JP2012253496A - Radio communication system, cell/antenna arrangement pattern optimization device, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform optimum cell arrangement and antenna arrangement in a radio communication system.SOLUTION: In the radio communication system, a base station includes n antennas. A constraint is provided in which the center of a cell which is a communication area including the base station and the n antennas are in the same arrangement pattern even if an origin of coordinate axis is shifted from the center of one cell to the center of another cell, and further even if the coordinate axis is rotated by 2π/n (n is the number of antennas). Under this condition, a reception power m(d,...,d)=Kf(l(d)ν,...,l(d)ν) at an arbitrary point (x, y) satisfies a target value v' at a probability 1-ε or more, and an asymptotic minimum coverage problem for covering the entire surface with a minimum number of cells is solved, for derivation of optimum cell arrangement pattern and antenna arrangement pattern.

Description

  The present invention relates to a radio communication system, a cell / antenna deployment pattern optimization apparatus, and a program, and more particularly to a radio communication system and a cell / antenna deployment pattern optimization apparatus for optimizing the arrangement of cells and antennas for mobile communication. And the program.

  In mobile communications, the first approximation of the path loss function m (d) for cell design (antenna deployment design)

がしばしば用いられる。ここで、dは、送受信装置間距離、αは定数である。そして、このパスロス関数が目標値vを満たす範囲をセルとすると、セルは、基地局を中心とする円となる。そして、サービスエリアである平面をこの円形のセルでもっとも効率的にカバーすると、円に内接する六角形により平面が分割されるパターンとなることがよく知られている。そして、この円形のセルと六角形により平面を分割するパターンは、無線システムのセル設計における第１近似として、評価や設計に重要な役割を果たしてきた。

Is often used. Here, d is the distance between the transmitting and receiving apparatuses, and α is a constant. If the range in which the path loss function satisfies the target value v is a cell, the cell is a circle centered on the base station. It is well known that when a plane that is a service area is most efficiently covered by this circular cell, the plane is divided by a hexagon inscribed in the circle. And the pattern which divides | segments a plane by this circular cell and a hexagon has played an important role for evaluation and design as a 1st approximation in the cell design of a radio | wireless system.

  In recent years, a wireless system using a plurality of antennas has appeared, and in particular, one base station transmits or receives the same signal using antennas installed at a plurality of points, and mainly performs error performance ( Macro diversity technology that improves the error rate characteristics) has begun to be used (Fig. 1). For example, as a system using a sector antenna, there is Non-Patent Document 1, and a configuration in which the base station side uses three antennas has been proposed. The cell antenna deployment pattern of a system using an omnidirectional antenna, which is the same as that of the present invention, was examined in Non-Patent Document 2, and n = 4 shown in FIG. 2 (n is the number of antenna points deployed in one base station) ) Pattern was recommended.

  In the case of using microdiversity, there may be a plurality of antennas in one place. Therefore, in the following description, an antenna is used to mean an antenna installed at one place. Therefore, the description of “one antenna” may actually be a plurality of antennas installed in one place.

  In a wireless system, received signal power is very important. The received signal power is divided into a component modeled by a path loss function that depends on the distance from the transmission point, a component called shadowing consisting of the influence of a shielding object, etc., and an instantaneous fluctuation component due to the influence of multipath, etc. Usually, you can think separately. Here, since the instantaneous fluctuation is often negligible by a technique such as microdiversity, it is important that path loss and shadowing can be considered.

In consideration of path loss and shadowing, in the existing 1-cell 1-antenna system, the received signal power m (d) is
m (d) = Kl (d) ν
It is represented by Where d is the distance between transmission and reception, l (d) is the path loss function,

がしばしば用いられる。Kは送信電力、アンテナゲイン等から定まる定数、νは、シャドウイングを表す確率変数である。

Is often used. K is a constant determined from transmission power, antenna gain, etc., and ν is a random variable representing shadowing.

Daisei Uchida et al., “Technological development efforts to realize wide area ubiquitous network”, March 2010. R. C. Bernhardt “Macroscopic Diversity in Frequency Reuse Radio Systems” IEEE J. Selected Areas in Communications, 5, 5, pp. 862-870, 1987.

  As described above, in the conventional wireless communication system, the cell arrangement is designed on the assumption that the base station constituting the communication cell is provided with only one antenna. In a wireless system in which one base station deploys omnidirectional antennas at multiple points, a method for optimal cell placement and antenna placement is not provided, and the cell is not circular and the plane is efficient. There is no known pattern to deploy to.

  The present invention has been made in view of the above points, and a method for determining a pattern for efficiently deploying a base station and an omnidirectional antenna with respect to a uniform plane, and a resulting antenna deployment pattern. It is an object of the present invention to provide a radio communication system, a cell antenna deployment pattern optimization device, and a program in which cells and antennas can be arranged.

  In particular, when the main cost factor of the base station system is the base station main apparatus, a pattern that covers the plane at a minimum cost is provided among the realistic deployment patterns. It should be noted that the case where the main cost cannot be said to be the base station main apparatus is also referred to as “shared antenna”. Further, in the present invention, shadowing is not considered, but when the number of antennas is the same, there is no difference in the countermeasures for shadowing, and therefore, it is based only on the distance attenuation term.

In order to solve the above problems, the present invention (Claim 1) is a wireless communication system including a plurality of base stations using antennas in which one base station is placed at n points.
The base station includes n antennas, and the center of a cell that is a communication area configured by the base station and the n antennas are
Even if the coordinate axis origin is moved from the center of one cell to the center of another cell, and the coordinate axis is rotated by 2π / n (where n is the number of antennas) The received power m _n (d ₁ ,..., d _n ) = Kf (l (d ₁ ) ν ₁ ,..., l (d _n ) ν _n ) at x, y) is the probability 1− Arranged by an optimal cell arrangement pattern and antenna arrangement pattern derived by solving an asymptotic minimum covering problem that satisfies the above-mentioned ε and covers the entire plane with the minimum number of cells.

In the present invention (Claim 2), when the number of antennas is 2 (n = 2), the plane is divided into congruent parallelograms, and the center of the cell is arranged at each vertex of the parallelogram,
When the number of antennas is 3 (n = 3), the plane is divided by a congruent regular hexagon, and the center of the cell is arranged at each vertex of the regular hexagon,
When the number of antennas is 4 (n = 4), the plane is divided into congruent squares, and the center of the cell is arranged at each vertex of the squares.
When the number of antennas is 6 (n = 6), the plane is divided by congruent equilateral triangles, and the center of the cell is arranged at each vertex of the equilateral triangle.

Further, the present invention (Claim 3) is a cell antenna arrangement pattern optimization device for optimizing cell arrangement and antenna arrangement in a radio communication system composed of a plurality of base stations,
The optimization device includes:
The received power m _n (d ₁ ,..., D _n ) = Kf (l (d ₁ ) ν ₁ ,..., L (d _n ) ν _n ) at an arbitrary point (x, y) depends on the constraint condition. Optimization that derives the optimal cell layout pattern and antenna layout pattern by solving the asymptotic minimum coverage problem that satisfies the value v 'with probability 1-ε or more and covers the entire plane with the minimum number of cells Means.

In the present invention (claim 4), the function form of the number of antennas n and f, the function form of the path loss function l (d), the parameter value such as α, the normalized target value v, and the target value non-achievable allowable value ε Having input means to input,
The optimization means includes
Based on the value obtained from the input means, an angle φεΦ (n) formed by a straight line along one side of the polygon having the center of the cell as a vertex and a straight line connecting the cell center and one of the antennas of the cell. And the boundary of the cell centered at the origin
R _n ((x, y) | → x ₁ (0,0, φ),…, → x _n (0,0, φ)) = 1−ε
(→ indicates a vector)
For any (x, y) above,
R _n ((x, y) | → x ₁ (i, j, F _{i, j} (φ)),…, → x _n (i, j, F _{i, j} (φ))) ≧ 1−ε
The constraint condition is that there exists (i, j) that satisfies the above condition, and the effective coverage size is considered under the constraint condition by solving the constrained optimization problem for the effective coverage size considering cell overlap. Optimal pattern deriving means for maximizing and deriving an optimal cell arrangement pattern and antenna arrangement pattern is included.

Further, according to the present invention (Claim 5), in the optimum pattern deriving means,
The effective covering size s ⁽ⁿ⁾ (p _n ),

（p_nはｎアンテナ時のパラメータ、｜Φ（n）｜はφが取り得る値の数、s_i ^(n,k)（p_n）はφφ_kのときにセル中心が原点にあるセルを含むｉ個のセルによって被覆される領域の大きさ）
で与え、前記p_nを調整し、前記有効被覆サイズs⁽ⁿ⁾（p_n）を前記拘束条件の下で、最大化する手段を含む。

(P _n is the parameter for n antennas, | Φ (n) | is the number of values that φ can take, and s _i ^{(n, k)} (p _n ) is the cell whose origin is at the origin when φφ _k. The size of the area covered by i cells)
And _pn is adjusted, and the effective covering size s ⁽ⁿ⁾ (p _n ) is maximized under the constraint conditions.

Further, the present invention (Claim 6), when the base station shares the antenna with a base station of a plurality of cells,
The input means includes
Means for further inputting the antenna cost, main part cost, or ratio thereof as a condition for sharing;
The optimization means includes
The solution of the optimization problem is obtained based on the constraint condition to which the condition for sharing is added, the center of the cell is arranged at a position determined by the obtained solution, and the n antennas are connected to the cell. Means for deriving an arrangement pattern to be arranged at each vertex of a regular n-gon centering on the center of.

  The present invention (Claim 7) is an optimization program for causing a computer to function as each means of the cell antenna arrangement pattern optimizing device according to any one of Claims 3 to 6.

According to the present invention, even if the coordinate axis origin is moved from the center of one cell to the center of another cell, a similar cell arrangement pattern is obtained, and the coordinate axis is 2π / n (n is the number of antennas included in one base station) ) By limiting the asymptotic minimum coverage (when the region Φ is a two-dimensional all-plane) problem by restricting the same cell position pattern from being rotated, the optimal cell position pattern and antenna An arrangement pattern can be derived, and cells and antennas can be arranged based on the pattern derived by the method. as a result,
・ When there are two antennas:
Cell center: each vertex when the plane is divided into parallelograms;
Antenna: Two points on a straight line centered on the center of the cell;
・ When there are three antennas:
Cell center: each vertex when the plane is divided into regular hexagons;
Antenna: each vertex of an equilateral triangle centered on the center of the cell;
・ When there are four antennas:
Cell center: each vertex when the plane is divided into squares;
Antenna: each vertex of a square centered on the center of the cell;
・ When there are 6 antennas:
Cell center: vertex when the plane is divided into equilateral triangles;
Antenna: Each vertex of a regular hexagon centering on the center of the cell. With this configuration, it is possible to cover the plane with the minimum number of cells.

It is a block diagram of the radio | wireless communications system used as the optimization object of this invention. This is the number of antenna points deployed in one base station. It is a block diagram of the cell antenna arrangement | positioning pattern optimization apparatus in one embodiment of this invention. It is an example in the case of the deployment pattern (phi) (n = 2) of the cell and antenna in one embodiment of this invention. It is an example in the case of the deployment pattern (phi) (n = 3) of the cell and antenna in one embodiment of this invention. It is an example in the case of the deployment pattern (phi) (n = 4) of the cell and antenna in one embodiment of this invention. It is a numerical example of the deployment pattern obtained when n = 3 in one embodiment of the present invention. It is a numerical example of the deployment pattern obtained when n = 4 in one embodiment of the present invention. It is an example of a sharing condition in the case of n = 4 in one embodiment of the present invention. It is an effective covering size according to the deployment pattern of the present invention. It is a comparison result of this invention and a prior art.

  Embodiments of the present invention will be described below with reference to the drawings.

  FIG. 1 shows a configuration of a wireless communication system to be optimized by the present invention.

  In the figure, antennas 11 to 14 are usually installed at different installation locations several kilometers away. Each of the antennas 11 to 14 includes base units 41 and 42 that perform signal processing and the like via remote units 21 to 24 having simple functions such as D / A conversion and links 31 to 34 such as dedicated lines. Connected to. In the case of FIG. 1, each of the base stations 41 and 42 is configured to include two antennas. The base stations 41 and 42 are connected to each other by a network 51 and provide a wide area service. A transmission / reception signal of the terminal 61 is received / transmitted by the antennas 11 and 12, processed by the remote units 21 and 22, modulated / demodulated by the main device 41, and other terminals that are communication partners via the network 51, here Then, it communicates with the fixed terminal 71.

  The wireless communication system of FIG. 1 is an example of the configuration. In the present invention, one base station uses an antenna placed at n points, and a plurality of cells that the base station configures are installed. Provide communication services. In the example of FIG. 1, the base stations 41 and 42 are configured to include two antennas (n = 2). At this time, the center of the cell is each vertex when the plane is divided into parallelograms, and the antennas are arranged at two locations on a straight line with the center of the cell as the midpoint. Although not shown in FIG. 1, when there are three antennas, the center of the cell is each vertex when the plane is divided into regular hexagons, and the antenna is an equilateral triangle centered on the center of the cell. Placed at each vertex. When there are four antennas, the center of the cell is each vertex when the plane is divided into squares, and the antenna is arranged at each vertex of the square centered on the center of the cell. Further, when there are six antennas, the center of the cell is a vertex when the plane is divided into equilateral triangles, and the antenna is arranged at each vertex of a regular hexagon centering on the center of the cell.

  Hereinafter, a process for determining such an arrangement pattern will be described.

[First Embodiment]
In the present embodiment, a cell / antenna deployment pattern optimization apparatus that determines an antenna arrangement pattern and a cell arrangement pattern of the system will be described for the radio communication system shown in FIG.

  Under ideal macro diversity and uniform plane, the received signal power is

のように書ける。ここで、nは１基地局のアンテナ配備地点数、d_iは第i配備地点から受信端末への距離、ν_iは第i配備地点・受信端末間のシャドーイングを表す確率変数、fは信号合成アルゴリズムにより定まる関数であり、各アンテナの平均雑音電力が同じ場合、選択合成では、

It can be written as Where n is the number of antenna deployment points of one base station, d _i is the distance from the i-th deployment point to the receiving terminal, ν _i is a random variable representing shadowing between the i-th deployment point and the receiving terminal, and f is the signal This is a function determined by the synthesis algorithm.

最大比合成では、

In maximum ratio synthesis,

である。そして、セルを面的に配置するためには、この受信信号電力の大きさが目標値v'を確率1-εで満たす必要がある。すなわち、セルは、

It is. In order to arrange the cells in a plane, the magnitude of the received signal power needs to satisfy the target value v ′ with a probability 1−ε. That is, the cell

で定まる外周の内部の点である（一般的には、上式で定まる図形は、内部に穴が生じ得る。ここでは、外周の内部の点であるとして、セル内部には、穴が無いものとする）。以下、「アンテナ配備地点」と「アンテナ位置」は同義で用いる。
上式で、εは、目標値不達成許容値、

(In general, the figure defined by the above formula may have a hole inside. Here, it is assumed that the point is inside the outer periphery, and there is no hole inside the cell. And). Hereinafter, “antenna deployment point” and “antenna position” are used interchangeably.
In the above equation, ε is a target value non-achievable allowable value,

→x_i= (x_i, y_j)は、２次元平面上の第i配備地点の位置、正規化目標値vはv=v'/K、である。なお、本明細書中ではベクトル標記として文中では「→」をベクトルである文字の前に付し、数式中では「→」を文字の上に付している。

→ x _i = (x _i , y _j ) is the position of the i-th deployment point on the two-dimensional plane, and the normalized target value v is v = v ′ / K. In the present specification, as a vector mark, “→” is added in front of a character that is a vector in the sentence, and “→” is added above the character in a mathematical expression.

  FIG. 3 shows a configuration of the cell antenna arrangement pattern optimization apparatus according to the first embodiment of the present invention.

  The optimization apparatus shown in FIG. 1 includes an input unit 1, an optimization unit 3, and an output unit 4.

  The input unit 1 inputs the function form of the number of antennas n and f, the function form of the path loss function l (d), the parameter value such as α, the normalized target value v, and the target value unachievable allowable value ε to the optimization unit 3 To do.

  The optimization unit 3 solves the optimization problem so as to maximize the effective coverage size under the constraint condition based on the value input from the input unit 1, and the obtained cell and antenna deployment pattern is output to the output unit 4. Output.

  In the present invention, as a deployment pattern of the base stations 41 and 42 and the antennas 11 to 14, a realistic set is assumed, and an asymptotic minimum covering pattern is given among the patterns belonging to the set.

  First, the minimum coverage for the region Φ is the minimum number of cells and satisfies the condition that there is always a cell covering (x, y) for any point (x, y) in the region Φ. Say. Note that the minimum number of cells is equivalent to maximizing the effective coverage size (area Φ divided by number of cells). Furthermore, when the region Φ is a two-dimensional whole plane, it is called asymptotic minimum coverage.

  Since the asymptotic minimum coverage problem cannot be solved when the cell shape is general, here, the deployment pattern is limited to a certain condition. The following notation is used to define the conditions.

-> C _j : Center position of the j-th cell (base station).

但し、→x_i,jは第ｊセルの第ｉアンテナ位置を表す。

However, → x _{i, j} represents the i-th antenna position of the j-th cell.

-> T _c (x): x cell center-> c translation. That is,

・→Q_n, →o((x, y))：(x, y)の原点周りの角度2π／nの回転。すなわち、

-> Q _n ,-> o ((x, y)): rotation of 2x / n around the origin of (x, y). That is,

・→Q_n,→c(→x)：→xのセル中心→c周りの角度2π／nの回転。すなわち、

-> Q _{n,-> c} (->x):-> cell center of x-> rotation of angle 2π / n around c. That is,

・→M_n(→x)：→xの、セル中心の平行移動とセル中心の回転の任意の組み合わせで、定義される移動。

-> M _n (-> x): A movement defined by any combination of cell center translation and cell center rotation of → x.

  The following conditions are to be satisfied for the deployment pattern to be considered.

1) For the center position of the jth cell → c _j , → M _n (c _j ) is also the cell center. That is,

を満たす整数ｊ'が存在すること。

There exists an integer j ′ that satisfies

2) For the antenna {→ x _{1, j} , ..., → x _{n, j} } of the j th cell

も、また、ある１つのセルのアンテナ位置となること。すなわち、

Is also the antenna position of a cell. That is,

を満たす整数j'が存在すること。

There exists an integer j ′ that satisfies

  The above condition means that even if the coordinate axis origin is moved from the center of one cell to the center of another cell, and the coordinate axis is rotated by 2π / n, the same deployment pattern is obtained. As a result, it means that cells having the same shape appear periodically and with symmetry of an angle of 2π / n.

  From the above conditions, it can be proved that the cell and antenna deployment patterns obtained by the optimization unit 3 are as follows.

  • For n = 2, the plane is divided into congruent parallelograms, and the center of the cell is at each vertex of the parallelogram.

  ・ For n = 3, the plane is divided into congruent regular hexagons, and the center of the cell comes to each vertex.

  ・ For n = 4, the plane is divided into congruent squares, and the center of the cell comes to each vertex.

  ・ For n = 6, the plane is divided by congruent equilateral triangles, and the center of the cell comes to each vertex.

  The antenna of each cell is deployed at each vertex of a congruent regular n-gon centered on the cell center.

Furthermore, L ₁ is the parallelogram when n = 2, the regular hexagon when n = 3, the square when n = 4, the equilateral triangle when n = 6, A line along one side, L ₂ is a line connecting the cell center and one of the antennas of the cell, and an angle between L ₁ and L ₂ is φ. Then, “φ is periodically 4 (in the case of n = 2, FIG. 4), 3 (in the case of n = 3, FIG. 5), 2 (in the case of n = 4, FIG. 6), It can also be proved that the value of is periodically taken.

For any integer i, j, (x (i, j), y (i, j)) is the cell center position, → x _k (i, j, φ) is the cell center (x (i, j, Let j), y (i, j)) be the k-th antenna position of the cell, 2a is the distance between adjacent antennas in the cell, and Φ (n) is a set of values that φ can take. (I.e.

である。）さらに、

It is. )further,

とする。（但し、Iはパスロスが目標値を満たしているかどうかで０，１のいずれかをとる）ここで

And (However, I takes either 0 or 1 depending on whether the path loss meets the target value)

である。

It is.

  Then, the asymptotic minimum covering problem becomes the following optimization problem with constraints.

[Restraint condition]
It is assumed that the constraint condition is input in advance from the input unit 1 and held in a memory (not shown) in the optimization unit 3.

  Arbitrary φ∈Φ (n) and cell boundary centered at the origin

上の任意の(x, y)に対して、

For any (x, y) above,

を満たす(i, j)が存在すること。ここでF_i,j(φ)は、各nについて、後に与える。

(I, j) that satisfies Here, F _{i, j} (φ) is given later for each n.

[optimisation]
Below, the optimization process in the optimization part 3 is demonstrated.

Effective coverage size s ⁽ⁿ⁾ (p _n ) is input from input 1

で与えられる。ここで、p_nは、nアンテナ時のパラメータ、|Φ(n)|は、φがとり得る値の数、s_i ^(n,k)(p_n)は、φ=φ_kのときに、セル中心が原点にあるセルを含むi個のセルによって被覆される領域の大きさである（以下、「有効被覆サイズ」と記す）。p_nを調整し、有効被覆サイズs⁽ⁿ⁾(p_n)を上記拘束条件のもとで最大化する。s_i ^(n,k)(p_n)は、各nについて、後に与える。

Given in. Here, _pn is a parameter for n antennas, | Φ (n) | is the number of values that φ can take, and s _i ^{(n, k)} (p _n ) is φ = φ _k This is the size of an area covered by i cells including a cell whose center is at the origin (hereinafter referred to as “effective covering size”). Adjust p _n and maximize the effective coverage size s ⁽ⁿ⁾ (p _n ) under the above constraints. s _i ^{(n, k)} (p _n ) is given later for each n.

(If the number of parameters included in _pn is large, the optimization is a burden on numerical calculation. In this case, the above optimization may be performed with φ _i = φ _j for any i, j. It is valid.)
(1) When the number of antennas n = 2:
Using arbitrary integers i and j, the cell center is

（但し、μ、ρはセル中心を頂点とする平行四辺形の辺の長さ）
で与えられ、当該セル中心をもつ２つのアンテナ位置は、

(However, μ and ρ are the lengths of the sides of the parallelogram with the cell center as the vertex.)
And the two antenna positions with the cell center are

となる。φは、Φ(2) = {φ₁, φ₂, φ₃, φ₄}のいずれかの値をとる。

It becomes. φ takes any value of Φ (2) = {φ ₁ , φ ₂ , φ ₃ , φ ₄ }.

[Restriction condition when n = 2]
R ₂ ((x, y) | → x ₁ (0, 0, φ), → x ₂ (0, 0, φ)) = 1−ε
For any point (x, y) that satisfies
R ₂ ((x, y) | → x ₁ (i, j, F _{i, j} (φ)), → x ₂ (i, j, F _{i, j} (φ))) ≧ 1−ε
There exists an integer i, j (| i | ≦ 1, | j | ≦ 1, (i, j) ≠ (0, 0), where

［n = 2の場合の最適化］
有効被覆サイズ

[Optimization when n = 2]
Effective coating size

は、以下の式（１４）で与えられる。

Is given by the following equation (14).

p₂ = {a, μ, ρ, θ, φ₁, φ₂, φ₃, φ₄}を調整し、拘束条件を満たしつつ有効被覆サイズs⁽²⁾(p₂)を最大化する。

p ₂ = {a, μ, ρ, θ, φ ₁ , φ ₂ , φ ₃ , φ ₄ } is adjusted, and the effective covering size s ⁽²⁾ (p ₂ ) is maximized while satisfying the constraint conditions.

[Obtained deployment pattern when n = 2]
The cell center is at the apex of the parallelogram, and the antenna is arranged at an angle with respect to the side of the parallelogram.

(2) When the number of antennas n = 3 It is assumed that the plane is divided by an equilateral triangle whose side is η and the cell center is at the apex of the equilateral triangle. At that time, the cell center is

で与えられる。特に、原点周辺のセル中心位置は

Given in. In particular, the cell center position around the origin is

で与えられる。ここで、

Given in. here,

である。セル中心が(x(i,j), y(i,j))のアンテナは、

It is. The antenna whose cell center is (x (i, j), y (i, j))

に位置する。ただし、φは、φ₁, φ₂, φ₃のいずれかの値をとる。

Located in. However, φ takes one of the values φ ₁ , φ ₂ , and φ ₃ .

[Restriction condition when n = 3]
The constraint conditions are as follows: φ = φ ₁ , φ ₂ , φ ₃
R ₃ ((x, y) | → x ₁ (0, 0, φ), → x ₂ (0, 0, φ), → x ₃ (0,0, φ)) = 1−ε
For any point (x, y) that satisfies
R ₃ ((x, y) | → x ₁ (i, j, F _{i, j} (φ)), → x ₂ (i, j, F _{i, j} (φ)), → x ₃ (i, j , F _{i, j} (φ))) ≧ 1−ε
There are integers i, j (| i | ≦ 1, | j | ≦ 1, i ≠ j) that satisfy here,

である。

It is.

[Optimization when n = 3]
Effective coating size

は、以下で与えられる。ただし、p₃ = {a, η,φ₁, φ₂, φ₃}である。

Is given below. However, p ₃ = {a, η, φ ₁ , φ ₂ , φ ₃ }.

p₃を調整し、有効被覆サイズs⁽³⁾(p₃)を拘束条件を満たしつつ最大化する。

Adjust p ₃ to maximize the effective covering size s ⁽³⁾ (p ₃ ) while satisfying the constraints.

[Deployment pattern obtained when n = 3]
The cell center is at the apex of the equilateral triangle, and the antenna is arranged at an angle with respect to the side of the equilateral triangle. Specific numerical examples are shown in FIG.

(3) In the case where the number of antennas n = 4 It is assumed that the plane is divided by a square whose side is ξ and the cell center is at the apex of the square. At that time, the cell center is

で与えられる。また、そのセルのアンテナ位置は、

Given in. The antenna position of the cell is

で与えられる。ただし、φは、φ₁, φ₂のいずれかの値である。

Given in. However, φ is one of φ ₁ and φ ₂ .

[Restriction condition when n = 4]
The constraint conditions are as follows: φ = φ ₁ , φ ₂
R ₄ ((x, y) | → x ₁ (0, 0, φ), → x ₂ (0, 0, φ),…, → x ₄ (0, 0,)) = 1−ε
For any point (x, y) that satisfies
R ₄ ((x, y) | → x ₁ (i, j, F _{i, j} (φ)), → x ₂ (i, j, F _{i, j} (φ)),…, → x ₄ (i , j, F _{i, j} (φ))) ≧ 1−ε
There exists an integer i, j (| i | ≦ 1, | j | ≦ 1, (i, j) ≠ (0, 0)) that satisfies here,

である。

It is.

[Optimization when n = 4]
Effective coating size

は、以下の式（２６）から決まる。ただし、p₄ = {a, ξ,φ₁, φ₂}

Is determined from the following equation (26). Where p ₄ = {a, ξ, φ ₁ , φ ₂ }

p₄を調整し、拘束条件を満たしつつ、有効被覆サイズを最大化する。

Adjust the p _4, while satisfying the constraint condition, to maximize the effective coating size.

[Obtained deployment pattern when n = 4]
The cell center is at the apex of the square, and the antenna is arranged at an angle with respect to the side of the square. A specific numerical example is shown in FIG.

[Second Embodiment]
In this embodiment, a case where a plurality of cells are shared will be described.

[In case of shared antenna]
The above is based on the premise that one antenna is used by one cell (one base station). However, when the cost of the antenna, the remote unit, etc. and the installation cost are high, it may be advantageous to share them among a plurality of cells (a plurality of base stations) from the viewpoint of cost.

In the present embodiment, the input unit 1 includes the number n _{s of} cells sharing one antenna in addition to the input in the first embodiment.
The antenna cost c _antenna , the base station main device cost c _main , or the ratio c _antenna / c _main is input to the optimization unit 3.
Therefore, the objective function is formulated again as a cost C _base minimization. Here, the cost C _base can be written as follows.

C_antennaは、アンテナ、リモートユニット等のコスト、n_sは、１つのアンテナを共用するセル数、C_mainは基地局主装置コスト、s_cは1セルの有効被覆サイズである。C_antenna、C_mainは定数である。従って、n, n_sが与えられたもとでは、有効被覆サイズs_cの最大化がC_baseの最小化と等価である。従って、アンテナを共用させるという拘束条件を付け加えた上で、前述の第１の実施の形態における最適化が適用可能である。

C _antenna is the cost of the antenna, remote unit, etc., n _s is the number of cells sharing one antenna, C _main is the base station main device cost, and s _c is the effective coverage size of one cell. C _antenna and C _main are constants. Therefore, given n and n _s , maximizing the effective covering size s _c is equivalent to minimizing C _base . Therefore, the optimization in the first embodiment described above can be applied after adding the constraint that the antenna is shared.

  The condition that the antenna is shared requires a condition for the antenna position, so that the degree of freedom of parameters for determining the antenna position is reduced. The case of n = 4 is illustrated in FIG. The conditions for sharing with two adjacent cells are

であり、４セルとの共用の条件がφ₁, φ₂ = π／4, 2a = ξとなる。4セル共用の場合は、図２(a)と同じになる。

The conditions for sharing with 4 cells are φ ₁ , φ ₂ = π / 4, 2a = ξ. In case of sharing 4 cells, it is the same as Fig.2 (a).

  The effects obtained by the present invention are specifically shown below.

  FIG. 10 shows the effective covering size / number of antennas. As shown in FIG. 10, it can be seen that the effective covering size per number of antennas according to the deployment pattern according to the present invention exceeds that of n = 1.

  FIG. 11 shows a comparison result with the case where the distance between antennas is determined so that the effective covering size is maximized with the antenna deployment pattern (n = 4) recommended in the paper cited in the existing technology. In either case, it can be seen that the present invention is approximately twice as advantageous in terms of effective coating size. In the present invention, an efficient deployment pattern is obtained by a two-stage deployment pattern of cell-centered deployment and antenna deployment, whereas in the proposal in this paper, the antenna position is considered to be deployed in a certain pattern. It is done.

  The operation of each component of the optimization device shown in FIG. 3 can be constructed as a program and installed in a computer used as the optimization device for execution, or distributed via a network. is there.

  The present invention is not limited to the above-described embodiments, and various modifications and applications can be made within the scope of the claims.

DESCRIPTION OF SYMBOLS 1 Input part 3 Optimization part 4 Output part 11-14 Antenna 21-24 Remote unit 31-34 Link 41,42 Base station main apparatus 51 Network 61 Terminal 71 Fixed terminal

Claims (7)

A wireless communication system comprising a plurality of base stations using antennas in which one base station is placed at n points,
The base station includes n antennas, and the center of a cell that is a communication area configured by the base station and the n antennas are
Even if the coordinate axis origin is moved from the center of one cell to the center of another cell, and the coordinate axis is rotated by 2π / n (where n is the number of antennas) The received power m _n (d ₁ ,..., d _n ) = Kf (l (d ₁ ) ν ₁ ,..., l (d _n ) ν _n ) at x, y) is the probability 1− The radio is characterized by an optimal cell arrangement pattern and antenna arrangement pattern derived by solving an asymptotic minimum covering problem that satisfies ε or more and covers the entire plane with the minimum number of cells. Communications system. When the number of antennas is 2 (n = 2), the plane is divided into congruent parallelograms, and the center of the cell is arranged at each vertex of the parallelogram,
When the number of antennas is 3 (n = 3), the plane is divided by a congruent regular hexagon, and the center of the cell is arranged at each vertex of the regular hexagon,
When the number of antennas is 4 (n = 4), the plane is divided into congruent squares, and the center of the cell is arranged at each vertex of the squares.
The radio communication system according to claim 1, wherein when the number of antennas is 6 (n = 6), the plane is divided by congruent equilateral triangles, and the center of the cell is arranged at each vertex of the equilateral triangle. A cell antenna deployment pattern optimizing device for optimizing cell arrangement and antenna arrangement in a wireless communication system composed of a plurality of base stations,
The optimization device includes:
The received power m _n (d ₁ ,..., D _n ) = Kf (l (d ₁ ) ν ₁ ,..., L (d _n ) ν _n ) at an arbitrary point (x, y) depends on the constraint condition. Optimization that derives the optimal cell layout pattern and antenna layout pattern by solving the asymptotic minimum coverage problem that satisfies the value v 'with probability 1-ε or more and covers the entire plane with the minimum number of cells An optimization device comprising: means. A function form of the number of antennas n, f, a function form of the path loss function l (d) and a parameter value such as α, a normalized target value v, and a target value non-achievable allowable value ε;
The optimization means includes
Based on the value obtained from the input means, an angle φεΦ (n) formed by a straight line along one side of the polygon having the center of the cell as a vertex and a straight line connecting the cell center and one of the antennas of the cell. And the boundary of the cell centered at the origin
R _n ((x, y) | → x ₁ (0,0, φ),…, → x _n (0,0, φ)) = 1−ε
(→ indicates a vector)
For any (x, y) above,
R _n ((x, y) | → x ₁ (i, j, F _{i, j} (φ)),…, → x _n (i, j, F _{i, j} (φ))) ≧ 1−ε
The constraint condition is that there exists (i, j) that satisfies the above condition, and the effective coverage size is considered under the constraint condition by solving the constrained optimization problem for the effective coverage size considering cell overlap. 4. The cell antenna deployment pattern optimizing device according to claim 3, further comprising an optimum pattern deriving unit for maximizing and deriving an optimum cell arrangement pattern and an antenna arrangement pattern. The optimum pattern derivation means includes:
The effective covering size s ⁽ⁿ⁾ (p _n ),

(P _n is the parameter for n antennas, | Φ (n) | is the number of values that φ can take, and s _i ^{(n, k)} (p _n ) is the cell whose origin is at the origin when φφ _k. The size of the area covered by i cells)
The cell antenna deployment pattern optimizing device according to claim 4, further comprising means for adjusting the _pn and maximizing the effective covering size s ⁽ⁿ⁾ (p _n ) under the constraint condition. When the base station shares the antenna with a base station of a plurality of cells,
The input means includes
Means for further inputting the antenna cost, main part cost, or ratio thereof as a condition for sharing;
The optimization means includes
The solution of the optimization problem is obtained based on the constraint condition to which the condition for sharing is added, the center of the cell is arranged at a position determined by the obtained solution, and the n antennas are connected to the cell. 5. The cell antenna deployment pattern optimizing device according to claim 4, further comprising means for deriving an arrangement pattern arranged at each apex of a regular n-gon centering on the center of the cell.   The optimization program for functioning a computer as each means of the cell antenna arrangement | positioning pattern optimization apparatus of any one of Claim 3 thru | or 6.

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