阅读说明：本技术 3d大规模mimo广覆盖预编码传输方法 (3D large-scale MIMO wide-coverage pre-coding transmission method ) 是由 高西奇 郭伟然 卢安安 于 2019-10-21 设计创作，主要内容包括：本发明公开了一种3D大规模MIMO广覆盖预编码传输方法,利用预编码产生广覆盖的功率图样,能够解决3D大规模MIMO公共信号传输的功率覆盖问题。本发明首先利用天线阵列高度和下倾角等信息,基于球心投影理论计算功率图样应当覆盖的角度范围,设置目标功率图样；然后再以预编码矩阵产生的功率图样与目标图样距离最小为目标,预编码矩阵属于oblique流形为约束构建优化问题；再基于流形优化理论,求得预编码矩阵。预编码矩阵产生的广覆盖的功率图样,其覆盖的角度范围可自由调整。本发明产生的辐射功率图样能抑制小区间干扰并且可以确保不同位置用户间的公平性。另外,本发明所提出的预编码,有利于充分利用基站端功放容量,进而取得高功率效率。(The invention discloses a 3D large-scale MIMO wide-coverage pre-coding transmission method, which can solve the problem of power coverage of 3D large-scale MIMO public signal transmission by utilizing pre-coding to generate a wide-coverage power pattern. Firstly, calculating an angle range to be covered by a power pattern based on a sphere center projection theory by utilizing information such as antenna array height, downward inclination and the like, and setting a target power pattern; then, the minimum distance between a power pattern generated by the pre-coding matrix and a target pattern is taken as a target, and the pre-coding matrix belongs to an obeque manifold and is taken as a constraint construction optimization problem; and then, based on the manifold optimization theory, a precoding matrix is obtained. The precoding matrix generates a wide-coverage power pattern, and the coverage angle range of the wide-coverage power pattern can be freely adjusted. The radiation power pattern generated by the invention can inhibit the interference among cells and can ensure the fairness among users at different positions. In addition, the precoding provided by the invention is beneficial to fully utilizing the power amplification capacity of the base station end, thereby obtaining high power efficiency.)

The 3D large-scale MIMO wide-coverage precoding transmission method is characterized by comprising the following steps: the method comprises the following steps:

(1) setting a required wide-coverage power pattern according to the height and the downward inclination angle of the base station antenna array and the corresponding emission angle of the user terminal in the cell coverage range, wherein the value of the required wide-coverage power pattern on a sampling point is in direct proportion to the square of the distance between the base station antenna array and the user terminal;

(2) constructing an optimization problem by taking the minimum correlation matrix distance between a power pattern generated by a precoding matrix and a required wide coverage power pattern as a target and the precoding matrix belonging to the oblique manifold as a constraint, and optimizing based on a conjugate gradient method constructed by manifold optimization to obtain an optimal precoding matrix;

(3) and performing wide-coverage precoding processing on the signals based on the obtained optimal precoding matrix and sending the signals, wherein the transmitting signal power on each antenna unit is the same.

2. The 3D massive MIMO wide-coverage precoding transmission method of claim 1, wherein: the distance between the base station antenna array and the user terminal is expressed as a function of the position coordinates of the user terminal in the plane and the height difference between the base station antenna and the user terminal.

3. The 3D massive MIMO wide-coverage precoding transmission method of claim 2, wherein: the distance between the base station antenna array and the user terminal is represented as:

wherein (X (theta)_t,φ_t),Y(θ_t,φ_t) Is the position coordinate of the user terminal in the plane, h is the height difference between the base station antenna and the user terminal;

wherein theta is_tRepresenting the pitch angle, phi, of the transmitted signal_tWhich is indicative of the azimuth of the transmitted signal,α is the mechanical down tilt.

4. The 3D massive MIMO wide-coverage precoding transmission method of claim 1, wherein: the samples of the desired wide coverage power pattern are expressed as:

wherein

5. The 3D massive MIMO wide-coverage precoding transmission method of claim 1, wherein: the power pattern generated by the precoding matrix is:

wherein M is_tIs the number of transmitting antennas, S_tIs the transmitted signal dimension, W is the precoding matrix, T_qIs a conversion matrix, Q-0, 1.., Q-1, which is a function of steering vectors and antenna element patterns.

6. The 3D massive MIMO wide-coverage precoding transmission method of claim 5, wherein: matrix T_qIs defined as:

where v (theta, phi) represents the steering vector, e (theta, phi) represents the pattern of the transmit antenna elements, and the indices 0, 1.

7. The 3D massive MIMO wide-coverage precoding transmission method of claim 1, wherein: the precoding matrix W satisfies:

wherein M is_tIs the number of transmitting antennas, S_tIs the dimension of the transmitted signal that is,

8. The 3D massive MIMO wide-coverage precoding transmission method of claim 1, wherein: the objective function of the precoding matrix optimization problem is represented as:

where B is the desired radiation power pattern and a is the radiation power pattern produced by the precoding matrix W.

9. The 3D massive MIMO wide-coverage precoding transmission method of claim 1, wherein: the step of optimizing the precoding matrix by adopting the conjugate gradient method comprises the following steps:

s1: setting a search direction, and if the cycle count is 0, setting the search direction as a negative Riemann gradient direction;

if the cycle count is larger than 0, setting the sum of the Riemann gradient direction with the negative search direction and the parallel conveying direction corrected based on the Hestenes-Stiefel rule;

s2: setting a search step according to Armijo linear search until the search step meets the Wolfe condition;

s3: establishing an updating equation by utilizing the searching direction and the step length, and updating the precoding matrix;

s4: comparing the current precoding matrix with the previous round precoding matrix: if the difference is less than the threshold, determining that the precoding matrix is converged; otherwise, it is determined that the precoding matrix is not converged, and the process returns to step S1.

Technical Field

The invention belongs to the technical field of communication, and relates to a 3D large-scale MIMO wide-coverage pre-coding transmission method.

Background

In order to improve user experience and meet the challenges brought by the rapid increase of wireless data service requirements and new service requirements, a new generation of mobile network needs to support scenes such as high quality, high transmission rate, high mobility, high user density, low time delay and the like. The large-scale Multiple-Input Multiple-output (MIMO) technology, which greatly improves the system capacity by providing a large-scale antenna array at a base station, is one of the key technologies of a new generation of wireless network in the future and is a research hotspot in recent years.

One of the challenges of massive MIMO is to design the signaling process for the common channels. Unlike dedicated channels, which have been widely studied for exchanging user-specific data, common channel transmission schemes are relatively rarely studied. Common channels play an important role in cellular systems, and much of the necessary common information and services are delivered to users over common channels. Since the common channel serves all users in the cell and not only certain active users, it is desirable that the radiated power of the signals transmitted by the base station hardly fluctuate in different spatial directions within the cell. All users in the cell can reliably receive the common signal.

Both the 180 degree omni-directional coverage scheme and the less than 180 degree wide coverage scheme are natural choices to meet the power requirements described above. There have been some documents that propose omni-directional precoding designs as well as wide-coverage precoding designs. However, these schemes have not been considered for application to three-dimensional (3D, 3-divisional) MIMO scenarios. Considering that 3D MIMO has an additional degree of freedom in the vertical direction compared to a uniform linear array for designing a power pattern in the pitch angle direction, designing a wide-coverage power pattern based on a uniform area array has a possibility of further improving synchronization performance. Synchronization performance is an important indicator in the initial cell discovery process. The channel state information of all users is not available in this process. In such a scenario, it is desirable to use a reasonably designed power pattern to ensure wide coverage of the cell range.

Generally, the miss probability can be used to characterize the synchronization performance of the system. In order to ensure the synchronization performance of the users in the whole cell range, the positions corresponding to all possible transmission angles can be considered to have equal missed detection probability. To ensure wide coverage over the considered angular range, a natural approach is to design the radiation power pattern of 3D massive MIMO by half-power beamwidth. However, this scheme does not take into account the shape of the cell and the path loss of different user terminals. If the scheme fails to match the shape of the cell coverage, the corresponding power pattern causes inter-cell interference. In addition, different user terminals have different path losses with respect to the base station. To ensure fairness among different users, the gains of the power patterns at different emission angles also need to be changed accordingly.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the defects of the prior art, the invention discloses a 3D large-scale MIMO wide-coverage pre-coding transmission method, which can realize wide coverage on a cell range, inhibit interference among cells, ensure fairness among different users and obtain high power efficiency.

The technical scheme is as follows: in order to achieve the purpose, the invention provides the following technical scheme:

the 3D large-scale MIMO wide-coverage precoding transmission method can calculate the angle range covered by the power pattern according to the cell range expected to be covered. By using M_t×S_tProcessing the transmitted signal by the dimensional wide-coverage precoding matrix W, so that the power of the signal can be adjusted in a set angle range, wherein S_tIs the dimension of the transmitted signal, M_tIs the number of transmit antennas. And the transmitted signal power on each antenna unit is the same, so that the power efficiency of each radio frequency channel and the antenna array is maximized. Specifically, the 3D massive MIMO wide coverage precoding transmission method of the present invention mainly includes the following steps:

(1) setting a required wide-coverage power pattern according to the height and the downward inclination angle of the base station antenna array and the corresponding emission angle of the user terminal in the cell coverage range, wherein the value of the required wide-coverage power pattern on a sampling point is in direct proportion to the square of the distance between the base station antenna array and the user terminal;

(2) constructing an optimization problem by taking the minimum correlation matrix distance between a power pattern generated by a precoding matrix and a required wide coverage power pattern as a target and the precoding matrix belonging to the oblique manifold as a constraint, and optimizing based on a conjugate gradient method constructed by manifold optimization to obtain an optimal precoding matrix;

(3) and performing wide-coverage precoding processing on the signals based on the obtained optimal precoding matrix and sending the signals, wherein the transmitting signal power on each antenna unit is the same.

Further, the distance between the base station antenna array and the user terminal is expressed as a function of the position coordinates of the user terminal in the plane and the height difference between the base station antenna and the user terminal. In particular, the distance between the base station antenna array and a certain user terminal can be expressed as

Wherein (X (theta)_t,φ_t),Y(θ_t,φ_t) Is the position coordinates of the user terminal in the plane and h is the height difference of the base station antenna and the user terminal.

Further, the position coordinates of the user terminal within the plane may be expressed as

And

wherein theta is_tRepresenting the pitch angle, phi, of the transmitted signal_tRepresenting the transmitted signal azimuth.And α is the mechanical downtilt.

Further, the desired wide coverage power pattern may be denoted as pattern B, which is a P × Q dimensional matrix. Use of

To indicate the corresponding transmission angle (theta) of the user terminal in the coverage area of the considered cell_p,φ_q). The samples of the required power pattern are given by:

wherein

Is a normal number.

Further, the power pattern generated by the precoding matrix W is a P × Q dimensional matrix. The power pattern generated by the precoding matrix W is:

further, the transformation matrix is a function of the steering vectors and the antenna element pattern, the matrix T_qIs defined by the formula:

wherein

Indicating the steering vector and e (theta, phi) the pattern of the transmit antenna element.

Further, the precoding matrix W satisfiesI.e. precoding matrix W in the oblique manifold

The above.

Further, the objective function of the precoding matrix optimization problem can be defined as:

further, the conjugate gradient method comprises the following steps:

s1: setting a search direction, and if the cycle count is 0, setting the search direction as a negative Riemann gradient direction;

if the cycle count is larger than 0, setting the sum of the Riemann gradient direction with the negative search direction and the parallel conveying direction corrected based on the Hestenes-Stiefel rule;

s2: setting step size mu according to Armijo linear search^(k)Until it meets the Wolfe condition;

s3: establishing an updating equation by utilizing the searching direction and the step length to update the precoding matrixWherein D^(k)Is the search direction, μ^(k)Is the search step size, operator

Representing projection of precoding back to manifold

S4: the current precoding matrix W^(k+1)With the preceding round precoding matrix W^(k)And (3) comparison: if the difference is less than the threshold, then it is determined that the precoding matrix converges to the optimal precoding matrix W^opt(ii) a Otherwise, it is determined that the precoding matrix is not converged, and the process returns to step S1.

Has the advantages that: the invention considers the shape of the cell and the path loss of different users based on the prior information such as the height of the antenna array of the base station, the mechanical downward inclination angle and the like, and the generated radiation power pattern can be matched with the shape of the cell, thereby being capable of inhibiting the interference between the cells. The invention considers the path loss between different user terminals and the base station, and the generated radiation power pattern can carry out gain compensation according to the loss, thereby ensuring the fairness among different users. In addition, the precoding provided by the invention can meet the requirement that each antenna has equal transmitting power, is beneficial to fully utilizing the power amplification capacity of the base station end and obtains high power efficiency. Compared with the prior art, the invention has the following advantages and beneficial effects:

the large-scale MIMO wide-coverage pre-coding transmission method can realize wide-angle coverage of the power pattern, and meanwhile, the pre-coding matrix meets the equal-power constraint condition, which means that the power amplification efficiency can be greatly improved. The number of the precoding matrix columns in the invention is not limited to 1, which means that the system has a plurality of transmission streams, and the power patterns and the transmission power generated by different data streams can be complementary, so that the equal power constraint condition can be met while the wide-angle coverage of the power patterns is realized more easily. The precoding matrix searching method provided by the invention is very flexible, and can be used in the scene of an omnidirectional antenna array element and the scene of a directional antenna array element. The method can be flexibly applied to scenes with different downward inclination angles. Compared with a wide-coverage precoding scheme based on half-power beam width, the method has better synchronization performance and less interference to adjacent cells.

Drawings

FIG. 1 is a flow chart of a method of an embodiment of the present invention;

FIG. 2 is a schematic diagram of a 3D massive MIMO system configuration;

FIG. 3 is a side view of FIG. 2, showing the relationship between the geometric quantities of space in the scene under consideration;

fig. 4 is an exemplary illustration of a radiation power pattern of a single antenna element;

FIG. 5 is a graph comparing the power pattern results of the proposed solution and the control solution;

FIG. 6 is a graph comparing the received power results of the proposed scheme and the control scheme;

FIG. 7 is a comparison chart of the probability of missed detection results of the proposed solution and the comparison solution in the line-of-sight channel scenario;

fig. 8 is a comparison chart of the probability of missed detection results of the proposed scheme and the comparison scheme under the non-line-of-sight channel scene.

Detailed Description

The technical solutions provided by the present invention will be described in detail below with reference to specific examples, and it should be understood that the following specific embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention.

The method is mainly suitable for a 3D large-scale MIMO system with a large-scale antenna array arranged on a base station side to serve a plurality of users simultaneously. As shown in fig. 1, in the 3D massive MIMO wide coverage precoding transmission method disclosed in the embodiment of the present invention, a required wide coverage power pattern is first set according to the height of a base station antenna array, a downward inclination angle, and a transmission angle corresponding to a user terminal in a cell coverage range, and a value of the required wide coverage power pattern on a sampling point is proportional to a square of a distance between the base station antenna array and the user terminal; then, constructing an optimization problem by taking the minimum correlation matrix distance between a power pattern generated by a precoding matrix and a required wide coverage power pattern as a target and the precoding matrix belonging to the oblique manifold as a constraint, and optimizing based on a conjugate gradient method constructed by manifold optimization to obtain an optimal precoding matrix; and finally, performing wide-coverage precoding processing on the signals based on the obtained optimal precoding matrix and sending the signals, wherein the transmitting signal power on each antenna unit is the same.

The following describes in detail a specific implementation procedure of the method for wide-coverage precoding transmission according to the present invention with reference to a specific communication system example, and it should be noted that the method of the present invention is not only applicable to the specific system model mentioned in the following example, but also applicable to system models of other configurations.

First, system model

Consider a 3D massive MIMO broadcast system. The large-scale antenna array configured by the base station has a plurality of sectors, and each sector consists of M_tThe individual antenna elements form a uniform rectangular array. Let M_yAnd M_zThe number of antennas along the y-axis and z-axis, respectively, then M_t＝M_yM_z. Each antenna unit may employ an omni-directional antenna or a sector antenna. Large-scale antenna arrays may also employ circular arrays or other array structures that are convenient to install. Each antenna unit in the large-scale antenna array is connected with the digital baseband processing unit through a respective transceiving radio frequency unit, an analog-digital/digital-analog conversion unit, a digital optical module and an optical fiber transmission channel. Let theta_tIs indicative of pitch angle phi_tRepresenting the azimuth, for a uniform rectangular array, the steering matrix can be represented as:

wherein

And

in the above two formulae, u_y＝cosθ_tsinφ_tAnd u_z＝sinθ_tIs the direction cosine. In addition, the spacing between adjacent antenna elements along the y and z axes, respectively, is designated as d_yAnd d_z. The carrier wavelength is denoted as λ. Defining a steering vector as

The notation vec (·) denotes the matrix arrangement as a column vector. Symbol

Representing unit imaginary number, superscript^TRepresenting a matrix transposition.

Consider that the user terminals are distributed in a two-dimensional planar environment and have a fixed height (typically 1.5 meters). Let point C denote the center of the uniform rectangular array and point O denote the location of the base station tower. A spherical coordinate system is constructed by selecting an origin C, and a Cartesian coordinate system is constructed by an origin O. In this case, the signal transmission direction may be expressed by a spherical coordinate system as (θ)_t,φ_t). The user terminal position may be represented by a cartesian coordinate system as (X, Y). A schematic diagram of the system configuration is shown in fig. 2.

In order to design a wide-coverage precoding, a simple downlink direct path scenario is considered. Let d (theta)_t,φ_t) Represents the distance between the user terminal and the geometric center of the base station antenna array, i.e. the distance can be regarded as the signal transmission direction (theta)_t,φ_t) The equation of (c). Order to

Representing the pattern of elements of each antenna on an array of base station antennas, where m_y＝1,2,...,M_yAnd m_z＝1,2,...,M_zCable for representing array elements of transmitting antennaQuotation marks. Assuming that all transmit antenna elements have the same element pattern, i.e.

At the same time, let e_r(θ_r,φ_r) Representing the pattern of elements of the user terminal receive antenna. Assuming that each user terminal is equipped with a single omnidirectional antenna element, i.e. e_r(θ_r,φ_r)＝1。

The path loss coefficient is 2 in the direct path scene. The log path loss model can thus be expressed as

Wherein r is 2, d₀Is a reference distance. When the transmission distance is d₀|e(θ_t,φ_t) When l, the path loss is P_L0. The channel vector can thus be modeled as

Wherein

And is

Second, synchronization performance index

Let L denote the number of complex baseband signal samples in one data stream, let S_tRepresenting the number of transmitted data streams. Receiving a signal

And transmitting a synchronization signal

The relationship between can be modeled as

y^T＝h^TWX+z^T， (6)

Wherein

Is a pre-coding of the signal to be transmitted,

is provided with independent elements in the same distribution

Gaussian additive white noise vector. Suppose that the synchronization signal X satisfies

The time course of each transmission of a synchronization signal by a base station is called a synchronization slot. Transmitting and receiving complex signal samples at a delay τ may be written as

Wherein it is assumed that

Indicating that the received signal and the transmitted synchronization signal are aligned, i.e. the timing offset τ and the correct value τ₀Are equal. Suppose that

Indicating a synchronization signal misalignment or signal loss. Thus, time synchronization can be modeled as a hypothesis testing problem in (8).

Line of T'_glrt(τ) represents a detection statistic of the maximum likelihood ratio. If T'_glrt(τ) is greater than threshold γ', synchronization is considered successful. The detection statistic of the maximum likelihood ratio is defined by

Wherein

Is the equivalent channel vector and v is the variance of the noise vector z. Equation (9) is equivalent to

Wherein

T_glrtAnd (tau) is a detection statistic corresponding to the threshold gamma, and superscript denotes the conjugation operation on the vector or matrix. And the probability of missed detection can be expressed as

Wherein

And

all the elements of (A) are independently and identically distributed

Therefore, according to equation (11), synchronization performance can be characterized by a probability of missed detection.

Thirdly, design criterion and constraint condition of precoding

As has been described in the foregoing, in the preferred embodiment,is an equivalent channel vector, the missed detection probability of equation (11) can be reconstructed as

Wherein

And is

The equivalent channel vector is given by

Wherein c is a constant. At this time, the process of the present invention,

probability of missed detection with respect to received powerThe monotonicity of (d) is given by the following relationship. For line-of-sight channel scenarios, the probability of missed detection of formula (11) relates to

Strictly monotonically decreases, wherein

Is the resulting radiation power pattern.

According to fig. 2, the distance between the base station antenna array and a certain user terminal, i.e. the length of the line segment CP', can be expressed as

Where h is the height difference between the base station antenna and the user terminal. For clarity of illustration of the geometric relationships, the side view of FIG. 2 is shown in FIG. 3.

As shown in fig. 2 and 3, the projection plane OP' is tangent to the spherical surface at the point O. The pitch and azimuth angles at point O are represented as (θ)₀,φ₀) Wherein phi ₀0. Let (theta)_t,φ_t) Representing the angle of a point P on a sphere, the position of the point P 'within a plane OP' can be expressed as

And

whereinAnd α is the mechanical downtilt.

To ensure coverage of user synchronization performance throughout the cell, we consider coverage at all possible angles (θ)_t,φ_t) Have equal probability of missed detection. Continuous pitch angle theta_tAnd azimuth angle phi_tCan be dispersed as theta_pPhi and phi_qWherein P-0, 1, P-1 and Q-0, 1, Q-1 denote the ordinal number of the sample point. Use of

To indicate the corresponding transmission angle (theta) of the user terminal in the coverage area of the considered cell_p,φ_q). To ensure equal probability of missed detection in the cell coverage, a power pattern a (θ) is generated_p,φ_q) Should be proportional to d²(θ_p,φ_q)。

Let b (theta)_p,φ_q) Is shown at an angle (theta)_p,φ_q) The desired radiation power pattern. The required radiation power pattern b (theta)_p,φ_q) The ensemble over PQ discrete angles is defined as matrix B. Because of the generated radiation power pattern a (theta)_p,φ_q) Should be proportional to d²(θ_p,φ_q) The sampling point of the required power pattern is given by

Wherein

And is

Is a normal number.

The distance between the desired radiation power pattern B and the generated radiation power pattern a can be described using the correlation matrix distance. The resulting radiation power pattern A is given by

Wherein

Therefore, equal missed detection probability criteria need to be met in the design of cell coverage

The operator tr (·) represents the trace of the matrix, | ·| non-woven phosphor_FThe Frobenius norm of the matrix is represented.

The transmit power of each antenna is typically limited by the respective power amplifier capacity. In large-scale MIMO systems, the capacities of these power amplifiers are generally the same. If only one power amplifier is fully used at the base station end, the power efficiency of the base station will be very low. Therefore, it is desirable to have equal maximum transmit power on each antenna to fully utilize the capacity of the base station side power amplifier.

To ensure equal average power consumption over each antenna element, each row of precoding W should have an equal 2-norm. Taking into account transmit power constraintsThe precoding matrix W should satisfy the following constraint condition

Fourth, precoding realization algorithm

According to equation (19), the radiated power pattern generated by W should ensure wide coverage within the cell. Defining an objective function J (W) as

According to equation (23), the precoding matrix W should be such that the transmitted signals on all antennas have equal average power. Note that the equal power constraint is equivalent to a complex oblique manifold

Namely, it is

Thus, the precoding matrix W can be obtained by solving the following optimization problem

The solution of the optimization problem (26) is facilitated within the framework of manifold optimization. The optimization method on the manifold can be regarded as popularization of the optimization method in the Euclidean space.

Let W^(k)Indicates the precoding obtained in the k-th cycle. The updated equation for solving the minimum of the cost function J (W) can be expressed as

Wherein D^(k)Is the search direction, μ^(k)Is the search step size. Operator

Projecting precoding back into manifold

Therefore, in the pre-weavingThe precoding satisfies the manifold constraint by using the projection after the code moves along the search directionConstruction of

Is composed of

Wherein

Search step size mu^(k)Is generally selected to satisfy the Wolfe condition. The conditions are given by

And

wherein 0 < c₁＜c₂< 1, symbol<>Indicating the determination of the inner product, sign, of two matricesThe representation is taken in the real part,representing the gradient over the manifold. For conjugate gradient methods, a typical value may be c₁＝10^-4And c₂0.1. For a real-valued function J (W) with a complex matrix variable W, the Wolfe condition should be equivalent to

And

the step size may be selected by an Armijo linear search to satisfy the Wolfe condition.

If searching for the direction D^(k)Given by negative Riemann gradients, i.e.

The steepest descent method can be implemented. Manifold

The Riemann gradient above can be expressed as

Wherein

Is the euclidean gradient of the cost function j (w). Euclidean gradients are given by

Wherein

And is

Although the steepest descent method can converge globally, its convergence speed may be very slow. The conjugate gradient method has a much faster convergence rate than the steepest descent method. The search direction of the conjugate gradient method can be expressed as

Wherein beta is^(k)From a variety of Hesteees-Stiefel gaugesIs defined as

And is

In the step (36), the step (c) is carried out,

andwriting and doing

And

the details of the precoding design process based on the conjugate gradient method are shown by the following steps:

s1: setting a search direction, if k is 0, then

If k > 0, then

S2: setting step size mu according to Armijo linear search^(k)Until it meets the Wolfe condition;

s3: establishing an updating equation by utilizing the searching direction and the step length to update the precoding matrix

S4: the current precoding matrix W^(k+1)With the preceding round precoding matrix W^(k)And (3) comparison: if the difference is less than the threshold value, thenDetermining that a precoding matrix converges on W^opt(ii) a Otherwise, it is determined that the precoding matrix is not converged, and the process returns to step S1.

Fifth, effect of implementation

In order to make those skilled in the art better understand the scheme of the present invention, the following provides a comparison between the results of the 3D massive MIMO wide-coverage precoding transmission method in the present embodiment and the existing methods in the line-of-sight channel scenario.

First, a design example of wide-coverage precoding is described. Considering a 3D massive MIMO system equipped with a uniform rectangular array, 32 columns of antennas are arranged in the horizontal direction and 64 rows of antennas are arranged in the vertical direction. Wherein the vertical and horizontal spacing of the antenna elements are set to half a wavelength. Suppose users are distributed in a 120-degree sector with a radius R of 200 meters. The heights of the base station and the user terminal are respectively set to be 25 meters and 1.5 meters. In this case, the height difference between the base station and the user terminal is h 23.5 m. The mechanical lower inclination angle is set as

The radiation power pattern distribution is plotted from-90 to 90 in pitch angle theta and azimuth angle phi. The radiation power pattern should be proportional to e (theta, phi)²Where e (θ, φ) is the antenna element pattern. In this design example, the antenna element pattern is selected from the 3GPP-3D channel model implemented with QuaDRiGa v2.0.0. The pattern of elements is shown in fig. 4.

Precoding proposed by the invention

Shown in fig. 5 (a). The proposed precoding will be based on the angle theta_δDesigned precoding is compared. Angle theta_δCorresponding to the half-power beam width in the pitch angle direction, the power pattern angle coverage is set to-60 DEG to phi 60 DEG andbased on angle theta_δThe power pattern resulting from the designed precoding is shown in fig. 5 (b) - (d).

As can be seen from the radiation power pattern in fig. 5 (a), the shape is a projection of a 120-degree sector onto a spherical surface. In addition, the power near 0 ° is much higher than the power near-40 °. This is because the distance between the base station and the user terminal in the vicinity of θ 0 ° is much longer than that in the vicinity of θ -40 °. In fig. 5 (b) to (d), the power pattern pitch angle direction half-power beam width corresponding angle is (b) θ_δ＝12°,(c)θ_δ24 ° and (d) θ_δ36 ° is set. The azimuth direction half-power beamwidth correspondence angles in (b) - (d) of fig. 5 are all set to 120 °. And as the half-power beamwidth increases in the azimuth direction, the maximum value of the power pattern decreases correspondingly.

The considered received power situation within and around the 120 sector is shown next. The channel vector may be described by a complex gain epsilon, as described in equation (5). Suppose that ε is set at point S (X (0,0), Y (0,0)) in the sector^*ε is 1. The point S corresponds to the direction of the sight of the uniform area array. Because the mechanical downward inclination angle is set as

According to the formulas (17) and (18), the coordinates of the point S are (R/2, 0).

The received power in and around the 120 ° sector with radius R-200 m is plotted. Precoding proposed by the invention in a sector

The generated reception power is shown in fig. 6 (a). The angle theta corresponds to the received power generated by the proposed scheme by different half-power beamwidths within a 120 deg. sector_δThe resulting received powers are shown in fig. 6 (b) - (d). In fig. 6 (b) to (d), the power pattern pitch angle direction half-power beam width correspondence angle is (b) θ_δ＝12°,(c)θ_δ24 ° and (d) θ_δ36 ° is set. The azimuth direction half-power beamwidth correspondence angles in (b) - (d) of fig. 6 are all set to 120 °.

Observing (a) in fig. 6, the precoding W proposed by the present invention^optMitigating received power attenuation due to path loss. In this case, the received power resulting from the proposed precoding is almost the same within a 120 ° sector. Fairness among users within a sector is ensured. Meanwhile, compared with precoding designed based on different half-power beam widths, the precoding proposed by the present invention has significantly less inter-cell interference.

Finally, the synchronization performance characterized by the probability of missed detection is evaluated. The signal-to-noise ratio is defined as SNR ═ 1/ν. The threshold value gamma is determined by the following closed expression, namely

Wherein

Let P_FA＝10^-4Then the corresponding threshold is γ ≈ 0.17149. The probability of missed detection in the line-of-sight channel scenario, with signal-to-noise ratio from-10 dB to 20dB, is plotted in fig. 7.

As can be seen from fig. 7, the probability of missed detection of the proposed scheme is lower than that of the scheme based on different half-power beamwidth designs. Therefore, in this scenario, the synchronization performance of the scheme proposed by the present invention is superior to that of the conventional wide-coverage precoding scheme.

To demonstrate synchronization performance in non-line-of-sight channel scenarios, QuaDRiGa v2.0.0 was chosen to generate a simulation environment. The channel generation scenario is selected as "3 GPP 3D UMa NLOS". Consider the distribution of users in a 120 degree sector. Other parameter settings are the same as before. Due to loss caused by multipath, the path loss coefficient in a non-line-of-sight channel scene is larger than 2, namely r is larger than 2. The probability of missed detection in the non-line-of-sight channel scenario, with signal-to-noise ratio from 0dB to 30dB, is plotted in fig. 8.

As can be seen from fig. 8, let r >2 in the design rule, the missed detection probability of the proposed scheme of the present invention can still be lower than that of the design scheme based on different half-power beamwidths. Therefore, the synchronization performance of the scheme provided by the invention is still better than that of the traditional wide-coverage precoding scheme in the scene.

In the examples provided herein, it is to be understood that the disclosed methods may be practiced otherwise than as specifically described without departing from the spirit and scope of the present application. The present embodiment is an exemplary example only, and should not be taken as limiting, and the specific disclosure should not be taken as limiting the purpose of the application. For example, some features may be omitted, or not performed.

The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and such improvements and modifications are also considered to be within the scope of the present invention.