranged at transmitter and receiver side.This application establishes corresponding channel model and constructs optimization problem of maximum system achievable rate according to statistical channel information, to transmit fluid antenna position, receive fluid antenna position and transmit covariance matrix as optimization variable, and uses alternate optimization, Cauchy-Schwarz inequality and Taylor expansion to solve optimization problem to realize achievable rate maximization.This application uses fluid antenna that can freely move in given area in MIMO system, compared with the case that traditional MIMO uses fixed position antenna, this application can utilize more spatial degrees of freedom, obtain higher achievable rate and diversity gain.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and fluid antennas, and in particular to a MIMO transmission method and system utilizing a fluid antenna. Background Technology

[0002] Over the past few decades, the evolution from single-antenna or single-input single-output (SSO) to multi-antenna or multiple-input multiple-output (MIMO) systems has been a significant trend in wireless communication system development. MIMO technology has significantly improved the capacity and reliability of wireless communication by utilizing spatial multiplexing, interference suppression, beamforming, and diversity gain. However, existing communication systems, due to the fixed location of antennas, cannot fully utilize spatial degrees of freedom within a given transmitter and receiver area. To overcome this limitation, fluid antenna technology has recently been introduced, allowing transmitter or receiver antennas to move freely within a designated area. By utilizing more degrees of freedom in the spatial domain, fluid antennas and MIMO can be combined to achieve higher spatial diversity gain.

[0003] Existing papers on fluid antennas all utilize instantaneous channel state information. However, because changes in antenna position lead to channel changes, it is typically difficult to obtain instantaneous channel state information in systems utilizing fluid antennas. On the other hand, the slow-changing nature of statistical channel state information makes it relatively easy to obtain. Therefore, it is necessary to investigate a MIMO transmission scheme that utilizes a fluid antenna and incorporates statistical channel state information within it. Summary of the Invention

[0004] Purpose of the invention: In view of the shortcomings of the prior art, the purpose of this invention is to provide a MIMO transmission method and system using fluid antennas. For scenarios where multiple fluid antennas are deployed on both the transmitter and receiver sides, the achievable rate of the system can be optimized and the complexity of implementing this optimization process can be reduced, making it easier to implement.

[0005] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] The MIMO transmission method using fluid antennas deploys multiple fluid antennas that can move freely within a given area on both the transmitter and receiver sides. By establishing a channel model and constructing an optimization problem to maximize the system's achievable rate based on statistical channel information, the position of the transmitting fluid antennas is optimized. Location of receiving fluid antenna And the emission covariance matrix Q optimizes the achievable rate of the system; the optimization problem is expressed as:

[0007]

[0008]

[0009]

[0010] ||t k -t l ||2≥D,k,l=1,2,...,N,k≠l,

[0011] ||r k -r l ||2≥D,k,l=1,2,...,M,k≠l,

[0012] tr(Q)≤P max

[0013] Where N and M are the number of transmitting fluid antennas and receiving fluid antennas, respectively. and These represent the movable regions of the transmitting and receiving fluid antennas, respectively, and the channel matrix H(t,r) = F. H (r)ΣG(t), The emission region is t0 = (0,0). T From the origin to the receiving region r0 = (0,0) T The path response matrix of the origin, L t and L r These represent the number of transmit paths and receive paths, respectively. Let N be the response matrices of the transmitting fluid antennas. Let I be the response matrices of M receiving fluid antennas. M Let P be an M×M dimensional identity matrix, where D is the minimum distance required between fluid antennas, and P is the minimum distance required between fluid antennas. max For maximum transmit power, det(·) represents the determinant of a matrix, ||·||2 represents the L2 norm of a vector, and tr(·) represents the trace of a matrix. This represents the expectation of the variable Σ; the optimization problem is solved using alternating optimization, the Cauchy-Schwarz inequality, and Taylor expansion.

[0014] Furthermore, the statistical channel state information is obtained through user feedback, direct estimation by the base station, or through uplink probe signals.

[0015] Furthermore, in the channel model, for the transmitter part, let the elevation angle and azimuth angle of the p-th transmission path be respectively... and The position t of the nth transmitting fluid antenna in the p-th transmission path n =(x n ,y n ) T With respect to the origin t0 = (0,0) T The difference in propagation distance between them is The signal phase difference between the nth transmitting fluid antenna and the origin in the p-th transmission path is Where λ is the signal wavelength; the transmission response vector is:

[0016]

[0017] The response matrices of all N transmitting fluid antennas are:

[0018] Furthermore, in the channel model, for the receiver section, let the elevation angle and azimuth angle of the q-th receiving path be respectively... and The position r of the m-th receiving fluid antenna in the q-th receiving path m =(x m ,y m ) T With respect to the origin r0 = (0,0) T The difference in propagation distance between them is The signal phase difference between the m-th receiving fluid antenna and the origin in the q-th transmission path is... Where λ is the signal wavelength; the received response vector is:

[0019]

[0020] The response matrices of all M receiving fluid antennas are:

[0021] Furthermore, the method of solving the optimization problem using alternating optimization, the Cauchy-Schwarz inequality, and Taylor expansion specifically includes:

[0022] The original objective function is replaced with its tight upper bound using Jensen's inequality.

[0023] The original problem is decomposed into an optimization problem of the transmit covariance matrix Q, an optimization problem of the receive fluid antenna position r, and an optimization problem of the transmit fluid antenna position t using alternating optimization, with the iteration number indicator i = 0.

[0024] Solve the Q-optimization problem of the emission covariance matrix using the Cauchy-Schwarz inequality;

[0025] The optimization problem of the receiving fluid antenna position r is solved by decoupling the antenna position variables and Taylor expansion.

[0026] The optimization problem of the transmitting fluid antenna position t is solved by using the Cauchy-Schwarz inequality, antenna position variable decoupling, and Taylor expansion.

[0027] The rate value obtained in the (i+1)th iteration is compared with the result of the i-th iteration. If the difference between the two results is less than the set threshold ε, the iteration is terminated; otherwise, the iteration number i is incremented by 1, and the iteration continues to solve the problem.

[0028] Furthermore, the tight upper bound of the original objective function for: Where, α 2 Let Σ be the response coefficient between the p-th transmit path and the q-th receive path. q,p The variance.

[0029] Furthermore, the optimization problem of the emission covariance matrix Q is solved, specifically including:

[0030] The Q-optimization problem of the emission covariance matrix is ​​expressed as:

[0031] max Q tr(G(t)QG H (t))

[0032] sttr(Q)≤P max

[0033] According to the Cauchy-Schwarz inequality, the objective function can be rewritten as:

[0034]

[0035] The condition for the equation to hold is that Q is G. H (t) is a multiple of G(t); according to the objective function, Q is a multiple of G when it reaches its maximum value. H (t) is a multiple of G(t) and tr(Q) = P max Find the optimal solution for Q based on these two conditions.

[0036] Furthermore, solving the optimization problem for the receiving fluid antenna position r specifically includes:

[0037] The optimization problem for the receiving fluid antenna position r is expressed as:

[0038]

[0039]

[0040] ||r k -r l ||2≥D,k,l=1,2,…,M,k≠l

[0041] After decoupling by antenna position variables, the optimization problem is transformed into the following problem and then solved using a second-order Taylor expansion:

[0042]

[0043]

[0044] ||r m -r k ||2≥D,k=1,2,...,M,k≠m

[0045] Where, f(r) m Let be the m-th column vector in matrix F(r). Remove f(r) from matrix F(r) m The remaining L after ) r A × (M-1) dimensional matrix, For L r ×L r 3D identity matrix.

[0046] Furthermore, solving the optimization problem for the position t of the transmitting fluid antenna specifically includes:

[0047] The optimization problem for the position t of the transmitting fluid antenna is expressed as:

[0048] max t tr(G(t)QG H (t))

[0049]

[0050] ||t k -t l ||2≥D,k,l=1,2,...,N,k≠l

[0051] By decoupling the antenna position variables using the Cauchy-Schwarz inequality, the optimization problem is transformed into the following problem, which is then solved using a second-order Taylor expansion:

[0052]

[0053]

[0054] ||t n -t k ||2≥D,k=1,2,...,N,k≠n

[0055] Among them, g(t) n Let be the nth column vector in matrix G(t).

[0056] Based on the same inventive concept, this invention also provides a MIMO transmission system utilizing fluid antennas, including a transmitter, a receiver, and a rate optimization module. Multiple fluid antennas capable of freely moving within a given area are deployed on both the transmitter and receiver sides. The rate optimization module establishes a channel model and constructs an optimization problem to maximize the system's achievable rate based on statistical channel information, optimizing the positions of the transmitting fluid antennas. Location of receiving fluid antenna And the achievable rate of the system by optimizing the Q-covariance matrix of the emission.

[0057] Beneficial Effects: This invention models a MIMO system utilizing a fluid antenna based on readily available statistical channel state information, establishing the relationship between the channel matrix and the fluid antenna position. Compared to traditional MIMO with fixed antenna positions, the use of a fluid antenna enables the MIMO system to achieve a higher achievable data rate. This invention employs alternating optimization, the Cauchy-Schwarz inequality, and Taylor expansion to optimize the rate of the MIMO system utilizing a fluid antenna, achieving a significant improvement in system rate while reducing the complexity of solving the optimization problem and implementing the physical layer, thus accelerating computation. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the overall method flow of an embodiment of the present invention;

[0059] Figure 2 This is a schematic diagram of the iterative algorithm flow in an embodiment of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0061] like Figure 1As shown in the figure, this invention discloses a MIMO transmission method using fluid antennas. First, multiple fluid antennas capable of free movement within a given area are deployed on both the transmitter and receiver sides. Then, a corresponding channel model is established, and statistical channel state information in the system is obtained. Next, a system rate expression is constructed based on the statistical channel information, and a rate optimization problem model is established. Finally, alternating optimization, the Cauchy-Schwarz inequality, and Taylor expansion are used to solve the optimization problem to optimize the achievable system rate. The optimization objective is the achievable ergodic rate, and the optimization variables are the transmitting fluid antenna position t, the receiving fluid antenna position r, and the transmitting covariance matrix Q. The constraints are that the power is less than or equal to the maximum value, the antenna positions must be within a given area, and the distance between antennas must be greater than or equal to a threshold value.

[0062] In this embodiment, the optimization problem is solved using alternating optimization, the Cauchy-Schwarz inequality, and Taylor expansion. Specifically, it includes:

[0063] The original objective function is replaced with its tight upper bound using Jensen's inequality.

[0064] The original problem is decomposed into an optimization problem of the transmit covariance matrix Q, an optimization problem of the receive fluid antenna position r, and an optimization problem of the transmit fluid antenna position t using alternating optimization, with the iteration number indicator i = 0.

[0065] Solve the Q-optimization problem of the emission covariance matrix using the Cauchy-Schwarz inequality;

[0066] The optimization problem of the receiving fluid antenna position r is solved by decoupling the antenna position variables and Taylor expansion.

[0067] The optimization problem of the transmitting fluid antenna position t is solved by using the Cauchy-Schwarz inequality, antenna position variable decoupling, and Taylor expansion.

[0068] The rate value obtained in the (i+1)th iteration is compared with the result of the i-th iteration. If the difference between the two results is less than the set threshold ε, the iteration is terminated; otherwise, the iteration number i is incremented by 1, and the iteration continues to solve the problem.

[0069] The method of this embodiment will be explained in more detail below with a specific scenario.

[0070] Part 1: Constructing a MIMO system model utilizing a fluid antenna

[0071] Specifically, consider a MIMO system consisting of a transmitter with N fluid antennas and a receiver with M fluid antennas. The coordinates of the nth transmitting fluid antenna and the mth receiving fluid antenna are denoted as follows: and in and Let N be the movable area for the transmitting fluid antenna and the receiving fluid antenna. The sets of positions for the N transmitting fluid antennas and the M receiving fluid antennas are respectively denoted by […]. and express.

[0072] The number of transmit paths and receive paths are denoted as L. t and L r For the transmitter section, the p-th (1≤p≤L) t The elevation and azimuth angles of the launch path are denoted as follows: and In the p-th transmission path, the position of the n-th transmitting fluid antenna is relative to the origin t0 = (0,0). T The difference in propagation distance between them can be written as:

[0073]

[0074] Correspondingly, the signal phase difference between the nth transmitting fluid antenna and the origin in the pth transmission path can be written as: Where λ is the signal wavelength. Therefore, the transmit response vector can be written as:

[0075]

[0076] The response matrices of all N transmitting fluid antennas can be denoted as:

[0077]

[0078] For the receiver section, the q-th (1≤q≤L) r The elevation and azimuth angles of the receiving path are denoted as follows: and In the q-th receiving path, the position of the m-th receiving fluid antenna is relative to the origin r0 = (0,0). T The difference in propagation distance between them can be written as:

[0079]

[0080] Similarly, the corresponding received response vector and received response matrix can be written out:

[0081]

[0082]

[0083] From the launch region t0 = (0,0) T From the origin to the receiving region r0 = (0,0) TThe path response matrix of the origin is defined as Σ q,p Let Σ be the response coefficient between the p-th transmit path and the q-th receive path. q,p Independent and identically distributed, and modeled as a group with a mean of zero and a variance of α. 2 The channel is a Gaussian distributed random variable. Therefore, the channel matrix can be written as:

[0084] H(t,r)=F H (r)ΣG(t)

[0085] The transmitted signal is recorded as The emission covariance matrix is The received signal can be written as:

[0086] y(t,r)=H(t,r)s+z

[0087] In the above formula, Let be the channel matrix between a transmitter with N fluid antennas located at position t and a receiver with M fluid antennas located at position r. It is additive white Gaussian noise. Let I represent a complex circular symmetric Gaussian distribution with zero mean and covariance matrix B. M It is an M×M dimensional identity matrix.

[0088] The reachable rate can be written as:

[0089]

[0090] The rate maximization problem can be written as:

[0091]

[0092]

[0093]

[0094] ||t k -t l ||2≥D,k,l=1,2,...,N,k≠l,

[0095] ||r k -r l ||2≥D,k,l=1,2,…,M,k≠l,

[0096] tr(Q)≤P max

[0097] Where D refers to the minimum distance required between the transmitting / receiving fluid antennas to avoid mutual coupling; P max This represents the maximum permissible transmit power.

[0098] Part Two: Iterative Algorithm Based on Alternating Optimization, Cauchy-Schwarz Inequality, and Taylor Expansion

[0099] The implementation process of the iterative algorithm based on alternating optimization, Cauchy-Schwarz inequality, and Taylor expansion is as follows: Figure 2 As shown, it specifically includes the following steps:

[0100] Step S1: Replace the original objective function with its immediate upper bound using Jensen's inequality.

[0101]

[0102] Reuse properties The upper bound can be rewritten as:

[0103]

[0104] Step S2: Use alternating optimization to decompose the original problem into an optimization problem of the transmit covariance matrix Q, an optimization problem of the receive fluid antenna position r, and an optimization problem of the transmit fluid antenna position t. Set the iteration number indicator i = 0.

[0105] Step S3: Solve the emission covariance matrix Q optimization problem, which specifically includes:

[0106] The Q-optimization problem of the emission covariance matrix can be expressed as:

[0107] max Q tr(G(t)QG H (t))

[0108] sttr(Q)≤P max

[0109] Since the trace operation follows the Cauchy-Schwarz inequality, the objective function can be rewritten as:

[0110]

[0111] The above equation holds true if Q is G. H Q is a multiple of G(t). Therefore, when the objective function reaches its maximum value, Q should satisfy the condition that G(t) is a multiple of G(t). H (t) is a multiple of G(t) and tr(Q) = P max Based on these two conditions, the optimal solution for Q can be obtained.

[0112] Step S4: Solve the optimization problem of the receiving fluid antenna position r, which specifically includes:

[0113] The optimization problem for the receiving fluid antenna position r is expressed as:

[0114]

[0115]

[0116] ||r k -r l ||2≥D,k,l=1,2,…,M,k≠l

[0117] make objective function It can be rewritten as:

[0118]

[0119] In the above equation, the position variables of the M receiving fluid antennas are decoupled. The m-th column vector f(r) is removed from the matrix F(r). m After that, we will use the remaining L r The ×(M-1) dimension matrix is ​​represented as Separate F(r) into f(r) m )and Then, the objective function It can be rewritten as:

[0120]

[0121] In the given At that time, maximize Equivalent to maximizing p(r) m )=f H (r m B m f(r m ),in It is a with r m An irrelevant positive definite matrix. The optimization problem for the location of the receiving fluid antenna can be rewritten as:

[0122]

[0123]

[0124] ||r m -r k ||2≥D,k=1,2,...,M,k≠m

[0125] The transformed optimization problem can be solved using a second-order Taylor expansion.

[0126] Step S5: Solve the optimization problem of the transmitting fluid antenna position t, which specifically includes:

[0127] The optimization problem for the position t of the transmitting fluid antenna can be expressed as:

[0128] max t tr(G(t)QG H (t))

[0129]

[0130] ||t k -t l ||2≥D,k,l=1,2,...,N,k≠l

[0131] Similarly, applying the Cauchy-Schwarz inequality, we can derive that maximizing the objective function is equivalent to maximizing

[0132]

[0133] In the given At that time, maximize Equivalent to maximizing tr(g(t) n )g H (t n C n ) = g H (t n C n g(t n ),in For t n The positive semi-definite matrix. Therefore, the optimization problem for the position of the transmitting fluid antenna can be rewritten as:

[0134]

[0135]

[0136] ||t n -t k ||2≥D,k=1,2,...,N,k≠n

[0137] The transformed optimization problem can be solved using a second-order Taylor expansion.

[0138] Step S6: Compare the rate value obtained in the (i+1)th iteration with the result of the ith iteration. If the difference between the two results is less than the set threshold ε, terminate the iteration and use the transmit covariance matrix obtained in step S3, the receive fluid antenna position obtained in S4, and the transmit fluid antenna position obtained in S5 as the final solution; otherwise, increment the iteration number i by 1 and return to step S3. Specifically, in this embodiment, the threshold ε can be set by a technician according to the actual situation, and its specific value is not limited in this embodiment.

[0139] Based on the same inventive concept, this invention also discloses a MIMO transmission system utilizing fluid antennas, including a transmitter, a receiver, and a rate optimization module. Multiple fluid antennas capable of freely moving within a given area are deployed on both the transmitter and receiver sides. The rate optimization module establishes a channel model and constructs an optimization problem to maximize the system's achievable rate based on statistical channel information. The system's achievable rate is optimized by optimizing the positions of the transmitting and receiving fluid antennas and the transmit covariance matrix. Specific implementation details are detailed in the above method embodiments and will not be repeated here.

[0140] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0141] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A MIMO transmission method utilizing a fluid antenna, characterized in that, Multiple fluid antennas capable of free movement within a given area are deployed on both the transmitter and receiver sides. An optimization problem is constructed to maximize the system's achievable rate by establishing a channel model and using statistical channel information. The location of the transmitting fluid antennas is then optimized. Location of the receiving fluid antenna and the emission covariance matrix Optimize the achievable speed of the system; the optimization problem is expressed as: ； Where N and M are the number of transmitting fluid antennas and receiving fluid antennas, respectively. and The movable areas of the transmitting and receiving fluid antennas are respectively defined by the channel matrix. , Launch area From the origin to the receiving area The path response matrix at the origin, and These represent the number of transmit paths and receive paths, respectively. for The response matrix of a transmitting fluid antenna. for A receiver fluid antenna response matrix, for 3D identity matrix The minimum distance required between fluid antennas, At maximum transmission power, This means finding the determinant of a matrix. This indicates taking the L2 norm of a vector. This indicates finding the trace of a matrix. Represents the variable Seeking expectations, The variance of additive white Gaussian noise is represented. The optimization problem is solved using alternating optimization, the Cauchy-Schwarz inequality, and Taylor expansion, including replacing the original objective function with its tight upper bound using Jensen's inequality. The original problem is decomposed into an emission covariance matrix using alternating optimization. Optimization problem: Location of the receiving fluid antenna Optimization problem and transmitting fluid antenna location Optimize the problem and set an iteration count indicator. The emission covariance matrix is ​​solved using the Cauchy-Schwarz inequality. Optimization problem; solving for the receiving fluid antenna position using antenna position variable decoupling and Taylor expansion. Optimization problem; solving for the transmitting fluid antenna position using Cauchy-Schwarz inequality, antenna position variable decoupling, and Taylor expansion. Optimization problem; the first The rate value obtained in the second iteration is the same as that in the third iteration. The results of the next iteration are compared; if the difference between the two results is less than a set threshold... If the iteration fails, the iteration ends; otherwise, the iteration count is incremented. Add 1 and continue iterating to solve the problem.

2. The MIMO transmission method using a fluid antenna according to claim 1, characterized in that, Statistical channel state information is obtained through user feedback, direct estimation by the base station, or through uplink probe signals.

3. The MIMO transmission method using a fluid antenna according to claim 1, characterized in that, The channel model, for the transmitter part, is denoted as... The elevation and azimuth angles of each launch path are respectively and In the In the launch path, the first The location of the transmitting fluid antenna and the origin The difference in propagation distance between them is ;No. In the transmission path, the first The signal phase difference between the transmitting fluid antenna and the origin is ,in The signal wavelength is given; the transmission response vector is: ； all The response matrix of the transmitting fluid antenna is: .

4. The MIMO transmission method using a fluid antenna according to claim 1, characterized in that, The channel model, for the receiver part, is denoted as the... The elevation and azimuth angles of each receiving path are respectively and In the In the receiving path, the first Location of the fluid receiving antenna and the origin The difference in propagation distance between them is ;No. In the transmission path, the first The signal phase difference between each receiving fluid antenna and the origin is ,in The signal wavelength is denoted as ; the received response vector is: ； all The response matrix of the receiving fluid antenna is as follows: .

5. The MIMO transmission method using a fluid antenna according to claim 1, characterized in that, The tight upper bound of the original objective function for: ,in, For the first The launch path and the first Response coefficient between each receiving path The variance.

6. The MIMO transmission method using a fluid antenna according to claim 1, characterized in that, Solve for the emission covariance matrix Optimization issues, specifically including: Emission covariance matrix The optimization problem is represented as: ； According to the Cauchy-Schwarz inequality, the objective function can be rewritten as: ； The condition for the equation to hold true is: yes Multiples of; based on when the objective function reaches its maximum value. yes multiples of and These two conditions are calculated The optimal solution.

7. The MIMO transmission method using a fluid antenna according to claim 1, characterized in that, Solving for the position of the receiving fluid antenna Optimization issues, specifically including: Location of receiving fluid antenna The optimization problem is represented as: ； in, For the first The launch path and the first Response coefficient between each receiving path The variance; by decoupling using antenna position variables, the optimization problem is transformed into the following problem and then solved using second-order Taylor expansion: ； in, For matrix The Middle Column vector, , For matrix Remove from The remaining 3D matrix , for 3D identity matrix.

8. The MIMO transmission method using a fluid antenna according to claim 1, characterized in that, Solving for the position of the transmitting fluid antenna Optimization issues, specifically including: Transmitting fluid antenna position The optimization problem is represented as: ； By decoupling the antenna position variables using the Cauchy-Schwarz inequality, the optimization problem is transformed into the following problem, which is then solved using a second-order Taylor expansion: ； in, For matrix The Middle Column vector, .

9. A MIMO transmission system utilizing a fluid antenna, characterized in that, The system includes a transmitter, a receiver, and a rate optimization module. Multiple fluid antennas capable of freely moving within a given area are deployed on both the transmitter and receiver sides. The rate optimization module establishes a channel model and constructs an optimization problem to maximize the system's achievable rate based on statistical channel information, optimizing the positions of the transmitting fluid antennas. Location of the receiving fluid antenna and the emission covariance matrix Optimize the achievable speed of the system; the optimization problem is expressed as: ； Where N and M are the number of transmitting fluid antennas and receiving fluid antennas, respectively. and The movable areas of the transmitting and receiving fluid antennas are respectively defined by the channel matrix. , Launch area From the origin to the receiving area The path response matrix at the origin, and These represent the number of transmit paths and receive paths, respectively. for The response matrix of a transmitting fluid antenna. for A receiver fluid antenna response matrix, for 3D identity matrix The minimum distance required between fluid antennas, At maximum transmission power, This means finding the determinant of a matrix. This indicates taking the L2 norm of a vector. This indicates finding the trace of a matrix. Represents the variable Seeking expectations, The variance of additive white Gaussian noise is represented. The optimization problem is solved using alternating optimization, the Cauchy-Schwarz inequality, and Taylor expansion, including replacing the original objective function with its tight upper bound using Jensen's inequality. The original problem is decomposed into an emission covariance matrix using alternating optimization. Optimization problem: Location of the receiving fluid antenna Optimization problem and transmitting fluid antenna location Optimize the problem and set an iteration count indicator. The emission covariance matrix is ​​solved using the Cauchy-Schwarz inequality. Optimization problem; solving for the receiving fluid antenna position using antenna position variable decoupling and Taylor expansion. Optimization problem; solving for the transmitting fluid antenna position using Cauchy-Schwarz inequality, antenna position variable decoupling, and Taylor expansion. Optimization problem; the first The rate value obtained in the second iteration is the same as that in the third iteration. The results of the next iteration are compared; if the difference between the two results is less than a set threshold... If the iteration fails, the iteration ends; otherwise, the iteration count is incremented. Add 1 and continue iterating to solve the problem.

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