CN111065109B - Rural area heterogeneous cellular network base station electromagnetic radiation prediction method - Google Patents
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Abstract
The invention discloses a rural area heterogeneous cellular network base station electromagnetic radiation prediction method, which comprises the following steps: the method comprises the steps of calculating the number average value mu of macro base stations through the area S in a region to be detected, establishing probability density distribution f (x) with the number x of the macro base stations, obtaining the value of the number N of the macro base stations under interval estimation, obtaining the distribution coordinates of the macro base stations in MATLAB according to a uniform distribution algorithm, taking the coordinates of the macro base stations as the mother points in the MATLAB by using an even generation method as a Voronoi diagram, and obtaining weak coverage points k and corresponding coordinates (M) according to the intersection points (nodes) of the edges of the Voronoi diagram j ，N j ) Obtaining probability distribution P (m) of the number of micro base stations in the area through the number k of weak coverage points, further obtaining specific values of the number of micro base stations under the condition, obtaining distribution coordinates of the micro base stations in MATLAB according to a uniform distribution algorithm in a circle, and finally predicting to obtain total electromagnetic radiation values of macro base stations and micro base stations in the rural area.
Description
Technical Field
The invention relates to a rural area heterogeneous cellular network base station electromagnetic radiation prediction method.
Background
With the infinite communication convenience brought to people by the mobile communication technology, the base station construction in the rural area is also explosively increased, and more people are panicked by electromagnetic radiation brought by the base stations, but in the currently disclosed documents and patents, only the influence brought by a single base station or a single base station is generally considered, the radiation value exposed by a plurality of layers of base stations in the rural area under the heterogeneous cellular network is not considered, and the effective estimation of the total electromagnetic radiation exposure level of each layer of base stations in the rural area is not considered according to the heterogeneous cellular network base station cluster distribution in the rural area.
Aiming at the defects of the prior art, the invention provides a rural area heterogeneous cellular network base station electromagnetic radiation prediction method. The method comprises the steps of calculating the number average value mu of macro base stations through the area S in a region to be detected, establishing probability density distribution f (x) with the number x of the macro base stations, obtaining the value of the number N of the macro base stations under interval estimation, obtaining the distribution coordinates of the macro base stations in MATLAB according to a uniform distribution algorithm, taking the coordinates of the macro base stations as the mother points in the MATLAB by using an even generation method as a Voronoi diagram, and obtaining weak coverage points k and corresponding coordinates (M) according to the intersection points (nodes) of the edges of the Voronoi diagram j ，N j ) Obtaining probability distribution P (m) of the number of micro base stations in the area through the number k of weak coverage points, further obtaining specific values of the number of micro base stations under the condition, and obtaining micro in MATLAB according to a uniform distribution algorithm in a circleAnd finally predicting the distribution coordinates of the base stations to obtain the total electromagnetic radiation values of the macro base stations and the micro base stations in the rural areas.
Disclosure of Invention
In order to solve the technical problems, the invention provides a rural area heterogeneous cellular network base station electromagnetic radiation prediction method, which comprises the following steps:
1. the method for predicting the electromagnetic radiation of the rural area heterogeneous cellular network base station is characterized by comprising the following steps of:
1) Establishing a rural area macro base station distribution model, calculating the number average value mu of macro base stations according to the area S in the area to be detected, and establishing probability density distribution f (x) with the number x of macro base stations to obtain the value of the number N of macro base stations under interval estimation;
2) Obtaining the position coordinate distribution (x) of macro base stations in the area in MATLAB by a uniform distribution algorithm according to the number N of macro base stations obtained in the step 1) i ，y i ) I is the reference number of the macro base station, i=1, 2,. -%, N;
3) Macro base station position coordinate distribution (x) obtained according to step 2) i ，y i ) By using a pair-to-pair generation method and taking macro base station coordinates as a mother point in MATLAB as a Voronoi diagram, signal weak coverage points (blind points) can be determined through intersection points (nodes) of edges of the Voronoi diagram, and weak coverage points k and corresponding coordinates (M) are obtained according to the Voronoi diagram j ，N j )；
4) According to the weak coverage point k obtained in the step 3), a rural area micro base station distribution model is established, the average value lambda of the number of micro base stations in the micro base station distribution model is calculated, the cumulative probability density distribution F (M) of the number M of the micro base stations is established, and the value of M under the condition of 95% probability is obtained, wherein the value is represented by M;
5) Obtaining the position coordinate distribution (x) of the micro base stations in the area in MATLAB by a circular uniform distribution algorithm according to the micro base station number M obtained in the step 4) j ，y j ) J is the reference number of the base station, j=1, 2,. -%, M;
6) The macro base station position coordinate distribution (x) obtained according to the steps 2) and 5) i ，y i ) Micro base station position coordinate distribution (x j ，y j ) Combined power density meterReach, predict macro base station electromagnetic radiation intensity S i Micro base station electromagnetic radiation intensity S i 。
2. In the step 1), the rural area macro base station distribution model is as follows:
wherein x is the number of macro base stations, f (x) is the probability when the number of the macro base stations is x, exp is an exponential function based on a natural constant e, mu is the average number of the macro base stations, the unit is one, sigma is the data variance of the statistical macro base stations, and the value is 0.76;
the expression of the macro base station number average value mu and the area S is as follows:
μ＝0.3972·S
wherein S is the area of the area to be measured, and the unit is km 2 ；
The probability of the number of macro base stations in the (mu-1.96 sigma, mu+1.96 sigma) interval is 95.4%, and the maximum integer in the interval is selected as the number N of macro base stations, and the expression is as follows:
N＝[μ+1.96σ]
wherein [ mu+1.96 sigma ] is a maximum integer not exceeding mu+1.96 sigma.
3. In the step 2), the coordinate expression of each macro base station in the area is obtained in MATLAB according to the uniform distribution algorithm by combining the number N of the macro base stations obtained in the step 1), wherein the coordinate expression is as follows:
x i ＝L·(μ 1 ) i
y i ＝L·(μ 2 ) i
wherein i is the index of the i-th macro base station, and the value is 1,2, N; x is x i Is the abscissa, y of the ith macro base station i L is the side length of the predicted square area, which is the ordinate of the ith macro base station, (mu) 1 ) i For continuous even distribution of random numbers on the ith macro base station abscissa, (mu) 2 ) i Random numbers are continuously and uniformly distributed on the ordinate of the ith macro base station.
4. The saidIn step 3), the macro base station coordinates (x) obtained in step 2) are combined i ，y i ) According to the couple generation method, taking macro base station coordinates as a mother point in MATLAB as a Voronoi diagram, and obtaining weak coverage point k and corresponding coordinates (M) through intersections (nodes) of Voronoi diagram edges j ，N j )。
5. In the step 4), in combination with the weak coverage point k obtained in the step 3), a micro base station distribution model in a rural area is established as follows:
where P (m) is the probability when the number of micro base stations is m, λ is the mean value of the number of micro base stations, and λ is expressed as follows:
λ＝k
where k is the number of weak coverage points in units of one;
the cumulative probability density distribution F (m) for the number m of micro base stations is expressed as:
wherein F (M) is the cumulative probability density when the number of micro base stations takes M, l is the number of micro base stations, the unit is one, the value is 0,1,2,..m, λ is the average value of the number of micro base stations, the unit is one, λ is substituted into the F (M) expression, the cumulative probability density of the micro base stations is obtained, and under the condition that F (n) =95% probability:
at this time, M is obtained.
6. In the step 5), the coordinate expression of each micro base station in the area is obtained in MATLAB according to the in-circle uniform distribution algorithm by combining the micro base station number M obtained in the step 4):
x j ＝M j +R j ·cosθ j
y j ＝N j +R j ·sinθ j
wherein j is the label of the j-th micro base station, and the value is 1, 2. X is x j Is the abscissa, y, of the jth micro base station j Is the ordinate of the j-th micro base station, M j Is the abscissa of the jth weak coverage point, N j Is the ordinate of the j-th weak coverage point, R j For a continuous uniform distribution of random numbers of radius r, the expression is:
wherein r is the coverage area of the micro base station, the value is 50, the unit is m, (mu) 1 ) j Continuously and uniformly distributing random numbers on the coverage area of the jth micro base station; θ j For the continuous and uniform distribution of random numbers of the j-th micro base station angle, the expression is:
θ j ＝2·π·(μ 2 ) j
wherein (mu) 2 ) j The random numbers are continuously and uniformly distributed for the j-th micro base station.
7. In the step 6), the macro base station coordinates (x) obtained in the step 2) and the step 5) are combined i ，y i ) Micro base station coordinates (x j ，y j ) According to the Euclidean distance formula in the plane:
wherein x is c ，y c Respectively the abscissa and the ordinate of the predicted point, R i The unit is m and R, which are the distances between the predicted point and the ith macro base station j The unit is m, which is the distance between the predicted point and the jth micro base station;
macro base station electromagnetic radiation intensity S i Micro base station electricIntensity of magnetic radiation S j The method comprises the following steps:
wherein S is i The unit is uw/cm for the electromagnetic radiation intensity of the macro base station 2 ，S j The unit is uw/cm for the electromagnetic radiation intensity of the micro base station 2 I is the macro base station number, the value is 1,2, & gt, N, j is the micro base station number, the value is 1,2, & gt, M, P i The unit is W, P, which is the transmitting power of macro base station j The unit is W, G, which is the transmitting power of the micro base station i The unit is dB and G is the antenna gain of the macro base station j The antenna gain in dB is the antenna gain of the micro base station.
The invention has the beneficial effects that: according to the method, a macro base station number average value mu is calculated according to an area S in a region to be detected, probability density distribution f (x) with the macro base station number of x is established, the value of the macro base station number N under interval estimation is obtained, distribution coordinates of the macro base stations are obtained in MATLAB according to a uniform distribution algorithm, a Voronoi diagram is made by taking the macro base station coordinates as a parent point in the MATLAB through an even generation method, and weak coverage points k and corresponding coordinates (M) are obtained according to intersection points (nodes) of the Voronoi diagram edges j ，N j ) The probability distribution P (m) of the number of micro base stations in the area is obtained through the number k of weak coverage points, the specific value of the number of micro base stations under the condition is further obtained, the distribution coordinates of the micro base stations are obtained in MATLAB according to a uniform distribution algorithm in a circle, and finally the total electromagnetic radiation values of macro base stations and micro base stations in the rural area are obtained through prediction, and the base station environment influence evaluation and environmental protection are guided, so that the method has a certain social value.
Drawings
Fig. 1 is a Voronoi diagram of a rural area macro base station of the present invention.
Detailed Description
The invention will be described in further detail with reference to specific embodiments. The present embodiment is performed on the premise of the present disclosure, and detailed implementation steps are given, but the scope of the present disclosure is not limited to the following embodiments.
The implementation object of the invention is a base station of three operators communication network system, and the working frequency bands are respectively: the mobile communication (890 MHz-909 MHz), the communication (954 MHz-960 MHz), the telecom (825 MHz-840 MHz), the place is a rural area, the area of the selected test area is 2km multiplied by 2km, the measuring equipment is composed of a frequency spectrograph (frequency range 9kHz-3 GHz) with the model of AT6030D produced by an Antai communication company and a PCD 82-50 omnidirectional antenna (frequency range 80MHz-3 GHz), the antenna factor is 30dB/m, and the cable loss is 3dB.
The invention provides a rural area heterogeneous cellular network base station electromagnetic radiation prediction method, which comprises the following steps:
1) Establishing a rural area macro base station distribution model, calculating the number average value mu of macro base stations according to the area S in the area to be detected, and establishing probability density distribution f (x) with the number x of macro base stations to obtain the value of the number N of macro base stations under interval estimation;
2) Obtaining the position coordinate distribution (x) of macro base stations in the area in MATLAB by a uniform distribution algorithm according to the number N of macro base stations obtained in the step 1) i ，y i ) I is the reference number of the macro base station, i=1, 2,. -%, N;
3) Macro base station position coordinate distribution (x) obtained according to step 2) i ，y i ) By using a pair-to-pair generation method and taking macro base station coordinates as a mother point in MATLAB as a Voronoi diagram, signal weak coverage points (blind points) can be determined through intersection points (nodes) of edges of the Voronoi diagram, and weak coverage points k and corresponding coordinates (M) are obtained according to the Voronoi diagram j ，N j )；
4) According to the weak coverage point k obtained in the step 3), a rural area micro base station distribution model is established, the average value lambda of the number of micro base stations in the micro base station distribution model is calculated, the cumulative probability density distribution F (M) of the number M of the micro base stations is established, and the value of M under the condition of 95% probability is obtained, wherein the value is represented by M;
5) Obtaining a zone in MATLAB by a uniform distribution algorithm in a circle according to the number M of the micro base stations obtained in the step 4)Intra-domain micro base station position coordinate distribution (x j ，y j ) J is the reference number of the base station, j=1, 2,. -%, M;
6) The macro base station position coordinate distribution (x) obtained according to the steps 2) and 5) i ，y i ) Micro base station position coordinate distribution (x j ，y j ) Combining with a power density expression, predicting the electromagnetic radiation intensity S of the macro base station i Micro base station electromagnetic radiation intensity S j 。
In the above step 1), since the measurement area is 2km×2km, i.e., s=4 km 2 The rural area macro base station average mu is calculated as follows:
μ＝0.3972·S＝0.3972×4＝1.5888
by the property of probability density function distribution, the probability of macro base station number interval is 95.4% in (mu-1.96 sigma, mu+1.96 sigma), sigma is statistical base station data variance, the value is 0.76, and the maximum value is generally selected as a reference value of base station planning according to operators, so that the maximum integer in the interval is selected as macro base station number N:
N＝[μ+1.96σ]＝[1.5888+1.96×0.76]＝[3.0784]＝3
wherein [ mu+1.96 sigma ] is a maximum integer not exceeding mu+1.96 sigma.
In the above step 2), according to N calculated in the step 1), the area to be predicted is 2km×2km, and in MATLAB, according to a uniform distribution algorithm, n=3, the coordinates of each macro base station in the area are:
(x 1 ，y 1 )＝(L·(μ 1 ) 1 ，L·(μ 2 ) 1 )＝(2000×0.29，2000×0.75)＝(580，1500)
(x 2 ，y 2 )＝(L·(μ 1 ) 2 ，L·(μ 2 ) 2 )＝(2000×0.75，2000×0.38)＝(1500，760)
(x 3 ，y 3 )＝(L·(μ 1 ) 3 ，L·(μ 2 ) 3 )＝(2000×0.55，2000×0.08)＝(1100，160)。
in the step 3), the macro base station position coordinate distribution (x) obtained in the step 2) is obtained 1 ，y 1 )、(x 2 ，y 2 )、(x 3 ，y 3 ) By using the couple generation method, a Voronoi diagram is made in MATLAB by taking macro base station coordinates as parent points, as shown in fig. 1 of the specification drawing, the number of weak coverage points is 1, and the weak coverage coordinates are 760 and 800.
In the step 4), according to the number of the weak coverage points obtained in the step 3) being 1, the average value λ of the number of the micro base stations in the micro base station distribution model is calculated as follows:
λ＝k＝1
substituting the calculated average value lambda of the number of the micro base stations into the cumulative probability density distribution F (m) of the number m of the micro base stations as follows:
the M is obtained from the F (M) =95% probability as follows:
m is calculated to be 3 by the above formula.
In the above step 5), according to M calculated in step 4), the area to be predicted is 2km×2km, and m=3 is calculated in MATLAB according to the algorithm of uniform distribution in a circle, and the coordinates of the micro base stations in the area of the weak coverage point (760, 800) are:
(x 1 ，y 1 )＝(760+R 1 ·cosθ 1 ，800+R 1 ·sinθ 1 )＝(760+(-25)，800+10)＝(735，810)
(x 2 ，y 2 )＝(760+R 2 ·cosθ 2 ，800+R 2 ·sinθ 2 )＝(760+25，800+(-20))＝(785，780)
(x 3 ，y 3 )＝(760+R 3 ·cosθ 3 ，800+R 3 ·sinθ 3 )＝(760+18，800+40)＝(778，840)。
in the step 6), the coordinates of the predicted points are taken to be (1000, 2000), and the predicted points are obtained according to the step 2)Each macro base station coordinate (x i ，y i ) The coordinates (x) of each micro base station obtained in the step 5) j ，y j ) The distance between the predicted point and each macro base station is calculated according to the in-plane Euclidean distance formula, and is as follows:
the distances of each micro base station in the predicted point and weak coverage point (760, 800) areas are calculated according to the in-plane Euclidean distance formula respectively:
distance R between predicted point and each macro base station and micro base station i 、R j Calculating the total value of the radiation intensity of each macro base station and each micro base station to the predicted point, wherein the unit is uw/cm 2 ，P i The transmitting power of macro base station is 20W, P j The transmitting power of the micro base station is 20W, G i The antenna gain of the macro base station is 12dB, G j The value of the antenna gain of the micro base station is 6dB, and the antenna gain is substituted into the expression of the total value of the predicted radiation intensity:
distance R between the predicted point and each macro base station i Substituting the total electromagnetic radiation value S of the predicted point i ＝1.36×10 -4 uw/cm 2 To prove the effectiveness of the invention, we measured the average electromagnetic radiation intensity obtained by the accumulation of electromagnetic radiation of the communication frequency bands of three operators in the field by using a spectrometer at the position of the predicted coordinate point (1000, 2000) in the predicted area, and compared the average electromagnetic radiation intensity with the predicted electromagnetic radiation intensity, wherein the measured value is 1.24 multiplied by 10 -4 uw/cm 2 。
Distance R between the predicted point and each micro base station j Substituting the total electromagnetic radiation value S of the predicted point j ＝1.15×10 -4 uw/cm 2 To prove the effectiveness of the invention, we measured the average electromagnetic radiation intensity obtained by the accumulation of electromagnetic radiation of the communication frequency bands of three operators in the field by using a spectrometer at the position of the predicted coordinate point (1000, 2000) in the predicted area, and compared the average electromagnetic radiation intensity with the predicted electromagnetic radiation intensity, wherein the measured value is 1.08x10 -4 uw/cm 2 。
By comparison, the predicted values and measured values of the electromagnetic radiation intensities of the macro base station and the micro base station in the rural area are very consistent, and the effectiveness of the invention is verified.
Claims (6)
1. The method for predicting the electromagnetic radiation of the rural area heterogeneous cellular network base station is characterized by comprising the following steps of:
1) Establishing a rural area macro base station distribution model, calculating the number average value mu of macro base stations according to the area S in the area to be detected, and establishing probability density distribution f (x) with the number x of macro base stations to obtain the value of the number N of macro base stations under interval estimation;
2) Macro base station obtained according to step 1)The number N is obtained by a uniform distribution algorithm in MATLAB to obtain the position coordinate distribution (x i ,y i ) I is the reference number of the macro base station, i=1, 2, …, N;
3) Macro base station position coordinate distribution (x) obtained according to step 2) i ,y i ) By using a pair-to-pair generation method and taking macro base station coordinates as a mother point in MATLAB as a Voronoi diagram, signal weak coverage points (blind points) can be determined through intersection points (nodes) of edges of the Voronoi diagram, and weak coverage points k and corresponding coordinates (M) are obtained according to the Voronoi diagram j ,N j )；
4) According to the weak coverage point k obtained in the step 3), a rural area micro base station distribution model is established, the average value lambda of the number of micro base stations in the micro base station distribution model is calculated, the cumulative probability density distribution F (M) of the number M of the micro base stations is established, and the value of M under the condition of 95% probability is obtained, wherein the value is represented by M;
5) Obtaining the position coordinate distribution (x) of the micro base stations in the area in MATLAB by a circular uniform distribution algorithm according to the micro base station number M obtained in the step 4) j ,y j ) J is the reference number of the base station, j=1, 2, …, M;
6) The macro base station position coordinate distribution (x) obtained according to the steps 2) and 5) i ,y i ) Micro base station position coordinate distribution (x j ,y j ) Combining with a power density expression, predicting the electromagnetic radiation intensity S of the macro base station i Micro base station electromagnetic radiation intensity S j :
According to the Euclidean distance formula in the plane:
wherein x is c ，y c Respectively the abscissa and the ordinate of the predicted point, R i The unit is m and R, which are the distances between the predicted point and the ith macro base station j For the predicted point and jThe distance of the micro base station is m;
macro base station electromagnetic radiation intensity S i Micro base station electromagnetic radiation intensity S j The method comprises the following steps:
wherein S is i The unit is uw/cm for the electromagnetic radiation intensity of the macro base station 2 ，S j The unit is uw/cm for the electromagnetic radiation intensity of the micro base station 2 I is the index of macro base station, the value is 1,2, …, N, j is the index of micro base station, the value is 1,2, …, M, P i The unit is W, P, which is the transmitting power of macro base station j The unit is W, G, which is the transmitting power of the micro base station i The unit is dB and G is the antenna gain of the macro base station j The antenna gain in dB is the antenna gain of the micro base station.
2. The method for predicting electromagnetic radiation of a rural area heterogeneous cellular network base station according to claim 1, wherein in the step 1), a rural area macro base station distribution model is as follows:
wherein x is the number of macro base stations, f (x) is the probability when the number of the macro base stations is x, exp is an exponential function based on a natural constant e, mu is the average number of the macro base stations, the unit is one, sigma is the data variance of the statistical macro base stations, and the value is 0.76;
the expression of the macro base station number average value mu and the area S is as follows:
μ＝0.3972·S
wherein S is the area of the area to be measured, and the unit is km 2 ；
The probability of the number of macro base stations in the (mu-1.96 sigma, mu+1.96 sigma) interval is 95.4%, and the maximum integer in the interval is selected as the number N of macro base stations, and the expression is as follows:
N＝[μ+1.96σ]
wherein [ mu+1.96 sigma ] is a maximum integer not exceeding mu+1.96 sigma.
3. The electromagnetic radiation prediction method of rural area heterogeneous cellular network base stations according to claim 1, wherein in the step 2), the number N of macro base stations obtained in the step 1) is combined, and the coordinate expression of each macro base station in the area is obtained in MATLAB according to a uniform distribution algorithm, wherein the coordinate expression is as follows:
x i ＝L·(μ 1 ) i
y i ＝L·(μ 2 ) i
wherein i is the index of the ith macro base station, and the values are 1,2, … and N; x is x i Is the abscissa, y of the ith macro base station i L is the side length of the predicted square area, which is the ordinate of the ith macro base station, (mu) 1 ) i For continuous even distribution of random numbers on the ith macro base station abscissa, (mu) 2 ) i Random numbers are continuously and uniformly distributed on the ordinate of the ith macro base station.
4. The method for predicting electromagnetic radiation of a rural area heterogeneous cellular network base station according to claim 1, wherein in the step 3), the macro base station coordinates (x) obtained in the step 2) are combined i ,y i ) According to the couple generation method, taking macro base station coordinates as a mother point in MATLAB as a Voronoi diagram, and obtaining weak coverage point k and corresponding coordinates (M) through intersections (nodes) of Voronoi diagram edges j ,N j )。
5. The method for predicting electromagnetic radiation of a rural area heterogeneous cellular network base station according to claim 1, wherein in the step 4), in combination with the weak coverage point k obtained in the step 3), a distribution model of micro base stations in a rural area is established as follows:
where P (m) is the probability when the number of micro base stations is m, λ is the mean value of the number of micro base stations, and λ is expressed as follows:
λ＝k
where k is the number of weak coverage points in units of one;
the cumulative probability density distribution F (m) for the number m of micro base stations is expressed as:
wherein F (M) is the cumulative probability density of the micro base stations when the number of the micro base stations takes M, l is the number of the micro base stations, the unit is one, the value is 0,1,2, …, M, λ is the average value of the number of the micro base stations, the unit is one, λ is substituted into the F (M) expression to obtain the cumulative probability density of the micro base stations, and under the condition that F (n) =95% probability:
at this time, M is obtained.
6. The method for predicting electromagnetic radiation of rural area heterogeneous cellular network base stations according to claim 1, wherein in the step 5), the coordinate expression of each micro base station in the area is obtained in MATLAB according to the in-circle uniform distribution algorithm by combining the number M of micro base stations obtained in the step 4) as follows:
x j ＝M j +R j ·cosθ j
y j ＝N j +R j ·sinθ j
wherein j is the label of the j-th micro base station, and the values are 1,2, … and M; x is x j Is the abscissa, y, of the jth micro base station j Is the ordinate of the j-th micro base station, M j Is the abscissa of the jth weak coverage point, N j For the j-th weak coverageOrdinate of point, R j For a continuous uniform distribution of random numbers of radius r, the expression is:
wherein r is the coverage area of the micro base station, the value is 50, the unit is m, (mu) 1 ) j Continuously and uniformly distributing random numbers on the coverage area of the jth micro base station; lambda (lambda) j For the continuous and uniform distribution of random numbers of the j-th micro base station angle, the expression is:
θ j ＝2·π·(p 2 ) j
wherein (mu) 2 ) j The random numbers are continuously and uniformly distributed for the j-th micro base station.
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