CN111405577A - Antenna position layout method for full-duplex cognitive radio - Google Patents

Antenna position layout method for full-duplex cognitive radio Download PDF

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CN111405577A
CN111405577A CN202010131295.1A CN202010131295A CN111405577A CN 111405577 A CN111405577 A CN 111405577A CN 202010131295 A CN202010131295 A CN 202010131295A CN 111405577 A CN111405577 A CN 111405577A
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CN111405577B (en
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周娟
朱晓东
沈莹
汪进
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Chengdu University of Information Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/14—Two-way operation using the same type of signal, i.e. duplex
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
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Abstract

The invention discloses an antenna position layout method for recognizing radio by full duplex, which comprises the following steps: s1, deducing the performance of the antenna under each channel and relevant shadow; s2, analyzing the influence of path loss and main user position distribution on the sensing performance of the antenna spectrum; s3, determining the optimal antenna position according to the criterion of minimizing the perception error probability; the determination of the optimal position of the transmitting antenna specifically comprises the following steps: p1, calculating the electric field intensity of the double antenna arrays; p2, the optimal antenna position is determined with the goal of maximizing the electric field strength. The invention provides the method for determining the optimal position of the receiving antenna, optimizes the antenna position layout of the full-duplex cognitive network, improves the operation quality of the cognitive radio network, and has important academic and market values.

Description

Antenna position layout method for full-duplex cognitive radio
Technical Field
The invention relates to simultaneous co-frequency full duplex communication of cognitive radio, in particular to antenna position layout of full duplex cognitive radio, and belongs to the technical field of communication.
Background
Radio resources are a natural asset of all mankind. Radio resources are not a renewable common resource. The limitation of radio resources is becoming more apparent today with the increasing development of mobile communication technology. With the updating of the technology, various radio application technologies are in the inky arena, and the originally intense competition degree of radio resources is also aggravated, so that the scarcity of the radio resources is more obvious, and simultaneously, the utilization of the radio resources in various countries is promoted more efficiently.
The radio spectrum is a substance that is actually present in nature and is also an electromagnetic wave. Electromagnetic waves are a magic invisible and inaccessible natural resource which can be used by human beings. Due to the limitation of current scientific technology, human beings cannot develop and utilize electromagnetic waves in ultra-high frequency band at present, so that radio spectrum resources are precious and cannot be copied at present. The method has the scarcity that any user occupies a certain frequency band under certain time, place and space conditions, and the use of the frequency band by other users in the time, place and space is excluded.
Cognitive radio is an important approach to addressing spectrum scarcity. In the cognitive radio dynamic spectrum access strategy, a system for allocating spectrum resources has the ability of learning and interacting with the external environment. A frequency band is assigned to one or more Primary Users (PUs) that have priority access to the frequency band. When the primary user does not use the frequency band or the influence on the primary user when other users (SU) use the frequency band is acceptable, the secondary users can share the frequency band resource. In this way, the utilization of the spectrum can be significantly improved.
In the conventional cognitive field, a communication device or system usually adopts time division duplex or frequency division duplex, wherein the time division duplex uses the division of time slots to distinguish uplink from downlink, and the frequency division duplex uses the division of frequency bands to distinguish uplink from downlink. The traditional duplex mode is not efficient enough for spectrum resource utilization.
In order to further improve the spectrum utilization efficiency and improve the inherent defect that the spectrum utilization efficiency of the traditional duplex communication is not high, researchers at home and abroad put forward the concept of full duplex in recent years. Full duplex means that the same frequency is used for receiving and transmitting simultaneously, time slots or frequency bands are not required to be divided for distinguishing receiving and transmitting, and compared with a traditional duplex communication mode, the full duplex theoretically improves the frequency spectrum utilization efficiency by one time.
The full-duplex communication is integrated into the cognitive radio network, so that not only can the spectrum efficiency be improved, but also the secondary user has the spectrum sensing capability while transmitting data. The cognitive radio technology and the full-duplex technology play different roles in improving the utilization rate of frequency spectrum resources, so that the combination of the cognitive radio technology and the full-duplex technology has important value.
The layout of the antenna positions influences the network operation quality to a certain extent, so that the optimization of the layout of the antenna positions has important significance for improving the system network quality.
The present invention mainly focuses on the two aspects of the antenna layout of a cellular cell and the antenna position optimization of a distributed antenna, the position optimization of the antenna of the cellular cell is researched by documents, under the condition that the cellular cells are arranged on a street in order, the conclusion that the optimal antenna position is in the middle of the road and at the corners of the street is obtained under the condition that a plurality of L OS paths exist in a coverage area as judgment conditions, the antenna position optimization of a linear cell distributed antenna is also researched by documents, the distributed antenna layout is carried out by using the principle of minimum cell average bit error rate, the conclusion that the antenna should be distributed by using cell center symmetry is obtained, the document [9] researches the optimal antenna position of a circular cell, the optimal circular radius is analyzed by optimizing multiple users and speed, so as to obtain the optimal antenna position distribution, the document provides a square distance design method, the distance algorithm is provided by using the principle of maximum average channel capacity for the circular distributed antenna cell, the position optimization of the distributed antenna in the emission selection is also provided by the criterion of maximum cell average distance, the traversal rule is provided, and the corresponding traversal method for the distributed antenna is not provided.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide an antenna position layout method for full-duplex cognitive radio, which optimizes the antenna position layout of a full-duplex cognitive network and improves the operation quality of the cognitive radio network, aiming at the defects of the prior art.
The technical scheme is as follows: the invention relates to an antenna position layout method of full duplex cognitive radio, main users are uniformly distributed in a cell with radius R,
the determination of the optimal position of the receiving antenna comprises the following steps:
s1, deducing the performance of the antenna under each channel and relevant shadow;
s2, analyzing the influence of path loss and main user position distribution on the sensing performance of the antenna spectrum;
s3, determining the optimal antenna position according to the criterion of minimizing the perception error probability;
the determination of the optimal position of the transmitting antenna specifically comprises the following steps:
p1, calculating the electric field intensity of the double antenna arrays;
p2, the optimal antenna position is determined with the goal of maximizing the electric field strength.
The technical scheme of the invention is further defined in that the determining step of the optimal position of the receiving antenna of the secondary user specifically comprises the following steps:
s1, the energy detector measures the energy of the received signal in a detection interval to obtain the average false negative probability of the composite Rayleigh-shadow channel
Figure BDA0002395839230000031
In the formula (3-3-13),
Figure BDA0002395839230000032
is the average signal-to-noise ratio, ξ010/ln (10), (dB) is the standard deviation of 10log ω, T is the energy detector threshold, the detection interval of N samples,
Figure BDA0002395839230000033
Figure BDA0002395839230000034
in the formula (3-3-9), (a, x) is an incomplete gamma function;
s2, according to the system model, the primary users are uniformly distributed in the circle with radius R, and the position set can be expressed as a set C { (x, y) | x2+y2≤R2And R is the radius of the cell, the receiving antenna of the secondary user is positioned on a hyperbolic curve in the circle, and the probability density function of the position of the primary user is averaged to obtain the area average probability of missing report:
Figure BDA0002395839230000035
in the formula (3-4-6), σ2Is the noise variance, Es is the energy of the transmitted signal during the detection time interval,
Figure BDA0002395839230000036
a constant determined for the antenna characteristics and the average attenuation,
Figure BDA0002395839230000037
η is the path loss coefficient;
s3, determining the optimal antenna position by using the criterion of minimizing the perception error probability:
position of secondary user receiving antenna
Figure BDA0002395839230000038
Determined by the hyperbola on which the secondary user receiving antenna is located, wherein,
Figure BDA0002395839230000039
c is half of the distance between the two transmitting antennas, n is the multiple of odd times and half of the wavelength of the distance between the two transmitting antennas and the receiving antenna,
the optimal receive antenna position can be described as:
Figure BDA0002395839230000041
formula (3-4-7) optimal solution (x)0,y0)*Can be obtained from convex optimization.
Further, in the dual antenna array, the antenna 1 and the antenna 2 are relatively close and have the same orientation, a binary array formed by two symmetrical antennas which are oriented along the z axis and arranged along the x axis has a distance of 2d, the observation point P is far away from the center of the array, and the coordinate is P (r1, θ, Φ), then the determination step of the optimal position of the transmitting antenna specifically is:
p1, mode value of the resultant field intensity of observation point P:
Figure BDA0002395839230000042
wherein, I1Is the excitation current of the antenna 1;
Figure BDA0002395839230000043
omega is the angular frequency of electromagnetic wave, mu is a constant determined by a conductive medium, l is the effective length of the antenna, m is the amplitude ratio of the excitation currents of the two array elements, phi is ξ +2kdsin theta cos phi, ξ is the phase difference of the excitation currents of the two array elements;
p2 considering only the electric field strength on the xoy plane,
Figure BDA0002395839230000044
due to the limitation of the cognitive radio conditions,
ξ ═ 0 and m ═ 1, then Ψ ═ 2kdcos Φ, so that the mode value of the resultant field strength of point P is observed:
Figure BDA0002395839230000045
in the formula (4-3-1), r is far enough to ensure that the observation point P is far enough1Setting 10 × 2d to 20d, and setting phi to be (0,2 pi);
the optimal distance is
Figure BDA0002395839230000046
In the formula (4-3-2), the optimal d value is solved only by maximizing the integral part;
order to
Figure BDA0002395839230000051
B2 kd, then
Figure BDA0002395839230000052
In the formula (4-3-6),
Figure BDA0002395839230000053
omega, mu, respectively the electromagnetic wave frequency, the magnetic permeability and the dielectric constant of the propagation medium;
taking out in vacuum environment
Figure BDA0002395839230000054
And k is>>1, then
Figure BDA0002395839230000055
(4-3-7) in the formula (4-3-7)
Figure BDA0002395839230000056
Within the interval, monotonically increases
Figure BDA0002395839230000057
Monotonically decreasing in the interval, so that when the frequency of the electromagnetic wave transmitted from the base station using the 4G technology is substantially 2000MHz
Figure BDA0002395839230000058
The optimum position of the two transmitting antennas is obtained.
Has the advantages that: the invention provides an antenna position layout method for full-duplex cognitive radio, which provides an optimal position determination method for a receiving antenna, optimizes the antenna position layout of a full-duplex cognitive network, improves the operation quality of the cognitive radio network and has important academic and market values. .
Drawings
FIG. 1 is an antenna distribution model (PU indicates primary user);
FIG. 2 electric field strength for dual antenna arrays;
FIG. 3 is a simplified dual antenna array model;
FIG. 4 shows simulation results of total energy radiated by the antenna at low frequency;
fig. 5 shows simulation results of total energy radiated by the antenna at high frequency.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the embodiments.
Example 1: the invention provides an antenna position layout method for recognizing radio by full duplex, which comprises the steps of firstly providing an optimal position determining method for a receiving antenna and then providing an optimal position determining method for a transmitting antenna.
Firstly, the determination of the optimal position of the receiving antenna comprises the following steps:
the determination of the optimal position of the receiving antenna comprises the following steps:
s1, deducing the performance of the antenna under each channel and relevant shadow;
s2, analyzing the influence of path loss and main user position distribution on the sensing performance of the antenna spectrum;
and S3, determining the optimal antenna position by using the criterion of minimizing the perception error probability.
The specific process is as follows:
the relationship of three antenna positions is shown in fig. 1, where primary users are evenly distributed in a cell with radius R. The PU represents the primary user.
The condition for suppressing self-interference by antenna position can be reasonably assumed: assuming that two transmitting antennas are located at two focuses of a hyperbola, the positions are (-c, 0) and (c, 0), respectively, and self-interference suppression conditions are known from the antenna positions, and when the odd multiple of the half wavelength n is determined, the receiving antenna is on the hyperbola determined by the two focuses to satisfy the conditions of the antenna positions required for self-interference suppression.
Assuming that the receiving antenna position is (x0, y0), the following relationship is satisfied:
Figure BDA0002395839230000061
wherein 2a is defined by hyperbola and the condition that the antenna position restrains self-interference, namely the difference between two transmitting antennas and the receiving antenna is obtained by odd times of half wavelength:
Figure BDA0002395839230000062
the following can be obtained:
Figure BDA0002395839230000063
b can be determined from the hyperbolic definition:
Figure BDA0002395839230000064
the secondary user received signal may be expressed as:
Figure BDA0002395839230000065
wherein: s (k) is the target signal to be detected. The signal is affected by the complex channel gain h and zero-mean additive white gaussian noise n (k), which is the communication channel from the cell site to the receiving antenna. Binary hypothesis H0And H1Respectively, indicates the absence and presence of a target signal from a cell base station.
S1, deducing the performance of the antenna under each channel and relevant shadow
The energy detector is used for measuring the energy of the received signal in an observation interval. The measured energy is compared to a predetermined threshold to determine the presence or absence of a primary user. In the detection interval of N samples, the false alarm probability, the detection probability and the false negative probability of the energy detector under the AWGN channel condition are respectively as follows:
Figure BDA0002395839230000071
Figure BDA0002395839230000072
Pm＝1-Pd(3-2-3)
where T and γ are the energy detection threshold and signal-to-noise ratio, respectively, (a, x) is the incomplete gamma function. The probability expression of false negatives can be further obtained:
Figure BDA0002395839230000073
wherein
Figure BDA0002395839230000074
In a cell environment with more buildings, the signal is blocked by the buildings, and the signal is attenuated due to the shadow effect. Also, due to the presence of many buildings, there are many paths for the signal to reach the receiving antenna, and the signal is subject to rayleigh fading. This section therefore studies the energy detection performance under the complex rayleigh-shadowing channel. Since the false alarm probability Pf is independent of the signal-to-noise ratio, we will focus on the false-positive probability.
The probability density function of γ under the rayleigh channel is:
Figure BDA0002395839230000075
wherein the content of the first and second substances,
Figure BDA0002395839230000076
is the average signal-to-noise ratio.
The probability density function of the shadows follows a log-normal distribution [21 ]:
Figure BDA0002395839230000077
wherein, ξ010/ln (10), (dB) is the standard deviation of 10log ω.
Thus, the probability density function of γ under the composite rayleigh-shaded channel is:
Figure BDA0002395839230000081
correspondingly, the average false-positive probability of the composite rayleigh-shadow channel is:
Figure BDA0002395839230000082
after equivalence:
Figure BDA0002395839230000083
in view of
Figure BDA0002395839230000084
In the high signal-to-noise ratio region, equation (3-3-6) can be simplified to:
Figure BDA0002395839230000085
from equation (3-2-5) we can see:
Figure BDA0002395839230000086
wherein:
Figure BDA0002395839230000087
thus, the formula (3-3-4) can be rewritten as:
Figure BDA0002395839230000088
according to the formula (3-3-2) there are:
Figure BDA0002395839230000089
wherein:
Figure BDA00023958392300000810
and has the following components:
Figure BDA00023958392300000811
the formula (3-3-10), the formula (3-3-11) and the formula (3-3-12) can be synthesized to obtain:
Figure BDA00023958392300000812
s2, analyzing the influence of path loss and main user position distribution on the antenna spectrum sensing performance
According to the system model, the primary users are uniformly distributed in a circle with the radius of R, and the position set can be expressed as a set C { (x, y) | x2+y2≤R2R is the cell radius. The secondary user receiving antenna is positioned on a hyperbolic line in the circle, and the distance between the secondary user receiving antenna and the primary user is as follows:
Figure BDA0002395839230000091
the primary and secondary user receive antenna path losses L may be expressed as:
L＝ζD-η(3-4-2)
wherein
Figure BDA0002395839230000092
A constant determined for the antenna characteristics and average attenuation, η is the path loss coefficient.
The master users obey uniform distribution, and the probability density is as follows:
Figure BDA0002395839230000093
considering the effect of path loss, the average signal-to-noise ratio in equation (3-3-15) is expressed as:
Figure BDA0002395839230000094
wherein sigma2As a variance of the noise, EsThe expression is that the energy of the sending signal in the detection time interval is:
Figure BDA0002395839230000095
averaging the probability density functions of the false positive probability formula given by (3-3-12) at the PU position to obtain the area average false positive probability:
Figure BDA0002395839230000096
s3, determining the optimal antenna position by using the criterion of minimizing the perception error probability
Position of receiving antenna
Figure BDA0002395839230000097
Determined by a hyperbola, c is half the distance between the two transmitting antennas, and the value of a is determined by the formula (3-1-3). The optimal receive antenna position can be described as:
Figure BDA0002395839230000098
optimal solution (x)0,y0)*Can be obtained from convex optimization.
According to the convex optimization theory, the optimal position of the receiving antenna is the intersection point of the hyperbola and the abscissa.
Secondly, the determination of the optimal position of the transmitting antenna comprises the following steps:
p1, calculating the electric field intensity of the double antenna arrays;
p2, the optimal antenna position is determined with the goal of maximizing the electric field strength.
The specific process is as follows: the specific process is as follows:
and in the range with the radius R, determining the optimal transmitting antenna position according to the maximum standard of the average power of the electromagnetic waves transmitted by the two antennas.
The initial energy of the electromagnetic wave excited by the antenna is determined by the antenna and its input power. When energy leaves the antenna in the form of electromagnetic waves and enters free space, the electromagnetic waves excited by the two antennas generate phenomena such as interference, the study on the change of the power of the electromagnetic waves along with the space position becomes difficult, and the average poynting vector can be used for replacing the power. The average poynting vector is a physical quantity describing the flow of electromagnetic energy in an electromagnetic field, in Wm2The formula is
Figure BDA0002395839230000101
In a homogeneous conducting medium, the electric field
Figure BDA0002395839230000102
And a magnetic field
Figure BDA0002395839230000103
The Helmholtz equation satisfied is:
Figure BDA0002395839230000104
in the formula:
Figure BDA0002395839230000105
wherein the ratio of mu to mu is,care all constants determined by the conductive medium. In discussing the propagation of electromagnetic waves in a conductive medium, equation (4-1-2) is generally rewritten as:
Figure BDA0002395839230000106
wherein:
Figure BDA0002395839230000107
assuming that the electromagnetic wave is a uniform plane wave propagating along the + Z-axis direction and the electric field has only an Ex component, the solution of equation (4-1-4) is:
Figure BDA0002395839230000108
since γ is a complex number, let γ be α + j β, put into the above equation:
Figure BDA0002395839230000109
in the formula e-αzThe factor representing the amplitude of the electric field exhibits an exponential decay with increasing propagation distance z is called decay factor α, which is called decay constant, with the unit Np/m.e-jβzThe factor is a phase factor, β is called the phase constant, and has the unit of rad/m.
The instantaneous values corresponding to equations (4-1-7) are in the form:
Figure BDA0002395839230000111
and obtaining a magnetic field expression of the electromagnetic wave by using Maxwell equations. By
Figure BDA0002395839230000112
The magnetic field strength in the conductive medium can be found as follows:
Figure BDA0002395839230000113
in the formula:
Figure BDA0002395839230000114
is the intrinsic impedance of the conductive medium. From the formula (4-1-9), the relationship satisfied between the complex vector of the magnetic field strength and the complex vector of the electric field strength is:
Figure BDA0002395839230000115
in a conductive medium, the average poynting vector is:
Figure BDA0002395839230000116
where phi is the initial phase of the electromagnetic wave. It can be seen that the magnitude of the average poynting vector is only related to the square of the modulus of the electric field intensity, i.e., the magnitude of the modulus of the electric field intensity can indicate the magnitude of the power of the electromagnetic wave.
P1 calculating electric field intensity of dual antenna array
The antenna array is shown in figure 2, and the two antennas are close to each other and are uniformly oriented. Two symmetrical antennas oriented along the z-axis and arranged along the x-axis form a binary array with a spacing of 2 d. Let the excitation current of the antenna 1 (array element 1) be I1Then, the excitation current of the antenna 2 (array element 2) is:
I2＝mI1ejξ(4-2-1)
where m is the amplitude ratio of the two array element excitation currents, and ξ is the phase difference between the two array element excitation currents.
Since the observation point P is far away from the center of the array, the radius can be approximately considered
Figure BDA0002395839230000121
Radius of vector
Figure BDA0002395839230000122
Parallel. So that the electric fields generated by the array elements at the observation points are all along
Figure BDA0002395839230000123
The direction, namely:
Figure BDA0002395839230000124
wherein
Figure BDA0002395839230000125
ω is the angular frequency of the electromagnetic wave, μ, a constant determined by the conductive medium. In the formula:
Figure BDA0002395839230000126
where l is the effective length of the antenna.
In addition, as long as the observation point is far enough, there is an approximation as follows:
Figure BDA0002395839230000127
therefore, the formula (4-2-2) can be rewritten as:
Figure BDA0002395839230000128
where Ψ is ξ +2kdsin θ cos φ, representing the electric field at observation point P
Figure BDA0002395839230000129
And
Figure BDA00023958392300001210
including the phase difference ξ of the excitation currents of the two array elements and the phase difference caused by the wave path difference caused by the radiation of the two array elements.
The resultant field for observation point P is therefore:
Figure BDA0002395839230000131
taking a die:
Figure BDA0002395839230000132
p2, determining the best antenna position with the goal of maximizing the electric field strength
Considering that the whole space is too complicated, only the electric field intensity on the xoy plane is considered, as shown in FIG. 3, then
Figure BDA0002395839230000133
Due to cognitive radio condition restrictions, ξ ═ 0 and m ═ 1, then according to the formula Ψ ═ ξ + kdsin θ cos Φ,when Ψ is 2kdcos Φ, the mode of the electric field strength is:
Figure BDA0002395839230000134
where l is the effective length of the antenna,
Figure BDA0002395839230000135
at this time, finding the optimum position of the two antennas becomes a value of 2d in which the average of the squares of the modes of the electric field intensity in a circle having a center at (d,0) and a radius at R, which is a constant value, is the maximum criterion.
In the actual environment, d<<R, so R1Upper limit of (d + R ≈ R). In addition, to ensure that the observation point P is far enough to satisfy the above formula establishment condition, r1The lower limit of (d) is set to 10 × 2d to 20d, and the range of (0,2 pi).
If the optimal distance is D, the problem can be expressed as:
Figure BDA0002395839230000136
for facilitating calculation
Figure BDA0002395839230000137
(all constants in this term), B ═ 2 kd.
Note that the denominator part in equation (4-3-2) is constant, so only the integral part needs to be maximized to be the optimal d value.
Figure BDA0002395839230000138
Let the above formula be K, will
Figure BDA0002395839230000141
Expanded by taylor's formula, i.e.:
Figure BDA0002395839230000142
the first two terms are taken as approximations, thus obtaining
Figure BDA0002395839230000143
Substituting B ═ 2kd into the above formula to give
Figure BDA0002395839230000144
Wherein the content of the first and second substances,
Figure BDA0002395839230000145
omega, mu, respectively, frequency of electromagnetic wave, permeability and permittivity of propagation medium, noting that under vacuum conditions
Figure BDA0002395839230000146
The frequency of electromagnetic wave emitted by the base station using the 4G technology is basically about 2000MHz, so k>>1, thereby further simplifying the formula (4-3-6). Due to k>>1，k4The influence of (c) is much larger than the constant term and the square term, so it can be simplified as:
Figure BDA0002395839230000147
formula (4-3-7) in
Figure BDA0002395839230000148
Within the interval, monotonically increases
Figure BDA0002395839230000149
Monotonically decreasing in the interval, so that the function K (d) is at a frequency of around 2000MHz
Figure BDA00023958392300001410
Taking a maximum value in the vicinity, i.e. when
Figure BDA00023958392300001411
The two transmitting antennas have the best position.
The method is applied to a specific scene, and double transmitting antennas with the same power and the same phase are considered. The antenna effective current i is 1A, the antenna effective length l is 5m, and the cell radius is 100 m. As can be seen from fig. 4 and 5, the transmitting antenna is optimally positioned
Figure BDA00023958392300001412
The neighborhood was taken to be 3 × 100/80 — 3.75m, i.e., the point where the average energy was the largest was indeed around 3.75 m.
All curves fall first and then rise and fall no matter how high or low the frequency is. The reason the curve initially trended downward is that the two antennas were too close. When d is 0, the two antennas are superposed, and the average energy of the whole cell is the highest at this time; as the antenna moves away, a significant portion is cancelled out due to the interference of electromagnetic waves and the energy received by the cell drops dramatically. The first curve will exhibit a downward trend;
the reason for the curve rising is then that the distance between the two antennas is relatively modest, the cell is able to receive the energy of both antennas, and the interference effect is not strong. When the distance between the two antennas is proper, the emitted electromagnetic wave is absorbed by the environment of the cell before interference, and the phenomena that most of the electromagnetic wave is counteracted and a small part of the electromagnetic wave is absorbed by the environment when the two antennas are too close to each other are avoided. Therefore, the second curve will slowly rise to the optimal position;
the reason for the slow decline of the curve is then that the two antennas miss the optimum position. Although the interference effect of the electromagnetic wave is weaker than that of the previous stage and most of the energy is absorbed by the environment, the energy of the electromagnetic wave is weaker when reaching the cell environment, so that the total energy obtained by the cell environment begins to decrease finally;
the reason why the curve is sharply decreased is that the distance between the two antennas is too far, the energy radiated by the antennas is very weak when reaching the environment of the cell, and the energy radiated by the antennas is inversely proportional to the square of the distance, so the curve is very fast to decrease.
The lowest point position on the left side of the curve is analyzed. The lowest point of the low frequency group curve is approximately within the range of 0.5-1, and the high frequency group curve is within the range of 0-0.5. Can be explained by the formula (4-3-6). The formula (4-3-6) is as follows:
Figure BDA0002395839230000151
in the actual simulation case, k >1 is always true. When 0< d <1, the first and second terms mainly act in the low frequency case, the first term is large, and the second term is small in the low frequency (k is just larger than 1), so the final value is relatively large; the frequency continues to increase (the magnitude of k is not sufficient to offset the effect of the cube of d), still giving priority to the first and second terms, but the second term is larger than before, so the final value is smaller and the graph conforms to equation (4-3-6).
As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A method for recognizing antenna position of radio in full duplex mode features that the primary users are uniformly distributed in the cell with radius R,
the determination of the optimal position of the receiving antenna comprises the following steps:
s1, deducing the performance of the antenna under each channel and relevant shadow;
s2, analyzing the influence of path loss and main user position distribution on the sensing performance of the antenna spectrum;
s3, determining the optimal antenna position according to the criterion of minimizing the perception error probability;
the determination of the optimal position of the transmitting antenna specifically comprises the following steps:
p1, calculating the electric field intensity of the double antenna arrays;
p2, the optimal antenna position is determined with the goal of maximizing the electric field strength.
2. The method as claimed in claim 1, wherein the step of determining the optimal position of the receiving antenna of the secondary user comprises:
s1, the energy detector measures the energy of the received signal in a detection interval to obtain the average false negative probability of the composite Rayleigh-shadow channel
Figure FDA0002395839220000011
In the formula (3-3-13),
Figure FDA0002395839220000012
is the average signal-to-noise ratio, ξ010/ln (10), (dB) is the standard deviation of 10log ω, T is the energy detector threshold, the detection interval of N samples,
Figure FDA0002395839220000013
(3-3-9), wherein (a, x) is an incomplete gamma function in the formula (3-3-9);
s2, according to the system model, the primary users are uniformly distributed in the circle with radius R, and the position set can be expressed as a set C { (x, y) | x2+y2≤R2And R is the radius of the cell, the receiving antenna of the secondary user is positioned on a hyperbolic curve in the circle, and the probability density function of the position of the primary user is averaged to obtain the area average probability of missing report:
Figure FDA0002395839220000014
in the formula (3-4-6), σ2As a variance of the noise, EsTo transmit the energy of the signal during the detection time interval,
Figure FDA0002395839220000015
a constant determined for the antenna characteristics and the average attenuation,
Figure FDA0002395839220000021
η is the path loss coefficient;
s3, determining the optimal antenna position by using the criterion of minimizing the perception error probability:
position of secondary user receiving antenna
Figure FDA0002395839220000022
Determined by the hyperbola on which the secondary user receiving antenna is located, wherein,
Figure FDA0002395839220000023
c is half of the distance between the two transmitting antennas, n is the multiple of odd times and half of the wavelength of the distance between the two transmitting antennas and the receiving antenna,
the optimal receive antenna position can be described as:
Figure FDA0002395839220000024
optimal solution (x) of formula (3-4-7)0,y0)*Can be obtained from convex optimization.
3. The method as claimed in claim 2, wherein in the dual antenna array, the antenna 1 and the antenna 2 are close and uniformly oriented, the distance between the two symmetric antennas is 2d, the observation point P is far from the center of the array, and the coordinates are P (r1, θ, Φ), the step of determining the optimal position of the transmitting antenna is specifically:
p1, mode value of the resultant field intensity of observation point P:
Figure FDA0002395839220000025
wherein, I1Is the excitation current of the antenna 1;
Figure FDA0002395839220000026
omega is the angular frequency of electromagnetic wave, mu is the constant determined by conductive medium, l is the effective length of antenna, m is the amplitude ratio of two array element exciting currents, psi is ξ +2kd sin theta cos phi, ξ is two array element exciting currentsThe phase difference of (a);
p2 considering only the electric field strength on the xoy plane,
Figure FDA0002395839220000027
due to cognitive radio condition constraints, ξ ═ 0 and m ═ 1, then Ψ ═ 2kdcos Φ, so the modulus of the resultant field strength of observation point P:
Figure FDA0002395839220000028
in the formula (4-3-1), r is far enough to ensure that the observation point P is far enough1Setting 10 × 2d to 20d, and setting phi to be (0,2 pi);
the optimal distance is
Figure FDA0002395839220000031
In the formula (4-3-2), the optimal d value is solved only by maximizing the integral part;
order to
Figure FDA0002395839220000032
B2 kd, then
Figure FDA0002395839220000033
In the formula (4-3-6),
Figure FDA0002395839220000034
omega, mu, respectively the electromagnetic wave frequency, the magnetic permeability and the dielectric constant of the propagation medium;
taking out in vacuum environment
Figure FDA0002395839220000035
And k is>>1, then
Figure FDA0002395839220000036
(4-3-7) in the formula (4-3-7)
Figure FDA0002395839220000037
Within the interval, monotonically increases
Figure FDA0002395839220000038
Monotonically decreasing in the interval, so that when the frequency of the electromagnetic wave transmitted from the base station using the 4G technology is substantially 2000MHz
Figure FDA0002395839220000039
The optimum position of the two transmitting antennas is obtained.
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