CN112737653B - Non-uniform antenna array system design method using spherical wave model - Google Patents

Non-uniform antenna array system design method using spherical wave model Download PDF

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CN112737653B
CN112737653B CN202011588123.3A CN202011588123A CN112737653B CN 112737653 B CN112737653 B CN 112737653B CN 202011588123 A CN202011588123 A CN 202011588123A CN 112737653 B CN112737653 B CN 112737653B
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optimal
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CN112737653A (en
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邓志伟
蒲旭敏
陈前斌
冯文婷
谭伟强
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention relates to the technical field of wireless communication, and discloses a method for designing a non-uniform antenna array system by using a spherical wave model, which comprises the following steps: s1, establishing an antenna array structure of the non-uniform transceiving antenna array; s2, establishing a channel model containing spherical wave characteristics according to the established antenna array architecture; s3, designing the optimal transmitting direction and the power distribution thereof by using the statistical channel information; and S4, finally, based on the maximum capacity criterion, under the optimal transmission strategy, giving the optimal antenna array element design criterion. The invention can provide the antenna design method criterion under different signal-to-noise ratios, so that the performance of the array antenna design method is better than that of other array antenna design methods.

Description

Non-uniform antenna array system design method using spherical wave model
Technical Field
The invention relates to the technical field of wireless communication, in particular to a non-uniform antenna array system design method using a spherical wave model.
Background
In recent years, with the widespread use of smart terminals such as mobile phones and tablets, the volume of mobile data traffic has increased explosively, and the existing wireless communication systems have been gradually unable to meet such enormous business demands. Therefore, research on the fifth Generation mobile communication technology (5th Generation,5G) has been successively conducted in the academic world and the industrial world. Compared with the existing fourth Generation mobile communication technology (4th Generation,4G), the massive MIMO (Multiple Input Multiple Output, MIMO) technology is one of the key technologies of 5G, and has become a hot spot of domestic and foreign research because it can significantly improve the spectral efficiency and energy efficiency of a communication system.
In MIMO systems, the use of plane wave models for communication severely underestimates the channel capacity of the system. Compared with plane waves, the system capacity can be remarkably increased by using a spherical wave model for communication; for the MIMO system of the spherical wave model, most of the prior arts relate to the design scheme of the uniform antenna array, and most of the design schemes are all studied on the influence of the antenna spacing, the antenna azimuth angle, the distance between the transmitting and receiving antennas, and the like of the uniform antenna on the system performance under the direct-view channel. Under the condition of a uniform antenna array in a three-dimensional space, the optimal precoding design method of the system is only researched at present.
However, how to study the non-uniform linear antenna array design and the precoding design method under rice channel and how to design the placement positions of the non-uniform antennas is a technical problem that needs to be solved in the field.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a non-uniform antenna array system design method using a spherical wave model, which can provide criteria of an antenna design method under different signal-to-noise ratios, so that the performance of the antenna array design method is better than that of other antenna array design methods.
The invention solves the technical problems by the following technical means:
a method for designing a non-uniform antenna array system by using a spherical wave model is characterized by comprising the following steps: the method for designing the precoding and array antenna design of the non-uniform antenna array system according to the spherical wave model specifically comprises the following steps:
s1, establishing an antenna array framework with non-uniform antenna arrays for receiving and transmitting, and establishing a signal model according to a spherical wave model;
s2, establishing a channel model, and assuming that the receiving end knows all state information of the channel and the transmitting end knows the statistical state information of the channel, obtaining the system capacity expression as follows:
Figure GDA0003474374730000021
wherein Q is a correlation matrix Q ═ E { SS ] of the transmitted signalHρ is ES/N0U is
Figure GDA0003474374730000022
Is a matrix of eigenvectors of
Figure GDA0003474374730000023
Feature decomposition diagonal matrix, ΛQIs a eigen-decomposition diagonal matrix of Q;
and deducing the upper bound of the traversal capacity of the channel by using a Jensen inequality and statistical information as follows:
Figure GDA0003474374730000024
s3, designing the optimal transmitting direction of the 2-transmitting M-receiving system: the method for obtaining the optimal transmitting direction and the optimal power distribution scheme of the 2-transmitting-M-receiving non-uniform antenna array system by utilizing the statistical information specifically comprises the following steps: deducing an optimal transmitting direction as a channel response matrix right singular matrix according to a receiving signal expression, and solving a 2-transmitting M receiving non-uniform linear antenna array system transmission matrix right singular matrix by using matrix analysis knowledge; proving that the capacity upper bound expression is a convex function about power, and solving an optimal power distribution scheme by using a KKT condition;
s4, solving the array antenna design method under different signal-to-noise ratios according to the capacity closed solution after the power distribution scheme specifically comprises the following steps: analyzing the concave-convex property of the capacity closed-type solution to obtain that the closed-type solution is a composite function, and obtaining a conclusion that the capacity of the non-uniform array antenna parameter is the maximum value of the endpoint value according to the monotonicity of the subfunction in the composite function; according to the capacity closed type solution function property, judging the monotonicity of a capacity function subfunction under different signal-to-noise ratios, and determining the optimal nonlinear uniform array antenna parameter value of the system;
s5, designing the optimal array antenna distribution according to the optimal transmission strategy; carrying out closed solution analysis on the transmission power distribution scheme, and designing an antenna method according to different signal-to-noise ratios; the method comprises the following specific steps:
when in use
Figure GDA0003474374730000031
The design criteria for an optimal irregular antenna array are as follows:
Figure GDA0003474374730000032
when it is satisfied with
Figure GDA0003474374730000033
And is
Figure GDA0003474374730000034
The design criteria for an optimal irregular antenna array are as follows:
Figure GDA0003474374730000035
when it is satisfied with
Figure GDA0003474374730000036
Or
Figure GDA0003474374730000037
And is
Figure GDA0003474374730000038
This optimal antenna design criterion is then:
Figure GDA0003474374730000039
further, in the step S3, the system performance of the signal is optimized according to the eigenvector matrix when the optimal transmission direction of the signal is equal to the channel response covariance matrix, and the optimal transmission direction of the system is obtained as
Figure GDA00034743747300000310
Wherein
Figure GDA00034743747300000311
Wherein L ist、LrRespectively, the length of the transmitting and receiving antenna arrays, λ the wavelength of the signal, D the distance between the antenna arrays, αr,lIndicating the normalized position of the l-th receiving antenna from the starting position.
Further, in step S3, according to the capacity upper bound obtained by the statistical information, a power allocation scheme of the transmit antenna of the 2-transmit-M-receive system is obtained, which optimizes the capacity; the method comprises the following specific steps:
when in use
Figure GDA0003474374730000041
The optimal power allocation scheme is
Figure GDA0003474374730000042
Figure GDA0003474374730000043
Wherein
Figure GDA0003474374730000044
When in use
Figure GDA0003474374730000045
Time of day, optimum powerThe distribution scheme is
Figure GDA0003474374730000046
The invention has the beneficial effects that:
under the irregular array antenna system, the non-uniform antenna array design method utilizing the spherical wave characteristics is better than the performance of the precoding scheme under the existing equal power, and under different signal-to-noise ratios, the array antenna design method provided by the invention is better than the performance of the existing array antenna design method.
Drawings
FIG. 1 is a diagram of a non-uniform antenna array of the present invention in three dimensions;
FIG. 2 is a graph comparing equal power to unequal power distribution for a Rice channel system of the present invention;
fig. 3 is a graph comparing system performance for different array antenna design methods with different signal-to-noise ratios.
Wherein, T in FIG. 1X、RXRespectively representing transmit and receive antenna arrays, thetat、θrRespectively representing the angles between the transmit antenna array and the receive antenna array and the longitudinal axis, D representing the distance between the transmit antenna array and the receive antenna array, phirIndicating the angle of the projection of the receiving antenna array with respect to the horizontal.
Detailed Description
The invention will be described in detail below with reference to the following drawings:
as shown in fig. 1-3:
examples 1,
In this embodiment, a non-uniform antenna array method design scheme using spherical wave characteristics is adopted when the number of antennas is 4, 24, and 100, as shown in fig. 1, the method includes the following steps:
s1, building an antenna array architecture of the non-uniform transmit-receive antenna array, and building a signal model according to the spherical wave model, specifically as follows:
Figure GDA0003474374730000051
wherein the content of the first and second substances,
Figure GDA0003474374730000052
is a received signal vector, ESIs the total energy of the transmitted signal per unit period,
Figure GDA0003474374730000053
is a matrix of the response of the channel,
Figure GDA0003474374730000054
is the vector of the transmitted signals and,
Figure GDA0003474374730000055
is an independent and identically distributed complex additive white Gaussian noise vector;
s2, establishing a channel model, specifically as follows:
Figure GDA0003474374730000056
wherein the content of the first and second substances,
Figure GDA0003474374730000057
is the channel response matrix for the direct path in the rice channel,
Figure GDA0003474374730000058
is a channel response matrix of a scattering path in the rice channel, and K represents the ratio of the powers of the direct path and the scattering path;
and assuming that the receiving end knows all the state information of the channel and the transmitting end knows the statistical state information of the channel, the system capacity expression is as follows:
Figure GDA0003474374730000061
wherein Q is a correlation matrix Q ═ E { SS ] of the transmitted signalHρ is ES/N0U is
Figure GDA0003474374730000062
Is a matrix of eigenvectors of
Figure GDA0003474374730000063
Feature decomposition diagonal matrix, ΛQIs a eigen-decomposition diagonal matrix of Q;
by using the Jensen inequality, the upper bound of the traversal capacity of the channel is as follows:
Figure GDA0003474374730000064
s3, obtaining the optimal transmitting direction of the 2-transmitting M-receiving system as
Figure GDA0003474374730000065
Wherein
Figure GDA0003474374730000066
S4, obtaining the optimal power distribution scheme of the transmitting antenna of the 2-transmitting-M-receiving system according to the capacity upper bound obtained by the statistical information; the method comprises the following specific steps:
when in use
Figure GDA0003474374730000067
The optimal power allocation scheme is
Figure GDA0003474374730000068
Figure GDA0003474374730000069
Wherein
Figure GDA0003474374730000071
When in use
Figure GDA0003474374730000072
The optimal power allocation scheme is
Figure GDA0003474374730000073
Example 2
Example 2 is compared with example 1, the only difference being that the antenna process is being designed.
In this embodiment when satisfying
Figure GDA0003474374730000074
The optimal non-uniform receiving antenna array design method is as follows:
Figure GDA0003474374730000075
example 3
Example 3 is compared with example 1, the only difference being that the antenna process is being designed.
In this embodiment when satisfying
Figure GDA0003474374730000076
And is
Figure GDA0003474374730000077
The optimal receiving antenna design method comprises the following steps:
Figure GDA0003474374730000078
example 4
Example 4 is compared with example 1, the only difference being that the antenna process is being designed.
In this embodiment when satisfying
Figure GDA0003474374730000079
Or
Figure GDA00034743747300000710
And is
Figure GDA00034743747300000711
The optimal antenna design method is as follows:
Figure GDA0003474374730000081
comparative examples
In the comparative example, when the number of antennas is selected to be 4, 24, and 200, the antennas are designed by using the existing unequal power allocation method in the rice channel system.
Finally, as shown in fig. 2, when the number of antennas is 4, 24, and 200, the performance of the non-equal power allocation algorithm proposed by us adopted under the rice channel system is improved compared with the traditional equal power allocation algorithm; system performance increases as the signal-to-noise ratio increases.
As shown in fig. 3, the system performance varies with the snr under different non-uniform antenna design methods under the condition that the number of receiving antennas is 4. It is apparent from the figure that the performance is optimal when the antenna design method is the antenna design method in embodiment 2 under low signal-to-noise ratio, and the performance of the system is optimal when the antenna design method is designed by adopting the method in embodiment 3 under high signal-to-noise ratio.
Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims. The techniques, shapes, and configurations not described in detail in the present invention are all known techniques.

Claims (1)

1. A method for designing a non-uniform antenna array system by using a spherical wave model is characterized by comprising the following steps: the method for designing the precoding and array antenna design of the non-uniform antenna array system according to the spherical wave model specifically comprises the following steps:
s1, establishing an antenna array framework with non-uniform antenna arrays for receiving and transmitting, and establishing a signal model according to a spherical wave model;
s2, establishing a channel model, and assuming that the receiving end knows all state information of the channel and the transmitting end knows the statistical state information of the channel, obtaining the system capacity expression as follows:
Figure FDA0003371186990000011
wherein Q is a correlation matrix Q ═ E { SS ] of the transmitted signalHρ is ES/N0U is
Figure FDA0003371186990000012
Is a matrix of eigenvectors of
Figure FDA0003371186990000013
Feature decomposition diagonal matrix, ΛQIs a eigen-decomposition diagonal matrix of Q;
and deducing the upper bound of the traversal capacity of the channel by using a Jensen inequality and statistical information as follows:
Figure FDA0003371186990000014
s3, designing the optimal transmitting direction of the 2-transmitting M-receiving system: the method for obtaining the optimal transmitting direction and the optimal power distribution scheme of the 2-transmitting-M-receiving non-uniform antenna array system by utilizing the statistical information specifically comprises the following steps: deducing an optimal transmitting direction as a channel response matrix right singular matrix according to a receiving signal expression, and solving a 2-transmitting M-receiving non-uniform linear antenna array system transmission matrix right singular matrix by utilizing matrix analysis; proving that the capacity upper bound expression is a convex function about power, and solving an optimal power distribution scheme by using a KKT condition;
s4, solving the array antenna design method under different signal-to-noise ratios according to the capacity closed solution after the power distribution scheme, which specifically comprises the following steps: analyzing capacity closed type solution concave-convex performance to obtain a closed type solution composite function, and obtaining a conclusion that the capacity of the non-uniform array antenna parameter is maximum by taking the endpoint value according to monotonicity of sub-functions in the composite function; according to the capacity closed type solution function property, judging the monotonicity of a capacity function subfunction under different signal-to-noise ratios, and determining the optimal nonlinear uniform array antenna parameter value of the system;
s5, designing the optimal array antenna distribution according to the optimal transmission strategy; carrying out closed solution analysis on the transmission power distribution scheme, and designing an antenna method according to different signal-to-noise ratios; the method comprises the following specific steps:
when in use
Figure FDA0003371186990000021
The design criteria for an optimal irregular antenna array are as follows:
Figure FDA0003371186990000022
when it is satisfied with
Figure FDA0003371186990000023
And is
Figure FDA0003371186990000024
The design criteria for an optimal irregular antenna array are as follows:
Figure FDA0003371186990000025
when it is satisfied with
Figure FDA0003371186990000026
Or
Figure FDA0003371186990000027
And is
Figure FDA0003371186990000028
This optimal antenna design criterion is then:
Figure FDA0003371186990000029
the step S3 of pushing to the optimal transmitting direction specifically includes: according to the characteristic vector matrix when the optimal signal transmitting direction is equal to the channel response covariance matrix, the system performance of the signal is optimal, and the optimal system transmitting direction is obtained
Figure FDA00033711869900000210
Wherein
Figure FDA00033711869900000211
Wherein L ist、LrRespectively, the length of the transmitting and receiving antenna arrays, λ the wavelength of the signal, D the distance between the antenna arrays, αr,lA normalized position representing the location of the ith receiving antenna from the starting point;
the step S3 of solving the optimal power distribution scheme is specifically to obtain a 2-transmission M-reception system transmitting antenna power distribution scheme with optimal capacity according to the capacity upper bound obtained by the statistical information; the method comprises the following specific steps:
when in use
Figure FDA0003371186990000031
The optimal power allocation scheme is
Figure FDA0003371186990000032
Figure FDA0003371186990000033
Wherein
Figure FDA0003371186990000034
When in use
Figure FDA0003371186990000035
The optimal power allocation scheme is
Figure FDA0003371186990000036
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