CN116633397B - Array topology optimization method and device for AP subarrays of distributed MIMO system - Google Patents
Array topology optimization method and device for AP subarrays of distributed MIMO system Download PDFInfo
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Abstract
The invention discloses a distributed MIMO system AP subarray array topological structure optimization method and device, and initial parameters of the distributed MIMO system AP subarrays are obtained; constructing a first optimization problem based on initial parameters with the maximum traversal and rate of the distributed MIMO system as targets; constructing an interference item and an auxiliary variable based on the first optimization problem, and simplifying the first optimization problem by combining the array element displacement vector of the AP subarray to obtain a third optimization problem; solving a third optimization problem by using an iterative search method based on a CVX tool box to obtain an arrangement mode of the non-uniform linear arrays in the AP subarrays; according to the method, the first optimization problem is built through the initial parameters of the AP subarrays, the third optimization problem is obtained based on the interference items and the array element displacement vectors in a simplified mode, the calculation amount of solving is greatly reduced, finally, the third optimization problem is solved by using an iterative search method based on a CVX tool box, the arrangement mode of the non-uniform linear arrays in the AP subarrays is obtained, and the communication efficiency of the distributed MIMO system can be improved.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a distributed MIMO system AP subarray array topological structure optimization method and device.
Background
Millimeter wave (mmWave) refers to electromagnetic waves having a frequency in the range of 30 to 300Ghz and a wavelength in the range of 1 to 10 mm. Millimeter wave communication has the potential to achieve gigabit per second (Gbps) data rates because its frequency band is several times higher than current systems. Furthermore, the extremely short wavelength of millimeter wave signals allows for the packaging of a large number of antenna elements on small terminals. Thus, using distributed massive MIMO technology instead of traditional MIMO helps the radiation beam to be narrower and spatially directed towards the user, thus achieving higher Spectral Efficiency (SE) and Energy Efficiency (EE).
Large-scale multiple-input multiple-output (MIMO) techniques to compensate for the large path loss of the millimeter wave band. Distributed MIMO is in fact one of the evolution of MIMO technology, combining MIMO with a distributed antenna system enables the formation of a distributed MIMO multi-antenna system. Multiple antennas are configured at the distributed remote antenna units, so that the communication capacity is doubled. Combining the traditional point-to-point MIMO technology with the basic principle of distributed antennas, a distributed MIMO (D-MIMO) system is introduced, which combines the advantages of spatial multiplexing and macro diversity. In the distributed MIMO system, since antennas are distributed at different positions, the distance between the distributed antenna units and users can be shortened, and the transmission power can be reduced, so that lower propagation loss and higher spatial multiplexing can be obtained.
However, in the distributed MIMO system, the antenna array topology of the distributed antenna unit affects the communication efficiency, and how to design the antenna array topology of the distributed antenna unit is a problem to be solved.
Disclosure of Invention
The invention aims to provide a distributed MIMO system AP subarray array topology optimization method and device, and the distributed MIMO system communication efficiency can be improved by constructing an optimization problem to optimize the AP subarray array topology.
The invention adopts the following technical scheme: an array topology optimization method of AP subarrays of a distributed MIMO system comprises the following steps:
acquiring initial parameters of AP subarrays of a distributed MIMO system;
constructing a first optimization problem based on initial parameters with the maximum traversal and rate of the distributed MIMO system as targets;
constructing an interference item and an auxiliary variable based on the first optimization problem, and simplifying the first optimization problem by combining the array element displacement vector of the AP subarray to obtain a third optimization problem;
and solving a third optimization problem by using an iterative search method based on the CVX tool box to obtain the arrangement mode of the non-uniform linear array in the AP subarray.
Further, constructing the interference term and the auxiliary variable based on the first optimization problem and combining the array element displacement vector of the AP subarray to simplify the first optimization problem includes:
establishing an interference item and carrying out equivalent conversion on the first optimization problem based on the interference item to obtain a second optimization problem;
and simplifying the second optimization problem based on the array element displacement vector and the auxiliary variable of the AP subarray to obtain a third optimization problem.
Further, the first optimization problem is:
wherein R is sum Representing that the downlink transmission of the distributed MIMO system can realize traversal and speed, wherein Deltax is the interval between adjacent array elements in the non-uniform linear array, and x is n Represents the specific position abscissa, x, of the nth array element in the non-uniform linear array in each AP subarray in the AP coordinate system n+1 Represents the specific position abscissa, d, of the n+1th array element in the non-uniform linear array in each AP subarray in the AP coordinate system min Is the minimum spacing threshold between adjacent array elements,n-th in non-uniform linear array representing each AP subarray t Specific position abscissa, L, of each array element in the AP coordinate system t The array aperture is a non-uniform linear array,k is the number of users, K is the total number of users, SINR k Representing the received signal-to-interference-and-noise ratio of the kth user.
Further, establishing the interference term and performing an equivalent transformation on the first optimization problem based on the interference term includes:
converting the first optimization problem using the Jensen inequality;
transforming the SINR term in the converted first optimization problem based on Mullen inequality and large number law;
let interference itemAnd integrate it into the transformed SINR term; wherein v (θ) k,j ) For the steering vector corresponding to the kth user and the jth AP, v (θ i,j ) The guiding vector corresponding to the ith user and the jth AP, lambda representing the wavelength, theta k,j Representing the corresponding azimuth angle, θ, between the kth user and the jth AP i,j Representing the corresponding azimuth angle between the ith user and the jth AP;
and generating a second optimization problem according to the transformed SINR term.
Further, the second optimization problem is:
further, the third optimization problem is:
wherein t represents an auxiliary variable, f (v) is a function of the array element position displacement vector,a＝[a 1 ,a 2 ,...,a Nt ]to determine N for AP subarrays t Array element position vector of dimension, a n1 For the nth to be determined 1 The positions of the array elements, a n2 For the nth to be determined 2 The position of each array element->For the nth to be determined at the ith-1 th iteration 1 The position of each array element->For the nth to be determined at the ith-1 th iteration 2 The position of each array element, ω=cos (θ k,j )-cos(θ i,j )，/>Represents the position shift of the n1 st array element at the ith iteration,/th iteration>Represents the position shift of the n2 th array element at the ith iteration,/th iteration>Is the position of the n+1th array element in the ith-1 th iteration, i is the iteration step number, < >>For the position shift of the n+1th array element at the ith iteration, +.>The position of the nth element during the i-1 th iteration, < >>Is the position displacement of the nth array element in the ith iteration, v i And represents the displacement vector of the array element at the ith iteration, and mu represents the upper limit threshold value of the position displacement of the array element.
Another technical scheme of the invention is as follows: an array topology optimization device of an AP subarray of a distributed MIMO system comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein the processor realizes the array topology optimization method of the AP subarray of the distributed MIMO system when executing the computer program.
The beneficial effects of the invention are as follows: according to the method, the first optimization problem is built through the initial parameters of the AP subarrays, the third optimization problem is obtained based on the interference items and the array element displacement vectors in a simplified mode, the calculation amount of solving is greatly reduced, finally, the third optimization problem is solved by using an iterative search method based on a CVX tool box, the arrangement mode of the non-uniform linear arrays in the AP subarrays is obtained, and the communication efficiency of the distributed MIMO system can be improved.
Drawings
Fig. 1 is a schematic diagram of a topology structure of a single-cell distributed MIMO downlink system according to an embodiment of the present invention;
fig. 2 is a schematic diagram of AP circular deployment and user distribution in an embodiment of the present invention;
fig. 3 is a schematic diagram of non-uniform linear array arrangement on an AP according to an embodiment of the present invention;
fig. 4 is a schematic diagram of traversal and rate change with signal-to-noise ratio achieved by different AP sub-array topologies in an embodiment of the invention.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
In the present invention, consider a single cell distributed MIMO downlink system as shown in fig. 1, which is composed of J antenna ports (i.e., APs) and K users (i.e., UEs), each AP is equipped with multiple array elements, and the antenna array topology equipped by each AP is the same, while serving multiple single antenna users. The AP is connected with a central processing unit (namely BBU) through an optical fiber, and is circularly dispersed at different geographic positions in a cell, and the appearance positions of all users are uniformly distributed in the cell. The total number of transmitting array elements in the system is M=N t ×J，N t Indicating the number of array elements on each AP. Consider the case where the APs are uniformly distributed on a circle of radius r, i.e., r min ＜＜r＜R，r min Is the minimum distance between the AP and the user and R is the cell radius.
According to the above model, the signal is processed by linear precoding before being transmitted to all users. In the downlink, w k,j Representing beamforming vector from jth AP to kth UE, assuming that the signal sent to kth user in the system is s k The signal transmitted by the jth AP is denoted by S, and is composed of a precoding superposition of all User (UE) signals served by the AP, denoted asThe signal received at the kth UE from the AP is:
wherein h is k,j Representing the channel vector between the jth AP and the kth user,representing complex Gaussian additive noise, σ, at the kth user 2 Variance of complex Gaussian additive noise, p k,j Representing transmission power from the jth AP to the kth UE, p i,j Representing transmission power from the jth AP to the ith UE, h i,j Is the channel vector, w, between the jth AP and the ith user i,j The beamforming vector from the jth AP to the ith UE is represented, and the precoding mode of MRT is adopted, so that the computational complexity is reduced, matrix inversion operation is avoided, and the beamforming vector can be represented as w i,j ＝h i,j ，s i Representing the signal sent by the system to the ith user.
In the embodiment of the invention, the input signal and the precoding vector are assumed to satisfy||w k,j || 2 ＝||w i,j || 2 Let P be the total transmit power of the system, P/K, equal to ρ, for each user on average.
As can be seen from the above equation, the signal received by the user comprises three parts, the first part being the desired signal, the second part being the interference signal, and the third part being the noise. The achievable traversal and rate of the system can be expressed as:
wherein SINR k For use inThe receiving signal-to-interference-and-noise ratio of the user k is specifically expressed as follows:
for the problem of optimization of the array topology of the AP subarrays, the following factors are considered in the invention:
considering the complex communication environment of a cell, the distributed MIMO system fully considers small-scale fading and large-scale fading when in channel modeling, an angle expansion-based Saleh-Valenzuela model is to be adopted, each scattering cluster is assumed to contribute to one propagation path, and the antenna array response of a receiving end is not required to be considered because a user is a single antenna, so that a channel between a kth UE (i.e. the user) and a jth AP can be expressed as follows:
wherein beta is k,j Representing the large scale fading coefficient, beta, between the jth AP and the kth user k,j ＝z k,j (r min /δ k,j ) v ，z k,j Represents shadow fading (obeying log-normal distribution, average value is mu) z Standard deviation is sigma z )，r min Representing the minimum distance threshold, delta, between an AP and a user k,j Is the distance between the jth AP and the kth user and v represents the path loss component.
The number of array elements on each AP in the distributed MIMO system is equal, L k,j Represents the number of propagation paths between the kth user and the jth AP,representing the complex gain of the first path between the jth AP and the kth user,following a complex gaussian distribution with zero mean and unit variance,/->Is a normalized transmit array response vector corresponding to the departure angle, < >>Indicating the departure azimuth of the corresponding first path between the kth user and the jth AP.
The distance between the jth AP and the kth user can be expressed as:
wherein the polar coordinate of the position of the jth AP is expressed as (r j ,φ j ) = (r, 2pi (J-1)/J), then the rectangular coordinates are expressed as (x) j ,y j )＝(r j cosφ j ,r j sinφ j ). Assuming that the moving users are independently and uniformly distributed in the cell, the polar coordinates of the users are expressed asThe rectangular coordinates are expressed as +.>
In the embodiment of the invention, each AP respectively establishes a rectangular coordinate system by taking the first array element as the origin, and N in each AP t The array elements are horizontally arranged on the x axis in a linear manner,n in non-uniform linear array t Specific position coordinates of each array element.
The invention discloses a distributed MIMO system AP subarray array topological structure optimization method, which comprises the following steps: acquiring initial parameters of AP subarrays of a distributed MIMO system; constructing a first optimization problem based on initial parameters with the maximum traversal and rate of the distributed MIMO system as targets; constructing an interference item and an auxiliary variable based on the first optimization problem, and simplifying the first optimization problem by combining the array element displacement vector of the AP subarray to obtain a third optimization problem; and solving a third optimization problem by using an iterative search method based on the CVX tool box to obtain the arrangement mode of the non-uniform linear array in the AP subarray.
According to the method, the first optimization problem is built through the initial parameters of the AP subarrays, the third optimization problem is obtained based on the interference items and the array element displacement vectors in a simplified mode, the calculation amount of solving is greatly reduced, finally, the third optimization problem is solved by using an iterative search method based on a CVX tool box, the arrangement mode of the non-uniform linear arrays in the AP subarrays is obtained, and the communication efficiency of the distributed MIMO system can be improved.
Therefore, the scheme design problem (namely the first optimization problem) of the optimization method of the array topology structure of the AP subarray of the distributed MIMO system provided by the embodiment of the invention is modeled as follows:
wherein R is sum Indicating that distributed MIMO system downlink transmission can achieve traversal and rate,n-th in non-uniform linear array representing each AP subarray t The abscissa of the specific position of each array element in the AP coordinate system, deltax is the interval between adjacent array elements in the non-uniform linear array, and x is n Represents the specific position abscissa, x, of the nth array element in the non-uniform linear array in each AP subarray in the AP coordinate system n+1 Represents the specific position abscissa of the n+1th array element in the non-uniform linear array in each AP subarray in the AP coordinate system,/L>，y n Represents the ordinate, a, of the specific position of the nth array element in the non-uniform linear array in each AP n ∈[-1,1]Represents the normalized position of the nth transmitting array element relative to the center on the transmitting NULA, d min Is the minimum spacing threshold value between adjacent array elements, L t Is a non-uniform lineArray aperture of the array.
Under the condition that the array aperture and the minimum spacing threshold are limited, the AP subarray is designed to be of a non-uniform linear array structure, so that R can be caused sum Maximization, the AP subarrays are therefore designed as non-uniform linear array structures.
In the embodiment of the invention, constructing the interference item and the auxiliary variable based on the first optimization problem and combining the array element displacement vector of the AP subarray to simplify the first optimization problem comprises the following steps: establishing an interference item and carrying out equivalent conversion on the first optimization problem based on the interference item to obtain a second optimization problem; and simplifying the second optimization problem based on the array element displacement vector and the auxiliary variable of the AP subarray to obtain a third optimization problem.
Specifically, establishing the interference term and performing the equivalence transformation on the first optimization problem based on the interference term includes: converting the first optimization problem using the Jensen inequality; transforming the SINR term in the converted first optimization problem based on Mullen inequality and large number law; let interference itemAnd integrate it into the transformed SINR term; wherein v (θ) k,j ) For the steering vector corresponding to the kth user and the jth AP, v (θ i,j ) The guiding vector corresponding to the ith user and the jth AP, lambda representing the wavelength, theta k,j Representing the corresponding azimuth angle, θ, between the kth user and the jth AP i,j Representing the corresponding azimuth angle between the ith user and the jth AP; and generating a second optimization problem according to the transformed SINR term.
More specifically, an approximation of the traversal system and rate is derived using the mathematical methods of the Jensen inequality, mullen inequality, etc., the received signal-to-interference-and-noise ratio (SINR) at the kth user k ) The method comprises the following steps:
the k-th user can thus achieve the following corresponding achievable rates:
R k ＝log 2 (1+SINR k ) (8)
the total achievable traversal and rate of the system is:
using the Jensen inequality, we get the traversal sum rate as:
since the numerator and denominator in the SINR term are independent of each other, according to the Mullen inequalityLaw of large numbers, ++>It can be calculated as:
to obtain the approximate expression, the numerator and denominator need to be calculated separately. Due to channel vector h k,j Complex gain alpha in (a) k Independent of each other and following a complex gaussian distribution with zero mean and unit variance, there is thereforeEqual to one, regarding the expected value in denominator, use +.>
According to the law of large numbers in mathematics, when the array element number of a single AP tends to infinity, the following can be obtained:
thus, it was obtained:
wherein Ω NULA The term of interference is represented by a term of interference,v(θ k,j ) For the steering vector corresponding to the kth user and the jth AP, v (θ i,j ) The steering vector for the i-th user and the j-th AP, lambda represents the wavelength,θ k,j for the corresponding azimuth angle between j APs and kth user, θ k,j Representing the corresponding azimuth angle, θ, between the kth user and the jth AP i,j Indicating the corresponding azimuth angle of departure between the i-th user and the j-th AP.
The approximate values of the traversal and rate are:
from traversal and rate approximationIt can be seen that the interference term Ω NULA Minimizing the achievable traversal rate to its maximum value, equivalently converting the optimization problem, and obtaining a second optimization problem as:
wherein Ω NULA Expressed by the extension and basic mathematical transformation:
wherein a= [ a ] 1 ,a 2 ,...,a Nt ]To determine N for AP subarrays t Array element position vector of dimension, a n1 For the nth to be determined 1 The positions of the array elements, a n2 For the nth to be determined 2 The location of the individual array elements.
Further, by introducing array element displacement vectorsAnd an auxiliary variable t for shifting the nth element in the x-axis direction by the iterative algorithm in the ith step +.>For the position displacement of array elements, give definitionIn the far field case, when->Smaller, using a first order Taylor expansion approximation can be obtainedThe objective function after conversion can be written as:
wherein,for the nth to be determined at the ith-1 th iteration 1 The position of each array element->For the nth to be determined at the ith-1 th iteration 2 The position of each array element, ω=cos (θ k,j )-cos(θ i,j )，/>Represents the position shift of the n1 st array element at the ith iteration,/th iteration>Representing the position displacement of the n2 th array element at the ith iteration.
The auxiliary variable t is the maximum value of the interference term value of the channel component, and the interference term value is minimized, and the form of the auxiliary variable t is consistent with f (v) and is used as an optimization variable. In the far field case, whenAnd when the method is smaller, converting the non-convex problem into a convex problem by using a first-order Taylor expansion approximation, and re-expressing a third optimization problem by using a second optimization problem, wherein the third optimization problem is specifically:
wherein v i Representing the displacement vector of the array element position, f (v) is a function of the displacement vector of the array element position, i is the iteration number, mu is a constant, is the upper threshold value of the displacement of the array element position,is the position of the n+1th array element in the ith-1 th iteration, i is the iteration step number, < >>For the position shift of the n+1th array element at the ith iteration, +.>The position of the nth element during the i-1 th iteration, < >>Is the position displacement of the nth array element in the ith iteration, v i Representing the array element displacement vector at the ith iteration, and a second constraint condition C 2 Indicating that the spacing of adjacent array elements meets a given minimum spacing.
Finally, when solving the optimization problem, the final non-uniform linear array arrangement mode is obtained by using iterative search by means of a CVX tool box, and the solving algorithm process is as follows:
the effectiveness of the method is illustrated in a simulation experiment mode, namely, the effectiveness of the AP subarray topological structure optimization method is verified through MATLAB simulation. And setting the path number to be 3 by adopting a geometric Saleh-Valenzuela narrow-band channel model, and leading the leaving random azimuth angles to follow the uniform distribution on [0,2 pi ]. Fig. 2 shows a circular deployment and user distribution diagram of an AP, where the number of APs is 8, the number of users is 4, the cell radius R is 100 meters, and the circular deployment radius r=0.65r. The number of the array elements equipped for each AP is 16, the number of the received array elements for each user is 1, the non-uniform linear array arrangement of the 16 array elements is shown in figure 3, and the array element position coordinates x= [ -1, -0.7757, -0.6532, -0.5531, -0.4139, -0.2953, -0.1771, -0.0590,0.0590,0.1771,0.2953,0.4139,0.5331,0.6532,0.7757,1].
Fig. 4 shows the traversal and rate versus signal-to-noise ratio achieved by different AP sub-array topologies. From the figure, it can be seen that in the distributed MIMO system, when the AP subarray topology is a non-uniform linear array, the system traversal and the rate are high, and the system performance when the non-uniform linear array is adopted is better than the result when the conventional uniform linear array is adopted, so as to improve the system performance.
The invention discloses an array topology optimization device of an AP subarray of a distributed MIMO system, which comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein the processor realizes the array topology optimization method of the AP subarray of the distributed MIMO system when executing the computer program.
Based on such understanding, the present invention may implement all or part of the flow of the method of the above embodiments, and may be implemented by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, and when the computer program is executed by a processor, the computer program may implement the steps of each of the method embodiments described above. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. The computer readable medium may include at least: any entity or device capable of carrying computer program code to a storage device, a recording medium, computer Memory, read-Only Memory (ROM), random access Memory (RAM, random Access Memory), electrical carrier signals, telecommunications signals, and software distribution media. Such as a U-disk, removable hard disk, magnetic or optical disk, etc. In some jurisdictions, computer readable media may not be electrical carrier signals and telecommunications signals in accordance with legislation and patent practice.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and in part, not described or illustrated in any particular embodiment, reference is made to the related descriptions of other embodiments.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
In the embodiments provided in the present invention, it should be understood that the disclosed apparatus/device and method may be implemented in other manners. For example, the apparatus/device embodiments described above are merely illustrative, e.g., the division of the modules or units is merely a logical functional division, and there may be additional divisions when actually implemented, e.g., multiple modules or components may be combined or integrated into another system, or some features may be omitted or not performed.
The modules described as separate components may or may not be physically separate, and components shown as modules may or may not be physical units, may be located in one place, or may be distributed over multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
The above embodiments are only for illustrating the technical solution of the present application, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention, and are intended to be included in the protection scope of the present application.
Claims (2)
1. The method for optimizing the array topology of the AP subarrays of the distributed MIMO system is characterized by comprising the following steps of:
acquiring initial parameters of AP subarrays of a distributed MIMO system; the AP subarrays are antenna arrays on the AP;
constructing a first optimization problem based on the initial parameters with the maximum traversal and rate of the distributed MIMO system as targets;
constructing an interference item and an auxiliary variable based on the first optimization problem, and simplifying the first optimization problem by combining an array element displacement vector of an AP subarray to obtain a third optimization problem;
solving the third optimization problem by using an iterative search method based on a CVX tool box to obtain an arrangement mode of the non-uniform linear array in the AP subarrays;
constructing an interference item and an auxiliary variable based on the first optimization problem and combining array element displacement vectors of the AP subarrays to simplify the first optimization problem comprises:
establishing an interference item and carrying out equivalent conversion on the first optimization problem based on the interference item to obtain a second optimization problem;
the second optimization problem is simplified based on the array element displacement vector and the auxiliary variable of the AP subarray, and a third optimization problem is obtained;
the first optimization problem is as follows:
wherein R is sum Representing that the downlink transmission of the distributed MIMO system can realize traversal and speed, wherein Deltax is the interval between adjacent array elements in the non-uniform linear array, and x is n Represents the specific position abscissa, x, of the nth array element in the non-uniform linear array in each AP subarray in the AP coordinate system n+1 Represents the specific position abscissa, d, of the n+1th array element in the non-uniform linear array in each AP subarray in the AP coordinate system min Is the minimum spacing threshold between adjacent array elements,n-th in non-uniform linear array representing each AP subarray t Specific position abscissa, L, of each array element in the AP coordinate system t The array aperture is a non-uniform linear array,k is the number of users, K is the total number of users, SINR k Representing the received signal-to-interference-and-noise ratio of the kth user;
establishing an interference term and performing equivalence transformation on the first optimization problem based on the interference term comprises:
converting the first optimization problem using the Jensen inequality;
transforming the SINR term in the first optimization problem after conversion based on Mullen inequality and large number law;
let interference itemAnd integrate it into the transformed SINR term; wherein v (θ) k,j ) For the steering vector corresponding to the kth user and the jth AP, v (θ i,j ) The guiding vector corresponding to the ith user and the jth AP, lambda representing the wavelength, theta k,j Representing the corresponding azimuth angle, θ, between the kth user and the jth AP i,j Representing the corresponding azimuth angle between the ith user and the jth AP;
generating a second optimization problem according to the transformed SINR term;
the second optimization problem is as follows:
the third optimization problem is as follows:
wherein t represents an auxiliary variable, f (v) is a function of the array element displacement vector,a＝[a 1 ,a 2 ,...,a Nt ]to determine N for AP subarrays t Array element position vector of dimension, a n1 For the nth to be determined 1 The positions of the array elements, a n2 For the nth to be determined 2 The position of each array element->For the nth to be determined at the ith-1 th iteration 1 The position of each array element->For the i-1 st time of laminationNth to be determined at time of generation 2 The position of each array element, ω=cos (θ k,j )-cos(θ i,j )，/>Represents the position shift of the n1 st array element at the ith iteration,/th iteration>Represents the position shift of the n2 th array element at the ith iteration,/th iteration>Is the position of the n+1th array element in the ith-1 th iteration, i is the iteration step number, < >>For the position shift of the n+1th array element at the ith iteration, +.>The position of the nth element during the i-1 th iteration, < >>Is the position displacement of the nth array element in the ith iteration, v i Represents the array element displacement vector at the ith iteration, and mu represents the upper threshold of the array element position displacement.
2. An array topology optimization device of an AP subarray of a distributed MIMO system, comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor implements the array topology optimization method of an AP subarray of a distributed MIMO system according to claim 1 when executing the computer program.
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