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CN104270820B - United vertical beam control and power distribution method in the extensive mimo systems of 3D - Google Patents

United vertical beam control and power distribution method in the extensive mimo systems of 3D Download PDF

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CN104270820B
CN104270820B CN201410380297.9A CN201410380297A CN104270820B CN 104270820 B CN104270820 B CN 104270820B CN 201410380297 A CN201410380297 A CN 201410380297A CN 104270820 B CN104270820 B CN 104270820B
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CN104270820A (en
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张国梅
王兵
吕刚明
李国兵
任俊臣
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CERTUSNET CORP
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Xian Jiaotong University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power

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Abstract

本发明公开了一种3D大规模MIMO系统中联合的垂直波束控制及功率分配方法，包括以下步骤：1)根据用户位置分布将每个小区划分为两个垂直扇区并在垂直扇区间复用一组相同的导频序列进行上行信道估计；2)在下行数据传输阶段，首先，基于上行信道估计的结果以及上行用户所属扇区的初始化结果，以最大比传输为下行预编码算法，最大化和速率为目标，联合优化各小区近扇区的3D天线阵列加权矢量wl0、发送功率pl0，以及远扇区的3D天线阵列加权矢量wl1、发送功率pl1；然后，根据优化后每个扇区的波束增益，将用户重新划分到波束增益较大的扇区；重复2)中步骤，直至用户所属扇区情况不变；至此，完成3D大规模MIMO系统中联合的垂直波束控制及功率分配。

The invention discloses a joint vertical beam control and power allocation method in a 3D massive MIMO system, comprising the following steps: 1) dividing each cell into two vertical sectors according to user position distribution and multiplexing between the vertical sectors A group of the same pilot sequence is used for uplink channel estimation; 2) In the downlink data transmission stage, firstly, based on the result of uplink channel estimation and the initialization result of the sector to which the uplink user belongs, the maximum ratio transmission is used as the downlink precoding algorithm to maximize and rate as the target, jointly optimize the 3D antenna array weight vector w l0 and transmit power p l0 of the near sector of each cell, and the 3D antenna array weight vector w l1 and transmit power p l1 of the far sector; then, according to the optimized the beam gain of each sector, and re-divide users into sectors with larger beam gains; repeat the steps in 2) until the situation of the sector to which the user belongs remains unchanged; so far, the joint vertical beam steering and joint vertical beam steering in the 3D massive MIMO system and the 3D massive MIMO system are completed. power distribution.

Description

Combined vertical beam control and power distribution method in 3D large-scale MIMO system
The technical field is as follows:
the invention belongs to the technical field of wireless communication, and particularly relates to a combined vertical beam control and power distribution method in a 3D large-scale MIMO system.
Background art:
in the end of 2010, the scientist Thomas l.marzetta in bell laboratories proposed the concept of Massive MIMO (LargeScale MIMO or Massive MIMO), where a base station equipped with hundreds of antennas serves tens of users using the same time-frequency resource at the same time. Research shows that when the number of base station antennas is large, the original random variable tends to be a determined value, so that the interference between users can be effectively reduced by a simple signal processing method; in addition, when the antenna scale of the base station is large, the equivalent signal-to-noise ratio is linearly increased along with the number of the base station antennas, which means that the more the number of the antennas is, the smaller the transmission power required for obtaining the same equivalent signal-to-noise ratio can be, so that the large-scale MIMO technology can greatly reduce the transmission power of an uplink and a downlink, and meets the requirement of 'green communication'. Massive MIMO has been regarded as one of the key technologies of 5 th generation mobile communication, and has become a research hotspot in recent years in the field of wireless communication.
Research has shown that when the number of base station antennas tends to infinity, uncorrelated interference and noise can be averaged out, leaving only pilot pollution as the determining factor limiting system performance. Therefore, how to effectively suppress the pilot pollution and reduce the performance loss caused by the pilot pollution becomes a key problem to be solved by the design of the massive MIMO system. The existing pilot pollution suppression method can be divided into the following aspects: high-precision channel estimation, robust precoding, pilot frequency structure design and pilot frequency optimal allocation. In the aspect of channel estimation, a channel estimation algorithm based on feature decomposition, a Bayesian channel estimation algorithm and the like are proposed; in the aspect of robust precoding algorithm, the robust precoding algorithm comprises a precoding algorithm through cooperation between base stations, a robust precoding algorithm based on MMSE (minimum mean square error) criterion and the like; in the aspect of pilot frequency structure design, the method is divided into a time-shifted pilot frequency structure and a redundant pilot frequency structure; in the aspect of pilot frequency optimization allocation, a pilot frequency optimization allocation scheme which aims at minimizing the mean square error of channel estimation, a pilot frequency allocation scheme which takes the total throughput of the system as a utility function and the like are included. The above techniques, however, only consider the effect of the antenna horizontal dimension characteristics on the system performance. In a practical system, considering the problem of the limitation of the size of the antenna and the large number of antennas, a 3D (three-dimensional) antenna array such as an area array becomes a practical antenna array suitable for a massive MIMO system, and the degree of freedom in the vertical plane brought by the 3D antenna array provides a new opportunity for further improving the system performance.
By using the active antenna, the 3D antenna array of the base station forms a plurality of vertical beams at the same time, so that the vertical splitting of a cell can be realized, and the overall performance of the system is improved by increasing the number of users simultaneously served by the base station or improving the signal to interference plus noise ratio (SINR) of the users through accurate beam adjustment. However, the number of antennas of a base station in a practical system may be large but is always limited, in which case uncorrelated interference and noise cannot be ideally cancelled out and still have a severe impact on the system performance. Introduction of the vertical splitting technique not only causes inter-sector interference problems, but also may enhance inter-cell interference. The influence of interference on the system performance can be effectively inhibited through the processes of downtilt optimization, power distribution, coordinated beam forming, vertical beam optimization combined with joint transmission and the like. However, most of the current research is still performed under the assumption of ideal Channel State Information (CSI), and the problem that the system performance is limited by pilot pollution when the number of antennas is large and the number of users is large is not involved, especially in the case that the pilot needs to be multiplexed between sectors when the number of users is large in each vertical sector, the problem of pilot pollution becomes more severe.
The invention content is as follows:
the invention aims to provide a combined vertical beam control and power distribution method in a 3D large-scale MIMO system aiming at a vertical splitting scene of the large-scale MIMO system adopting an antenna area array structure, which indirectly reduces the deterioration influence of pilot frequency pollution on the system performance on one hand, and effectively coordinates various interferences existing in the system to reduce the interference influence on the other hand.
Compared with the prior art, the invention adopts the following technical scheme:
the combined vertical beam control and power distribution method in the 3D large-scale MIMO system comprises the following steps:
1) in an uplink channel estimation stage, dividing each cell in a cooperation cluster into two virtual vertical sectors according to user position distribution, and enabling the two vertical sectors to reuse one group of same pilot frequency sequences so as to increase the number of users simultaneously served by each base station, wherein the channel estimation adopts an LS estimation algorithm;
2) in the downlink data transmission stage, firstly, each cell sets two fixed antenna downward inclination angles according to user position distribution, each cell forms two vertical sectors which are a near sector and a far sector respectively, and the sector to which each user belongs is initialized; secondly, based on the result of the uplink channel estimation and the initialization result of the sector to which each cell user belongs, the 3D antenna array weighting vector w of the near sector of each cell is optimized in a combined manner by taking maximum ratio transmission as a downlink precoding algorithm and taking the maximum sum rate as a targetl0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1(ii) a Thirdly, according to the optimized wave beam gain of the near sector and the far sector of the cell where the user is located, the user is divided into the sectors with larger wave beam gain in the cell again; repeating the first step to the third step until the sector condition of the user is unchanged; so far, joint vertical beam control and power allocation in the 3D large-scale MIMO system are completed.
The invention is further improved in that the method specifically comprises the following steps:
1) and (3) uplink channel estimation: dividing each cell into two virtual vertical sectors according to the user position distribution, using one vertical beam to receive the uplink pilot signals sent by all users in the two virtual sectors in each cell, carrying out LS channel estimation, and carrying out LS channel estimation on a near sector user k in a cell l0The LS channel estimation result is
2) Downlink vertical beam forming and power distribution joint optimization: for user k in cell l, maximum ratio transmission is carried out based on uplink channel estimation information, and the user and rate R can be obtainedlkThe expression of (1); the optimization target is to maximize the sum rate of all users in the cooperative cluster, and the optimization target is the 3D antenna array weighting vector w of each cell near sectorl0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1I.e. the optimization problem is
Wherein:for a near sector user k in cell l0The sum of the rates of (a) and (b),for the remote sectors in cell lFamily k1L is the total number of cells in the cooperative cluster, Kl0Is the total number of users, K, in the celll0The total number of users of the remote sector in the cell l;
in order to reduce inter-cell interference and meet total power constraints, the constraint condition of the optimization problem is set to be that the correlation of the beam between sectors is smaller than a threshold rhomaxAnd the total transmitting power of the two sectors does not exceed P;
3) in order to reduce the complexity of solving the optimization problem, iterative solution is carried out by using a particle swarm algorithm;
the first step is as follows: initializing 3D antenna array weighting vectors w for each cell near sectorl0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1Setting a 3D antenna array weighting vector w of each cell near sectorl0Has an update speed vw，l0And a transmission power pl0Has an update speed vp，l0Setting a 3D antenna array weighting vector w of each cell remote sectorl1Has an update speed vw，l1And a transmission power pl1Has an update speed vp，l1；
The second step is that: setting the total sum rate of the system as a utility function, and continuously updating the 3D antenna array weighting vector w of each cell near sector by taking the maximum utility function as a targetl0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1；
The third step: if the maximum iteration times are reached or the difference value of the utility functions of two adjacent iterations is smaller than a preset constant delta, stopping the iteration process, wherein the constant delta is smaller than 0.01;
according to the iterated 3D antenna array weighting vector w of each cell near sectorl0And 3D antenna array weight vector w for each cell remote sectorl1Array antenna gains for serving near and far sectors, respectively, where user i in cell l is in the near sector of base station lThe gain of the area array antenna is A (theta)D，l0，θlli)，θD，l0Down tilt angle, theta, of the near sector antenna for celllliThe pitch angle from user i in cell l to base station l, and the array antenna gain of user i in cell l in the far sector of base station l is A (theta)D，l1，θlli)，θD，l1The downtilt angle of the remote sector antenna of the serving cell l; the gain of the near sector array antenna of user i in cell l at base station l is A (theta)D，l0，θlli)，θD，l0A downtilt angle of a near sector antenna of a serving cell;
4) the sector to which the user belongs is re-divided according to the beam gain of the user in each sector, and the adjustment process is as follows:
if A (theta)D，l0，θlli)≥A(θD，l1，θlli) If the user is a near sector user;
if it isThen the user is a remote sector user;
repeating the steps 2) to 4), if the sector condition of the user does not change, stopping to obtain the final 3D antenna array weighting vector w of the near sector of each celll0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1。
The invention is further improved in that, in step 1), a near-sector user k is present in the cell l0The LS channel estimation result of (1) is:
in the formula: y islThe calculation formula of the signal received by the base station l is:
wherein: k is the total number of users served by each cell, L is the total number of cells in the coordinated cluster, ΨkFor near sector user k0And remote sector user k1The same pilot sequence is transmitted in 1 x tau dimension in uplink,for cell/. near-sector user k0The channel matrix to the base station/,for cell l remote sector user k1The channel matrix to the base station/,for cell j near sector user k0The channel matrix to the base station/,for cell j remote sector user k1Channel matrix to base station l, A (-) is the 3D antenna pattern of the base station, θD，lIs the downtilt angle of the base station i antenna array,for a near sector user k in cell l0Looking at the elevation angle of the base station i,for a remote sector user k in cell l1Looking at the elevation angle of the base station i,for a near sector user k in cell j0Looking at the elevation angle of the base station i,for a remote sector user k in cell j1Elevation angle, z, looking at base station llIs additive white Gaussian noise of base station l, andN0is noise power spectral density, I is unit array;
denotes ΨkThe conjugate transpose of (c).
The invention is further improved in that, in step 2), the problem is optimizedThe concrete form is as follows:
in the formula:andmean elevation angles of users in the near sector and the far sector of the cell l are respectively represented;
the optimization problem includes two constraints: c1The premise that the correlation between the antenna beams of two sectors in each cell is smaller than a threshold value is shown, and the transmission power of the base station is kept unchanged after the weighting vector w is adjusted;
C2means that the total power of two sectors per cell is less than the total power P of the base station;
Br(θ)∈CM×1is the directional diagram of the base station antenna array, and M is the number of base station antennas;
p (θ) represents a probability density function of the user distribution;
ρ represents the correlation coefficient between two sector antenna beams per cell;
indicates that the antenna has a downtilt angle ofThe antenna array weight vector for the near sector of cell i,to representThe conjugate transpose of (1);indicates that the antenna has a downtilt angle ofThe antenna array weight vector for the far sector of cell/,to representThe conjugate transpose of (1);
pl0indicating the base station service power, p, of the near sector of the celll1Representing the base station serving power of the remote sector of cell/.
The invention further improves that in step 3), a 3D antenna array weighting vector w of a near sector of each cell is initializedl0And its update speed vw，l0The calculation formula is as follows:
in the formula: e to U (0,1), d is the spacing of two antenna elements, and d ═ dy＝dz，dyAnd dzRespectively representing the horizontal spacing and the vertical spacing of the antennas;
m and n represent the mth row and nth column antenna element of the planar antenna array;
is (N-1) NVThe update speed at time 1 of the j-th particle of + m elements,is (N-1) NVInitial position at time 0 of j-th particle of + m elements, NVRepresenting the number of vertical antennas of the antenna array;
λ represents the wavelength of the user transmit beam;
initializing the transmit power p of the near sector of each celll0The calculation formula is as follows:
in the formula:is Pl0The update rate at time 1 of the jth particle,is Pl0Initial position at time 0 of the jth particle;
initializing 3D antenna array weighting vectors w for each cell remote sectorl1And an update speed vw，l1The calculation formula is as follows:
in the formula:is (N-1) NVUpdate speed at time 1 of the jth particle of + m elements;
is (N-1) NVAn initial position at time 0 of a jth particle of + m elements;
the formula for the iteratively updated for each particle at time τ is as follows:
wherein: v. ofj(τ) update speed, x, of jth particle time τj(τ) the position of the jth particle time τ, c1, c2 being normal numbers, called the learning factor; r1 and r2 are [0, 1 ]]A is an inertial weight factor; p is a radical ofj(τ -1) is the local optimum, p, for the jth particle time τ -1g(τ -1) is the global optimum of all particles at time τ -1.
The invention is further improved in that, in the step 4),
in the formula:is an antenna array with a downward inclination angle thetaD，l0Then, the weighting vector of the cell l near sector antenna array; b isr(θlli)∈CM×1Is the directional pattern of the base station antenna array, Br(θlli) (N-1) NV+ m elements being Br，m，n(θlli) Representing the m-th row and n-th column of antenna elementsGain, expressed as
In the formula:for vertical patterns of individual antenna elements, theta3dBRepresenting the half-power angle, thetaDRepresenting the downtilt angle, theta, of the antenna arraylliFor the pitch angle, d, of users i in cell l to base station lyAnd dzRepresenting antenna horizontal and vertical spacing;
in the formula:is an antenna array with a downward inclination angle thetaD，l1The weight vector of the far sector antenna array.
Compared with the prior art, the invention has the following technical effects:
the invention introduces 3DMIMO into the large-scale MIMO system in consideration of the practical problem that the antenna array in the large-scale MIMO system is an area array. By utilizing the 3D characteristics of the antenna array, optimizing the antenna weighting vector and the power distribution of each sector are considered, and inter-sector and inter-cell interference in the 3D large-scale MIMO system is effectively coordinated, so that the influence of pilot pollution on the system performance is indirectly inhibited, and the spectrum efficiency of the system is improved.
Description of the drawings:
FIG. 1 is a schematic diagram of a 3D massive MIMO system model;
FIG. 2 is a graph of channel estimation error versus time;
fig. 3 is a graph comparing the average spectral efficiency of a cell when r is 0.5;
fig. 4 is a graph comparing the average spectrum efficiency of cells when r is 5/6.
The specific implementation mode is as follows:
the present invention will be described in further detail with reference to the accompanying drawings and examples.
Considering a 3D massive MIMO transmission scenario, 7 horizontal sectors are shared in a cooperative cluster, an antenna array with an area array structure is adopted, each horizontal cell serves 12 single-antenna users, and the number of antennas of a base station is simulated from 20 to 100, so that the method of the present invention is compared with a conventional 2D massive MIMO system, a 3D massive MIMO system with a fixed downtilt method, and a 3D massive MIMO system with only a downtilt angle and power adjustment method, to show the effect that the present invention can achieve, as shown in fig. 1.
As can be seen from fig. 2, after dividing each cell into two vertical sectors using the vertical sectorization technique and multiplexing a set of same pilots among the vertical sectors, the pilot pollution is more serious than that of the conventional massive MIMO system, and the channel estimation error is increased. Meanwhile, the smaller the pilot frequency multiplexing factor between sectors is, i.e. the more the number of users using the same pilot frequency sequence is, the more the pilot frequency pollution is, and the higher the channel estimation error is.
Fig. 3 and fig. 4 compare the change of the average cell spectrum efficiency with the number of antennas in 4 scenarios, which are respectively the joint optimization of the downtilt angle and downtilt angle power of each fixed sector in the conventional 2D massive MIMO system, the 3D massive MIMO system, and the antenna weighting vector power joint optimization scheme proposed by us. As can be seen from fig. 3, when r is 0.5, that is, when pilots are completely multiplexed between sectors, pilot pollution is the most serious, and when a conventional massive MIMO system and a vertical sectorization technique are used to fix downtilt and power average allocation, the cell average spectral efficiency of the system is poor, and the cell average spectral efficiency by optimizing downtilt and power systems is better than that of the conventional 2D massive system, while the antenna weight vector power joint optimization scheme proposed by us can achieve the best cell average spectral efficiency. As can be seen from fig. 3, when r is 5/6, since the pilot pollution is severe compared to the conventional massive MIMO system due to the partial multiplexing of pilots among sectors, the pilot length is increased, and therefore the average spectrum efficiency of the cell in the 3D massive MIMO system is reduced, but the proposed scheme can still achieve the best system performance.
Examples
Considering a 3D massive MIMO system, L horizontal sectors form a cooperative cluster, and each horizontal sector consists of an array with the number M (N in the vertical direction)vRoot, horizontal direction NtRoot), where the number of M may reach hundreds. Each horizontal sector simultaneously serves K (K < M) single-antenna users, and the users are uniformly distributed. By mechanical downtilt, each cell is divided into two vertical sectors, by thetal0And thetal1The antenna downtilt angles for the near and far sectors, respectively, served by the ith cell are shown in fig. 1. The total power of the base station is P, and the near sector power of the serving cell is Pl0The power of the far sector is Pl1The uplink transmission power of the user is pr。
And a block fading channel model is adopted, and the fast fading coefficient is kept unchanged in the coherent interval of T OFDM symbols. The M × 1-dimensional uplink channel vector from user k to target base station j in cell l can be expressed aswherein beta isjlkRepresenting large-scale fading coefficients, including path loss and shadow fading, hjlkRepresents a small-scale fading coefficient, hjlkEach element of (a) obeys a complex gaussian distribution with a mean of 0 and a variance of 1. The overall gain of the antenna array is a (-) and,andrespectively representing users i in cell j0At corresponding near and far sector beam gains from base station l, where θD，lFor base station l downtilt angle (pitch angle), thetallkIs the elevation angle from which user k looks at base station l in cell l.
The technical means for indirectly inhibiting the pilot pollution by the 3D coordinated beam forming and power distribution combined optimization scheme provided by the invention are as follows:
1. uplink channel estimation
Since the present invention is primarily concerned with vertical sectorization, the gain of the antenna in each direction of the horizontal plane is assumed to be 1. When estimating the uplink channel, the users are virtually divided into near sector users and far sector users according to the geographical position of the user distribution, and the same group of orthogonal pilot frequency is multiplexed between the two groups of users. And the base station antenna is only provided with a downward inclination angle, namely, the base station uses a vertical beam to receive pilot signals transmitted by all users in two sectors. Suppose the number of users in each sector is the same and is K', and the near sector user K of each cell0And remote sector user k1Using the same 1 x τ -dimensional pilot sequence Ψk(K' ≦ τ ≦ K), we define the pilot multiplexing factor between sectors asThen whenWhen the signal received by the base station is
Wherein: a (-) is the 3D antenna pattern of the base station (assuming the 3D antenna pattern of the mobile station is 1), θD，lFor base station l downtilt angle (pitch angle), thetallkIs the elevation angle from which user k looks at base station l in cell l. z is a radical oflIs additive white Gaussian noise of base station l, and(N0is the noise power spectral density);
the gain of the array antenna in formula (1) is defined as
Wherein:is a weighting vector of dimension M x 1 of the antenna array, Br(θ)∈CM×1Is the directional pattern of the base station antenna array, Br(N-1) N of (theta)V+ m elements being Br，m，n(theta) representing the gain of the antenna element in the mth row and the nth column, and the expression is
In the formula (3)For vertical patterns of individual antenna elements, theta3dBRepresenting the half power angle, dyAnd dzIndicating antenna horizontal and vertical spacing.
Under the assumption that the elevation angle of each base station antenna and the elevation angle of each user are known, the near sector user k in the cell l0The LS channel estimation result of (1) is:
as can be seen from equation (4), the LS estimation result of the channel not only includes the channel information of the target user, but also includes the channel information of all users using the same pilot frequency in other vertical sectors of the cell and in each vertical sector of other cells, and it can be seen that after vertical sectorization, because more users using the same pilot frequency are also more intensive, the pilot frequency pollution is more serious than that of the conventional massive MIMO system, and the reduction of the channel estimation accuracy may offset the improvement of the system and rate performance caused by the vertical sector splitting to some extent.
2. Downlink data transmission
In TDD transmission mode, the downlink channel is the transpose of the uplink channel. Here, it is not assumed that the number of service users in each sector is the same. The base station end adopts the maximum ratio transmission, then the user i of the sector near the cell j0The received downlink signal is
Wherein, Pl0And Pl1Respectively representing the near and far sector transmit power of cell/,indicating that base station l sends to user k in cell l0The data symbols of (a) are transmitted,is additive white gaussian noise.Andrespectively representing users i in cell j0Corresponding near and far sector beam gains from base station/.
For calculating expressions of users and rates, noteThe formula (21) is rewritten as
The first term is the expected signal, the second term is the interference between users in the sector in the cell, the third term is the interference between sectors in the cell, the fourth term is the interference between the sectors, and the fifth term is the noise.
Assuming that the user data symbols are independent of each other and have a power of 1, and that the noise power is normalized and the pilot overhead is taken into account, the near-sector user i of cell j can be calculated from equation (24)0The instantaneous rate is expressed as
On the premise that the channel estimation result of each user is known,sum of transmission power with each sectorIt is related.
3. Antenna array weighting vector and power distribution joint optimization problem
Based on the above analysis, our optimization problem is established as: the maximum sum rate of all users in the system is taken as an optimization target, and the weighting vector and power distribution of each sector antenna are taken as optimization objects in a specific form
W in formula (8)l0And wl1The antenna weight vectors for the near and far sectors of cell l.Andrepresenting the average elevation angle of users in the near and far sectors of cell l, respectively. The optimization problem includes two constraints: c1The premise that the correlation between the antenna beams of two sectors in each cell is smaller than a threshold value is shown, and the transmission power of the base station is kept unchanged after the weighting vector w is adjusted; c2Indicating that the total power of the two sectors per cell is less than P.
The optimization problem of equation (8) is a nonlinear non-convex optimization problem. The traditional solution thought is to fix the weighting vector, distribute power according to the KKT condition, then fix the beam power to optimize the weighting vector, alternate in this way, and obtain the final solution through multiple iterations, and since the calculation form of the formula (8) is very complicated, the calculation complexity of the solution process is too high. To reduce complexity, particle swarm optimization can be used to find a "sufficient" sub-optimal solution. The solving steps are as follows:
(a) initialization: selecting proper critical downward inclination angle according to the distribution condition of users, dividing the users into two sectors, and calculating the average elevation angle of the users in each sectorAndthe initial position and update speed of each particle for each variable is initialized.
Pl0The update speed and initial position of the jth particle of (a) may be initialized as:
wl0(N-1) N ofVThe update speed and initial position of the jth particle of + m elements can be initialized as:
wl1(N-1) N ofVThe update speed and initial position of the jth particle of + m elements can be initialized as:
wherein epsilon-U (0,1), d ═ dv＝dzIs the spacing of two antenna elements.
(b) Iteration: and updating the updating speed and position of each particle according to an iterative formula of the particle swarm.
Wherein c1 and c2 are normal numbers and are called learning factors; r1 and r2 are [0, 1 ]]Is a weighting factor of inertia. p is a radical ofjIs the local optimum of the jth particle, pgIs a global optimum.
(c) Judging whether the wave beam weighting vector of each sector of each cell meets the correlation condition limitation, and if not, enabling rhomax＝ρmax+0.01, the update is iterated again. Judging whether the power of each sector is in the range, if the power is out of the range,and (5) updating again.
(d) Defining an evaluation function fmThe local and global optima for the particles may be for the overall sum rate of the systemThrough fmAnd (4) calculating.
(e) And stopping if the maximum iteration number is reached or the difference value of the utility functions of the two adjacent iterations is smaller than delta (a preset small constant).
4. Self-adaptive adjustment of sector to which user belongs
The above optimization process is performed in the case where whether the user belongs to the near sector or the far sector in the cell is already divided. Theoretically, each user should be served by a downlink beam with a large antenna gain. Therefore, we consider that after the optimization processing is completed and the antenna beam direction and the transmission power of each sector are adjusted, the home sector of the user is adjusted, and all users are guaranteed to be served by the downlink beam with larger antenna gain. For user i in cell l, the adjustment process is as follows:
● if A (theta)D，l0，θlli)≥A(θD，l1，θlli) If the user is a near sector user;
● if A (theta)D，l0，θlli)＜A(θD，l1，θlli) Then the user is a far sector user.
After the above adjustment, if the sector assignment of the user is changed, the optimization of the equation (8) is executed again, otherwise, the optimization is ended.
The specific computational complexity contrast for each scheme is given below:
the complexity of the joint optimization of the downtilt angle and the power by using the particle swarm optimization is O (S)2M2) Where S is the number of particles, the complexity of the antenna and weight vector and power joint optimization proposed by us is O (CS)2M3) And C is the adjustment times of the sector to which the user belongs.
In conclusion, the scheme of the invention improves the performance of the system under the condition of certain computation complexity. Meanwhile, the uplink channel estimation problem is considered in the optimization problem, and the pilot frequency pollution problem in a large-scale MIMO system is indirectly inhibited unlike the assumption of 3DMIMO ideal CSI.

Claims (1)

  1. A combined vertical beam control and power allocation method in a 3D massive MIMO system is characterized by comprising the following steps:
    1) in an uplink channel estimation stage, dividing each cell in a cooperation cluster into two virtual vertical sectors according to user position distribution, and enabling the two vertical sectors to reuse one group of same pilot frequency sequences so as to increase the number of users simultaneously served by each base station, wherein the channel estimation adopts an LS estimation algorithm;
    2) in the downlink data transmission stage, in the first step, each cell is set according to the distribution of user positionsTwo fixed antenna downward inclination angles, two vertical sectors are formed in each cell, namely a near sector and a far sector, and the sector to which each user belongs is initialized; secondly, based on the result of the uplink channel estimation and the initialization result of the sector to which each cell user belongs, the 3D antenna array weighting vector w of the near sector of each cell is optimized in a combined manner by taking maximum ratio transmission as a downlink precoding algorithm and taking the maximum sum rate as a targetl0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1(ii) a Thirdly, according to the optimized wave beam gain of the near sector and the far sector of the cell where the user is located, the user is divided into the sectors with larger wave beam gain in the cell again; repeating the first step to the third step until the sector condition of the user is unchanged; so far, the combined vertical beam control and power distribution in the 3D large-scale MIMO system is completed;
    the method specifically comprises the following steps:
    (1) and (3) uplink channel estimation: dividing each cell into two virtual vertical sectors according to the user position distribution, using one vertical beam to receive the uplink pilot signals sent by all users in the two virtual sectors in each cell, carrying out LS channel estimation, and carrying out LS channel estimation on a near sector user k in a cell l0The LS channel estimation result isThe method comprises the following specific steps:
    <mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mover> <mi>b</mi> <mo>^</mo> </mover> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> <mrow> <mi>L</mi> <mi>S</mi> </mrow> </msubsup> <mo>=</mo> <mfrac> <mrow> <msub> <mi>y</mi> <mi>l</mi> </msub> <msubsup> <mi>&amp;Psi;</mi> <mi>k</mi> <mi>H</mi> </msubsup> </mrow> <mrow> <mi>K</mi> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>b</mi> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mrow> <msub> <mi>llk</mi> <mn>1</mn> </msub> </mrow> </msub> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>&amp;NotEqual;</mo> <mi>l</mi> </mrow> <mi>L</mi> </munderover> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mrow> <msub> <mi>ljk</mi> <mn>0</mn> </msub> </mrow> </msub> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>ljk</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mrow> <msub> <mi>ljk</mi> <mn>1</mn> </msub> </mrow> </msub> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>z</mi> <mi>l</mi> </msub> <msubsup> <mi>&amp;Psi;</mi> <mi>k</mi> <mi>H</mi> </msubsup> </mrow> <mrow> <mi>K</mi> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    in the formula: y islThe calculation formula of the signal received by the base station l is:
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mi>l</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> </msub> <mi>A</mi> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> <mo>)</mo> <msub> <mi>&amp;Psi;</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mrow> <msub> <mi>llk</mi> <mn>1</mn> </msub> </mrow> </msub> <mi>A</mi> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> <mo>)</mo> <msub> <mi>&amp;Psi;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>&amp;NotEqual;</mo> <mi>l</mi> </mrow> <mi>L</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mrow> <msub> <mi>ljk</mi> <mn>0</mn> </msub> </mrow> </msub> <mi>A</mi> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>llk</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> <mo>)</mo> <msub> <mi>&amp;Psi;</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mrow> <msub> <mi>ljk</mi> <mn>1</mn> </msub> </mrow> </msub> <mi>A</mi> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <msub> <mi>ljk</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> <mo>)</mo> <msub> <mi>&amp;Psi;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>z</mi> <mi>l</mi> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    wherein: k is the total number of users served by each cell, L is the total number of cells in the coordinated cluster, ΨkFor near sector user k0And remote sector user k1The same pilot sequence is transmitted in 1 x tau dimension in uplink,for cell/. near-sector user k0The channel matrix to the base station/,for cell l remote sector user k1The channel matrix to the base station/,for cell j near sector user k0The channel matrix to the base station/,for cell j remote sector user k1Channel matrix to base station l, A (-) is the 3D antenna pattern of the base station, θD,lIs the downtilt angle of the base station i antenna array,for a near sector user k in cell l0Looking at the elevation angle of the base station i,for a remote sector user k in cell l1Looking at the elevation angle of the base station i,for a near sector user k in cell j0Looking at the elevation angle of the base station i,for a remote sector user k in cell j1Elevation angle, z, looking at base station llIs additive white Gaussian noise of base station l, andN0is noise power spectral density, I is unit array;
    denotes ΨkThe conjugate transpose of (1);
    (2) downlink vertical beam forming and power distribution joint optimization: for user k in cell l, maximum ratio transmission is carried out based on uplink channel estimation information, and the user and rate R can be obtainedlkThe expression of (1); the optimization target is to maximize the sum rate of all users in the cooperative cluster, and the optimization target is the 3D antenna array weighting vector w of each cell near sectorl0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1I.e. the optimization problem isThe concrete form is as follows:
    <mrow> <mtable> <mtr> <mtd> <mrow> <munder> <mi>max</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>w</mi> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </munder> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>L</mi> </munderover> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> </munderover> <msub> <mi>R</mi> <mrow> <msub> <mi>lk</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> </munderover> <msub> <mi>R</mi> <mrow> <msub> <mi>lk</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>C</mi> <mn>1</mn> </msub> <mo>:</mo> <msubsup> <mi>w</mi> <mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mi>l</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <msub> <mi>w</mi> <mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msubsup> <mi>w</mi> <mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>l</mi> <mn>1</mn> </mrow> <mi>H</mi> </msubsup> <msub> <mi>w</mi> <mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi>&amp;rho;</mi> <mo>=</mo> <mfrac> <mrow> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;pi;</mi> </mrow> <mi>&amp;pi;</mi> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>w</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <mi>B</mi> <mi>r</mi> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>w</mi> <mrow> <mi>l</mi> <mn>1</mn> </mrow> <mi>H</mi> </msubsup> <mi>B</mi> <mi>r</mi> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>p</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&amp;theta;</mi> </mrow> <mrow> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;pi;</mi> </mrow> <mi>&amp;pi;</mi> </msubsup> <msup> <mrow> <mo>|</mo> <msubsup> <mi>w</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <mi>B</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mi>p</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&amp;theta;</mi> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;pi;</mi> </mrow> <mi>&amp;pi;</mi> </msubsup> <msup> <mrow> <mo>|</mo> <msubsup> <mi>w</mi> <mrow> <mi>l</mi> <mn>1</mn> </mrow> <mi>H</mi> </msubsup> <mi>B</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mi>p</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&amp;theta;</mi> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>&amp;rho;</mi> <mi>max</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <msub> <mi>C</mi> <mn>2</mn> </msub> <mo>:</mo> <msub> <mi>p</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>p</mi> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>&amp;le;</mo> <mi>P</mi> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    in the formula:andmean elevation angles of users in the near sector and the far sector of the cell l are respectively represented;
    the optimization problem includes two constraints: c1The premise that the correlation between the antenna beams of two sectors in each cell is smaller than a threshold value is shown, and the transmission power of the base station is kept unchanged after the weighting vector w is adjusted;
    C2means that the total power of two sectors per cell is less than the total power P of the base station;
    Br(θ)∈CM×1is the directional diagram of the base station antenna array, and M is the number of base station antennas;
    p (θ) represents a probability density function of the user distribution;
    ρ represents the correlation coefficient between two sector antenna beams per cell;
    indicates that the antenna has a downtilt angle ofThe antenna array weight vector for the near sector of cell i,to representThe conjugate transpose of (1);indicates that the antenna has a downtilt angle ofThe antenna array weight vector for the far sector of cell/,to representThe conjugate transpose of (1);
    pl0indicating the base station service power, p, of the near sector of the celll1Represents the base station service power of the remote sector of the cell l;
    wherein:for a near sector user k in cell l0The sum of the rates of (a) and (b),for a remote sector user k in cell l1L is the total number of cells in the cooperative cluster, Kl0Is the total number of users, K, in the celll1The total number of users of the remote sector in the cell l;
    in order to reduce inter-cell interference and meet total power constraints, the constraint condition of the optimization problem is set to be that the correlation of the beam between sectors is smaller than a threshold rhomaxAnd the total transmitting power of the two sectors does not exceed P;
    (3) in order to reduce the complexity of solving the optimization problem, iterative solution is carried out by using a particle swarm algorithm;
    the first step is as follows: initializing 3D antenna array weighting vectors w for each cell near sectorl0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1Setting a 3D antenna array weighting vector w of each cell near sectorl0Has an update speed vw,l0And a transmission power pl0Has an update speed vp,l0Setting a 3D antenna array weighting vector w of each cell remote sectorl1Has an update speed vw,l1And a transmission power pl1Has an update speed vp,l1；
    The second step is that: setting the total sum rate of the system as a utility function, and continuously updating the 3D antenna array weighting vector w of each cell near sector by taking the maximum utility function as a targetl0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1；
    The third step: if the maximum iteration times are reached or the difference value of the utility functions of two adjacent iterations is smaller than a preset constant delta, stopping the iteration process, wherein the constant delta is smaller than 0.01;
    according to the iterated 3D antenna array weighting vector w of each cell near sectorl0And 3D antenna array weight vector w for each cell remote sectorl1Array antenna gains of a serving near sector and a far sector are respectively calculated, wherein the near sector array antenna gain of a user i in a cell l at a base station l is A (theta)D,l0,θlli)，θD,l0Down tilt angle, theta, of the near sector antenna for celllliThe pitch angle from user i in cell l to base station l, and the array antenna gain of user i in cell l in the far sector of base station l is A (theta)D,l1,θlli)，θD,l1The downtilt angle of the remote sector antenna of the serving cell l;
    wherein a 3D antenna array weighting vector w for each cell near sector is initializedl0And its update speed vw,l0The calculation formula is as follows:
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>v</mi> <msub> <mi>w</mi> <mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <mi>&amp;epsiv;</mi> <mn>2</mn> </mfrac> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>cos</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <mi>m</mi> <mi> </mi> <mi>sin</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi> </mi> <mi>cos</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mrow> <mo>(</mo> <mfrac> <mi>&amp;epsiv;</mi> <mn>2</mn> </mfrac> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>j</mi> <mi> </mi> <mi>sin</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <mi>m</mi> <mi> </mi> <mi>sin</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi> </mi> <mi>cos</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>w</mi> <msub> <mi>w</mi> <mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <mi>m</mi> <mi> </mi> <mi>sin</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi> </mi> <mi>cos</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mi>j</mi> <mi> </mi> <mi>sin</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <mi>m</mi> <mi> </mi> <mi>sin</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi> </mi> <mi>cos</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    in the formula: e to U (0,1), d is the spacing of two antenna elements, and d ═ dy＝dz，dyAnd dzRespectively representing the horizontal spacing and the vertical spacing of the antennas;
    m and n represent the mth row and nth column antenna element of the planar antenna array;
    is (N-1) NVThe update speed at time 1 of the j-th particle of + m elements,is (N-1) NVInitial position at time 0 of j-th particle of + m elements, NvRepresenting the number of vertical antennas of the antenna array;
    λ represents the wavelength of the user transmit beam;
    initializing the transmit power p of the near sector of each celll0The calculation formula is as follows:
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>v</mi> <msub> <mi>P</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> </msub> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>P</mi> <mo>&amp;times;</mo> <mi>&amp;epsiv;</mi> <mo>-</mo> <mfrac> <mi>P</mi> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>l</mi> <mn>0</mn> </mrow> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>P</mi> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    in the formula:is Pl0The update rate at time 1 of the jth particle,is Pl0Initial position at time 0 of the jth particle;
    initializing 3D antenna array weighting vectors w for each cell remote sectorl1And an update speed vw,l1The calculation formula is as follows:
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>v</mi> <msub> <mi>w</mi> <mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <mi>&amp;epsiv;</mi> <mn>2</mn> </mfrac> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>cos</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <mi>m</mi> <mi> </mi> <mi>sin</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi> </mi> <mi>cos</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mrow> <mo>(</mo> <mfrac> <mi>&amp;epsiv;</mi> <mn>2</mn> </mfrac> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>j</mi> <mi> </mi> <mi>sin</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <mi>m</mi> <mi> </mi> <mi>sin</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi> </mi> <mi>cos</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>w</mi> <msub> <mi>w</mi> <mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <mi>m</mi> <mi> </mi> <mi>sin</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi> </mi> <mi>cos</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mi>j</mi> <mi> </mi> <mi>sin</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <mi>m</mi> <mi> </mi> <mi>sin</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mi> </mi> <mi>cos</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    in the formula:is (N-1) NVUpdate speed at time 1 of the jth particle of + m elements;
    is (N-1) NVAn initial position at time 0 of a jth particle of + m elements;
    the formula for the iteratively updated for each particle at time τ is as follows:
    <mrow> <mtable> <mtr> <mtd> <mrow> <msup> <mi>v</mi> <mi>j</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>av</mi> <mi>j</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>&amp;lsqb;</mo> <msup> <mi>p</mi> <mi>j</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mi>x</mi> <mi>j</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>&amp;lsqb;</mo> <msup> <mi>p</mi> <mi>g</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mi>x</mi> <mi>j</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>x</mi> <mi>j</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>x</mi> <mi>j</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>v</mi> <mi>j</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    wherein: v. ofj(τ) update speed, x, of jth particle time τj(τ) the position of the jth particle time τ, c1, c2 being normal numbers, called the learning factor; r1 and r2 are [0, 1 ]]A is an inertial weight factor; p is a radical ofj(τ -1) is the local optimum, p, for the jth particle time τ -1g(τ -1) is the global optimum of all particles at time τ -1;
    (4) the sector to which the user belongs is re-divided according to the beam gain of the user in each sector, and the adjustment process is as follows:
    if A (theta)D,l0,θlli)≥A(θD,l1,θlli) If the user is a near sector user;
    if A (theta)D,l0,θlli)＜A(θD,l1,θlli) If the user is a remote sector user;
    wherein,
    in the formula:is an antenna array with a downward inclination angle thetaD,l0Then, the weighting vector of the cell l near sector antenna array; b isr(θlli)∈CM×1Is the directional pattern of the base station antenna array, Br(θlli) (N-1) NV+ m elements being Br,m,n(θlli) Representing the m-th row and n-th column of antenna elementsGain, expressed as
    <mrow> <msub> <mi>B</mi> <mrow> <mi>r</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>l</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>G</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>l</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <msub> <mi>md</mi> <mi>z</mi> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>l</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>D</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <msub> <mi>nd</mi> <mi>y</mi> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>l</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>D</mi> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    In the formula:for vertical patterns of individual antenna elements, theta3dBRepresenting the half-power angle, thetaDRepresenting the downtilt angle, theta, of the antenna arraylliFor the pitch angle, d, of users i in cell l to base station lyAnd dzRepresenting antenna horizontal and vertical spacing;
    <mrow> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>l</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>w</mi> <msub> <mi>&amp;theta;</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mi>H</mi> </msubsup> <msub> <mi>B</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>l</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    in the formula:is an antenna array with a downward inclination angle thetaD,l1Weight vector of time-of-flight far-sector antenna array；
    Repeating the steps (2) to (4), and stopping if the sector condition of the user does not change to obtain the final 3D antenna array weighting vector w of the near sector of each celll0And a transmission power pl0And a 3D antenna array weighting vector w for the far sectorl1And a transmission power pl1。
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